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IX SIMPOSIO IBEROAMERICANO SOBRE PROTECCIÓN DE SISTEMAS ELÉCTRICOS

DE POTENCIA

MEMORIA TÉCNICA Monterrey, México. Mayo 2008

ii

MENSAJE DEL COMITE ORGANIZADOR

El Comité Organizador del IX Simposio Iberoamericano sobre Protección de Sistemas Eléctricos de Potencia da la más cordial bienvenida a todos los participantes. Es un honor para nosotros recibirlos en Monterrey y tener la posibilidad de compartir estos días con ustedes. El Simposio Iberoamericano sobre Protección de Sistemas Eléctricos de Potencia es un evento en que los ingenieros de toda Iberoamérica pueden intercambiar experiencias entre sí y con especialistas de los países de mayor nivel de desarrollo tecnológico. Se mantienen vigentes los objetivos originales del Simposio y su intención de promover el acercamiento entre universidades, centros de investigación, fabricantes de equipos y empresas eléctricas de diversos países. En las ocho ediciones anteriores del evento han participado poco más de 1400 ingenieros de 25 países, se han presentado 278 ponencias, se han dictado 21 conferencias magistrales y se han desarrollado 9 mesas redondas. La exposición de equipos ha sido un elemento importante del evento, en que se ha contado con la participación de las firmas más reconocidas en la especialidad a nivel mundial. Más de 500 ingenieros de varios países han asistido a los 17 cursos tutoriales que se han impartido en el marco de estos ocho Simposios. En el IX Simposio se presentarán 21 ponencias por especialistas de 7 países, se dictarán tres conferencias magistrales y un panel, que estarán a cargo de personalidades reconocidas internacionalmente y versarán sobre aplicaciones de mediciones fasoriales sincronizadas, y sistemas de protección de área amplia. Nuevamente se contará con una exposición industrial, en que participarán los fabricantes más innovadores del mundo, y con dos cursos tutoriales, dedicados a los temas de protección de líneas de transmisión, y protección de generadores. El Comité Organizador desea hacer patente su reconocimiento y gratitud a la Universidad Autónoma de Nuevo León, a la Facultad de Ingeniería Mecánica y Eléctrica y a la Comisión Federal de Electricidad de México por el apoyo y estímulo que han dado en la organización de este IX Simposio. Esperamos que el evento satisfaga las expectativas de todos los participantes y constituya una experiencia útil para su desarrollo profesional.

Comité Organizador Monterrey, Nuevo León, Mayo de 2008.

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IX SIMPOSIO IBEROAMERICANO

SOBRE PROTECCION DE SISTEMAS ELECTRICOS DE POTENCIA

Auspiciado por: Universidad Autónoma de uevo León

M.C. José Antonio González Treviño, Rector

Facultad de Ingeniería Mecánica y Eléctrica

Ing. Esteban Baez Villarreal, Director

Comisión Federal de Electricidad

Ing. Alfredo Elías Ayub, Director General Ing. Nestor F. Moreno Díaz, Director de operación Ing. Noe Peña Silva, Subdirector de Transmisión Ing. Luis Carlos Hernández Ayala,Subdirector de Generación Ing. José Abel Valdez Campoy, Subdirector de Distribución Ing. Gustavo A. Salvador Torres, Subdirector del CENACE Ing. Román Ramírez Rodríguez, Coordinador de

Protecciones, Control y Comunicaciones Ing. Felipe de Jesús Vaquero Esparza, Gerente de

Protecciones y Medición

Instituto de Ingenieros en Electricidad y Electrónica

Comité Organizador: Dr. Ernesto Vázquez Martínez PRESIDENTE Ing. José Juan Luna Guzmán SECRETARIO EJECUTIVO

Dra. Gina María Idárraga Ospina Dr. Arturo Conde Enríquez Dr. Manuel Antonio Andrade Soto

Dr. Marco Tulio Mata Jiménez LOGÍSTICA Ing. Ramiro Patiño Bedolla Ing. Sergio David González Cantú Ing. Gerardo Manuel Robledo Leal EXPOSICIÓN INDUSTRIAL

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IX SIMPOSIO IBEROAMERICANO

SOBRE PROTECCION DE SISTEMAS ELECTRICOS DE POTENCIA

Empresas representadas en la Exposición Industrial:

• ABB, IC.

• ALLECTRO, S.A. de C.V.

• AREVA

• DIMAT, S. A.

• EUROSMC S.A.

• FOKEL MEXICAA S.A. de C.V.

• GE MULTILI

• HD ELECTRIC

• MABREX, S.A. de C.V.

• OMICRO ELECTROICS CORP. USA

• POWER MEASUREMET LTD, Una empresa de Scheneider Electric

• RADIA RESEARCH IC.

• SCHWEITZER EGIEERIG LABORATORIES, IC.

• SCHWEITZER EGIEERIG LABORATORIES, S.A. de C.V.

• SERVERO CORPORATIO

• SIEMES SA DE CV

• SIEMES AG

• TRASMISIO Y DISTRIBUCIO S.A. de C.V.

• ZIV P+C

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I N D I C E

Mensaje del Comité Organizador ii Comité Organizador iii Empresas representadas en la Exposición Industrial iv

Application of modern relays to dual-breaker line terminals 1

Bogdan Kasztenny (GE, Canadá), Ilia Voloh (GE Multilin, USA)

Método para el ajuste del alcance resistivo en características cuadriláteras de relés de distancia

15

Elmer Sorrentino (Universidad Simón Bolivar, Caracas, Venezuela), Eliana Rojas (ABB, Caracas, Venezuela), Jesús Hernández (SENECA, Porlamar, Venezuela)

Localización de fallas en líneas aéreas paralelas con múltiples terminales y con alimentación en dos de sus extremos

21

Luis de Andrade (C.A. La Electricidad, Caracas, Venezuela), Elmer Sorrentino (Universidad Simón Bolivar, Caracas, Venezuela)

Directional comparison protection over radio channels for subtransmission lines: field experience in Mexico

27

Servando Sánchez, Alfredo Dionicio, Martín Monjarás, Manuel Guel, Guillermo Gonzáles, y Octavio Vázquez (Comisión Federal de Electricidad, México), José L. Estrada (Altos Hornos de México, S.A. de C.V.), Héctor J. Altuve, Ignacio Muñoz, Iván Yánez, y Pedro Loza (Schwetizer Engineering Laboratorios, Inc.)

Implementación de un esquema de protecciones de sobrecorriente entre relevador-restaurador-restaurador con aumatismo y comunicación en un sistema de distribución en lazo

37

J.J. Tenorio y C. Guerrero (Luz y Fuerza del Centro, México D.F., México) D. Sebastian (Instituto Politécnico Nacional, SEPI ESIME ZAC., México D.F., México), R. Méndez (Instituto Politécnico Nacional, ESIME ZAC., México D.F., México)

Windfarm system protection using Peer-to-Peer communitacions 45

Michael L. Reichard (GE Energy’s Applications & System Engineering group, USA), Dale Finney (GE Multilin, Canada), John T. Garrity (GE Multilin, USA)

Case study: Design and implementation of IEC 61850 from multiple vendors at CFE La Venta II

51

vi

Victor Manuel Flores, Daniel Espinosa (Comisión Federal de Electricidad, México), Julian Alzate, Dave Dolezilek (Schweitzer Engineering Laboratories, Inc., USA)

High-speed control scheme to prevent instability of a large multi-unit power plant 67

Vahid Madani (WECC, USA), Edward Taylor (WECC, USA), Davis Erwin (PG&E system protection, USA), Anatoliy Meklin (Pacific Gas & Electric Company, USA), Mark Adamiak (GE, USA)

Operation simulation of out of step relays using COMTRADE files and power system simulation analysis

79

Juan M. Gers (GERS, USA), James Ariza (Megger, USA)

Backup transmission line protection for ground faults and power swing detection using synchrophasors

89

Armando Guzmán, Venkat Mynam, Greg Zweigle (Schweitzer Engineering Laboratories, Inc., USA).

Wide area measurement & control system in Mexico 101

Enrique Martínez Martínez (Comisión Federal de Electricidad, México)

Implementation and performance of synchrophasor function within microprocessor based relays

107

Bogdan Kasztenny (GE, Canada), Mark Adamiak (GE, USA)

Aplicaciones de la medición de sincrofasores pensadas por el operador del sistema eléctrico Español

127

S. López, J. Gómez (Red Eléctrica de España, España), R. Cimadevilla (ZIV P+C, España)

Estimando el fasor dinámico con diferenciadores máximamente lisos 139

Miguel Ángel Platas Garza y José Antonio de la O (UANL, México)

Aplicación de seccionadores fusibles de potencia con relés de falla a tierra en redes de distribución de media tensión con neutro aislado y/o delta

147

Luis Sánchez Pantoja, José Luis Mamani (EDELNOR S.A.A., Perú)

Detection of high-impedance faults in power distribution systems 155

Daqing Hou (Schweitzer Engineering Laboratories, Inc., USA)

Experiencias con protecciones diferenciales de bus digitales 167

Bladimir Hernández Acosta (CFE, SATT, Coatzacoalcos, México), Eduardo O. Mora Alcaraz (CFE, GRTOR, México)

Fundamentals of adaptive protection of large capacitor banks 173

Bogdan Kasztenny (GE, Canada), Joe Schaefer, Ed Clark (Florida Power & Light Company, USA)

Dynamic simulations help improve generator protection 189

Ramón Sandoval (Comisión Federal de Electricidad, México), Armando Guzmán, Héctor J. Altuve (Schweitzer Engineering Laboratories, Inc., USA)

Propuesta de una lógica de protección considerando el contenido subsíncrono del par eléctrico en terminales del turbogenerador

213

Jose A Castillo J., David Sebastián Baltasar (SEPI-ESIME-IPN, México), Carlos A. Rivera S. (UAM-Azcapotzalco, México)

vii

Enhanced motor protection with the slipdependent thermal model: A case study

221

Patrick Whatley (Plant Power and Control Systems, LLC, USA), Mark Lanier, Lee Underwood, Stan Zocholl (Schweitzer Engineering Laboratories, Inc., USA) Índice de Autores 233

ota: Las versiones en formato electrónico estarán disponibles en la página WEB del evento a partir del

mes Agosto de 2008

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Abstract—Modern line relays are capable of connecting both

sets of currents, and multiple sets of voltages in dual-breaker

applications. This allows novel applications such as integrated

Breaker Failure (BF) and AutoReclosure (AR), as well as solving

performance problems that may occur when summing the

currents externally while applying more traditional line relays.

This paper is concerned with the following aspects of application

of multi-function line protection relays at dual-breaker terminals:

First, applications of breaker fail functions are discussed

including opportunities to optimize performance, as well as

maintain redundancy & security when using integrated BF. Both

internal and external initiations are considered; integration with

BFs of adjacent zones is discussed as well.

Second, application of tripping and reclosing in dual-breaker

arrangement is discussed. This includes treatment of the middle

breaker, restraining from reclosing breakers that were not

tripped, sequential vs simultaneous reclosing, breaker transfer or

substitution, etc.

Third, security of distance, ground directional, current

differential and phase comparison functions are analyzed with

respect to situations where a large through current is feeding a

close-in external fault while the actual line current supplied

towards the terminal from the remote end is relatively small.

Even minor CT errors is response to the through current can

override the actual line current and make the current measured

via summation of the two CTs appear inverted, potentially

causing a misoperation. Modern relays measure the two currents

of a ring-bus or breaker-and-a-half configuration individually,

and can apply appropriate security measures to avoid the

problem. This paper presents such security logic for all typical

line protection functions.

Finally, stub-bus protection is discussed as applied to dual-

breaker terminals.

Index Terms—Automatic reclosing, breaker failure protection,

CT errors, security, transmission line protection.

I. INTRODUCTION

tandard practice today with respect to protecting dual-breaker line terminals – breaker-and-a-half or ring-bus – is to sum the two breaker currents externally and feed a

single-input line relay (distance, line current differential or phase comparison) with the total current flowing into the protected line. Breaker failure protection requires monitoring the two breakers and currents separately, and is typically

implemented as a stand-alone device outside of the main protection relay. Reclosing and synchrocheck control functions require monitoring and controlling both breakers as well as measuring two pairs of voltages for the purpose of synchrocheck, are also – in majority of cases – implemented outside of the main line protection device. This paper discusses several protection and control aspects

in relation to dual-breaker line terminals. First, breaker failure and reclosing functions are discussed

as applied to dual-breaker configurations. Second, the paper talks about protection security as related

to saturation of Current Transformers (CTs) under fault currents flowing locally through the two breakers. When the two currents are summated externally, the CT errors – if significant – can override the potentially low actual line current, and cause stability problems for the main line protection. Not only sensitive ground overcurrent functions are jeopardized, but also distance, current differential, or phase comparison. The paper explains the problem and presents solutions. Stub bus protection is also discussed as pertaining to dual-

breaker configurations. The paper looks at the above applications from the point of

view of a modern microprocessor-based relay. New generation of line relays support dual CT inputs to monitor both breakers individually, and three voltage points to provide for the main line protection, and synchrocheck across both breakers. These relays often include two breaker failure, two synchrocheck, and dual-breaker auto-reclose functions. This allows integrating protection, breaker failure and reclose functions into a single relay. The paper points to advantages and disadvantages of such integration, and provides some guidance regarding dual-breaker line applications.

II. CAPABILITIES OF MODERN LINE IEDS

Modern microprocessor-based line protection relays (or Intelligent Electronic Devices, IEDs) allow for protection and control of the dual-breaker line arrangement from a single device. Application of separate breaker failure and/or synchrocheck relays is no longer dictated by limitations of the main protection relay, but driven by the user’s protection philosophy to either combine the required functions, mostly for the for cost benefit, or to keep them separate for security, retaining present testing and maintenance practices, avoiding

Application of Modern Relays to Dual-Breaker Line Terminals

Bogdan Kasztenny, Fellow, IEEE, Ilia Voloh, Senior Member, IEEE

S

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re-training the personnel, etc. With reference to Figure 1, a modern IED capable of the

dual-breaker application supports two three-phase current inputs in order to measure both the currents individually for the breaker failure protection (50BF), backup overcurrent protection (51P), and associated meetering functions. The two currents are added internally in the relay’s software to become the input for the distance (21) or high-set overcurrent (50) functions. When properly implemented, the line current differential (87L) and phase comparison (87PC) functions use individual currents for stability under through fault conditions. Such modern IED typically support one three-phase voltage

input required for the main (distance) or backup protection (distance backup on line current differential or phase comparison relays), and at least two single-phase voltage inputs in order to facilitate synchrocheck (25) across both the breakers. A dual-breaker autorecloser (79) controlling both breaker simultaneously and capable of advanced reclose modes (sequential, simultaneous, breaker out of service, etc.) completes the application. A suite of backup and auxiliary functions are typically attached to the voltages and the three currents (breaker 1, breaker 2, line). In addition to the required AC inputs these IED are

designed to support enough binary inputs (breaker status, external breaker fail initiate) and output contacts (trip for both breakers, reclose per breaker, breaker fail re-trip and trip, etc.) to facilitate protection and control of a dual-breaker line terminal from a single IED.

CB-1

CB-2

CT-1

CT-2

VT-1

VT-2

VT

(1Φ)

(1Φ)

(3Φ)

25

(1)

25

(2)

50

BF

50

BF

Σ 21 87

79

(1/2)

CLOSE

CLOSE

TRIP/STATUS

TRIP/STATUS

LINE PROTECTION

IED

Fig. 1. Modern dual-breaker line IEDs

III. BREAKER FAILURE CONSIDERATIONS

Being a backup function, the BF protection may be required to use a different CT core, an independent current path, independent relay hardware, and a separate tripping path. This requirement is naturally met when using a stand-alone BF relay, but can as well be accomplished on multi-function relays without a separate BF device, at the expense of extra signaling between the relays. Figure 2 presents four approaches to distributing the Fault

Detection (FD) and BF functions between multiple relays.

Figure (a) is a traditional scheme with a dedicated BF relay. Figure (b) presents a simple scheme with an integrated BF

function per each fault detection function. No external BFI signals are used. Dependability is directly proportional, while security is

adversely proportional, to the number of operational copies of a given protection function. Predominately, we deploy one BF function per breaker, and the associated performance characteristics primarily in terms of spurious operations, are closely related to this practice. Currently this performance is considered satisfactory. Wide penetration of simple integrated BF schemes that

follow the approach of Figure 2a with co-dependency on the common signal path and relay hardware, and with 2 to 4 BF elements per each breaker, may significantly elevate the risk of large outages due to BF misoperations. This danger can be alleviated while integrating the BF

functions but at price of increased complexity. Figure (c) shows a crosscheck scheme. Each fault detection

function initiates its own BF function. This BF function is placed on the other relay so that a crosscheck is made between detecting the fault and detecting the BF condition. This scheme calls for wiring the BFI signals, and cross-monitoring of relay fail safe outputs so that upon the failure of one of the relays the other relay could switch to its own internal BF function. Figure (d) presents a solution with a single BF allocated

statically to one of the relays. Figure (e) shows an integrated and single BF but in a

switchover scheme. Normally both relays initiate the same integrated BF (one internally and one externally). Upon the failure of the relay that normally performs the BF function, the other relay switches to its own integrated BF element. The configuration of a stand-alone BF relay (Figure 2a) fits

naturally the past protection practice with external summation of CTs for the line relay. Traditional line relays did not measure the two currents individually and could not integrate the BF function for both the breakers anyway. With modern line relays the BF for dual-breaker terminals

can be integrated using any of the approaches outlined in Figure 2. For example, Figure 3a shows the “one BF per each fault detection function” approach of Figure 2b; and Figure 3b shows an implementation of the crosscheck scheme of Figure 2c. Note that with the BF initiation from the adjacent zone for

one of the two breakers, the other breaker of the dual breaker arrangement needs to be tripped. With this respect the solution of Figure 3a requires wiring the BF Trip signals while avoiding wiring the BFI signals; and solution of Figure 3b calls for wiring more BFI signals, but some BF trips are routed internally in the relays.

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Relay 1

FD

Relay 2

BF

FD

Breaker Relay

Zones intersecting at theprotected CB

(a) Dedicated BF relay

Relay 1

FD

BF

Relay 2

FD

BF


(b) One BF per each FD function

Relay 1

FD

BF

Relay 2

FD


(d) Single, internal BF

Relay 1

FD

BF

Relay 2

FD

BF

Only if R1 fails

Only if R2 fails


(c) Cross-check scheme

Relay 1

FD

BF

Relay 2

FD

BF

Only if R1 fails


(e) Single, internal BF with switch-over

Fig. 2. Allocations of Fault Detection (FD) and BF functions between relays

FD1 FD2

FD

CB2CB1

(b) Cross-check scheme

Relay 3

FD BF2BF1

Relay 2

FD2BF2

Relay 1

BF1FD1

(a) One BF per each FD function

Relay 3

FD BF2BF1

Relay 2

FD2BF2

Relay 1

BF1FD1

Fig. 3. Selected BF schemes of Figure 2 as applied to dual-breaker line terminals

Advantages of integrating BF in dual-breaker applications

are: • Cost and space advantage by eliminating stand-alone

Breaker Failure relay(s). • Simplified wiring and interlocking. Every wiring

termination is a potential point of failure, so reducing the amount of wiring increases reliability.

• BF simpler and easier to test thus reducing probability of spurious BF trips due to human errors during maintenance.

• More flexible initiation logic such as from voltage or frequency triggered trips.

• Easier application of multiple setting groups (banks) to adapt the BF function to changing system conditions.

• Direct access to the existing DTT/pilot channels via line relays for tripping remote breakers.

Disadvantages of utilizing integrated BF in dual-breaker

applications are: • Impact on security: The BF function uses same current

inputs, hardware and software, and the tripping paths as the fault detection function. This minor disadvantage can be addressed by crosschecking as explained in Figures 2c and 3b.

• Impact on security: Multiple copies of the BF function operational for the same breaker potentially increase the probability of misoperation. As a backup function, the BF should not be duplicated or quadrupled. This problem can be solved by using a switchover scheme of Figure 2e or a pre-selected BF location of Figure 2d.

The above advantages and disadvantages should be

weighted accordingly taking into account other factors, relaying philosophy and maintenance practice in particular. Factors to consider are: • Preferred degree of security and reliance on remote versus

local backup. • Degree of integration of primary (fault detection) and

backup (BF) functions on a single multi-function relay. • Existing maintenance/testing practice, willingness and

capacity to adjust. • Preferences with respect to simplicity and cost targets.

IV. AUTOMATIC RECLOSING CONSIDERATIONS

Similarly to the BF protection function, the Autoreclosure (AR) control function can reside in a stand-alone dedicated breaker control relay, one per each breaker; or can be integrated in a multi-function line relay. In any case, fundamental AR issues are the same; initiation,

blocking, lockout, switch onto the fault logic, dead time for different types of the faults and different shot counts, tripping during evolving faults in single-pole tripping and reclosing applications, sequential reclosing of the two beakers (master/follower), dynamic switchover to the follower when

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the master is out of service, etc. Proper treatment of the middle breaker is yet additional

factor specific to dual-breaker applications. The middle breaker is controlled from both the line zones that intersect at the breaker. In the case of integrated BF, multiple BF functions for the

same breaker may not be viewed as beneficial from the security point of view, but are certainly acceptable as a simple solution. On the other hand, multiple copies of the AR function for

the same breaker are typically considered not acceptable. The AR is a complex and sequential controller. Paralleled, not synchronized instances of the AR would cause performance problems and pose testing and maintenance challenges. As a result, solutions depicted in Figure 2a (stand-alone AR), 2c (single pre-selected internal AR) or 2d (internal AR in a switch-over scheme or “hot stand-by”) can be considered. The “one AR at a time” philosophy applies to multiple

possible allocations of the AR function (A and B systems, 2 adjacent zones). Beyond the common requirements ARs for dual-breaker

applications should support the following features: • Allowing choosing sequence of reclosing (1-2, 2-1 or

simultaneous reclose operation). • Ability to transfer the close command from one breaker to

another if the breaker pre-selected to close first is taken out of service or failed to close.

• Ability to recognize that breaker was open prior to the line fault either manually or by adjacent protection. If used, lockout relays solve this problem. If the operational philosophy relies on the reclosers to lockout under the time-extended trip commands, the dual breaker AR needs to be designed/configured accordingly to lockout one breaker while permitting to control the other.

• If required for a given system topology, ability to check synchronism across each breaker individually, as the transmission system may become electrically isolated across each breaker and/or remote terminals.

• When required, ability to perform single-pole operation including tripping and reclosing under evolving faults considering simultaneous or near simultaneous faults on the parallel line that call for tripping and reclosing of the common (middle) breaker.

V. PROTECTION SECURITY UNDER CT SATURATION

Fed with externally added currents (Figure 4a) a typical line relay responds to a vectorial sum of the two local currents. If both the CTs operate with no errors, the sum of the currents is an accurate representation of the line current at this terminal. If one of the CTs saturates, the produced error signal will effectively superimpose on the true line current and cause potential problems for the protection security. The situation is particularily dangerous if the feed through the line is weak, and the CT carrying the reverse current saturates on a close in external fault (Figure 4b). A portion of the missing reverse

current will leave the forward current not balanced, and appear to the relay in the forward or tripping direction. It may appear that line current differential relays would not

have problems with saturated CTs. This is true only if a given relay measures all currents of its differential zone individually and produces proper restraint or other countermeasures to the problem of CT errors. If fed with externally added currents, a line current differential relay produces the restraint signal as per its design equations based on the summation of the two local currents. Because the relay does not respond to the individual currents, but to the sum of thereof, a combination of restrained and unrestrained differential principles is effectively applied, and as such, it may face stability problems. For example, with weak feed from the remote terminal(-s), and a large through fault current along the breaker-and-a-half diameter, CT saturation errors would manifest themselves as a spurious differential current while relatively small restraint would be produced from the small, remote-end currents (high through-diameter current not seen by the relay, low through-line current seen by the relay as depicted in Figure 4b).

(a)

DISTANCE /

DIFFERENTIAL

DISTANCE /

DIFFERENTIALCOMMUNICATION

CHANNEL

(b)

CT-1

CT-2

Relay Measurement

(c)

CT-1 + CT-2 is the line

current only if the CTs are

accurate

This measurement is not

affected by the large

through current

Fig. 4. Dual-breaker arrangement: external CT summation (a), through fault under weak remote and strong local systems (b),

through fault in a single-breaker application (c). This problem does not exist in single breaker applications

(Figure 4c). With the line current measured directly in single-breaker applications there is no danger of producing a large error signal even if the line CT saturates. If an error occurs due to CT saturation, it is properly restrained by the principle of percent differential protection. The problem in the dual-breaker configuration

demonstrates itself not only under severe CT saturation, but could become significant under relatively small CT errors,

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including linear errors related to the CT accuracy class. As long as the through current of the line is considerably higher compared with the error current produced by the CTs, there is no danger of the CT error signals overriding the actual through line current. When the error current is comparable with the through current, the protection system is in danger of misoperation. The through current could be low for long lines and/or when the remote system is relatively weak. The short circuit level of the local system alone controls the current flowing along the dual-breaker diameter. With the local terminal strong, and the remote terminal weak, any relay could be brought to its design limits by saturating one or more CTs on the diameter. Distance relays are also exposed to this problem. During

close-in reverse faults, the voltage is depressed to very low levels, and stability of the relay is maintained solely by the directional integrity of the currents as measured. If, under such circumstances, CT that carries the current away from the terminal saturates (CT1 in Figure 4b), an error current appears in the direction of the line. With enough error current, the through line current becomes overridden, and the actual reverse fault direction may be seen as forward by the relay. As a result, with the voltage depressed and the current elevated and flowing spuriously in the forward direction, distance functions may pickup inadvertently. This includes a directly tripping underreaching zone 1, as well as an overreaching zone 2 typically used by communication-assisted schemes. In both cases, a false trip could occur. Current-reversal logic, application of a blocking or hybrid

permissive schemes, or similar approaches, may enhance the performance and solve the problem partially. These approaches, however, often rely on a reverse-looking distance zone 4. The latter may spuriously drop out when the effective current gets inverted from the true reverse to a false forward direction due to CT errors. Extending the blocking action by using timers is a crude solution, but would jeopardize dependability and speed of operation on evolving external-to-internal faults. Ground directional overcurrent functions, neutral and

negative-sequence specifically – being both fast and sensitive – are good supplements enhancing performance of communication-assisted schemes [4]. They, however, face similar security problems in the dual-breaker applications. With reference to Figure 5 consider an external line-to-line fault on the diameter. In this case performance of all four CTs (A1, A2, B1 and B2) affects the neutral current. With any of the CTs saturating, a spurious neutral current will be created. There is no real neutral current through the line for this type of fault. Therefore, the operating signal for the Neutral Directional Overcurrent function is entirely driven by CT errors. The remote terminal will see the fault via its distance function and key permission to trip, unless separate pilot channels are used to key from distance and ground directional functions. Combined with the spurious operation of the neutral directional function at the local terminal, the received permission would cause a false trip. The above problem with sensitive ground directional

overcurrent functions also exists in single-breaker applications. However, in single-breaker applications the relay would measure the elevated phase currents. Modern relays allow for positive-sequence restraint in neutral or negative-sequence directional overcurrent functions, effectively solving the problem [4]. In a dual-breaker terminal with external CT summation, the positive-sequence restraint would not work.

DISTANCE /

DIFFERENTIAL

CT-1

CT-2

A B C

INEUTRAL

= 0

Fig. 5. Danger of a spurious neutral current in a dual-breaker line

application Phase comparison relays supplied with the external sum of

the currents would face the same stability problems in dual-breaker applications. Contrary to the commonly understood immunity of the phase comparison principle to CT saturation, the 87PC function requires all currents of its zone to be measured individually and included in its coincidence timing. Only by looking at the two local currents individually, a phase comparison relay would have a chance to recognize the through fault condition and develop a proper countermeasure as per the principle of phase comparison.

VI. SUPERVISION LOGIC FOR IMPEDANCE-BASED PROTECTION

This section outlines a simple supervisory logic to ensure security of the main line protection during through current conditions on the dual-breaker diameter with weak feed through the line. The logic can be programmed from a number of standard Instantaneous Overcurrent elements (IOCs) and Phase Directional (Ph Dir) elements of a relay. The supervisory logic has been developed to meet the

following requirements: • The supervision should not penalize the speed of response

to internal faults (trip time) or sensitivity of the relay to high-resistance internal faults. Therefore, permission to trip should be given all the time unless a through fault condition is detected.

• Permission to trip should be maintained during transitions from load conditions, possibly a reverse load, to internal faults.

• The supervision should allow the relay to trip an evolving

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external-to-internal fault, in particular with both faults present at the same time, i.e. before the external fault is cleared by the associated protection system.

• The supervision should respond to elevated phase currents as the high phase currents cause CT errors and the latter could jeopardize security of the line protection. Responding to sequence components is not preferred because under evolving faults flows of negative-sequence and neutral currents may be considerably changed from expected.

• The supervision shall be easily applied to distance, differential, and overcurrent directional functions.

A. Protection Elements used by the Supervisory Logic With reference to Figures 1 and 6 the following elements are used: • IOC 1 to respond to forward current of CT-1. The element

shall be set at 2-3 times the nominal of CT-1, and is used to unblock the relay on external-to-internal evolving faults.

• IOC2 to respond to elevated current of CT-1; set at 1.5-2 times the nominal of CT-1 and used to supervise the blocking action.

• PHS DIR 1 to respond to reverse current direction at CT-1.

• IOC3 – similar to IOC1, but for CT-2. • IOC4 – similar to IOC2, but for CT-2. • PHS DIR 2 – similar to PHS DIR 1, but for CT-2. The directional functions in one particular application [1-3]

use quadrature polarization with memory action, if required.

PHASE IOC1 A PKP

PHS DIR1 A BLK AND

BKR 1 A FWD

PHASE IOC2 A PKP

PHS DIR1 A BLK

AND

BKR 1 A REVPHASE IOC4 A PKP

(a)

BKR 1 A REV

BKR 1 B REV

BKR 1 C REV

BKR 2 A REV

BKR 2 B REV

BKR 2 C REV

BKR 1 A FWD

BKR 2 A REV AND

BKR 1 B FWD

BKR 2 B REV AND

BKR 1 C FWD

BKR 2 C REV AND

BKR 2 A FWD

BKR 1 A REV AND

BKR 2 B FWD

BKR 1 B REV AND

BKR 2 C FWD

BKR 1 C REV AND

OR

0.25 cycle

0 cycle

AND

CT SAT SUPV0.75 cycle

2.5 cycle

OR

OR

(c)

(b)

Fig. 6. Supervisory logic to cope with CT errors in the dual-

breaker configuration

B. Supervisory Logic A reverse direction for CB-1 (Figure 6a) is declared if both

currents are elevated (IOC2 and IOC4) and the directional element sees a reverse direction (PHS DIR 1 BLK). Similar logic is implemented for CB-2, and phases B and C. The reverse direction flags will be asserted only if an elevated current is flowing through the diameter, and the direction is reverse in one of the breakers. A forward direction for CB-1 (Figure 6b) is declared if the

current is elevated in the CB-1 leg and appears in the forward direction. Declaration of the forward direction is not impacted by the situation in the second leg of the diameter. Similar logic is implemented for CB-2, and phases B and C. As shown in Figure 6c, the blocking action is established if

any of the three phases shows a through current flowing outside of the zone, either through CB-1 or CB-2. For security, the blocking action gets artificially extended

for extra 2.5 cycles after being present for 0.75 of a cycle (switch off transient logic to cope with clearance of the external fault). The blocking action gets cancelled if any of the currents is

elevated, appears in the forward direction, and is not accompanied by the reverse direction in the other breaker in the same phase. A 0.25 cycle delay is added for security.

C. Performance Analysis and Explanation During load conditions (current below some 1.5 times CT

nominal) none of the IOCs is picked up and the trip permission is asserted permanently. During internal fault conditions with very weak feed from

the local terminal, the current is not elevated and may appear in the reverse direction as dominated by the load – permission is maintained as none of the IOCs picks up. During high current internal faults, none of the directional

elements operates in the reverse direction, and the trip permission is maintained. During external faults with one breaker opened, the

blocking action is not established, but it is not needed either. During external faults with both breakers closed, the

blocking action is established as long as both the currents flowing through the diameter are above the pickup of IOC2 and IOC4. During evolving external-to-internal faults in different

phases, the blocking action is first established (phase A for example), and then canceled when the second fault appears in the forward direction in a different phase (phase B for example). The output flag, CT SAT SUPV of Figure 6c, shall be used

to supervise distance and ground directional functions of a distance relay, and the differential function of a line current differential relay, if required.

D. Transient Response Examples Figure 7 presents an external fault example. The trip

supervision is removed in 0.5 of a power cycle when using one particular IED [1-3] to implement the logic of Figure 6c. Figure 8 shows an evolving fault example. The trip

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supervision is removed in 1 cycle after the external fault, but is re-established in 0.75 of a cycle after the fault evolves into internal.

Fig. 7. External Fault. Phase-to-phase fault through the diameter

causes enough CT error to operate spuriously the Neutral Directional OC function. The CT logic blocks in 0.5 cycle.

Fig. 8. External-to-Internal Evolving Fault Example. The relay

trips single-pole the correct phase despite the pre-existing external fault. The CT logic unblocks in 0.75 of a cycle.

VII. LINE CURRENT DIFFERENTIAL SOLUTION

This section presents a description of a line current differential algorithm [5-6], but extended to dual-breaker applications. The concept [5-6] has been originally implemented for a

single-breaker arrangement. In such an application, each relay [2] sends phasors of local current in all three-phases calculated using a half-cycle estimator (6 numbers) as well as dynamic terms used for adaptive restraint (3 numbers). Some extra data is appended to this core of the packet such as relay ID, virtual I/Os for teleprotection, time stamps to facilitate

synchronization with the use of the ping-pong algorithm [6], GPS-driven time stamps to facilitate channel asymmetry compensation [7], CRC-check, etc. The presented solution targets communications channels of

64kbps. The baud-rate of the channel imposes certain limitation for the packet size. Application to dual-breaker configurations calls for producing a proper restraining signal out of all the currents of the zone. For example, in three-terminal applications with each of the terminals being breaker-and-a-half or ring-bus, 6 three-phase currents surround the line differential zone. Exchanging all these currents between the terminals would increase the packet size. The following design targets have been stated for the line

current differential function capable of secure operation at multi-breaker terminals: • The packet size should remain unchanged. A total of 9

numbers must represent currents at each terminal in terms of phasors (real, imaginary) and static and dynamic restraint factors.

• Window resizing shall be applied for fast relay operation. • Proper restraint shall be produced to secure the

differential system on external faults through the local terminal’s breakers.

• Up to four currents could be used at each terminal in order to facilitate combined bus and line protection for small buses.

• Backwards compatibility of the operating principle shall be maintained if the relay is applied in a single breaker configuration.

The following subsections address the above design constraints and goals.

A. Phasor Estimation The input currents are sampled at 64 samples per cycle and

pre-filtered using an optimized MIMIC filter aimed at removing dc component(-s) and other low-frequency oscillations. The optimized filter is a Finite Response Filter (FIR) with the window length of approximately 1/3rd of a power system cycle. The digitally pre-filtered currents are converted into

phasors by applying half-cycle Fourier algorithm. The half-cycle values are either used as calculated, or two consecutive half-cycle measurements are combined into an equivalent full-cycle measurement. The operation of switching from full- to half-cycle upon detecting disturbance in currents is referred to as “window resizing” and is implemented to speed up operation of the relay. The differential system transmits half-cycle values, and the resizing is done independently at each terminal of the line. Half-cycle magnitudes are also calculated and transmitted

in order to reflect properly through fault conditions at each terminal of the line. In addition “a goodness of fit” factor is calculated for each

current in order to measure the error between the waveform and its Fourier-estimated phasor [7]. The goodness of fit factor is further used to produce an extra restraint to countermeasure

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the estimation error, and increase security of the relay. Conceptually, the goodness of fit factor is proportional to the following value:

21

0)()()()(

2cos∑

−

=−

Θ+⋅⋅

⋅−='

nkknkk '

nXx

πδ (1)

In equation (1), the present magnitude and phase estimate

(X,Θ) at the k-th sample is compared with the actual waveform (x) over the duration of the data window ('), and the sum of squares error measure is calculated.

B. Consolidating Local Currents – the Outgoing Packet Each terminal of the current differential system consolidates

the local signals into an outgoing packet. Compression of information takes place in order to reduce the packet size and distribute the calculations between the two or three relays of the line current differential system. This is possible without compromising operating equations or accuracy if the operating equations are shaped accordingly. First, the phasors (real, imaginary) of all the local currents

are summated to give a sub-sum of the total differential current of the protected line:

...__2__1__ ++= AREAREARELOC III (2)

Equation (2) is applies to up to four local current inputs and

holds true for both real and imaginary parts, in all three phases. Equation (2) is not a differential current, but a portion of the differential current that involves the local currents only. Second, the measure of a through fault current is estimated

locally using magnitudes of all the local currents via the following equation:

( ) ( ) ( )( ),...,max 2__2

2__1

2__ AMAGAMAGATRADLOC III = (3)

Equation (3) selects, on a per phase basis, the largest among

the local currents to be a measure of the local restraint. Figure 9 illustrates the principles behind equations (2) and

(3). Third, the protection system applies differential

characteristic locally to each of the restraining currents. The presented system does not use an explicit restraining characteristic, but the total operating and restraining value [5-6]. The latter incorporates values of the pickup, slopes (S1, S2) and breakpoint (B). The following equations are used to accommodate the characteristic:

• In two-terminal applications:

If ( ) 22__ BI ATRADLOC <

Then ( ) ( ) ( )2__2

12

___ 2 ATRADLOCATRADRESTLOC ISI ⋅⋅= (4a)

Else:

( ) ( ) ( ) ( )( ) ( )212

22

__2

22

___ 22 BSBSISI ATRADLOCATRADRESTLOC ⋅⋅+⋅−⋅⋅=

(4b) • In three-terminal applications:

If ( ) 22__ BI ATRADLOC <

Then ( ) ( ) ( )2__2

12

___ 3

4ATRADLOCATRADRESTLOC ISI ⋅⋅= (4c)

Else:

( ) ( ) ( ) ( )( ) ( )212

22

__2

22

___3

4

3

4BSBSISI ATRADLOCATRADRESTLOC ⋅⋅+⋅−⋅⋅=

(4d) The adaptive portion of the restraint is a geometrical sum of

errors derived from equation (1) and a measure of the clock synchronization error [5-6]. The traditional and adaptive restraints are combined geometrically using a concept of an extra arbitrary multiplier:

( ) ( )2__2

_____ AADALOCAATRADRESTLOCARESTRIA'TLOC IMULTII ⋅+=

(5)

(a)

I1 I2 I3 I4

I1+I2+I3+I4LINE

(b)

I1 I2 I3 I4

I4 = I1+I2+I3In the worst-case, with no

restraint from the remote

terminal, the maximum local

current (most likely the fault

current) becomes the

restraint

Fig. 9. The differential current is created from partial sums of all the local currents (a). The restraining current is created based on the

maximum local current (b).

The multiplier increases the impact of signal distortions on the restraint, and is used to provide better restraint during CT saturation conditions on through line faults. Values defined by equations (1-5) are based on half-cycle

windows, and constitute the following outgoing packet:

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K,,,,,, ____________ CIMLOCBIMLOCAIMLOCCRELOCBRELOCARELOC IIIIII

CRESTRAI'TLOCBRESTRAI'TLOCARESTRAI'TLOC III ______ ,,,K (6)

C. Total Differential and Restraint Currents The local and remote data when received are used to

calculate the total differential and restraining signals for the current differential system. Before the data is used, a decision is made to either use the

full- or half-cycle measurements. The half-cycle data is used one time after detecting a fault. After such half-cycle window is used, the relay switches back to the full-cycle version when proceeding into the fault. Also, when a packet is lost, the next packet that arrives triggers window resizing. This is simply to enable protection using the latest packet even though the previous packet required to calculate the full-cycle quantities is lost due to the communication channel impairments. The following equations are used to combine the half-cycle

values into full-cycle measurements:

=AREPHASORLOCI ___ ( ))(__)(__5.0 previousARELOCpresentARELOC II +⋅ (7a)

( ) =2___ ARESTRAI'TPHASORLOCI ( ) ( )[ ]2)(__

2)(__5.0 previousARESTRAI'TLOCpresentARESTRAI'TLOC II +⋅ (7b)

Equation (7b) is accurate; equation (7b) is a good

approximation. Equations (7) apply to both local and remote signals, all three phases, and real and imaginary parts. Next, the relay calculates the total differential and restraint

currents:

=AREDIFFI __

AREPHASORREMAREPHASORREMAREPHASORLOC III ___2___1___ ++ (8a)

( ) ( ) += 2___

2_ ARESTRAI'TPHASORLOCAREST II

( ) ( )2___22

___1 ARESTRAI'TPHASORREMARESTRAI'TPHASORREM II ++ (8b)

And applies the so-called fault severity equation in order to

decide if the line should not should not be tripped [5-6]:

( ) ( )( )2_22

_ ARESTADIFFA IPIS +−= (9)

The relay (87L function) operates if the fault severity, S, is

positive. P is the pickup of the characteristic (the slopes and

breakpoints were already accommodated before sending the data in equations (4)). As indicated by all the equations, the algorithm is fully

phase-segregated.

D. CT Saturation Detection The algorithm has a built-in immunity to saturated CTs

owing to the concept of the dynamic restraint. The goodness of fit (1) becomes degraded on saturated waveforms, producing a measure of error (1), which added to the restraining signal allows for extra security. In order to boost this natural effect, the system is using an

adaptive multiplier in order to increase further the impact of the dynamic portion of the restraint (5) on the overall performance of the relay. The multiplier is calculated adaptively per phase as follows:

( )AAA MULTMULTMULT 21 ,max= (10)

The first component is based on local currents only, and as

such is instantaneous. This component is meant to detect through fault condition on the local diameter of the breaker-and-a-half or ring-bus configuration. The second component is based on local and remote

currents, and as such is lagging the real time by the channel propagation time. This component is meant to detect through fault conditions between terminals of the line. The first multiplier is calculated as follows: Step 1. Select the greatest current from the local currents.

The selection is based on half-cycle magnitudes: I1_MAG, I2_MAG, I3_MAG, I4_MAG. Assume the largest current is in the k-th circuit (k = 1,2,3 or 4). Step 2. Calculate two auxiliary currents:

REkREX II __ = (11a)

IMkIMX II __ = (11b)

REXREREREREREY IIIIII __4_3_2_1_ −+++= (11c)

IMXIMIMIMIMIMY IIIIII __4_3_2_1_ −+++= (11d)

The X-current is the maximum current among the local

currents. The Y-current is the sum of all the local currents but the maximum current. Note that during through faults with no feed from the remote terminals IX = -IY if no CT saturation. With CT saturation the currents differ, but remain approximately out of phase. Step 3. Calculate the multiplier as follows:

If puIpuI YX 3&3 >> (12a)

then If ( )( ) oYX IIangleabs 90, > (12b)

then ( )( )oYX IIangleabsMULT

180

5,: ⋅= (12c)

else 1:=MULT (12d) else 1:=MULT (12e)

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Equations (12) check if both currents (the maximum among

the local currents, and the sum of all the other local currents) are large enough to cause significant CT saturation. If so, the relative direction of the two currents is checked. If the angle is less than 90 degrees, the multiplier stays at the “neutral” value of 1.00. If the angle is larger than 90 degrees, the multiplier is proportional to the angle difference and could reach the maximum value of 5.00 if the currents are exactly out of phase. The second multiplier is calculated applying exactly the

same procedure, but instead of using local currents, the procedure uses the sum of the local currents, and the remote currents. In other words the currents into the line at each of up to three terminals of the line, regardless of the number of local currents at each terminal of the line. The second multiplier detects through fault conditions of the entire line. Figure 10 illustrates operation of the presented algorithm

under through fault conditions. In this example the traditional restraint of 15pu, is additionally augmented by adding the dynamic factor. The dynamic restraint is naturally increased by saturated CT, and artificially multiplied by the multiplier. In this example, the T3 terminal sees CT saturation in the circuit carrying the current out of the line toward the fault. This CT saturation will jeopardize stability of all terminals. However, all terminals will use high values of the multiplier to boost the effect of dynamic restraint, and will not misoperate.

E. Field Example A permanent AG fault occurred on line L2 in the system of

Figure 11. The line was tripped and reclosed from the A2 breaker. Shortly after a line current differential relay protecting the L1 line misoperated. Note that this installation used line current differential relays fed with externally summated currents. Figure 11 shows traces of the phase A currents at both ends

of the L1 line. The remote end current is not distorted. The local current is heavily distorted and suspicious. Detail analysis reveals that the A1 and A2 breakers carried about 22kA of fault current, or 22kA/0.8kA = 27.5 times rated when A2 closed onto the fault. The CTs saturated quickly due to a combination of large ac current, remanent flux due to the original fault, and dc offset. The through current in the L1 circuit was only 1.36kA. Relatively minor errors of the CTs carrying 22kA augmented considerably the true “1.36kA reverse” signal causing a false operation. The remote end relay measured 1.36kA∠-20° (correct)

while the local relay measured 1.77kA∠-112° (incorrect, due to CT saturation). As a result, the differential signal appeared to be 2.19kA.

The restraining signal calculated by the relays was 1.73kA (assuming a pickup of 0.16kA and a slope setting of 50%). The operating (differential) signal was far above the restraining signal, hence the spurious trip. Should the L1 relay at the A terminal be deployed in a

dual-breaker manner, and measured the A1 and A2 current separately, it would apply the restraint of:

0.16kA + 0.5*(max(23.3kA,21.9kA,1.36kA)) = 11.8kA The above restraint is several times higher than the

operating signal resulting in no operating for this external fault case.

2 pu

This CT should carry 19pu.

For illustration 15pu is

assumed to reflect CT

saturation error causing a

spurious differential current

of 4 pu.

4 pu

5 pu

2 pu

T1

6 pu -15 pu

T2

T3

ILOC = 6 pu ILOC = 7 pu

I LOC = -9 pu

ITRAD = 4 puITRAD = 5 pu

I TR

AD = 15 pu

(a)

2 pu

All three terminals apply the

multiplier of 5 to further

increase the traditional

restraint driven by the local

value of 15pu at T3

4 pu

5 pu

2 pu

T1

6 pu -15 pu

T2

T3

6 pu 7 pu

-9 pu

(b)

M1 = 1 (2pu vs 4pu)

M2 = 5 (6+7pu vs -9pu)

M = max(1,5) = 5

M1 = 1 (2pu vs 5pu)

M2 = 5 (7+6pu vs -9pu)

M = max(1,5) = 5

M1 = 5 (6pu vs -15pu)

M2 = 5 (-9pu vs 6+7pu)

M = max(5,5) = 5

Fig. 10. An example of calculating the restraints (a) and multipliers for CT saturation algorithm (b).

VIII. PHASE COMPARISON SOLUTION

As explained in section 5, phase comparison principle would face security problems when fed from externally summated currents in dual-breaker applications. In order to maintain the excellent immunity to CT saturation of the original (“single-breaker”) phase comparison principle, one needs to process the two currents individually and use both the phase and magnitude information to detect the through fault condition. The dual breaker logic consolidates two pieces of

information: fault detector flags signaling the rough current levels, and the “phase” pulses signaling current direction [8]. The fault detector flags (Fault Detector Low and Fault

Detector High) are OR-ed between the two breakers (breakers 1 and 2):

21 FDLORFDLFDL = , 21 FDHORFDHFDH = (13)

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Station A

21.9kA

A1

A2

A3

~

L1

L2

~

87L

L1

Fault

B1

B2

B3

~

~

87L

L1

87L

L2

1.36kA

23.3kA

Σ

87L

L2Σ

Σ

Σ

115kV Station B

1.76kA

800/5A

Fig. 11. System configuration for the presented filed case The rationale behind it is that regardless which breaker, or

both carry a current; the elevated current condition (FDL) shall be declared to signal permission or blocking as per the scheme type, and fault location; similarly with the trip supervision condition (FDH). It is the “pulse” combination logic that ensures security and

dependability of the 87PC function. With this respect a distinction must be made between tripping and blocking schemes. For tripping (permissive) phase comparison schemes, a

positive polarity is declared for the terminal if one breaker displays positive polarity when its FDL flag is set, while the other breaker either does not show the negative polarity or its FDL flag is dropped out (Figure 12a). This is similar to a Hybrid POTT scheme when a given terminal sends a permissive signal unless is restrained locally by a reverse fault condition. Note that this logic displays the following desirable features: • Under through fault conditions, when both currents are

elevated and out of phase, the positive pulses in one breaker get “erased” by the negative pulses in the other breaker.

• Under reverse or forward fault with one breaker opened or its current below the lower fault detector, the logic behaves as for a single breaker. The elevated current in the closed breaker drives the response of the scheme. In this way a small out-feed can be tolerated and will not impair dependability of the scheme.

• Under forward fault with both breakers closed and both currents above the fault detection level, the two-breaker

logic effectively creates a coincidence pulse out of the two individual pulses (logical AND). This corresponds to a multi-terminal phase comparison where all individual current pulses are AND-ed before feeding the trip integrators.

The above logic is used for keying in permissive schemes,

and regardless of the scheme type for derivation of local pulses sent to the trip integrators of the phase comparison relay. Transmission logic for the blocking logic follows a different

reasoning (Figure 12b). Here, a blocking action must be established if any of the two breakers sees a reverse direction. It must be kept in mind that the positive and negative pulses do not necessarily complement each other, and therefore one must not substitute the “not positive polarity” by “negative polarity”. Figure 13 shows a sample response of the permissive logic

to a through fault condition at a two-breaker terminal. The terminal does not produce permissive pulses and inhibits as expected. Figure 14 shows a case of an internal fault with strong feed

from both the breakers. More information on modern implementations of the phase

comparison principle, including dual-breaker applications and the CT saturation issue, can be found in [8].

AND

LOC1P_RAW

FDL1

OR

FDL2

FDL2

AND

LOC1N_RAW

OR

AND

LOC2P_RAW

FDL2

OR

FDL1

FDL1

AND

LOC2N_RAW

LOCP_RAW

(a)

AND

LOC1P_RAW

FDL1

FDL2

OR

LOCP_RAW

(b)

AND

LOC2P_RAW

FDL2

FDL1

AND

LOC1P_RAW

LOC2P_RAW

AND

LOC1P_RAW

LOC2N_RAWAND

LOC2P_RAW

LOC1N_RAW

OR

AND

FDL1

FDL2

Figure 12. Dual-breaker logic for the phase comparison relay [8]: Permissive (a) and blocking (b) transmit schemes.

IX. STUB BUS PROTECTION AND ISSUES

In dual-breaker applications a line disconnect can be opened while the two breakers are closed to facilitate continuous service of other circuits. At the same time the line may be energized from the other end or ends, to service tapped loads or transmit power between the other two line terminals (Figure 15). Under such circumstances the following needs to be

assured: • The stub bus zone between the two breakers and the

opened disconnect is properly protected. In single-breaker

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application a simple overcurrent function supervised with the “disconnect opened” signal is sufficient. In dual-breaker applications such simple solution would face security problems under through fault conditions and saturated CTs as explained in section 5. Either a differential-type stub bus protection is implemented with the use of proper restraint to counterbalance the impact of saturated CTs, or the supervisory logic presented in section 6 is adopted for tripping.

• When tripping on stub bus faults, no DTT is to be sent to the remote end(-s) as they are already isolated from the fault by the opened disconnect switch. Upon failure of one of the breakers, no BF trip is to be sent to the remote ends either.

Fig. 13. Illustration of dual-breaker logic: permissive, dual-

comparison scheme, through fault condition (relay [3] COMTRADE record).

Figure 14. Illustration of the dual-breaker logic: permissive single-comparison scheme, internal fault condition (relay [3] COMTRADE

record).

DSw

CB2CB1Line

Terminal 1

LineTerminal 2

LineTerminal 3

LineProtectionZone

Stub-busProtectionZone

Fig. 15. Stub bus situation (three-terminal line)

• A fault in the stub bus zone must not result in tripping the

remote line terminals. Solutions to this requirement depend on the applied protection principle, as explained below.

• Permissive directional comparison schemes typically do not have a problem. A permanent permission is keyed under the circumstances (disconnect opened while the breakers are closed); an echo scheme is used; or an overreaching zone 1 is applied at the remote end under the circumstances. In three-terminal applications or with tapped loads, it may happen that the remote end will “see” the fault in the stub bus zone despite the opened disconnect (Figure 16). This creates security problems if permanent permission or an echo scheme is used. If the fault current closes through the third line terminal, no permission will be sent from that terminal. But if the line closes via an unmonitored tapped load, the problem remains. Avoiding too sensitive overreaching functions at the remote end solves the problem.

• Under the circumstances blocking directional comparison schemes are practically equivalent to permissive schemes with permanent permission or echo as described above. Making sure the overreaching forward looking fault detectors never pickup for faults in the stub bus zone soles the problem.

• With the respect of the stub bus protection and application phase comparison relays can be dealt with as the same way as direction comparison schemes.

• Line current differential schemes require the relay under the stub bus condition to transmit zero currents regardless

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of its actual measurements. In this way under the stub bus fault, the 87L function will not trip the line at the remote terminal(s).

DSw

CB2CB1Line

Terminal 1

LineTerminal 2

LineTerminal 3

Forward,Overreaching FaultDetector

PermissiveEcho

Figure 16. Example of fault detectors too sensitive and causing problems under remote stub bus faults

X. CONCLUSIONS

This paper presents practical application solutions for

protection of lines in dual breaker applications. Integration of breaker failure and autoreclose is discussed

first. Next a problem of stability under CT saturation when using

externally summated currents for protection is described. A simple supervisory logic that could be implemented on

modern line relays is presented to ensure security under CT saturation during through faults on the breaker-and-a-half or ring-bus diameter. A novel line current differential system is described suitable

not only for dual-breaker configurations, but also for applications with up to four local inputs at each of the up to three terminals of the line. The solution is designed to produce correct restraining signal as per the principle of differential protection without sending all the raw local currents between all terminals of the line. Phase comparison algorithm addressing the security

concern related to CT saturation in dual-breaker applications is also presented. Finally notes are included on stub bus protection as related

to dual-breaker applications. Modern multi-input multi-function line protection relays

allow more sophisticated applications on dual-breaker line terminals.

REFERENCES

[1] GE Publication GEK-112989A, 2005, D60 Line Distance Relay, Instruction Manual.

[2] GE Publication GEK-112994A, 2005, L90 Line Differential Relay, Instruction Manual.

[3] GE Publication GEK-106412A, 2005, L60 Phase Comparison Relay, Instruction Manual.

[4] B.Kasztenny, D.Sharples, B.Campbell, M.Pozzuoli, “Fast Ground Directional Overcurrent Protection – Limitations and Solutions”, in Proc. 27th Annual Western Protective Relay Conference, Spokane, WA, October 24-26, 2000.

[5] A.Adamiak, G.Alexander, W.Premerlani, “A New Approach to Current Differential Protection for Transmission Lines”, in Proc. Electric Council of 'ew England – Protective Relaying Committee Meeting, Portsmouth, NH, October 22-23, 1998.

[6] M.Adamiak, G.Alexander, W.Premerlani, E.Saulnier, B.Yazici, “Digital Current Differential System”, U.S. Patent 5 809 045, September 15, 1998.

[7] G.Brunello, I.Voloh, I.Hall, J.Fitch, “Current Differential Relaying – Coping with Communications Channel Asymmetry”, in Proc. of the 8th Developments in Power System Protection Conference, Amsterdam, April 5-8, 2004, pp.821-4.

[8] B.Kasztenny, I.Voloh, E.A.Udren, “Rebirth of the Phase Comparison Line Protection Principle”, in Proc. of the 59th Annual Conference for Protective Relay Engineers, April 4-6, 2006, College Station, Texas.

Bogdan Kasztenny holds the position of Protection and System

Engineering Manager for the protective relaying business of General Electric. Prior to joining GE in 1999, Dr.Kasztenny conducted research and taught protection and control at Wroclaw University of Technology, Texas A&M University, and Southern Illinois University. Between 2000 and 2004 Bogdan was heavily involved in the development of the Universal RelayTM series of protective IEDs. He authored more than 160 papers, is the inventor of several patents, Senior Member of the IEEE, and the Main Committee of the PSRC. Dr.Kasztenny is a registered professional engineer in the province of Ontario. In 1997, he was awarded a prestigious Senior Fulbright Fellowship. In 2004 Bogdan received GE’s Thomas Edison Award for innovation.

Ilia Voloh received his Electrical Engineer degree from Ivanovo State Power University, Soviet Union. He then was for many years with Moldova Power Company in various progressive roles in Protection and Control field. Currently he is an Application Engineer with GE Multilin. His areas of interest are current differential relaying, phase comparison, distance relaying and advanced communications for protective relaying.

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15

VVII II II SSiimmppooss iioo IIbbeerrooaammeerr ii ccaannoo ssoobbrree PPrroo tteecccc iióónn ddee SSiiss tteemmaass EElléécc tt rr ii ccooss ddee PPootteenncc iiaa

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Resumen— En este artículo se presenta un método para el

ajuste del alcance resistivo de la característica cuadrilátera en

relés de distancia. El método se basa en el análisis de la

impedancia aparente vista por el relé y en la definición explícita

de las características deseables de la protección para cada zona

analizada. En el método propuesto, el ajuste del alcance resistivo

depende del ajuste del alcance reactivo y se calcula asumiendo

que éste ha sido previamente definido. El método se aplicó en un

ejemplo con 18 relés de distancia y su solución se comparó con

una solución simplificada, que consiste en ajustar el alcance

resistivo multiplicando el alcance reactivo por un factor constante

único, lo que permite apreciar las diferencias con respecto al

método propuesto.

Palabras claves—Ajuste de la función de distancia, alcance

resistivo en características cuadriláteras de relés de distancia.

I. INTRODUCCIÓN

L ajuste de las diferentes zonas de los relés de distancia se ha realizado tradicionalmente de acuerdo a reglas simples

[1]-[4]. Una revisión bibliográfica sobre el tema [5] clasificó las otras opciones que se han propuesto para efectuar dicho ajuste, según su fundamento conceptual (basadas en sistemas expertos, optimización matemática, protección adaptativa o métodos probabilísticos). Las reglas tradicionales de ajuste más conocidas se han desarrollado para el alcance ante fallas sólidas [1]-[5]. Cuando existe un ajuste independiente del alcance resistivo, como en el caso de las características cuadriláteras, es deseable definirlo mediante el análisis de las fallas a través de impedancia. Los métodos tradicionales que analizan las fallas a través de impedancia suelen hacerlo calculando una resistencia de falla típica [1],[2]; tales métodos no suelen considerar que la impedancia aparente vista por el relé está influenciada por diversos factores [6]. Una opción aún más simplista consiste en ajustar el alcance resistivo multiplicando el alcance reactivo por un factor único [7]. En este artículo se presenta un método para el ajuste del

alcance resistivo de la característica cuadrilátera en relés de distancia, basado en analizar la impedancia aparente vista por el relé y en usar una definición explícita de las características deseables de la protección para cada zona analizada.

Elmer Sorrentino labora en la Universidad Simón Bolívar, Caracas, Venezuela. Eliana Rojas labora en ABB, Caracas, Venezuela. Jesús Hernández labora en SENECA, Porlamar, Venezuela.

II. CRITERIOS DE AJUSTE PROPUESTOS

A. Consideraciones básicas preliminares

-En este artículo se considera que el ajuste reactivo (XR) se ha evaluado previamente, usando reglas tradicionales. Como tales reglas no son universales, especialmente para las zonas temporizadas, se indica la regla empleada para cada zona. -Los criterios usados en este artículo para el ajuste de XR

son relativamente complejos. Esto se realizó con el fin de ilustrar mejor la posibilidad de adaptación del método propuesto para el ajuste del alcance resistivo (RR). -Se asume que los tiempos de las zonas 2, 3 y 4 están

predefinidos, sin posibilidad de variarlos para mejorar la selectividad. Además, se asume la inexistencia tanto de teleprotección (disparo asistido por comunicaciones) como de protección ante falla de interruptor (50BF) y/o de protección diferencial de línea (87L). -Estas consideraciones suelen incidir en la forma de ajustar

XR para cada zona con criterios tradicionales. El método que se propone en este artículo para ajustar RR podría adaptarse a otros modos de ajustar XR. Para explicar con mayor facilidad las ideas se consideró necesario usar, como ejemplo, un modo específico de ajustar XR.

B. Características cuadriláteras analizadas

La característica cuadrilátera puede tener diversas formas y la figura 1 muestra el primer cuadrante para 3 casos distintos. En este artículo se asume que el criterio de ajuste está definido por el primer cuadrante en el plano R-X. Por simplicidad en la descripción del método propuesto, se

asumirá que la forma de la característica es la más simple (figura 1a). Sin embargo, los conceptos desarrollados pueden ajustarse a otras formas de la característica cuadrilátera (por ejemplo, como las mostradas en las figuras 1b y 1c), y sólo se requeriría adaptarse al manejo de las condiciones específicas que definan la geometría de la característica.

R

jX ZL+

θL+

XR

RR

R

jX ZL+

θL+

XR

RR

θL+R

jX ZL+

θL+

RR

θL+

XR α

a b c

R

jX ZL+

θL+

XR

RR

R

jX ZL+

θL+

XR

RR

θL+R

jX ZL+

θL+

RR

θL+

XR α

a b c

Fig. 1. Ejemplos de distintas formas de zonas cuadriláteras.

Método para el ajuste del alcance resistivo en características cuadriláteras de relés de distancia

Elmer Sorrentino Eliana Rojas Jesús Hernández

E

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C. Ajuste del alcance resistivo de la zona 1

C.1. Criterio usado para el alcance reactivo Se considerará que la zona 1 sólo debe actuar ante fallas en

la línea. Esto implica evitar que opere ante fallas en la barra remota, por selectividad. Se asumirá que el ajuste del alcance reactivo de la zona 1 (XR1) se realiza al 80% de la reactancia de la línea protegida (XL+): XR1 = 0,8 XL+.

C.2. Criterio usado para el alcance resistivo En concordancia con lo anterior, el alcance resistivo de la

zona 1 (RR1) debe ajustarse para evitar que opere ante fallas en la barra remota, considerando el efecto de las resistencias de falla. Esto implica el análisis de tres casos: a) Fallas en la barra remota cuya impedancia aparente (ZAP)

tienda a entrar en la característica de la zona 1 (figura 2a). Para que exista margen de seguridad, se limitará el ajuste resistivo (RR1-A) al valor de la parte real de ZAP en el que la parte imaginaria de ZAP sea el 90% de XL+. b) Fallas en la barra remota cuya ZAP tienda a ser paralela a

XR1 (figura 2b). Se considerará que el posible error de medición del relé es proporcional al módulo de ZAP. Por ello, cuando la parte imaginaria de ZAP menos el 5% del módulo de ZAP sea igual al 85% de la XL+, la correspondiente parte real de ZAP limitará el ajuste resistivo (RR1-B). c) Fallas en la barra remota cuya ZAP tienda a alejarse de XR1

(figura 2c). En este caso RR1 no está limitado por ZAP. El ajuste de RR1 será el menor de los valores RR1-A y RR1-B, si

ambas situaciones pueden suceder. Si el ajuste de RR1 no está limitado por ZAP, RR1 podría ser ajustado a un valor muy alto.

ZAP variando RF

R

jX

ZL+

θL+

XR1=0,8XL+

RR1-A

Si ImImImImZAP=0,9XL+,⇒ RR1-A=ReReReReZAP

ZAP variando RF

R

jX

ZL+

θL+

XR1=0,8XL+

RR1-B

Si [ImImImImZAP-0,05|ZAP |]=0,85XL+,⇒ RR1-B=ReReReReZAP

ZAP variando RF

R

jX

ZL+

θL+

XR1=0,8XL+

RR1 no está limitado por ZAP

a

b

c

ZAP variando RF

R

jX

ZL+

θL+

XR1=0,8XL+

RR1-A


ZAP variando RF

R

jX

ZL+

θL+

XR1=0,8XL+

RR1-A


ZAP variando RF

R

jX

ZL+

θL+

XR1=0,8XL+

RR1-B

Si [ImImImImZAP-0,05|ZAP |]=0,85XL+,⇒ RR1-B=ReReReReZAP

ZAP variando RF

R

jX

ZL+

θL+

XR1=0,8XL+

RR1 no está limitado por ZAP

a

b

c

Fig. 2. Criterios usados para el ajuste del alcance resistivo de la zona 1.

D. Ajuste del alcance resistivo de la zona 2

D.1. Criterio usado para el alcance reactivo Se considerará que el principal objetivo de la zona 2 es

cubrir el tramo de la línea que no está cubierto por la zona 1. Esto implica ajustar el alcance reactivo para cubrir más del 100% de la impedancia de la línea protegida, con el fin de garantizar sensibilidad ante fallas internas en la línea. Este criterio indicado se utiliza frecuentemente; sin embargo, suele requerirse tomar previsiones para mantener selectividad cuando hay líneas cortas adyacentes a la barra remota, pues el inicio de la zona 2 de la protección de línea corta adyacente podría solaparse con el fin de la zona 2 de la línea en estudio. Se asumirá que el ajuste del alcance reactivo de la zona 2

(XR2) se realiza con el siguiente criterio: -Se evalúa el ajuste mínimo deseable para el alcance

reactivo de la zona 2 (X2-MIN-1) como el 120% de la reactancia de la línea protegida (XL+): X2-MIN-1 = 1,2 XL+. -Se evalúa el ajuste máximo deseable para el alcance

reactivo de la zona 2 (X2-MAX) como el 80% de la reactancia total vista hasta el inicio de la zona 2 de la línea adyacente al extremo remoto que represente una menor reactancia adicional (XL+,ADY,CORTA): X2-MAX = 0,8(XL++0,8XL+,ADY,CORTA). -Si X2-MAX es mayor que X2-MIN-1, entonces no hay conflicto

alguno entre esos valores y el ajuste será: XR2 = X2-MIN-1. -Si X2-MAX es menor que X2-MIN-1, entonces no es posible

satisfacer la sensibilidad deseada garantizando selectividad y: -Se evalúa el promedio de los valores mencionados

previamente (X2-PROM=[X2-MIN-1+X2-MAX]/2) y se evalúa el ajuste mínimo admisible (X2-MIN-2) para el alcance reactivo de la zona 2 como el 110% de XL+ (X2-MIN-2=1,1 XL+). -Si X2-PROM es mayor que X2-MIN-2, entonces no hay

conflicto alguno entre esos valores y se realizará el siguiente ajuste: XR2 = X2-PROM. -Si X2-PROM es menor que X2-MIN-2, entonces se asumirá

que no es posible garantizar selectividad con esa línea adyacente corta y el ajuste será: XR2 = X2-MIN-2. En la práctica, la solución para este caso es recomendar el uso de una protección unitaria para la línea adyacente corta (diferencial de línea y/o teleprotección) y/o un cambio en el tiempo de actuación de la zona 2 de la línea en estudio. Sin embargo, se considerará que el análisis de dichas soluciones está fuera del alcance del presente trabajo.

D.2. Criterio usado para el alcance resistivo El ajuste del alcance resistivo de la zona 2 (RR2) se define en

términos similares a lo descrito para el ajuste reactivo. La sensibilidad deseable será considerada para cubrir fallas

al 100% de la línea protegida con el valor típico de resistencia de falla (RF-TIP) multiplicado por un factor de seguridad (FS1) y la sensibilidad mínima admisible utiliza un factor de seguridad (FS2) menor: FS2<FS1; RF1=(FS1)RF-TIP; RF2=(FS2)RF-TIP (por lo tanto, RF2<RF1). El ajuste mínimo deseable y admisible (R2-MIN-1 y R2-MIN-2,

respectivamente) corresponde a la parte real de la impedancia aparente vista por el relé ante fallas al 100% de la línea protegida, con las resistencias de falla que consideran los

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distintos factores de seguridad (RF1 y RF2), como se ilustra

en la figura 3a.

ZAP variando RF hasta RF2

R

jX

ZL+

θL+R2-MIN-2

Zona 1 de la líneaadyacente, vista porel relé en estudio

R

jX

ZL+

θL+

R2-MAX=0,9R2-R1-ADY

a

b


R2-MIN-1

Fallas en lalínea protegida

Fallas fuera de lalínea protegida

ZL+,ADY

R2-R1-ADY


R

jX

ZL+

θL+R2-MIN-2

Zona 1 de la líneaadyacente, vista porel relé en estudio

R

jX

ZL+

θL+

R2-MAX=0,9R2-R1-ADY

a

b


R2-MIN-1

Fallas en lalínea protegida

Fallas fuera de lalínea protegida

ZL+,ADY

R2-R1-ADY

Fig. 3. Límites para el ajuste del alcance resistivo de la zona 2.

El ajuste máximo deseable para el alcance resistivo de la zona 2 (R2-MAX) se evalúa considerando fallas a través de resistencia, al inicio de líneas adyacentes al terminal remoto, que se salgan de la zona 1 de la línea adyacente. Esto implica hallar el límite de resistencia de falla (RF-LIM-ADY) que es capaz de detectar el relé de la línea adyacente al inicio de su zona 1 y evaluar, con dicha resistencia de falla, la parte real de la impedancia aparente vista por el relé de la línea en estudio, ante fallas al 100% de la línea protegida (R2-R1-ADY): se considerará que el ajuste máximo deseable corresponde al 90% de este último valor (R2-MAX = 0,9 R2-R1-ADY), como se ilustra en la figura 3b. El algoritmo de ajuste del alcance resistivo de la zona 2 es

similar al descrito para el ajuste del alcance reactivo: -Si R2-MAX es mayor que R2-MIN-1, entonces no hay conflicto

alguno entre esos valores y el ajuste será: RR2 = R2-MIN-1. -Si R2-MAX es menor que R2-MIN-1, entonces no es posible

satisfacer la sensibilidad deseada garantizando selectividad y: -Si R2-MAX es mayor que R2-MIN-2, entonces no hay

conflicto entre esos valores y el ajuste será: RR2 = R2-MAX. -Si R2-MAX es menor que R2-MIN-2, entonces se asumirá que

no es posible garantizar selectividad para algunos valores de resistencia de falla y el ajuste será: RR2 = R2-MIN-2.

D.3. Comentario sobre ambos criterios En ambos ajustes, la acción a tomar si se cumple la primera

condición (X2-MAX>X2-MIN-1, o R2-MAX>R2-MIN-1) podría ser distinta, para aumentar aún más la sensibilidad de la zona 2. Es decir, el ajuste en tales casos podría ser el valor máximo en vez del mínimo, o un promedio de ambos valores. Un análisis detallado de esas opciones está fuera del alcance del presente trabajo; sin embargo, la figura 4 ayuda a ilustrar este concepto. En el ejemplo de la figura 4 se asume que el ajuste resistivo

(RR2) ha quedado acotado por la sensibilidad mínima admisible (R2-MIN-2). En tal caso, incrementar la sensibilidad

del alcance reactivo (usar XR2-CASO2, en vez de XR2-CASO1) implicaría incrementar la pérdida de selectividad ante fallas resistivas en la línea adyacente que se salgan de la zona 1 de la protección de la línea adyacente.

R

jX

ZL+

θL+

Aumentar XR implicaperder selectividad siZAP cae en esta zona

ZL+,ADY

RR2-MIN-2

XR2-CASO1

XR2-CASO2

Zona 1 de la línea adyacente

R

jX

ZL+

θL+

Aumentar XR implicaperder selectividad siZAP cae en esta zona

ZL+,ADY

RR2-MIN-2

XR2-CASO1

XR2-CASO2

Zona 1 de la línea adyacente

Fig. 4. Ejemplo de la posible pérdida de selectividad asociada a un aumento

de la sensibilidad del alcance reactivo de la zona 2.

E. Ajuste del alcance resistivo de la zona 3

E.1. Criterio usado para el alcance reactivo Se asumirá que el principal objetivo de la zona 3 es actuar

como respaldo ante fallas en líneas adyacentes al extremo remoto de la línea en estudio [8]. Sin embargo, por ser ésta la función de respaldo más rápida, se le otorgará prioridad a la selectividad entre las zonas 3 de las distintas líneas, ya que se asume que las fallas no cubiertas como respaldo por la zona 3 de una línea serán cubiertas por su zona 4, que es más sensible (tiene más alcance o es simplemente una función direccional). De forma ideal, el ajuste del alcance reactivo de la zona 3

(XR3) se debiera realizar al 80% de la reactancia aparente total vista por el relé en estudio, ante fallas al final de la zona 2 del relé del extremo remoto que proteja la línea adyacente con menor reactancia de ajuste para su zona 2 (XR2-ADY,CORTA). En este caso, se debe considerar la amplificación (FINFEED) debido a la contribución de corriente de cortocircuito en el extremo remoto, con el menor valor factible que se pueda considerar del FINFEED: XR3 = 0,8 (XL++(FINFEED)XR2-ADY,CORTA). Sin embargo, hallar el valor anterior, en la práctica, puede

no ser sencillo. Por tal razón, en el presente artículo se ha preferido realizar el ajuste de XR3 al 75% de la menor reactancia aparente total (XL++XAP-MENOR-ADY) vista por el relé en estudio ante fallas al final de una de las líneas adyacentes al extremo remoto, considerando el valor de FINFEED para el caso base del flujo de carga: XR3 = 0,75 (XL++XAP-MENOR-ADY).

R

jX

ZL+

θL+

X=(XL++XAP-MENOR-ADY)

RR3

XR3ZAP variando RF

Si:(ImImImImZAP=1,1XR3)

OR

([ImImImImZAP-0,05|ZAP|]=1,05XR3), ⇒ RR3=ReReReReZAP

R

jX

ZL+

θL+

X=(XL++XAP-MENOR-ADY)

RR3

XR3ZAP variando RF

Si:(ImImImImZAP=1,1XR3)

OR

([ImImImImZAP-0,05|ZAP|]=1,05XR3), ⇒ RR3=ReReReReZAP

Fig. 5. Criterios usados para el ajuste del alcance resistivo de la zona 3.

E.2. Criterio usado para el alcance resistivo

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El ajuste del alcance resistivo de la zona 3 (RR3, figura 5) es

similar al descrito para RR1, considerando la evaluación de fallas a través de resistencias al final de la línea adyacente al extremo remoto usada en el caso del ajuste de XR3. Si la parte imaginaria de la impedancia aparente (ZAP) vista por el relé en estudio se acerca al 110% de XR3 o si al restarle el 5% del módulo de ZAP se acerca al 105% de XR3, la correspondiente parte real de ZAP será el valor de ajuste resistivo (RR3). De forma similar a la zona 1, si el ajuste de RR3 no está limitado por ZAP, RR3 podría ser ajustado a un valor muy alto.

III. SISTEMA USADO COMO EJEMPLO

A. Descripción del sistema de potencia

La figura 6 muestra el modelo del sistema usado como ejemplo y sus datos están en las tablas 1, 2 y 3.

LM

LR

LA

PMTPLM

LCAGUA

C1:26km

C1:26km

C2:12,2kmC1:22km C2:6,11k

mC2:6,87km

C1:3,37km

C1:10,03km

C1:9,96km

LM

LR

LA

PMTPLM

LCAGUA

C1:26km

C1:26km

C2:12,2kmC1:22km C2:6,11k

mC2:6,87km

C1:3,37km

C1:10,03km

C1:9,96km

Fig. 6. Esquema del sistema a 115 kV usado como ejemplo.

Tabla 1: Parámetros de líneas (r, x en Ω/km; b en µmho/km). r+ x+ b+ r0 x0 b0 C1 0,1211 0,4959 3,347 0,3160 1,102 1,938

C2 0,1714 0,4928 3,421 0,3630 1,151 1,860

Tabla 2: Datos de los generadores equivalentes. X+=X-(Ω) X0(Ω) P(MW) Q(MVAR) LCA 7,3 3,3 Slack Slack

GUA 15,9 15,9 120 74,37

LM 120,0 53,0 20 12,39

Tabla 3: Datos de las cargas. LCA LM LA PMT LR PLM GUA P(MW) 73 48 31 38 56 38 30 cos(φ) 0,900 0,900 0,900 0,900 0,936 0,900 0,850

B. Función de distancia ante fallas a tierra

La impedancia aparente vista por la función de distancia ante fallas a tierra (ZPh-G) depende de la forma de polarización usada [9]. En el ejemplo que se desarrolla en el presente artículo se asume que el relé usa una forma de polarización específica, que se rige por la siguiente expresión: ZPh-G = VPh-G / (IPh+K0IR) (1)

VPh-G: Voltaje fase-tierra de la fase fallada, medido por el relé. IPh: Corriente de la fase fallada, medida por el relé. IR: Corriente residual (IA + IB + IC), medida por el relé. K0: Factor de compensación residual. Se asumirá que el factor K0 se ajustará exactamente al valor

complejo que logra hacer que la impedancia vista por el relé sea la impedancia de secuencia positiva de la línea hasta el punto de falla cuando la falla es sólida. Es decir:

K0 = (ZL0 - ZL+) / (3 ZL+) (2) ZL+: Impedancia de secuencia positiva de la línea. ZL0: Impedancia de secuencia cero de la línea.

C. Flujos de carga pre-falla

La impedancia aparente vista ante fallas a través de una resistencia (RF) depende del flujo de carga pre-falla, medido en la localidad del relé [6],[9]. La determinación exacta de la peor condición posible para cada zona de cada relé en estudio está fuera del alcance del presente artículo. Un simple análisis preliminar (que no pretende ser una regla general) permitió sugerir el uso de las siguientes condiciones de flujo de carga pre-falla, medido en la localidad del relé en estudio: -Caso Base: Usar la topología del sistema que corresponde

con la descripción básica realizada en la sección III-A. -Caso 1: Usar la topología del sistema que corresponde a la

operación sin una de las líneas, y considerar un valor aproximado del flujo de carga correspondiente. Para el sistema en estudio, los resultados se muestran en la tabla 4 (QMÁX). -Caso 2: Considerar, además de las condiciones del caso 1,

que el flujo de potencia reactiva puede ser controlado por los operadores del sistema. Si se asume que la potencia reactiva puede ser la mitad del valor previo, para el sistema en estudio, los resultados se muestran en la tabla 4 (QMÍN). La aplicación de dichos casos se realizó del siguiente modo: a) Para el ajuste resistivo de zona 1, se usó el Caso 1 cuando

el flujo de carga prefalla es positivo y el Caso 2 cuando es negativo. En el sistema en estudio, coincidencialmente, los signos de P y Q son siempre iguales, en los casos simulados. b) Para el ajuste resistivo de zona 2, se usó el Caso Base. c) Para el ajuste resistivo de zona 3, se usó el Caso Base.

Tabla 4: Flujos de carga pre-falla, por la localidad del relé en estudio, para los Casos 1 y 2 (QMÁX y QMÍ', respectivamente).

Línea Línea Flujo prefalla (línea en estudio)

En fuera de Sentido P QMÁX QMÍN

estudio servicio de P y Q MW MVAR MVAR

GUA-LM PLM-LCA GUA->LM 90 56 28,0

LM-LA PMT-LR LM->LA 70 33 16,5

LA-PMT PMT-LR LA->PMT 38 18 9,0

LA-PMT LM-LA LA->PMT -31 -15 -7,5

PMT-LR PMT-LR LR->PMT 70 33 16,5

LR-PLM PLM-LCA PLM->LR 87 36 18,0

LR-PLM LCA-LR PLM->LR -38 -18 -9,0

PLM-LCA LCA-LR LCA->PLM 125 54 27,0

LCA-GUA GUA-LM LCA->GUA 90 56 28,0

LCA-LM GUA-LM LCA->LM 68 33 16,5

LCA-LR PLM-LCA LCA->LR 125 54 27,0

D. Resistencia típica de fallas a tierra (RF)

El valor de la resistencia de fallas a tierra depende de múltiples factores. Cada valor de RF tiene una determinada probabilidad de ocurrencia [10]; sin embargo, en el presente trabajo se requiere usar un valor típico para establecer el alcance deseable de la zona 2. Dicho valor fue supuesto de manera arbitraria (5Ω) y el resultado final, considerando los

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valores de seguridad mencionados, fue utilizar dos valores

extremos de RF: RF1=(FS1)RF-TIP= 20Ω; RF2=(FS2)RF-TIP= 10Ω.

IV. AJUSTES OBTENIDOS

Los ajustes obtenidos para la zona 1 se muestran en la tabla 5. En un estudio realizado previamente sobre el mismo sistema [11], los valores del alcance reactivo son idénticos a los de la tabla 5, por usar exactamente el mismo criterio; sin embargo, en dicho estudio se usó un factor único de XR/RR (igual a 2)

para definir el alcance resistivo de la característica en cada localidad. Al examinar la tabla 5, es posible destacar que el factor XR/RR varía entre 0,77 y 33,41, para el caso analizado. Por otra parte, el valor máximo de resistencia de falla, en el

extremo remoto, para el cual se definió el ajuste del RR1, varía entre 0,97Ω y 17,39Ω; sin embargo, debe destacarse que hay 5 casos en los que el alcance resistivo no fue limitado por el lugar geométrico de la impedancia aparente vista por el relé ante fallas en el extremo remoto, sino por la carga admisible en la línea de transmisión.

Tabla 5: Ajustes de la zona 1 y valor de la resistencia de falla, en el extremo remoto, que definió el ajuste (ver figura 2).

Todos los valores de impedancias están en ohmios primarios.

Línea Ext. 1 Ext. 2 (Ext.1-Ext.2) XR1 RR1 RF,MÁX XR1/RR1 XR1 RR1 RF,MÁX XR1/RR1 GUA-LM 10,31 12,11 3,86 1,17 10,31 18,06 5,56 1,75

LM-LA 4,81 7,75 8,71 1,61 4,81 88* N/A 18,30

LA-PMT 2,41 4,39 4,98 1,82 2,41 5,06 5,92 2,10

LR-PMT 2,71 4,95 5,67 1,83 2,71 88* N/A 32,49

PLM-LR 1,34 2,98 2,70 2,23 1,34 104,79 17,39 78,38

LCA-PLM 3,95 8,30 8,62 2,10 3,95 132* N/A 33,41

LCA-GUA 10,31 16,60 6,16 1,61 10,31 7,89 0,97 0,77

LCA-LM 8,73 14,17 8,77 1,62 8,73 132* N/A 15,12

LCA-LR 3,98 8,39 8,54 2,11 3,98 132* N/A 33,17 'ota: El asterisco (*) indica que dicho valor fue limitado exclusivamente por la carga máxima admisible de la línea (figura 2c).

Tabla 6: Ajustes de la zona 2 (ver figuras 3 y 4). Todos los valores de impedancias están en ohmios primarios.

Línea Ext. 1 Ext. 2 (Ext.1-Ext.2) XR2 RR2 XR2 RR2 GUA-LM 14,82 25,28 15,47 46,42

LM-LA 6,98 15,75 7,21 40,39

LA-PMT 3,61 42,03 3,61 27,97

LR-PMT 4,06 11,14 3,92 88*

PLM-LR 2,01 19,34 2,01 31,33

LCA-PLM 5,47 13,77 5,93 42,20

LCA-GUA 14,47 31,42 14,47 60,14

LCA-LM 12,83 22,19 12,49 132*

LCA-LR 5,51 14,62 5,97 76,59 'ota: El asterisco (*) indica que dicho valor fue limitado exclusivamente por la carga máxima admisible de la línea.

R

jX

ZL+

θL+

XR2

XR1

RR2 RR1

R

jX

ZL+

θL+

XR2

XR1

RR2 RR1 Fig. 7. Ejemplo gráfico de un resultado no convencional: el ajuste resistivo

de la zona 2 puede ser menor que el de la zona 1.

Los ajustes obtenidos para la zona 2 se muestran en la tabla 6. Es posible apreciar que el ajuste resistivo de zona 2 (RR2) es, en algunos casos, inferior al ajuste de zona 1 (RR1). Dicha situación corresponde al extremo 2 de LM-LA, PLM-LR, LCA-PLM, LCA-LR, en los cuales el ajuste de zona 1 es un valor muy alto (mayor a 88 ohmios primarios). Este resultado se ilustra en la figura 7, no es convencional y se debe a que el ajuste resistivo de la zona 2 debe ser acotado para disminuir el riesgo de pérdida de selectividad (ya que el ajuste reactivo de zona 2, XR2, es mayor que el ajuste de zona 1, XR1).

Tabla 7: Ajustes de la zona 3 (ver figura 5). Todos los valores de impedancias están en ohmios primarios.

Línea Ext. 1 Ext. 2 (Ext.1-Ext.2) XR3 RR3 XR3 RR3 GUA-LM 18.01 19,58 21.92(1) 132*

LM-LA 7.55 19,88 44.89 88*

LA-PMT 5.18 11,32 7.36 15,32

LR-PMT 5.33 14,28 4.39 39,25

PLM-LR 8.26 43,46 4.19 132*

LCA-PLM 5.57 132* 8.43(1) 132*

LCA-GUA 21.92(1) 50,24 33.16 132*

LCA-LM 22.34 67,41 13.47(1) 132*

LCA-LR 6.05 132* 8.43(1) 132*

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'ota: El asterisco (*) indica que dicho valor fue limitado exclusivamente por la carga máxima admisible de la línea. 'ota 1: Estos valores no fueron hallados por el criterio indicado en la sección II.E, por no ser posible (la reactancia daría negativa). Para hallarlos, se sumaron los valores de las menores reactancias de líneas adyacentes para, luego, multiplicar ese valor por 0,75. Los ajustes obtenidos para la zona 3 se muestran en la tabla

7. Es posible apreciar que el ajuste resistivo de zona 3 (RR3) es, en algunos casos, inferior al ajuste de zona 2 (RR2). Dicha situación corresponde al extremo 1 de GUA-LM y LA-PMT, y al extremo 2 de LA-PMT y LR-PMT. Este resultado es similar al que se destacó previamente para la zona 2 y que se ilustró en la figura 7. En el caso de que el ajuste resistivo de zona 3 sea inferior al

ajuste resistivo de zona 2, esto implica que la zona 2 tiene más sensibilidad ante fallas a través de resistencia. En tales casos, como la zona 3 no es tan sensible, una falla fuera de la línea protegida, con un valor de resistencia de falla suficientemente alto, debiera ser despejada por la zona 4. Es decir, la zona 4 debiera ser suficientemente sensible para garantizar el respaldo en estos casos. En los casos donde el ajuste resistivo de zona 2 sea inferior

al ajuste de zona 1, o cuando el ajuste resistivo de zona 3 sea inferior al ajuste de zona 2, este resultado no convencional puede evitarse si se impone la condición de que el valor del ajuste resistivo sea mayor mientras mayor sea el alcance reactivo de la zona. Dicha condición permitiría, a su vez, dos resultados posibles: usar el valor menor, o el mayor, entre ambos. Sin embargo, en caso de imponer la condición de que el valor del ajuste resistivo sea mayor mientras mayor sea el alcance reactivo de la zona, debe cuidarse que se actualice la posible interacción entre ambos resultados: por ejemplo, en la figura 3b se muestra que el análisis del ajuste resistivo de zona 2 depende del resultado previo del ajuste resistivo de la zona 1 de un relé adyacente al extremo remoto.

I. CONCLUSIONES

-Se presentó un método para el ajuste del alcance resistivo de la característica cuadrilátera en relés de distancia. El método se basa en el análisis de la impedancia aparente vista por el relé y en la definición explícita de las características deseables de la protección para cada zona analizada. -En el método propuesto, el ajuste del alcance resistivo

depende del ajuste del alcance reactivo y se calcula asumiendo que éste ha sido previamente definido. -El método propuesto se aplicó en un ejemplo con 18 relés

de distancia y su solución se comparó con una solución simplificada, que consiste en ajustar el alcance resistivo multiplicando el alcance reactivo por un factor constante. -Se obtuvo el resultado del ajuste resistivo para las 3 zonas

de los 18 relés de distancia del ejemplo empleado. -Este trabajo puede ser complementado en el futuro con el

análisis de otros posibles modos de ajustar el alcance reactivo y cambiar, en consecuencia, el criterio de ajuste del alcance resistivo para observar las variaciones en los resultados.

REFERENCIAS

[1] Areva T&D, “Network protection & automation guide”, 2002. [2] G. Ziegler, “Numerical distance protection. Principles and applications”,

Siemens AG, 1999. [3] ABB Power T&D Company Inc, “Protective relaying. Theory and

applications”, editado por W. Elmore, Marcel Dekker Inc, 1994. [4] R. Mason, “The art and science of protective relaying”, John Wiley &

Sons Inc, 1956. [5] V. De Andrade, E. Sorrentino, “Revisión bibliográfica sobre los

métodos para ajustar el alcance de los relés de distancia”, Memorias del I Congreso Venezolano de Redes y Energía Eléctrica, Lechería, Venezuela, 2007, en CD.

[6] T. Rodolakis, D. , “Effect of loads, shunts and system uncertainties on short circuit relay settings”, IEEE Trans. on Power Apparatus and Systems, Dec. 1981, págs. 4701-4709.

[7] ABB Relay, “Distance Relay Type Razoa”, 1985. [8] S. Horowitz, A. Phadke, “Third zone revisited”, IEEE Trans. on Power

Delivery, Jan. 2006, págs. 23-29. [9] E. Sorrentino, “Polarización de la función de distancia ante fallas a

tierra y su efecto sobre el alcance resistivo en zonas cuadriláteras”, Memorias del Décimo Segundo Encuentro Regional Iberoamericano del CIGRÉ, Foz do Iguazú, Brasil, 2007, en CD.

[10] J. Barnard, A. Pahwa, “Determination of the impacts of high impedance faults on protection of power distribution systems using a probabilistic model”, Electric Power Systems Research, 1993, págs. 11-18.

[11] E. Rojas, “Coordinación de las protecciones de distancia del sistema a 115 kV de Seneca incluyendo El Guamache”, Informe final de Pasantía Larga, Universidad Simón Bolívar, Venezuela, 2007.

Elmer Sorrentino obtuvo el grado de Ingeniero Electricista (1984) y Master en Ingeniería Eléctrica (1986) en la Universidad Simón Bolívar (USB, Venezuela), ambos con honores. Desde 1984 es Profesor en la USB y ha sido ingeniero consultor para diversas empresas. Sus áreas de trabajo son: protección de sistemas eléctricos, análisis de sistemas de potencia y máquinas eléctricas. Eliana Rojas obtuvo el grado de Ingeniero Electricista (2007) en la Universidad Simón Bolívar (Venezuela), recibiendo mención honorífica por la calidad de su trabajo de grado. Desde 2007 labora en ABB como Ingeniero Líder de Producto en el área de Productos de Automatización. Jesús Hernández obtuvo el grado de Ingeniero Electricista (1998) en la Universidad de Oriente (Venezuela). Desde 2000 labora en SENECA (Sistema Eléctrico del Estado Nueva Esparta C.A), en el área de protección del sistema eléctrico. Actualmente se desempeña como Jefe de Protección y Automatización de SENECA.

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Resumen— En este artículo se presenta un método para la

localización de fallas en líneas paralelas multiterminales de

transmisión, con alimentación sólo en dos de sus extremos. El

método utiliza la información de las tensiones y corrientes en los

dos extremos de alimentación, sin que exista sincronización entre

los registradores de fallas ubicados en dichos extremos. El método

fue comprobado mediante el análisis de registros reales de fallas

en los cuales se tenía un alto grado de certidumbre con respecto a

las ubicaciones reales de las fallas. En el presente artículo se

muestra que los métodos que no consideran el efecto de las líneas

paralelas ni de las derivaciones arrojan resultados erróneos y, por

ello, se concluye que es conveniente utilizar métodos como el

desarrollado en el presente trabajo.

Palabras claves—Localización de fallas, líneas paralelas, líneas

multiterminales, impedancias mutuas de líneas aéreas.

I. INTRODUCCIÓN

OS algoritmos de localización de fallas suelen ser usados para intentar encontrar el punto donde ha ocurrido una

falla en líneas de transmisión [1]-[13], usando la información almacenada mediante mediciones durante la falla (registros de fallas). Los métodos más comunes usan la información de tensiones y corrientes de un extremo de la línea y, considerando que podría haber una resistencia de falla, intentan evaluar la distancia a la cual ocurrió la falla. Algunos métodos no toman en cuenta ciertos aspectos particulares de las líneas, como topologías multiterminales y/o el efecto de líneas paralelas. Debido a ello y/o a otros factores, hay casos en los cuales el resultado del algoritmo de localización de fallas podría no ser confiable. En este artículo se presenta un método para localizar fallas

en líneas multiterminales paralelas con alimentación en sólo dos extremos, usando la información de los registradores de fallas de los dos terminales con fuentes y considerando que los registros no están sincronizados en el tiempo.

II. MÉTODO USADO COMO BASE

El método desarrollado está basado en un algoritmo creado hace más de 25 años [1]-[3] por Takagi y sus colaboradores,

Luis De Andrade labora en C.A. La Electricidad de Caracas, Caracas,

Venezuela (e-mail: [email protected]). Elmer Sorrentino labora en la Universidad Simón Bolívar, Caracas,

Venezuela (e-mail: [email protected]).

el cual será denominado algoritmo de Takagi en este artículo. El algoritmo de Takagi fue desarrollado para líneas de dos terminales, sin incluir el efecto de líneas paralelas y se basa en descomponer el sistema en condiciones de falla, usando el principio de superposición, en dos subsistemas: sistema en condición pre-falla y sistema en falla pura (figura 1).

ER

Red Pre-falla

ES

ZS

V’S

S R

I’S I’R V’R

ZRF

ES ER

ZS

VS

S R

IS IFS IFR IRVR

ZR

RFIF

Red en Falla

F

Red en Falla Pura

ZS

V’’S

S R

I’’S I’’FS I’’FR I’’R V’’R

ZR

IF

F

ERER

Red Pre-falla

ESES

ZSZS

V’SV’S

S R

I’SI’S I’RI’R V’RV’R

ZRZRF

ESES ERER

ZSZS

VSVS

S R

ISIS IFSIFS IFRIFR IRIRVRVR

ZRZR

RFRFIFIF

Red en Falla

F

Red en Falla Pura

ZSZS

V’’SV’’S

S R

I’’SI’’S I’’FSI’’FS I’’FRI’’FR I’’RI’’R V’’RV’’R

ZRZR

IFIF

F

Fig. 1. Subsistemas planteados en el algoritmo de Takagi.

Usando los parámetros de la línea (A, B, C, D) en función de la distancia a la falla (x), se puede deducir: VF = A(x)VS + B(x) IS (1) IFS” = C(x)VS” + D(x) IS” (2) A(x) = D(x) = cosh (λx) (3) B(x) = Z0 sinh (λx) (4) C(x) = (sinh (λx)) / Z0 (5) λ: constante de propagación de la línea (variable compleja). Z0: impedancia característica de línea (variable compleja). Definiendo K(x)=IFS”/IFR”, se obtiene:

VF = IF RF = -RF IFS” (1+K(x)) (6) La gran virtud del algoritmo de Takagi es que K(x) está

definido para la red en falla pura y, por ende, se puede asumir que es aproximadamente un número real (IFS” e IFR” están prácticamente en fase). Como la resistencia de falla (RF) es un número real, la parte imaginaria de -RF(1+K(x)) se asume nula y para encontrar la distancia a la falla (x) sólo se requiere resolver la siguiente ecuación: ImImImIm [A(x)VS + B(x) IS] / [C(x)VS” + D(x) IS”] = 0 (7)

Localización de fallas en líneas aéreas paralelas con múltiples terminales y con alimentación

únicamente en dos de sus extremos

Luis de Andrade Elmer Sorrentino

L

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⋅

=

2,

2,

1,

1,

2,

2,

1,

1,

)()()()(

)()()()(

)()()()(

)()()()(

S

S

S

S

mm

mm

mm

mm

FS

FS

FS

FS

I

V

I

V

xDxCxDxC

xBxAxBxA

xDxCxDxC

xBxAxBxA

I

V

I

V

III. MÉTODO PROPUESTO

A. Inclusión del caso de fallas bifásicas a tierra

En el desarrollo original del algoritmo de Takagi están descritas las expresiones requeridas para el caso de fallas trifásicas, bifásicas y monofásicas [1]-[3]; sin embargo, no hay expresiones para el caso de fallas bifásicas a tierra. Usando consideraciones similares al algoritmo de Takagi, la primera adecuación desarrollada en este trabajo consistió en desarrollar la expresión ante fallas bifásicas a tierra, usando una formulación similar al algoritmo original: ImImImIm [2V 0

F – V +F – V -

F] / I0FS” = 0 (8)

B. Inclusión de las diferentes características de tramos

En el presente trabajo se consideró que la línea puede estar compuesta por diferentes tramos y los tramos pueden tener distintos conductores y/o distintas estructuras de apoyo. Por ende, cada tramo tiene sus propios parámetros eléctricos. El análisis de una línea se comienza estudiando el tramo

inicial desde uno de sus extremos, a partir del registro de tensión y corriente en dicho extremo. Si el algoritmo indica que la falla se encuentra fuera de este tramo, entonces calcula las tensiones y corrientes al final de dicho tramo y se utiliza esta información para iniciar el análisis en el siguiente tramo. Este proceso se repite hasta que el resultado del cálculo arroje que la falla se encuentre dentro de un determinado tramo.

C. Inclusión del caso de líneas multiterminales, con alimentación sólo en dos extremos

Los tramos de línea que conectan los extremos alimentados conforman la línea troncal y las derivaciones (taps o TOFF) a los demás terminales pueden ser consideradas ramales. El análisis se puede dividir en dos casos: a) tramos de la línea troncal; b) tramos pertenecientes a las derivaciones. El cálculo en los tramos de la línea troncal se reduce a

aplicar el algoritmo de Takagi, a partir de las tensiones y corrientes de uno de los extremos. El cálculo en los tramos de una derivación (tap o TOFF) requiere estimar la corriente al proveniente de cada extremo alimentado, para poder usar las condiciones al inicio de la derivación (VT, IT), como se ilustra en la figura 2. Dichas condiciones se estiman a partir de la información de los registradores ubicados en ambos extremos de la línea troncal.

Fig. 2. Esquema para el análisis de líneas multiterminales.

La localización de falla desde el extremo S se realiza con la

estimación de los valores en el punto de la derivación (ITS, VT) y con una estimación de la contribución desde el otro extremo

(ITR). Dichos valores pueden hallarse fácilmente a partir de los registros de voltaje y corriente (S y R) pues las longitudes de los tramos hasta el punto de la derivación son conocidas. Sin embargo, para la estimación de la corriente total en el

punto de la derivación (IT) se requiere que las señales ITS e ITR estén sincronizadas. Si los equipos de registro ubicados en ambos extremos (S y R) no están sincronizados, como es el caso analizado en este artículo, es necesario sincronizar de forma artificial dichas corrientes. La sincronización artificial es una posible fuente de error en el resultado final y, por ello, se desea que el error de sincronización sea pequeño. El método utilizado para sincronizar artificialmente los

registros de ambos extremos está basado en asumir que la diferencia angular entre las tensiones pre-falla en ambos extremos es insignificante. Es decir, se usa el valor que tiene dicha diferencia angular, antes de la corrección, para corregir la fase de las variables que se desean sincronizar. Al examinar la ecuación 7, se observa que hay dos valores

de corriente (IS e IS”, en falla y falla pura, respectivamente) y algo análogo ocurre con los valores que se desean estimar en el punto de la derivación (IT e IT”). Para sumar las señales ITS e ITR en falla pura no se requiere corregir el ángulo de ITR, pues se puede asumir que dichos valores deben estar en fase, ya que ésa es una de las bases del algoritmo de Takagi. Sin embargo, para sumar las señales ITS e ITR en falla sí se requiere corregir el ángulo de ITR, pues en falla no se puede asumir que estén en fase. La localización de falla desde el extremo S puede indicar

varias soluciones posibles, en la línea troncal y/o en ramales. Al realizar un cálculo similar desde el extremo R, se obtiene una gama de posibles localizaciones, para una misma falla, vista desde cada uno de los extremos alimentadores. De todas las posibles localizaciones, en sólo una hay coincidencia (con suficiente precisión) entre los resultados indicados desde cada extremo: ese punto es el resultado del algoritmo propuesto.

D. Inclusión del efecto de líneas paralelas

El algoritmo de Takagi fue formulado usando el modelo de parámetros distribuidos de líneas de transmisión, el cual suele ser descrito de manera elemental [14]-[15] para las líneas monofásicas. En el algoritmo de Takagi [1]-[3] se asume que dicho modelo puede extenderse al análisis de líneas trifásicas. En la revisión bibliográfica realizada no se consiguió la

representación en parámetros distribuidos de los efectos mutuos entre líneas de transmisión paralelas. Por ello, para la adaptación del algoritmo de Takagi al caso de las líneas paralelas, se dedujo un modelo de parámetros distribuidos que tomase en cuenta los efectos mutuos entre las líneas. Por simplicidad, se muestra el resultado correspondiente a líneas paralelas idénticas. Es decir, sin considerar los efectos mutuos, cada una de las líneas paralelas representadas tendría la misma matriz [A, B, C, D]. La nueva matriz, desarrollada para representar los efectos mutuos, tiene dimensión 4x4: (9)

E S E R

Z S V S

S R

I S I TS I TR I R V R Z R

R F

I F

Z L

Load

V T

V F

I T

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Se ha mantenido la nomenclatura de las ecuaciones 1 y 2,

(VFS, IFS, VS, IS) y los subíndices 1 y 2 representan a las dos líneas paralelas. Am, Bm, Cm y Dm son los parámetros que representan el acople de las líneas paralelas:

(10)

(11) (12)

(13) (14) (15)

(16) (17) (18) (19)

ZL es la impedancia serie de la línea, YL es la admitancia en derivación de la línea y ZM es la impedancia mutua entre las líneas en estudio. ZL, YL y ZM son valores complejos, por unidad de longitud. Si la impedancia mutua entre las líneas es nula (ZM=0), los términos que representan el acople de las líneas paralelas (Am, Bm, Cm, Dm) son nulos y los demás parámetros (A, B, C, D) retornan al valor correspondiente a la inexistencia de efectos mutuos. Los valores descritos se utilizan sólo para la red de

secuencia cero, ya que se asume que el efecto mutuo en las redes de secuencia positiva y negativa es insignificante. Es decir, para las redes de secuencia positiva y negativa se utiliza el modelo convencional de parámetros distribuidos.

IV. SISTEMA DE POTENCIA USADO COMO EJEMPLO

El sistema usado como ejemplo es una línea doble circuito a 69kV (figura 3), perteneciente a C.A. La Electricidad de Caracas, con fuente de alimentación en las subestaciones Convento y Papelón, y con derivaciones para alimentar de manera radial otras cinco subestaciones. En las S/E’s que no tienen fuentes, el enlace de barras está normalmente abierto. La figura 3 muestra la longitud de cada tramo, así como el

calibre y material del conductor de fase. Además de haber diferencias entre los tipos de conductores de fase, también se usan distintos conductores de guarda y hay diferencias en la distribución geométrica de los conductores de fase, debido a que los tipos de estructuras de apoyo varían en algunos tramos.

V. RESULTADOS

A. Obtenidos con casos simulados

El algoritmo desarrollado fue probado con casos simulados mediante el uso de un software comercial para análisis de fallas [16], utilizando un valor de resistencia de falla igual a 5 Ω. La distancia teórica introducida en dicho software fue tomada como referencia para la comparación de los resultados que se muestra en la tabla 1. Es necesario destacar que el algoritmo desarrollado sólo indicó erróneamente el ramal ante fallas en la derivación Palo Verde, a 6.63 km de la S/E Convento, en el caso de fallas trifásicas y monofásicas sin considerar el efecto mutuo de la línea paralela (en esos 2 casos indicó que la falla era en el troncal). Por otra parte, los resultados mostrados en la tabla 1 indican que el error obtenido en los casos simulados suele ser inferior a 1 km, lo que podría ser considerado como una precisión satisfactoria.

B. Obtenidos con registros reales

De la base histórica de datos de los registros de las fallas en la línea usada como ejemplo, sólo se consideraron los casos donde existía certidumbre en cuanto a la localización efectiva de la falla. Se consideró que existía tal certidumbre cuando la inspección post-falla, en sitio, había arrojado resultados claros y precisos en cuanto a la ubicación de la falla. Dicha condición sólo se cumplió en el caso de 2 fallas bifásicas (sin contacto con tierra) y 5 fallas monofásicas. Una de las fallas bifásicas corresponde a un incendio que

sólo permite asegurar que la falla ocurrió en el troncal, a una distancia estimada desde la S/E Convento entre 8.58 y 12.14 km, y el resultado del algoritmo fue 11.50 km. En la otra falla bifásica, la localización real fue estimada a 16.3 km de la S/E Convento, en el ramal Lagunitas, y el resultado del algoritmo fue 16.44 km, en el mismo ramal. Las 5 fallas monofásicas en las que existía certidumbre en

cuanto a la localización real de la falla fueron en el troncal. Los resultados para tales casos se muestran en la tabla 2 y permiten confirmar que el algoritmo desarrollado se comporta de forma adecuada, así como permiten confirmar que la inclusión del efecto mutuo entre líneas paralelas ayuda a mejorar el valor estimado de la distancia a la falla. Es necesario destacar que en estas fallas reales, los equipos

actualmente instalados para la localización de fallas, en los dos extremos con alimentación, arrojan resultados inconsistentes ya que la distancia indicada por uno de los extremos no es compatible con la indicada desde el otro extremo. Dichos equipos no están específicamente diseñados para líneas multiterminales ni para considerar el efecto mutuo entre líneas paralelas, así como tampoco permiten incluir tramos de características distintas (en una misma línea de transmisión). En la tabla 3 se indica el resultado arrojado por tales equipos para los mismos casos indicados en la tabla 2.

( )

( )( )

( ) LMLm

L

MLm

LMLm

L

MLm

YZZ

YZZZ

YZZ

YZZZ

⋅−=

−=

⋅+=

+=

−

−

+

+

λ

λ

0

0

[ ]

[ ]

[ ]

[ ]

−

−

+

+

−−++

−+

−

−

+

+

−−++

−+

−=

−=

−==

+=

+=

+==

m

m

m

mm

mmmmm

mmmm

m

m

m

m

mmmm

mm

Zx

ZxxC

xZxZxB

xxxDxA

Zx

ZxxC

xZxZxB

xxxDxA

00

00

00

00

2)sinh(

2)sinh()(

2)sinh()sinh()(

2)cosh()cosh()()(

2)sinh(

2)sinh()(

2)sinh()sinh()(

2)cosh()cosh()()(

λλ

λλ

λλ

λλ

λλ

λλ

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Fig. 3. Línea multiterminal paralela usada como ejemplo. Los interruptores de unión de barras están abiertos en los 5 terminales radiales (Palo Verde, Tapias, Lagunita, Caicaguana y Sureste) y cerrados en los dos terminales con presencia de fuentes (Papelón y Convento).

Tabla 1. Distancias, consideradas desde la S/E Convento, estimadas para los casos simulados.

Ubicación (ramal)

Distancia Referencia (km)

Distancias estimadas por el algoritmo propuesto (km) Errores con respecto a la referencia (km)

3φ 2φ 2φ-g 1φ

3φ 2φ 2φ-g 1φ

Con mutuas

Sin mutuas

Con mutuas

Sin mutuas

Con mutuas

Sin mutuas

Con mutuas

Sin mutuas

Troncal 3.28 3.81 3.55 4.76 5.28 3.42 4.09 0.53 0.28 1.49 2.01 0.14 0.81 Troncal 8.15 8.71 8.38 8.43 9.34 8.17 9.37 0.56 0.23 0.28 1.19 0.02 1.22 Troncal 10.40 11.06 10.66 10.49 11.74 10.40 11.77 0.66 0.26 0.09 1.34 0.00 1.37 Troncal 12.05 12.84 12.36 11.21 11.74 12.72 13.28 0.79 0.31 -0.84 -0.31 0.67 1.23 Troncal 13.80 14.94 14.20 13.67 14.59 14.47 14.66 1.14 0.40 -0.13 0.79 0.67 0.86 Troncal 17.20 18.09 18.42 18.47 19.05 18.10 19.10 0.89 1.22 1.27 1.85 0.90 1.90 Palo Verde 6.63 7.04 6.77 6.81 6.85 6.86 7.50 0.41 0.14 0.18 0.22 0.23 0.87 Tapias 10.10 10.21 10.17 9.84 9.97 10.22 10.32 0.11 0.07 -0.26 -0.13 0.12 0.22 Lagunita 11.58 11.81 11.74 11.49 12.06 11.75 12.19 0.23 0.16 -0.09 0.48 0.17 0.61 Caicaguana 13.17 13.24 13.22 13.29 13.43 13.21 13.37 0.07 0.05 0.12 0.26 0.04 0.20 Sureste 14.67 14.70 14.69 14.64 14.76 14.68 14.76 0.03 0.02 -0.04 0.09 0.01 0.09 Palo Verde 7.19 7.44 7.36 6.96 6.81 7.40 7.52 0.25 0.17 -0.23 -0.38 0.21 0.33 Tapias 12.55 12.54 12.52 11.67 11.51 12.67 12.78 -0.01 -0.03 -0.88 -1.04 0.12 0.23 Lagunita 15.29 15.38 15.33 14.55 13.83 15.36 15.79 0.09 0.04 -0.74 -1.46 0.07 0.50 Caicaguana 14.01 14.05 14.03 13.76 13.41 14.00 14.23 0.04 0.02 -0.25 -0.60 -0.01 0.22 Sureste 15.51 15.49 15.49 15.32 15.19 15,57 15,44 -0.02 -0.02 -0.19 -0.32 0.42 -0.45

Tabla 2. Distancias, consideradas desde la S/E Convento,

estimadas con el algoritmo desarrollado para casos reales, a partir de los datos de los registradores de falla.

Ubicación real (km)

Distancia estimada (km) Error de estimación (km) Con Mutuas

Sin Mutuas

Con Mutuas

Sin Mutuas

8.58 9.21 9.98 0.63 1.40

15.97 14.69 13.86 -1.28 -2.11

14.55 16.43 16.87 1.88 2.32

14.55 14.65 15.14 0.10 0.59

22.50 21.79 21.76 -0.71 -0.75

16.3 16.44 16.44 0.86 0.86

Tabla 3. Distancias, consideradas desde la S/E Convento, estimadas con los equipos de localización de fallas

actualmente instalados en las S/E’s con alimentación.

Ubicación real (km)

Distancia estimada por equipo en S/E Convento (km)

Distancia estimada por equipo en S/E Papelón (km)

8.58 6.07 12.92 15.97 6.01 12.65 14.55 13.8 8.05 14.55 8.86 10.35 22.50 13.2 19.78 16.3 15.2 6.45

652.4 Al 350 Cu 350 Cu 350 Cu 350 Cu 350 Cu

S/E Sureste

1.2 Km

4/0 Al

8.3 Km 1.5 Km 2.0 Km 1.3 Km 3.2 Km 6.55 Km

S/E Papelón

S/E Convento

S/E Caicaguana

S/E Palo Verde

S/E Tapias

S/E Lagunita

1.2 Km

652.4 Al 5.3 Km

2/0 Cu

3.5 Km

4/0 Al

0.8 Km

652.4 Al

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I. CONCLUSIONES

-Se presentó un método para la localización de fallas en líneas multiterminales paralelas de transmisión, alimentadas sólo en dos de sus extremos. El método utiliza la información de tensiones y corrientes en los dos extremos de alimentación, sin que exista sincronización entre los registradores de fallas ubicados en dichos extremos -El método fue comprobado mediante fallas simuladas con

un software comercial y mediante el análisis de registros reales de fallas en los cuales se tenía un alto grado de certidumbre con respecto a las ubicaciones reales de las fallas. -Los métodos que no consideran el efecto de las líneas

paralelas ni de las derivaciones arrojan resultados erróneos y, por ello, es conveniente utilizar métodos como el desarrollado en el presente trabajo.

REFERENCIAS

[12] T. Takagi, Y. Yamakoshi, J. Baba, K. Uemura, T. Sakaguchi, “A New Algorithm of an Accurate Fault Location for EHV/UHV Transmission Lines: Part I – Fourier Transformation Method”, IEEE Trans. on PAS, March 1981, págs. 1316-1323.

[13] T. Takagi, Y. Yamakoshi, J. Baba, K. Uemura, T. Sakaguchi, “A New Algorithm of an Accurate Fault Location for EHV/UHV Transmission Lines: Part II – Laplace Transform Method”, IEEE Trans. on PAS, March 1982, págs. 564-573.

[14] T. Takagi, Y. Yamakoshi, M. Yamaura, R. Kondow, T. Matsushima, “Development of a new type fault locator using the one-terminal voltage and current data”, IEEE Trans. on PAS, Aug. 1982, págs. 2892-2898.

[15] A. Mazón, J. Mifiambres, M. Zorrozua, I. Zamora, R. Alvarez-Isasi, “New method of fault location on double-circuit two-terminal transmission lines”, Electric Power Systems Research, 1995, págs. 213-219.

[16] Z. Qingchao, Z. Yao, S. Wennan, Y. Yixin, W. Zhigang, “Fault location of two-parallel transmission line for non-earth fault using one-terminal data”, IEEE Trans. on PWRD, July 1999, págs. 863-867.

[17] L. Ying-Hong, L. Chih-Wen, Y. Chi-Shan,” A new fault locator for three-terminal transmission lines-using two-terminal synchronized voltage and current phasors”, IEEE Trans. on PWRD, April 2002, págs. 452-459.

[18] M. Abe, N. Otsuzuki, T. Emura, M. Takeuchi, “Development of a new fault location system for multi-terminal single transmission lines”, IEEE Trans. on PWRD, Jan. 1995, págs. 159-168.

[19] S. Brahma, “Fault location scheme for a multi-terminal transmission line using synchronized voltage measurements”, IEEE Trans. on PWRD, April 2005, págs. 1325-1331.

[20] S. Brahma, “New fault-location method for a single multi-terminal transmission line using synchronized phasor measurements”, IEEE Trans. on PWRD, July 2006, págs. 1148-1153.

[21] A. Girgis, D. Hart, W. Peterson, “A new fault location technique for two-and three-terminal lines”, IEEE Trans. on PWRD, Jan.1992, págs. 98-107.

[22] D. Tziouvaras, J. Roberts, G. Benmouyal, “New multi-ended fault location design for two or three-terminal lines”, Schweitzer Eng. Lab., 2004, http://www.selinc.com/techpprs/6089.pdf, consultada el 15/11/2008.

[23] T. Nagasawa, M. Abe, N. Otsuzuki, T. Emura, Y. Jikihara, M. Takeuchi, “Development of a new fault location algorithm for multi-terminal two parallel transmission lines”, IEEE Trans. on PWRD, July 1992, págs. 1516-1532.

[24] T. Funabashi, H. Otoguro, Y. Mizuma, L. Dube, A. Ametani, “Digital fault location for parallel double-circuit multi-terminal transmission lines” IEEE Trans. on PWRD, April 2000, págs. 531-537.

[25] J. Grainger, W. Stevenson, “Análisis de Sistemas de Potencia”, McGraw-Hill, 1996.

[26] H. Saadat, “Power System Analysis”, McGraw-Hill, 1999.

[27] DigSilent GmbH, “Manual of Power Factory Version 13.1”, Germany,

November 2005. Luis de Andrade obtuvo el grado de Ingeniero Electricista (2001) en la Universidad Simón Bolívar, donde actualmente estudia la Especialización en Sistemas de Potencia. Desde 2001 labora en C.A. La Electricidad de Caracas y actualmente se desempeña como Ingeniero Senior en el Dpto. de Protecciones y Controles de la Gerencia de Transmisión. Sus áreas de trabajo son: protección y análisis de fallas en el sistema de transmisión. Elmer Sorrentino obtuvo el grado de Ingeniero Electricista (1984) y Master en Ingeniería Eléctrica (1986) en la Universidad Simón Bolívar (USB) de Venezuela, ambos con honores. Desde 1984 es Profesor en la USB y ha sido ingeniero consultor para diversas empresas. Sus áreas de trabajo son: protección de sistemas eléctricos, análisis de sistemas de potencia y máquinas eléctricas.

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27

IIXX SSiimmppooss iioo IIbbeerrooaammeerr ii ccaannoo ssoobbrree PPrroo tteecccc iióónn ddee SS iiss tteemmaass EElléécc tt rr ii ccooss ddee PPootteenncc iiaa

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Directional Comparison Protection Over Radio Channels for Subtransmission Lines:

Field Experience in Mexico

Servando Sánchez, Alfredo Dionicio, Martín Monjarás, Manuel Guel, Guillermo González, and Octavio Vázquez, Comisión Federal de Electricidad, México

José L. Estrada, Altos Hornos de México, S.A. de C.V. (AHMSA)

Héctor J. Altuve, Ignacio Muñoz, Iván Yánez, and Pedro Loza, Schweitzer Engineering Laboratories, Inc.

Abstract—In this paper, we first review the need for

communications-assisted protection of subtransmission lines,

describe the communications channels available, and compare

applicable protection schemes. We show the advantages of

directional comparison protection over digital point-to-point

radio channels for this application. Later we present a summary

of the applications of directional comparison protection over

radio channels in Mexico. We also provide statistical data on the

field performance of protection schemes and radio channels

installed in Mexico. We then present and discuss several cases of

protection scheme operation for actual faults. Finally, we provide

guidelines for applying directional comparison protection over

radio channels to subtransmission lines.

I. INTRODUCTION

In the Mexican power system, many subtransmission lines

are short, looped lines, and some of them are multiterminal or

multitapped lines. Overcurrent and distance protection

schemes are not a good solution for these line configurations.

Low-cost communications-based protection schemes are now

available for subtransmission lines using digital point-to-point

radio channels.

Comisión Federal de Electricidad (CFE), the largest

Mexican electric utility, has 13 directional comparison

schemes with digital radio channels in operation on 115 kV

subtransmission lines. The first scheme was implemented in

2000. Some of the lines terminate at a substation owned by an

industrial customer. Altos Hornos de México (AHMSA) has

four directional comparison schemes with digital radio

channels operating in an industrial 34.5 kV network. Standard

NRF-041-CFE [1] includes directional comparison protection

over a digital radio channel as an accepted primary protection

scheme for lines up to 10 km long, with nominal voltages

between 69 and 161 kV.

This paper presents the experience of CFE and an industrial

customer in the design and operation of directional

comparison schemes with digital radio channels. The paper

provides real statistical data on the performance of protection

schemes and radio channels and discusses several cases of

protection scheme operation for actual faults. Finally, the

paper provides guidelines for applying directional comparison

protection over radio channels to subtransmission lines.

II. SUBTRANSMISSION LINES REQUIRE COMMUNICATIONS-BASED PROTECTION SCHEMES

A. Line Configurations

Overcurrent and distance protection schemes are the

traditional solution for radial subtransmission lines. However,

many subtransmission lines are short, looped lines, and some

of them are multiterminal or multitapped lines. Overcurrent

and distance protection is difficult to apply for these line

configurations. In addition, protection coordination requires

high operating times.

B. High-Speed Fault Clearing

Fast fault clearing preserves system stability, reduces

equipment damage, and improves power quality. In the past,

high-speed tripping was considered necessary only for

transmission systems.

Modern distribution and subtransmission systems also

require high-speed protection. Loads are becoming more

sensitive to voltage sags caused by faults because of the use of

electronic equipment and computer-controlled processes. The

Information Technology Industry Council (ITIC) created the

ITIC Curve (an updated version of the CBEMA Curve) to

represent the voltage tolerance of computer equipment (see

Fig. 1). A voltage variation is tolerable if the point defined by

the measured percent deviation from nominal and time

duration is between both curves shown. For example, a fault

causing the voltage to sag to 70 percent of nominal should not

last more than 0.5 s.

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500

400

300

200

100

0

Unacceptable Voltage

Variance Region (UVVR)

UVVR

120140

8070

Percent of Nominal Voltage

Duration of Disturbance (s)

11090

Steady

State100.50.020.0030.0011.67x10

-4

Fig. 1. ITIC Voltage Tolerance Curve Defines Transient and Steady State Voltage Tolerance Limits for a Given Load

Delayed fault clearing may cause voltage stability

problems. For example, in areas with a large amount of air

conditioning load, the voltage sag caused by a fault can

initiate a voltage collapse [2]. Distribution or subtransmission

systems with distributed generation also require high-speed

tripping to preserve transient stability.

Typical clearing times of overcurrent and distance

protection schemes are above 0.5 s for many faults, which is

unacceptable for modern subtransmission lines.

III. COMMUNICATIONS-BASED PROTECTION SCHEMES

A. Directional Comparison Protection

Directional comparison schemes use a communications

channel for the relays to exchange information on the status of

their directional elements. For this reason, directional

comparison does not require a high bandwidth channel.

Fig. 2 shows the basic elements of a directional comparison

scheme. At each line terminal, forward- and reverse-looking

instantaneous directional overcurrent or distance elements

provide information for the scheme logic. The forward-

looking elements at each terminal are set to overreach the

remote terminal with sufficient margin to detect all in-section

faults. For an internal fault, both forward-looking elements

operate. For an external fault, one forward-looking and one

reverse-looking element operate. The scheme uses this

information at each line terminal to provide fast tripping for

internal faults. Underreaching elements (not shown in the

figure) at each terminal provide instantaneous protection,

which is independent of the communications-assisted tripping

logic.

A BProtection Zone

A Forward Elements

B Reverse ElementsB Forward Elements

A Reverse Elements

Fig. 2. Directional Comparison Schemes Use Forward- and Reverse-Looking Directional Overcurrent or Distance Elements

Directional comparison schemes for subtransmission lines

in Mexico use Permissive Overreaching Transfer Trip (POTT)

logic. A pilot trip (TRIP) occurs for an internal fault if any

local forward-looking element operates and a permissive trip

(PTRX) is received from the remote terminal (see Fig. 3). At

either end, the forward-looking element pickup keys the

transmitter (KEY). For faults close to one of the line

terminals, the breaker of that line terminal trips

instantaneously via pickup of the underreaching distance or

directional overcurrent element. The remote breaker trips in

pilot time. An external fault is a reverse fault as seen from one

line terminal. The forward-looking element of this line

terminal does not operate. Therefore, no local tripping signal

is issued, and no permissive trip signal is sent to the other

terminal. The scheme does not operate for this out-of-section

fault.

TRIP

KEY

ANDPTRX

Forward-Looking Elements

Fig. 3. Basic Permissive Overreaching Transfer Trip Logic

This POTT scheme uses the reverse-looking elements in

the logic required to prevent misoperation for current reversals

in parallel or looped lines and to ensure tripping when one line

terminal is open or has a weak source. This logic is not shown

in Fig. 3 for simplicity.

Table I, adapted from [3], summarizes the main

characteristics of POTT schemes. A communications channel

failure causes the POTT scheme to fail to operate for internal

faults. For channels that could fail as a result of the internal

fault, one solution is a Directional Comparison Unblocking

(DCUB) scheme. DCUB has the same basic logic as the

POTT scheme, but it opens a time window that allows a trip

without receipt of the trip signal when the channel fails. A

radio channel is suited for POTT logic because it is

completely independent from the protected line.

Using a logic processor, we can apply the POTT scheme to

lines having up to 15 terminals. The logic processor receives

and processes logic information from all line terminals to

make a tripping decision and sends the tripping signal to all

line terminals. A POTT scheme can be implemented over a

channel with a bandwidth of 9.6 kbps or higher.

B. Line Current Differential Protection

In a digital line current differential scheme, the relays

exchange current data over the communications channel.

Using current information from all line terminals, each relay

executes a differential protection algorithm.

Current data may consist of digitized current samples or

phasor values. Some systems combine the three phase currents

into a single signal to reduce the amount of data to transmit.

Modern channels support phase-segregated systems, which

communicate information on all three phase currents

separately.

Table I summarizes the main characteristics of line current

differential schemes. A combination of phase and sequence

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differential elements in the same relay provides very fast

operation for phase faults and very high fault resistance

coverage for ground faults. Continuous channel monitoring is

important to deal with channel loss problems. Making the

differential comparison only when the channel is healthy

improves differential scheme security [4]. Line current

differential protection requires a digital channel with a

bandwidth of 56 kbps or higher.

TABLE I PROTECTION SCHEME COMPARISON

Permissive

Overreaching

Transfer Trip

(POTT)

Current

Differential

Operating Speed 1.5–2 cycles 1–1.5 cycles

Fault Resistance Coverage

Lower Higher

Maximum Number of Line Terminals

15 3

Bandwidth Requirement 9.6–38.4 kbps 56–115 kbps

Loss-of-Signal Consequence

Failure to Trip Failure to Trip

Loss-of-Signal Mitigation

Add Trip Window (DCUB)

Continuous Channel

Monitoring

Upgrading Existing Protection Requires Major Panel Changes

No Yes

IV. COMMUNICATIONS CHANNELS

Two communications channels are currently used in

Mexico for subtransmission line protection: spread-spectrum

radio and fiber-optic cable.

A. Spread-Spectrum Radio

Spread-spectrum radio is a good solution for

subtransmission line protection. If a tower for elevating the

antenna is not required, the cost of a spread-spectrum radio

system is approximately $4,000 (U.S.) per line terminal

(including installation). Once the system is installed, there are

no additional recurring costs, such as license fees. The radio

channel is physically independent from the protected line, and

all of the radio equipment except the antenna can be installed

in a protected enclosure.

Spread-spectrum radios use multiple frequencies in the

900 MHz and 2.4 GHz license-free ISM band to provide a

point-to-point connection. Another radio using the same

frequency at the same time may interfere with the signal;

however, the spread-spectrum system spends a very short time

at each frequency within the band. Frequency interferences

typically cause very short periods of channel unavailability.

Table II, adapted from [3], summarizes the main

characteristics of spread-spectrum radio channels.

B. Direct-Connected Optical Fiber

A direct fiber connection has significant operational

advantages over spread-spectrum radio (see Table II). For

subtransmission line applications, the main limitation is cost.

The typical cost of an optical ground wire (OPGW) or an all-

dielectric self-supporting (ADSS) direct fiber channel is in the

order of $3 per foot, equivalent to $10,000 (U.S.) per

kilometer (including installation). Because of data

transmission capability, point-to-point fiber-optic cable is

suited for current differential relaying.

TABLE II COMMUNICATIONS CHANNEL COMPARISON

Spread-

Spectrum Radio

Direct Fiber-

Optic Cable

Channel Unavailability (Typical)

0.0003 Very Low

Longest Failure (Typical)

1 s Very Short

Cost (10 km, Two Terminals)

$8,000 (U.S.) $150,000 (U.S)

Communications Delay 4 ms 0.1 ms

Data Rate 115.2 kbps 4 Gbps

V. DIRECTIONAL COMPARISON SCHEMES IN OPERATION

The Appendix provides data on the subtransmission lines

in Mexico that have directional comparison protection

schemes over radio channels. Line length ranges from 0.8 to

12.07 km, with 4.95 km as the average length. All lines are

two-terminal lines with no load taps. Some of the lines are

part of a looped system with generation at several buses.

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TABLE III PERFORMANCE OF DIRECTIONAL COMPARISON PROTECTION SCHEMES OVER RADIO CHANNELS IN SUBTRANSMISSION LINES IN MEXICO

)o. Line

)umber of

Years in

Operation

Internal Faults External Faults

Total Correct

Trips

Average Scheme

Operating Time

(Cycles)

Maximum Scheme

Operating Time

(Cycles)

Total Correct

)o Trips

1 73160 2 0 0 1 1

2 73370 2 1 1 1.125 1.125 0 0

3 73040 2 1 1 4.75* 4.75* 0 0

4 73360 2 0 0 1 1

5 73200 2 1 1 2.25 2.25 0 0

6 73350 2 0 0 1 1

7 73180 2 0 0 1 1

8 73590 0.75 1 1 2.25 2.25 3 3

9 73110 7 2 2 1.59 1.68 5 5

10 73090 4 2 2 1.5 2.0 3 3

11 HBB435 – HAM402 4 0 0 1 1

12 HAM403 – HPG435 4 1 1 2.0 2.0 0 0

13 HBA432 – MPC412 0.6 0 0 0 0

14 HBA412 – MPC413 0.6 0 0 0 0

15 73260 3 1 1 1.875 1.875 3 3

16 73440 5 1 1 1.5 1.5 4 4

17 73390 4 1 1 1.44 1.44 4 4

* This fault started as external and evolved to an internal fault; the current-reversal logic delay caused the 4.75 cycles operating time.

VI. FIELD OPERATION EXPERIENCE

A. Protection Operation Data

Table III summarizes the performance of directional

comparison protection schemes over radio channels currently

in operation in Mexico. All schemes have POTT logic, with

some schemes in operation since 2000. The total time of

operation is 46.95 years. The average time of operation is 2.76

years.

These schemes have properly cleared all 12 internal faults

and have remained secure for all 27 external faults. The

average scheme operating time is 1.73 cycles (measured from

fault inception to the emission of the breaker tripping signal).

The longest operating time has been 2.25 cycles. In this

analysis, we do not consider the 4.75-cycle operating time for

the 73040 line fault. Since this fault evolved from external to

internal, the current-reversal logic introduced an additional

time delay, as discussed in Section VII.

B. Radio Channel Data

Some digital relays have the capability of continuously

monitoring the performance of the radio channel. The relay

report provides historic data on the number of channel

failures, the longest recorded failure, and the resulting channel

unavailability. This information is important to evaluate the

impact of channel failures on the protection scheme reliability

and to take corrective actions.

Table IV provides data on radio channel performance for

some of the schemes in operation in Mexico. These data show

that radio channels have performed very reliably, with

unavailabilities between 0.00001 and 0.000585. The longest

unscheduled channel outage has been 4.184 s. Channel

failures have not coincided with faults. No relay has been

disabled because of a channel failure.

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TABLE IV RADIO CHANNEL PERFORMANCE DATA

Line Time Period Total Failures* Relay Disabled Longest Failure (s) Unavailability

73370 07/26/07

07/27/07 256 0 0.108 0.000103

73040 07/18/07

07/27/07 256 0 4.184 0.000098

73590 05/16/07

05/25/07 256 0 1.626 0.000156

73110 05/16/07

05/25/07 256 0 0.8 0.000049

73090 05/16/07

05/25/07 256 0 0.038 0.000585

HBB435 – HAM402 07/04/03

08/21/03 256 0 0.896 0.000010

73260 04/14/07

06/29/07 256 0 515.73 ** 0.000089

* 256 failures is the maximum buffer length in the relay’s report.

** This time does not correspond to a failure, but to a programmed disconnection.

VII. EXAMPLES OF SCHEME OPERATION FOR ACTUAL FAULTS

A. Internal Fault Case

The 73370 line connects substations Azteca and Gemini in

the 115 kV subtransmission ring of the Ciudad Juárez

Distribution Zone, CFE North Distribution Division, which

serves important industrial customers and includes a

generating station (see Fig. 4).

Fig. 4. Subtransmission 115 kV Looped System Serving the City of Ciudad Juárez, Chih., Mexico

The 73370 line has a directional comparison protection

scheme with direct relay-to-relay communications over a

spread-spectrum radio channel. This scheme was implemented

using existing digital directional overcurrent relays. The

POTT logic uses phase (67P2), negative-sequence (67Q2),

and ground (67G2) directional elements as the overreaching

forward-looking elements required for tripping and keying the

transmitter. The logic also uses reverse-looking 67P3, 67Q3,

and 67G3 elements for current-reversal and weak infeed logic.

A single-phase-to-ground fault occurred on this line on

October 31, 2006. The fault current contributions were 4988 A

from the Azteca terminal and 4265 A from the Gemini

terminal. From the oscillogram recorded at the Azteca

substation (Fig. 5), we conclude the following:

• The fault starts on cycle 4.1.

• The phase (67P2), negative-sequence (67Q2), and

ground (67G2) overreaching directional elements

operate on cycle 4.5. The internal bit KEY of the

POTT logic asserts, and a transfer trip signal is

transmitted via relay-to-relay communications using

the internal bit TMB1A.

• RMB1A bit asserts on cycle 5.35, indicating reception

of the transfer trip signal from the remote end, and bit

PTRX asserts to complete the tripping logic (see

Fig. 3). Bit TRIP asserts to initiate local breaker

tripping 1.25 cycles after fault inception.

• The scheme operating time is 1.25 cycles.

• The local breaker clears the fault on cycle 9.5.

• The total fault clearing time is 5.4 cycles.

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Fig. 5. Oscillogram Recorded at the Azteca Terminal of the 73370 Line

Since the relays are not time synchronized, the fault starts

on cycle 5.1 in the Gemini substation oscillogram (Fig. 6).

Protection operation is exactly the same as that of the Azteca

terminal. Bit TRIP asserts to initiate local breaker tripping

1.25 cycles after fault inception. Total fault clearing time is

4.9 cycles.

The POTT protection scheme operated correctly to clear

this internal fault in 5.4 cycles.

Fig. 6. Oscillogram Recorded at the Gemini Terminal of the 73370 Line

The fault records also serve to evaluate the

communications channel performance. The ROK bit remains

asserted during the fault, indicating good reception of the

channel signal. We can measure the transmission time as the

time difference between the remote TMB1A bit assertion and

the local RMB1A bit assertion. This time is 0.8 cycles for both

line terminals.

B. External Fault Case

Fig. 7 shows part of the 115 kV subtransmission loop of

the city of Querétaro. Several lines of this looped system have

directional comparison protection schemes with direct relay-

to-relay communications over a spread-spectrum radio

channel. The POTT logic uses overreaching forward-looking

67P2, 67Q2, and 67G2 directional elements, and also reverse-

looking 67P3, 67Q3, and 67G3 directional elements.

Fig. 7. Part of the Subtransmission 115 kV Looped System Serving the City of Querétaro, Qro., Mexico

A single-phase-to-ground fault occurred on February 2,

2002 on the 73540 line connecting Satélite (SAT) and

Querétaro (QRO) substations. The directional comparison

protection scheme of the adjacent 73110 line correctly did not

operate for this external fault. This line connects substations

Querétaro Poniente (QPE) and Satélite (SAT).

From the oscillogram recorded at the QPE substation

(Fig. 8), we conclude the following:


• The phase (67P2), negative-sequence (67Q2), and

ground (67G2) overreaching directional elements

operate on cycle 4.25. The internal bit KEY of the

POTT logic asserts, and a transfer trip signal is

transmitted via relay-to-relay communications using

the internal bit TMB1A.

• A transfer trip signal is not received from the remote

end, bit RMB1A does not assert, and there is no local

tripping for this external fault.

• Operation of the faulted line primary protection clears

the fault on cycle 8.8.

Fig. 8. Oscillogram Recorded at the QPE Terminal of the 73110 Line

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The oscillogram recorded at the SAT substation (Fig. 9)

shows that:


• The reverse-looking negative-sequence (67Q3) and

ground (67G3) directional elements operate on

cycle 4.0. Phase directional element 67P3 operates

0.25 cycles later. The logic blocks transmission of the

transfer trip bit TMB1A (no forward-looking elements

asserted).

• RMB1A bit asserts on cycle 5.0, indicating reception

of the transfer trip signal from the remote end.

However, bit TRIP does not assert for the external

fault because forward-looking elements are not

asserted.

• Operation of the faulted line primary protection clears

the fault on cycle 9.3.

Fig. 9. Oscillogram Recorded at the SAT Terminal of the 73110 Line

C. Evolving Fault Case

The 73040 line connects substations La Cuesta (CUE) and

Parque (PQE) in the 115 kV Ciudad Juárez subtransmission

looped system (see Fig. 4). On July 11, 2005, a lightning

storm caused several faults on this system. Fig. 10 shows the

oscillogram recorded at La Cuesta substation for a fault that

evolved from external to internal. This is the worst-case

scenario for protection operation speed because the POTT

current-reversal logic delays operation for the internal fault.

The sequence of events is as follows:

• The reverse-looking negative-sequence directional

element 67Q3 remains operated during the initial

phase-to-phase external fault. The fault current is

below the 67P3 element pickup.

• The 67Q3 element resets on cycle 4.3, indicating

clearance of the external fault. This reset activates the

POTT current-reversal logic (not shown in Fig. 3),

which blocks local tripping and prevents transmission

of the transfer trip signal for a preset time.

• An internal fault starts on cycle 4.5.

• The forward-looking negative-sequence element 67Q2

operates on cycle 5.2. The fault current is below the

67P2 element pickup.

• RMB1A and PTRX bits assert on cycle 5.7, indicating

reception of the transfer trip signal from the remote

end; however, the current-reversal logic blocks local

tripping.

• The current-reversal logic timer expires on cycle 9.25.

Bits KEY and TMB1A assert to send a transfer trip

signal. Bit TRIP also asserts to initiate breaker

tripping 4.75 cycles after fault inception.

• The scheme operating time is 4.75 cycles because of

the current-reversal logic delay.

• The breaker clears the fault on cycle 13.0. Total fault

clearing time is 8.5 cycles.

Fig. 10. Oscillogram Recorded at the La Cuesta Terminal of the 73040 Line

VIII. APPLICATION GUIDELINES FOR DIRECTIONAL

COMPARISON SCHEMES OVER RADIO CHANNELS

A. General Application Considerations

Use directional comparison over radio channels to provide

fast fault clearing in new or existing subtransmission and

distribution lines at very low cost. POTT logic is a good

choice for radio channels.

Add the radio channel for approximately $4,000 per line

terminal to upgrade existing schemes when relays are suited

for the application.

The relays should have these features:

• Phase and ground directional overcurrent and/or

distance elements. When available, use negative-

sequence directional elements to provide good fault

resistance coverage for unbalanced faults.

• Programmable functions to transmit and receive relay

internal bits over a direct relay-to-relay

communications channel.

Listed below are some general guidelines to select and set

directional overcurrent/distance elements for POTT logic.

• Use forward-looking directional Level 1 or distance

Zone 1 elements to directly trip the breaker.

– Set to underreach the remote line terminal.

– For short lines, it may be necessary to block

these elements.

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Zone 2 elements to enable local breaker tripping and

to initiate transfer trip transmission.

– Set to overreach the remote line terminal.

• Use reverse-looking directional Level 3 or distance

Zone 3 elements for the current reversal and weak

infeed logic when required.

– Set to overreach the Level 2 or Zone 2 elements

of the remote terminal.


Zone 4 elements to provide time-delayed remote

backup protection.

– Set to overreach the longest adjacent line to the

remote terminal.

• Evaluate the need to add a 0.25 to 0.5 cycle security

time delay to negative-sequence elements to avoid

temporary false channel keying because of unequal

breaker pole opening or closing.

B. Multiterminal Line Applications

Use a logic processor to apply directional comparison

protection to multiterminal lines. The logic processor must

have programmable logic to receive, process, and transmit

relay internal bits over a communications channel.

Fig. 11 shows the directional comparison scheme for a

three terminal line. This scheme is applicable to lines having

more than three terminals. The logic processor, installed at

Terminal 3 in this example, communicates with relays at

Terminal 1 and Terminal 2 via digital radio or fiber-optic

channels. The processor also communicates locally with the

Terminal 3 relay via fiber or copper wires.

Terminal 1 Terminal 2

Relay 1 Relay 2

Relay 3Logic

Processor

Terminal 3

Communications

Channels

Fig. 11. Directional Comparison Protection for a Multiterminal Line Using a Logic Processor

Fig. 12 shows the processor logic for the Terminal 3

scheme. The same logic applies for the other line terminals.

When transfer trip signals PTRX1 and PTRX2 are received

for the remote terminals, bit KEY12 asserts to send a transfer

trip signal to the Terminal 3 relay. This operation converts the

multiterminal line into a two-terminal line as seen from

Terminal 3. Bit PTRX12 asserts in Relay 3, indicating

reception of the transfer trip signal from the logic processor.

The POTT scheme of the Terminal 3 relay operates according

to the logic diagram shown in Fig. 3, with PTRX12 replacing

PTRX.

KEY12ANDPTRX1

PTRX2

Fig. 12. Processor Logic for Terminal 3 Directional Comparison Scheme in a Three-Terminal Line

A directional comparison scheme using this logic is under

commissioning on the 73750 line, which is part of the San

Juan del Río 115 kV looped system, in the state of Querétaro,

Mexico [5]. The 73750 line connects substations San Juan

Potencia, San Juan del Río, and IND-4 (an industrial customer

with cogeneration). This scheme uses direct fiber-optic

communications.

IX. CONCLUSIONS

• Modern subtransmission lines require fast fault

clearing to preserve transient and voltage stability and

to meet load voltage tolerance requirements.

Overcurrent and distance protection do not provide

high-speed tripping for all internal faults.

• Directional comparison protection using point-to-point

digital radio channels provides fast fault clearing at

low cost for subtransmission and distribution lines.

• In Mexico, the first subtransmission line directional

comparison scheme over radio channels was

commissioned in 2000. There are 17 schemes in

operation today.

• The schemes in service in the Mexican power system

have correctly cleared all 12 internal faults, with an

average operating time of 1.73 cycles. The longest

operating time has been 2.25 cycles. The schemes

have remained secure for all 27 external faults.

• Channel monitoring data show a very reliable

performance of the radio channels. Unavailability has

been no higher than 0.000585. The longest channel

outage has been 4.184 s. Channel failures have not

coincided with faults. No relay has been disabled

because of a channel failure.

• Using a logic processor, we may apply directional

comparison protection to lines having more than two

terminals. The logic sends a transfer trip signal to each

line terminal when it receives tripping signals from all

the other terminals.

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X. APPENDIX

TABLE V SUBTRANSMISSION LINES WITH RADIO CHANNELS IN MEXICO

)o. User Location Line Voltage

(kV)

Length

(km)

1 Juárez Zone, North Distribution Division, CFE Cd. Juárez, Chih. 73160 115 6.05







8 Querétaro Zone, Bajío Distribution Division, CFE Querétaro, Qro. 73590 115 5.2



11 AHMSA Monclova, Coah. HBB-435 – HAM-402 34.5 4.0

12 AHMSA Monclova, Coah. HAM-403 – HPG-435 34.5 0.8

13 AHMSA Monclova, Coah. HBA432 – MPC412 34.5 1.87

14 AHMSA Monclova, Coah. HBA412 – MPA413 34.5 1.40

15 Tlaxcala Zone, Centro Oriente Distribution Division, CFE Tlaxcala, Tlax. 73260 115 6.6

16 Uruapan Zone, Centro Occidente Distribution Division, CFE Uruapan, Mich. 73440 115 12.07

17 Uruapan Zone, Centro Occidente Distribution Division, CFE Uruapan, Mich. 73390 115 9.58

XI. REFERENCES

[1] /ormalized Protection Schemes for Transmission Lines, 2005. CFE Std.

NRF-041-CFE – 2000, Comisión Federal de Electricidad, México (in

Spanish).

[2] J. B. Roberts, A. Reyes, and T. Stulo, “Sympathetic Tripping Problem

Analysis and Solutions,” Proceedings of the 24th Annual Western

Protective Relay Conference, Spokane, WA, October 1997.

[3] R. Moxley and K. Fodero, “High-Speed Distribution Protection Made

Easy: Communications-Assisted Protection Schemes for Distribution

Applications,” Proceedings of the 31st Annual Western Protective Relay

Conference, Spokane, WA, October 2004.

[4] D. Carroll, J. Dorfner, T. Lee, K. Fodero, and C. Huntley, “Resolving

Digital Line Current Differential Relay Security and Dependability

Problems: A Case History,” Proceedings of the 29th Annual Western

Protective Relay Conference, Spokane, WA, October 2002.

[5] M. Monjarás, J. M. Jaramillo, and I. Muñoz, “Protection Scheme for a

Three-Terminal 115 kV Line Using Directional Comparison Relays,”

Proceedings of the 19th IEEE Mexico Section Summer Meeting on

Power and Industrial Applications, Acapulco, Gro. Mexico, July 2006

(in Spanish).

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XII. BIOGRAPHIES

Servando Sánchez received his BSEE degree in Electrical Engineering and his M. Sc. degree in Power Electronics from the Technological Institute of Morelia, in Morelia, Mich., Mexico. He has worked for the Mexican electric utility Comisión Federal de Electricidad (CFE) since 1984. From 1991 to 1996 he was head of the Substation Protection Department of the Morelia Distribution Zone, Centro-Occidente Distribution Division (CODD). From 1996 to 2001 he was head of the CODD Substation Protection Department. Mr. Sánchez has been the head of the Substations Department, CODD since 2001. He has also conducted research work at CFE and has authored and coauthored technical papers related to line protection. His main research interests are in power system protection and power transformer monitoring.

Alfredo Dionicio Barrón received his BSEE degree in Industrial and Electrical Engineering from the Querétaro Regional Technological Institute in 1991. He completed a set of graduate courses on power systems at the Guanajuato University in 1994. He has worked for Comisión Federal de Electricidad (CFE) since 1991. From 1991 to 1992 he was a Rural Electrification Supervisor at the Bajío Distribution Division (BDD). From 1992 to 1994 he was head of the Distribution Section at the Celaya Distribution Zone, BDD. Mr. Dionicio has been the head of the Protection Office of the Querétaro Distribution Zone, BDD since 1994.

Martín R. Monjarás M. received his BSEE degree in Electrical Engineering from the University of Guanajuato in 1990. He has worked for Comisión Federal de Electricidad (CFE) since 1991. From 1991 to 1994 he was head of the Distribution Section at the San Juan del Río Distribution Zone, Bajío Distribution Division (BDD). From 1994 to 1997 he was head of the Substations, Lines and Protection Office at the San Juan del Río Distribution Zone. Mr. Monjarás has been the head of the BDD Substation Protection Department since 1997.

Manuel Guel received his BSEE degree in Electrical Engineering from the Autonomous University of San Luis Potosí, Mexico. Since 1984 he has worked for Comisión Federal de Electricidad (CFE). From 1991 to 2004 he was head of the Substation Protection Department of the Golfo Centro Distribution Division (GCDD) in Tampico, Tam. Mr. Guel has been the head of the Communications and Control Department, GCDD since 2004.

Guillermo González Cavazos received his BSEE degree in Electronic Engineering from the Technological Institute of La Laguna, in Torreon, Coahuila, Mexico. Since 2002 he has worked for Comisión Federal de Electricidad (CFE). From 2002 to 2004 he served as a field engineer of the Protection and Measurement Department of the Juarez Transmission and Transformation Sub-Area. Since 2004 Mr. Gonzalez has been the head of the Communications and Control Office of the Juarez Distribution Zone, North Distribution Division (NDD). He has worked on the expansion and installation of radio frequency and fiber-optic channels for protection, voice, and data communications.

Octavio Vázquez Gamboa received his BSEE degree in Industrial and Electrical Engineering in 1981 from the Technological Institute of Puebla, in Puebla, Pue., Mexico. From 1980 to 1982 he was the head of the Electrical Maintenance Office at Industrias Polifil, S.A. de C.V. During 1983 he was the head of the Electrical Maintenance Department at Aceros Tlaxcala. He has worked for Comisión Federal de Electricidad (CFE) since 1984. From 1984 to 1989 he was the head of a Protection Office of the Southeastern Distribution Division (SDD). From 1990 to 1993 he was the head of a Substations and Lines Office of the SDD. From 1994 to 2000 Mr. Vázquez was the head of the SDD Substation Protection Department. In 2001 Mr. Vázquez was made the head of the Substation Protection Department of the Central-Eastern Distribution Division in Puebla, Pue. He is a member of the CFE Protection Panel Committee and has served as an instructor in distribution system protection courses at CFE Celaya and Campeche Training Centers. Mr. Vázquez has authored and coauthored technical papers on distribution system protection and is currently developing power quality monitoring systems for CFE.

José L. Estrada received his BSEE degree in Electrical Engineering in 1977 from the National Polytechnic Institute, Mexico City, Mexico. Since 1980 he has worked for Altos Hornos de México, S.A. de C.V. (AHMSA) the largest steel mill in Mexico, as a high voltage project manager. Mr. Estrada is also an Adjunct Professor at the Mechanical and Electrical Engineering School of the Coahuila University, in Monclova, Coahuila, Mexico.

Héctor J. Altuve received his BSEE degree in 1969 from the Central University of Las Villas, Santa Clara, Cuba, and his Ph.D. in 1981 from Kiev Polytechnic Institute, Kiev, Ukraine. From 1969 until 1993, Dr. Altuve served on the faculty of the Electrical Engineering School at the Central University of Las Villas. He served as professor, Graduate Doctoral Program, Mechanical and Electrical Engineering School, at the Autonomous University of Nuevo León, Monterrey, Mexico, from 1993 to 2000. In 1999 through 2000, he was the Schweitzer Visiting Professor at Washington State University’s Department of Electrical Engineering. In January 2001, Dr. Altuve joined Schweitzer Engineering Laboratories, Inc., where he is currently a Distinguished Engineer and Director of Technology for Latin America. He has authored and coauthored more than 100 technical papers and holds three patents. His main research interests are in power system protection, control, and monitoring. Dr. Altuve is an IEEE Senior Member and a PES Distinguished Lecturer.

Juan Ignacio Muñoz González received his BSEE degree in Electrical Engineering from the University of Guanajuato in 1978. From 1981 to 1997 he worked for Comisión Federal de Electricidad (CFE) as a protection engineer in the distribution and transmission areas. From 1988 to 1997 he was also an Adjunct Professor of the Engineering Sciences Department at the Iberoamerican University, León Campus. From 1997 to 2000 he was a technical support engineer for INELAP-PQE. Since 2000 Mr. Muñoz has worked for Schweitzer Engineering Laboratories, Inc., where he is currently the project administration manager of its Mexico subsidiary. Mr. Muñoz is an IEEE Member and also a Member of the College of Mechanical and Electrical Engineers of the State of Guanajuato.

Iván Yánez received his BSEE degree in Electrical Engineering in 1994 from the Technological Institute of Hermosillo, Hermosillo, Son., Mexico. From 1995 to 1998 he worked for Comisión Federal de Electricidad (CFE) as a protection engineer in the Transmission and Transformation Northwestern Area. He worked on the single-pole tripping and reclosing project for the 230 kV CFE Northwestern System. In 1999 he joined Schweitzer Engineering Laboratories, Inc., where he is currently a field application engineer in the Monterrey, Mexico office.

Pedro Loza received his BSEE degree in 1998 from the National Autonomous University of México (UNAM). He completed the courses for an M.Sc. Degree in Power Systems at UNAM and is currently working on his thesis. From 1998 to 1999, Mr. Loza worked in the Electric Research Institute in Cuernavaca, Mor., Mexico where he conducted research on small signal stability. In September 2000, he joined Schweitzer Engineering Laboratories, Inc., where he worked as a design engineer, and is currently a field application engineer in the Mexico City office.

© 2007 by Comisión Federal de Electricidad, México, Altos Hornos de México, S.A. de C.V., and Schweitzer Engineering Laboratories, Inc.

All rights reserved. 20070904 • TP6294-01

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Resumen –– Este trabajo describe la aplicación de dispositivos de

protección microprocesados, con capacidades de comunicación, en

la protección de redes de distribución en lazo; se utiliza

comunicación por radiofrecuencia por su economía y

confiabilidad actual.

Haciendo uso de la inteligencia distribuida se establece el

denominado esquema automático de protección. Para ello se

utiliza la lógica interna del equipo microprocesado y su protocolo

propietario, el cual permite intercambiar 8 bits de datos entre

restauradores adyacentes. Dicho esquema, aísla automáticamente

las secciones con falla y reenergiza las secciones no falladas

después de un cierto número de operaciones de recierre.

Previendo la posibilidad de la pérdida del canal de comunicación,

antes, durante o posterior a la operación del esquema, se

configuró un sistema de protección tradicional (relevador –

restaurador) que permita proteger a la red de distribución ante

tal situación.

Palabras Clave – coordinación relevador –restaurador-

restaurador, coordinación con radio frecuencia, automatismo en

la red de distribución.

I. INTRODUCCIÓN En la historia del suministro de energía eléctrica, la preocupación por mantener la continuidad de este servicio ha sido una constante; la evolución en cuanto a la naturaleza de la carga que se alimenta, ha marcado la pauta. Hoy en día, debido a la carga sensible, la intolerancia a la interrupción del servicio eléctrico sigue creciendo. Ante esta situación, la necesidad de actualizar el sistema de distribución convencional y los esquemas de protección asociados, siguen siendo una prioridad. Aunque el sistema de distribución es usualmente radial en diseño [1], la continuidad de servicio es su principal defecto, por ello los intentos por superar esta deficiencia han resultado en muchas formas y arreglos de este tipo de sistema [2,3]. Entonces, muchos sistemas de distribución están siendo actualizados de sistemas radiales para reducir interrupciones a los clientes y mejorar el servicio de suministro eléctrico, sin embargo la cuestión económica está involucrada al momento de seleccionar. Ahora bien, independientemente de la elección

se deben cubrir ciertos principios y características; el sistema de distribución debe proveer servicio con mínima variación de voltaje y mínima interrupción y cuando estas sucedan, deben ser de corta duración y afectar al menor número de usuarios. La razón principal para implementar la automatización en la red de distribución (AD) es la mejora en la confiabilidad. Aún cuando los índices de confiabilidad consideran una interrupción si el tiempo de pérdida de suministro es mayor a 5 minutos [4], cuando la automatización utiliza inteligencia distribuida (la cuál se define posteriormente) y es aplicada en alimentadores de distribución, la restauración de segmentos no fallados generalmente ocurre en menos de un minuto Arquitectura de la red

Ocasionalmente la forma de un circuito en lazo es confundido con un circuito en anillo. En el sistema de transmisión, un lazo es un circuito que comienza desde un punto de suministro o bus, es llevado hacia varios puntos de carga y retornado al mismo punto o bus. Un anillo es un circuito o circuitos con varias fuentes de potencia de amarre [5]. En distribución, la diferencia básicamente radica en que el arreglo en lazo, los ramales son conectados en tap; dichos ramales son protegidos por fusibles o seccionalizadores, mientras que en el arreglo en anillo se colocan elementos de seccionamiento en ambos lados del punto de conexión del ramal y uno más protegiendo al ramal. Aún cuando no es claro donde comienza uno y donde termina el otro, la literatura indica que existen arreglos tanto en anillo cerrado o abierto, como en lazo cerrado o abierto. Los arreglos en anillo generalmente son cerrados y se utilizan en redes subterráneas con un diseño como el que se muestra en la figura 1.1a o 1.1b, con una fuente; sin olvidar que se somete a mucho más clientes a caídas de voltaje por fallas [6]. Dada la posibilidad de conectar transformadores en paralelo, las figuras 1.1(c) y 1.1(d) no son recomendadas para los arreglos cerrados, además existe la posibilidad de incrementar dramáticamente el nivel de falla. En estos arreglos se mejora en gran medida ambos factores; la confiabilidad y la calidad de la energía en el suministro [7,8].

Implementación de un Esquema de Protecciones de Sobrecorriente entre Relevador-Restaurador-Restaurador

con Automatismo y Comunicación en un Sistema de Distribución en Lazo

1J. J. Tenorio 2D. Sebastian 3R. Méndez 4C. Guerrero [email protected] [email protected] [email protected] [email protected] 1 Luz y Fuerza del Centro, Gerencia de Aseguramiento de la Calidad, México D.F., México

2 Instituto Politécnico Nacional, SEPI ESIME ZAC., Programa. de Postgrado en Ing. Eléctrica, México, D.F. , México 3 Instituto Politécnico Nacional, ESIME ZAC., Departamento de Ingeniería Eléctrica, México, D.F. , México 4 Luz y Fuerza del Centro, Gerencia de Redes de Distribución, México D.F., México

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NA

NCNC

NCNC

Tr. 1 Tr. 2

Subest. dedist. 1

Subest. dedist. 2

Subest. dedistribución

Subest. dedistribución

Sub. Sub.dist. 1 dist. 2

TrTr1 Tr2 Tr1 Tr2

Fig. 1.1 (b) Fig. 1.1 (c) Fig. 1.1 (d)

InterruptorFusibleRestaurador Normalmente cerrado (NC)o Normalmente abierto (NA)

Subestación de

distribución

Fig. 1.1 (a) Fig. 1.1 (e)

Transf. dedistribución

Figura 1. Arquitecturas utilizadas en arreglos de lazo ó anillo

Los arreglos en lazo generalmente son en lazo abierto y se utilizan en redes de distribución aéreas. En estos, la cantidad de equipo de desconexión es menor, los ramales son tomados del lazo principal (taps) para obtener la cobertura de área, tal como se observa en la figura 1.1(e). Aunque se pueden alimentar por una o dos fuentes, tal como se muestra en los tres circuitos de las figuras 1.1(b), 1.1(c) y 1.1(d), se evita usar el arreglo de la figura 1.1(b) para no perjudicar a los alimentadores adyacentes de caídas de tensión excesivas, al existir fallas en cualquiera de los alimentadores relacionados a un mismo transformador. Con el arreglo de la figura 2.1(d) se soluciona este problema. Estos arreglos utilizan esquemas de protección de sobrecorriente y aún cuando se reducen los tiempos de interrupción la calidad del suministro a los clientes no es resuelta porque no resuelve el problema de las interrupciones momentáneas [9]. Entonces, los arreglos cerrados proporcionan una mayor calidad de suministro que los arreglos abiertos. Sin embargo, los arreglos abiertos son más ampliamente usados en sistemas de distribución porque son implementados usando desconectadores (llámese restauradores, seccionalizadores o cuchillas) de bajo costo y por tanto es el que se utilizará en la aplicación de este trabajo.

Evolución de la automatización y su aplicación al arreglo en

lazo abierto.

Dado que la AD y el SCADA crecieron de manera independiente, estas son diferentes pero muy similares [10]; debido al parecido, actualmente hay quién maneja que el desarrollo de la AD está basado en plataforma SCADA [11]. Una diferencia importante es el control, en el SCADA el operador se apoya en el control supervisorio y en la AD no existe intervención de este. Muchas funciones ejecutadas por la segunda, particularmente la adquisición de datos, son parte integral de la primera porque no se pueden tomar decisiones sin datos.

La AD es un campo muy amplio, dentro de ella habitan un sin número de funciones. Una lista completa de las funciones de AD se encuentra en la referencia [12], pero para facilitar el análisis se pueden clasificar en tres categorías [13,14]:

• Funciones para la automatización de la subestación • Funciones para la automatización del alimentador

• Funciones para la automatización con la interface del

cliente

Las funciones de la AD en el alimentador incluyen, principalmente:

• Seccionamiento automático y • Control de voltaje del alimentador.

El seccionamiento automático, trata con la identificación, localización y aislamiento de falla y restauración del servicio. El control de voltaje, involucra la colocación de capacitores y control del regulador de voltaje. Dadas las funciones de la AD, la IEEE la define como: “un sistema que permite a una compañía suministradora monitorear remotamente, coordinar y operar componentes de distribución en tiempo real desde sitios remotos”. Dentro de todas las funciones que existen en el sistema de distribución, aquellas que pueden ser automatizadas se pueden clasificar en dos categorías, llamadas, funciones de monitoreo y funciones de control. El sistema de protección es una parte de estos esquemas, es decir que, la automatización de la protección está contenida en la AD. Control de la automatización

El control utilizado para llevar a cabo el aislamiento de la falla y la restauración de las secciones sanas del esquema en lazo puede variar, existen dos estrategias con que se enfrenta la reconfiguración después de una contingencia en la red: La inteligencia central (control remoto) e inteligencia distribuida, en esta última puede o no utilizarse un sistema de comunicación (sistema convencional).

Considerando la evolución del control sobre la red de lazo abierto, el primero en utilizarse fue el sistema convencional (sin comunicación) donde se utiliza la caída de tensión como señal para iniciar el proceso de seccionamiento y transferencia automática a fin de recuperar el suministro a la mayor cantidad de usuarios. Los tiempos de operación son altos, del orden de minutos, y esto puede ser una causa por la cual la norma IEEE Std. 1366 [4] aún maneje 5 minutos para que se declare una interrupción. El control remoto se refiere al uso del sistema SCADA, con él se desminuyó el tiempo de interrupción del servicio a entre 15 y 40 minutos [16], otras experiencias indican que se lograron tiempos de restauración de 60 segundos [17] y 1 segundo [18]. Los tiempos alcanzados se deben al medio de comunicación, tipo y al número de seccionadores involucrados. Sin embargo, en general, el control remoto significa la intervención del factor humano para lograr el aislamiento de la falla y la restauración del servicio

La inteligencia distribuida es la vía para la reconfiguración automática [19,20], se aplica fácilmente al arreglo de lazo

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abierto y tiene la característica de flexibilidad y adaptabilidad (ausentes en el control remoto) que se requieren para satisfacer las necesidades crecientes de los clientes del sistema de distribución, lo que permite que sea más sencilla su expansión a redes más complejas; redes multifuente[20,21,22] ó redes inteligentes[23,24], basado desde luego en sistemas abiertos. En este tipo de control no existe dispositivo maestro, la reconfiguraciòn se procesa localmente programando un algoritmo dentro del control de los desconectadores. Además, con la inteligencia distribuida se logra un grado de protección local en caso de pérdida de comunicación.

II. IMPLEMENTACIÓN A continuación se desarrolla un ejemplo práctico aplicado, a nivel de laboratorio, a un circuito de lazo abierto y utilizando automatización de la protección; dicho arreglo se muestran en la figura 2. La aplicación está limitada por la disponibilidad de tres dispositivos electrónicos inteligentes (DEI’s) microprocesados con capacidad de recierre[25], los cuales simulan la operación de los restauradores y están indicados en la figura 2 como RB, RE y RC. Nótese que en el circuito de dicha figura 2, no existe comunicación entre los relevadores de la subestación y los restauradores más próximos a ella. Por sencillez, en adelante, el hecho de mencionar restaurador, control, equipo, DEI, se refiere a una misma definición; al control de los restauradores.

Figura 2 Red de distribución en lazo de 7 elementos.

La comunicación entre los controles RB, RE y RC fue a través de 4 equipos de radiofrecuencia (radios), con un rango de 902 a 928 MHz. Debido a la baja potencia de radiación de estos equipos no se requiere permiso especial ni licencia de la Secretaría de Comunicaciones y Transporte[26]. En la figura 3 aparece la conexión física de los restauradores con los radios.

Figura 3. Conexión física de los DEI’s con los radios

Los radios se configuraron de acuerdo a las referencias [27,28,29]. Al activar el canal de comunicaciones el protocolo propietario (presente en los 3 DEI’s) está listo para intercambiar 8 bits de datos de restaurador a restaurador[29,30,31], tal como se ilustra en la figura 4. En cada control, el estado de una ecuación lógica permite la transmisión de uno a ocho bits y, de igual forma, una vez que dichos bits se reciben, están disponibles para usarse en alguna lógica.

Figura 4. Representación de la comunicación restaurador a restaurador

Lógicas utilizadas por el esquema automático de protección

Los relevadores microprocesador presentes en la figura 2, tienen lógica con la capacidad suficiente para contruir el esquema automático de protección. Estos dispositivos utilizan elementos de control y protección y los combinan con operadores lógicos tales como *(AND), +(OR), !(NOT), /flanco ascendente, \(flanco descendente) y ()(paréntesis) para crear ecuaciones de control (denominadas ecuaciones de control SELogic). Dichas ecuaciones (en adelante llamadas simplemente como: lógicas) permiten crear esquemas de control y protección. Se hicieron algunas modificaciones a las lógicas de las referencias [32,33] a efecto de adecuarlas al esquema automático de protección de este trabajo, dichas lógicas se presentan a continuación:

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LOGICA 1. Lógica de encendido/apagado

Figura 5. Lógica de encendido/apagado del esquema

LOGICA 2. Lógica de inicio del esquema por contingencia 2a. Por pérdida de potencia

Figura 6. Lógica 2a: Lógica de pérdida de potencial

2b. Por cortocircuito

Figura 7. Lógica 2b: Lógica de cortocircuito

LOGICA 3. Lógica de seccionamiento.

Figura 8. Lógica 2b: Lógica de cortocircuito

LOGICA 4. Lógica de ECO 4a. ECO por cortocircuito

Figura 9. Lógica 4a: Lógica de ECO por cortocircuito

4b. ECO por pérdida de potencial. TMB2A=LT11 AND NOT (52A) OR RMB2B AND NOT (LT12) TMB2B=LT11 AND NOT (52A) OR RMB2A AND NOT (LT12)

LOGICA 5. Lógica de cierre

Figura 10. Lógica de cierre

LOGICA 6. Lógica de evento

Figura 11. Lógica de evento

LOGICA 7. Lógica de simulador de interruptor

Figura 11. Lógica de simulador de interruptor

Como ya se dijo, el tipo de control utilizado para la implementación de la AD, es inteligencia distribuida, lo que significa que las lógicas mencionadas se encuentran dentro de cada control de la red usada. Una característica propia de la AD es su flexibilidad, lo que permite que el esquema sea fácilmente expandible. En la figura 12 se muestran las lógicas contenidas en cada restaurador. Si se requiere reducir o expandir el esquema, será sencillo saber las lógicas que se deben insertar en el nuevo elemento.

Figura 12. Distribución de las lógicas del esquema sobre la red en

lazo de 7 elementos El desempeño del esquema ante fallas en las secciones del alimentador 1, es similar a las fallas que pudieran suceder en las secciones del alimentador 2, por ello únicamente se analiza

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el funcionamiento de las lógicas del esquema ante fallas que se ilustran en la figura 12, además esto subsana la limitación que se tiene de la cantidad de equipo porque ante una falla en las secciones S1 a S3 los restauradores R1 y R2 no operan, tan solo actúa la lógica L5 informando de la ocurrencia de la contingencia. La magnitud de corriente y la pérdida de potencial, son las señales que inician el proceso de apertura y cierre de los restauradores a efecto de liberar la falla y restablecer a la mayor cantidad de usuarios. En la figura 13, se muestra un diagrama de flujo donde se ilustra la secuencia de las lógicas del esquema automático de protección aplicado a la red de la figura 2. El objetivo del diagrama, es mostrar la operación de las lógicas ante la detección de pérdida de potencial y corriente de falla. La parte superior del diagrama indicado, muestra la secuencia de las lógicas de los restauradores involucrados cuando existe pérdida de potencial en las secciones S1 ó S4 (por falla en estas secciones ó por pérdida de la subestación). La parte inferior muestra la secuencia de las lógicas al existir falla en las secciones S2 a S5.

Figura 13. Diagrama de flujo con la operación de las lógicas del

esquema automático de protección a) Ejemplos de la operación del esquema

El objetivo del esquema es minimizar el tiempo de interrupción de aquellos clientes que aunque son alimentados por el mismo circuito no están directamente afectados por el punto de falla. Para ello, el esquema debe reconocer que ha ocurrido una falla permanente, aislar la sección con falla y cerrar el punto normalmente abierto para restaurar el servicio a las secciones sin falla. b) Falla permanente entre las secciones S1 y S2

Cuando la falla 1 de la figura 12 es permanente, el relevador “r1” se bloquea. El esquema se inicia cuando el temporizador SV4, de la lógica 2a en RC, ha finalizado su conteo de 300 ciclos. Todas las condiciones de esta lógica se cumplen, se activa el bit LT11, dispara el restaurador RC y se bloquea; al bloquearse, en este mismo control se cumplen las condiciones de la lógica L4a2 de ECO y se transmite la señal TMB2 al restaurador RB. La figura 14 muestra los eventos detectados por el restaurador RC. En dicha figura se ilustra la secuencia

de los bits involucrados desde que se detecta pérdida de potencial (línea 6: bit 27A1 habilitado) y hasta que se envía la señal al restaurador RB (línea 1: bit TMB2 habilitado), todo ello transcurre en 5 ciclos (70 ms).

Figura 14. Secuencia de eventos, detectados por el restaurador RC,

ante una falla permanente en la sección S1.

La señal RMB2, busca el punto normalmente abierto para cerrarlo, primero “pregunta” a RE y finalmente lo encuentra en RB a través de la lógica L4a1. En este restaurador la señal activa la lógica L4b, la cual cierra (CL=...+/LT12) a RB. En la figura 15 se muestran los eventos detectados por el restaurador RB, en la línea 3 aparece la recepción del bit RMB2A y en la línea 2 aparece habilitado el bit LT12, el cual cierra a este restaurador normalmente abierto. Esto ocurre en 4 ms.

Figura 15. Secuencia de eventos, detectados por el restaurador RB,


Desde que el temporizador SV4, de la lógica 2a en RC, termina su conteo, el temporizador SV7 de la lógica encendido/apagado (L1), permitirá un espacio de tiempo de 300 ciclos para que el esquema concluya tanto el seccionamiento como la transferencia automática y posteriormente lo apagará (RST10), de esta manera se evita que ante una falla posterior se lleve a cabo seccionamiento involucrando al esquema. Esto se ilustra, en la línea 1 de la figura 15, con el bit LT10 deshabilitado. Una vez que el esquema ha cumplido su ciclo, la red se ha reconfigurado, y en el caso de presentarse una falla posterior a ello, el desempeño de la protección de la nueva red, dependerá de la coordinación de protecciones tradicional.

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c) Falla permanente en las secciones S2 a S5

Cuando es permanente la falla 2, de la figura 12, el control RC se bloquea y se cumplen todas las condiciones de la lógica de inicio L2b de RC, se activa el bit LT13 (línea 14 de la figura 16) y envía señal de transmisión TMB1 (líneas 12 ó 13 de la figura 16) hacia RE.

Figura 16. Secuencia de eventos, detectados por el restaurador RC,

ante una falla permanente en la sección S2 La figura 17, muestra la secuencia de eventos detectados por RE, en la línea 7 se recibe señal (RMB1A) de RC, con dicha señal se cumplen las condiciones de la lógica de seccionamiento L3 y se habilita el bit LT11 (línea 6), entonces se activa la señal de disparo (línea 4, bit TRIP activado) y bloqueo (línea 5, bit 79LO habilitado), RE abre definitivamente sus contactos (línea 3, bit 52A deshabilitado). Después de habilitarse LT11, en este mismo control RE se cumplen las condiciones de la lógica ECO L4a1 y se transmite señal (TMB2) al restaurador RB (línea 2 de la figura 17).

Figura 17. Secuencia de eventos, detectados por el restaurador RE,

ante una falla permanente en la sección S2 RB recibe (RMB2) la señal de RE en; la lógica de ECO L4a1 y la lógica de cierre L4b. En la figura 18 se muestran los eventos detectados por el restaurador RB, en la línea 3 aparece la recepción del bit RMB2A y en la línea 2 aparece habilitado el bit LT12, el cual cierra a RB (normalmente abierto)

Figura 18. Secuencia de eventos, detectados por el restaurador RB,


Desde el momento en que se habilita el bit LT13 (lógica 2b en RB), el temporizador SV5 (lógica 1) permite el intervalo de tiempo de 300 ciclos para que el esquema concluya y se apague (RST10=1). Esto se ilustra en la línea 1 de las figuras 17 y 18 con el bit LT10 deshabilitado. Nuevamente, después de que el esquema cumple su ciclo, el desempeño de la protección de la red ante la nueva configuración, dependerá de la coordinación de protecciones tradicional. Como una forma sencilla de evaluar los beneficios de implementar el esquema automático, en la tabla 1 se presenta una relación de tiempos en el seccionamiento y transferencia automática. Tabla 1. Tiempos comparativos de transferencia y

seccionamiento en redes de distribución Tipo de maniobra Tiempo

Operación manual 2.5 horas Automático sin comunicación 5 minutos Control remoto (inteligencia centralizada)

1 minuto

Automatización en distribución (Inteligencia distribuida)

1 segundo

Implementación del Esquema automático de protección

5 segundos (300 ciclos)

Los tiempos de la tabla 1 están sustentados en la bibliografía que aparece en las referencias. Aún cuando existen trabajos donde se muestra que el control remoto ha conseguido tiempos de hasta 1 segundo, es claro que las características de flexibilidad y adaptabilidad de la automatización en distribución le dan un nivel superior comparado con el control remoto.

El tiempo máximo, que toma el esquema automático, para llevar a cabo tanto el seccionamiento como la transferencia, está definido por los temporizadores SV5 y SV7 de la lógica 1. Los registros de eventos de las figures 14 a 18 muestran que se logran tiempos inferiores, sin embargo dado que se trata de un trabajo de laboratorio dónde la distancia entre los radios está en un promedio de 2 metros (cuando el máximo alcance permitido es 15 km), 5 segundos es un tiempo significante para concluir que es atractivo utilizar el esquema. Además, considerando que en las redes ya existentes dónde se utilizan dispositivos microprocesados sola hay necesidad de agregar equipos de radiofrecuencia, este equipo es aproximadamente un 10% del costo total de un restaurador, la inversión no es elevada.

III. CONCLUSIÓN Este es un trabajo desarrollado a nivel de laboratorio, todas las simulaciones realizadas están encaminadas a validar prácticamente los conceptos teóricos del esquema en lazo propuesto. La estructura en la que se presentan las ecuaciones de control, del esquema automático, aplicado a los elementos

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del esquema en lazo, permite que sea relativamente sencillo aumentar o disminuir el número de elementos de la red; esta es la característica de adaptabilidad que permite a la inteligencia distribuida ser una vía futura para la reconfiguración automática De acuerdo con los resultados, el agregar comunicación punto a punto a un esquema de protección tradicional aumenta significativamente su desempeño, evitando la pérdida de carga en las secciones no falladas, además reduce la duración de la interrupción; en resumen, el sistema de comunicación es el elemento fundamental para lograr tiempos más cortos de restablecimiento del servicio eléctrico. Para implementar la automatización del esquema en lazo, se utilizó un medio de comunicación por radiofrecuencia, en la actualidad este es un medio de transmisión económico y es el que más se justifica en los sistemas de distribución Aún cuando en este trabajo, se utiliza la lógica de un tipo específico de relevador, en la actualidad todos los equipos microprocesados de los diferentes fabricantes que existen a nivel mundial ofrecen una característica similar, la cual se puede usar como herramienta para crear nuevos esquemas que ayuden a disminuir los tiempos de interrupción en el sistema de distribución.

Otro aspecto inherente al relevador usado es el protocolo de comunicación propietario, posiblemente no todos los fabricantes dispongan de un protocolo con el mismo potencial, sin embargo, con la aparición de la norma IEC 61850, el panorama es alentador porque con ellos se conseguirán sistemas abiertos, que evitarán la dependencia cada vez menor de tales protocolos propietarios.

IV. REFERENCIAS

[1] Burke J. J.: Power Distribution Engineering – Fundamental and

Application, Marcel Decker, 1994, chapter 4. [2] Westinghouse Electric Company: Electric Transmission and

Distribution Reference Book, Five Edition, 1964, chapter 20 [3] Settembrini R., “Seven Distribution Systems: How Reabilities

Compare”, Electrical Word, May 1992, pp. 41-45 [4] IEEE Std. 1366 – 2003: IEEE Guide for Electric Power Distribution

Reliability Indices [5] Westinghouse Electric Corporation: Electric Utility Engineering

Reference Book; Distribution Systems, First Edition, 1965, Chapter 3 and 4

[6] Roberts J., Zimmerman K., “Trip and restore Distribution Circuits at Transmission speeds”, presented at the 25th Annual Western Protective Relay Conference, Spokane, Washington, October 2001

[7] Tobias J. C., Sautriau D. J., Hull D. J., Fabraay S., “Improved Quality of Supply in MV Distribution Networks Using Directional Blocking Scheme”, IEE Conference Publication No. 438, CIRED 1997, pp. 4.29.1-4.29.5

[8] Fairman J. R., Zimmerman K., Niemira J. K., “International Drive Distribution Automation and Protection”, proceedings of the 26th Annual Western Protective Relaying Conference, Spokane, WA, October, 2000.

[9] Tobias J. C., Leeuwerke R. P., Brayford A. L., Robinson A., “The use of sectionalizing Circuit Breakers in Urban MV Distribution Network”, IEE Conference Publication No. 459, Trends in Distribution Switchgear, 10-12 November 1998, pp. 102-108

[10] Pahwa A.: otes of the course ”Flexible Control of Distribution

Systems”, July 1997, URL:www.eece.ksu.edu/~pahwa [11] Causey W., “Getting Smarter: New Approaches to Distribution

Automation”, Energybiz Magazine: Transmission and Distribution Automation, Vol. 3, Issue 1, Jan-Feb 2006, pp. 52-53.

[12] J.B. Bunch, “Guidelines for Evaluating Distribution Automation”, EPRI Report EL-3728, November 1984, Chapter 2.

[13] Gruenemeyer D., “Distribution Automation: How Should it be Evaluated”, Paper presented at the 35th Annual Rural Electric Power Conference, 20-30 April 1991, pp. C3/1-C3/10

[14] Brown L., Skeen W., Daryani P., Rahimi F., “Prospects for Distribution Automation at Pacific Gas & Electric Company”, IEEE Transactions on Power Delivery, Vol. 6, No. 4, Oct. 1991, pp. 1946-1954

[15] Cooper Power Systems.: Electrical Distribution – System Protection, Bulletin 90020, Third Edition, 1990, Section A, pp. 144-149

[16] Kitagawa M., “Automated Distribution System”, IEEE Transactions on Power Delivery, Vol. PWRD-2, No. 2, April 1987, pp. 493-501

[17] Atwell E., Gamvrelis T., Kearns D., Landman R., “Automated Distribution Squeme Speeds Service Restoration”, IEEE Computer Applications in Power, Vol. 9, Issue 1, January 1996, pp. 33-37

[18] Kato K., Nagasaka H., Okimoto A., Kunieda T., Nakamura T., “Distribution Automation Systems for High Quality Power Supply”, IEEE Transactions on Power Delivery, Vol. 6, No. 3, July 1991, pp. 1196-1203.

[19] Coffey J., “The Improvement Of Customer Service on overhead Circuits by System Automation”, IEE Colloquium on Remote Control and Automation on 11 kV Networks Beyond The Primary Substations, 22 November 1999, Ref. No. 1999/195, pp. 3/1-3/7

[20] Yuan Q., Zeng Y., Wu Y., “A Novel Scheme for Automatic Loop-Reconfiguration Following a Fault”, International Conference on Power System Technology, POWERCON’98, Vol. 1, 18-21 August 1998, pp. 255-259.

[21] Royster T., “Virginia Power Implements Recloser Loop Schemes”, The Line, August 1998, pp. 3,4,11

[22] Stazzesky D.M., Craig D., Befus C., “Advanced Feeder Automation Is Here”, IEEE Power & Energy Magazine, September/October 2005, pp. 56-63.

[23] Fanning R., Huber R, “Distribution Vision 2010: Planning for Automation”, IEEE Power Engineering Society General Meeting, Vol. 3, 12-16 June 2005, pp. 2614-2615.

[24] Wolf G., “Intelligent Distribution”, Transmission and Distribution World, January 2007

[25] Schweitzer Engineering Laboratories: “Instruction Manual for SEL-351”, 2006.

[26] Mata R., Dionicio A., “Sistema de adquisición de datos de subestaciones de distribución: vía radio” IEEE sección México, RVP-AI/2007-DIS03, Julio 2007

[27] Freewave Technologies, Ref. #5424, “Using the FGR-115MB Radio with Schweitzer Engineering Labs Mirrored Bits Communications”, September 2004.

[28] Freewave Technologies, “Spread Spectrum Wireless Data Transceiver User Manual, Ver. 6.3”, 2005

[29] Costello D., Fodero K., “Mirrored Bits Communications with Free Wave Technologies Spread Spectrum Radios”, Schweitzer Engineering Laboratories, Application Guide AG2000-02, Vol II, 2000

[30] Behrendt K. C., “Relay to Relay Digital Logic Communication for Line Protection, Monitoring and Control”, 51th Annual Georgia Tech Protective Relay Conference, Atlanta, Georgia, May 1997

[31] Behrendt K., Fodero K., “Implementing Mirrored Bits Technology Over Various Communication Media”, Schweitzer Engineering Laboratories, Application Guide AG2001-12, Vol. II, , 2001

[32] Hataway G., “Minimize Distribution Outages With High-Speed Automatic Network Reconfiguration Using SEL-651R Advanced Recloser Controls”, Schweitzer Engineering Laboratories, Application Guide AG2004-09, Vol. III, , 2004

[33] Hataway G., Warren T., Stephens C., “Implementation of a High-Speed Distribution Network Reconfiguration Scheme”, IEEE 59th Annual Conference for Protective Relay Engineers, 4-6 April 2006, pp. 1-7.

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V. AUTORES José Javier Tenorio Huertas obtuvo el titulo de Ingeniero Electricista por parte de la ESIME IPN en el año 1996. De 1996 a 2002 laboró en la empresa Alstom T&D en las áreas de servicio postventa y desarrollo de proyectos. Ingresó a laborar a Luz y Fuerza del Centro en el año 2002 donde actualmente desempeña el cargo de Ingeniero 20-A. Durante el periodo 2005-2007 realizó estudios de maestría en el área de sistemas eléctricos de potencia en la SEPI-ESIME-IPN. David Sebastián Baltazar. Profesor Titular (TCE). Ingeniero Industrial en Eléctrica por el Instituto Tecnológico de Morelia (1991). Maestro en Ciencias en Ingeniería Eléctrica por la SEPIESIME-ZAC del IPN (1993). Y Doctor en Ciencias en Ingeniería Eléctrica en la Sección de Estudios de Posgrado e Investigación de ESIMEZAC del IPN (1999). Actualmente, Coordinador de los Programas de Posgrado en Ingeniería Eléctrica del IPN Raúl Méndez Albores, es lngeniero Electricista, egresado de la Escuela Superior de Ingeniería Mecánica y Eléctrica del lnstituto Politécnico Nacional, de 1981-1982 realizo estudios de Maestría con Especialidad en Sistemas Eléctricos de Potencia en la Sección de Graduados e Investigación de la ESIME; de 1976 a 2004 laboró en Luz y Fuerza, donde desempeñó diferentes cargos incluido el de Gerente de Aseguramiento de la Calidad. Es profesor en el Departamento de Ingeniería Eléctrica de la ESIME (IPN) donde actualmente imparte las materias de: Protección por Relevadores y Técnica de las Altas Tensiones. Carlos guerrero Gómez. Egresado de la ESIME del IPN en 1974 como Ingeniero Electricista, ha laborado en diferentes Centros de Operación desempeñando todas las categorías en el grupo de ingenieros, actualmente se desempeña como Gerente de Operación de Redes de Distribución de LyFC.

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Abstract—Windfarm electrical systems present some unique

challenges for protection. The grid tie and wind turbine

generators provide multiple sources of fault currents to be

considered. Collector feeders become isolated ungrounded

systems during faults due to separation from the centralized

collector bus reference ground. Ground faults on feeders will

result in unfaulted phase voltages rising to line levels. In

addition, severe transient overvoltages can be produced, which

can degrade insulation, resulting in eventual equipment failure.

This paper reviews the overall requirements for comprehensive

windfarm protection. It also focuses on the particular problem of

feeder ground faults. A novel, yet simple solution is presented that

makes use of peer-to-peer (GOOSE) messaging via the IEC 61850

protocol. The characteristics of the GOOSE message are

discussed with respect to speed and reliability and

communications architecture is presented. The performance of

the resulting protection scheme is quantified.

Index Terms—GOOSE messaging, IEC61850, peer-to-peer

communications, windfarm electrical system protection.

I. INTRODUCTION

ITH the recent development of new technologies, wind

energy is quickly becoming an important contributor to

the power system. As such, the protection of wind

turbines and the overall wind farm system is a topic which

warrants further attention. As technology has progressed from

smaller, isolated systems towards larger, wind farms

interconnected to the transmission system, issues regarding

unit and collector system protection are yet to be fully

addressed so as to provide adequate protection for the wind

farm as an integrated system, as opposed to a collection of

individual generation units. Improvements in wind farm

system protection will result in increased wind farm

availability; yielding better economics and quicker investment

payback.

II. WIND-TURBINE PROTECTION CONSIDERATIONS

The type of wind turbine unit will have some bearing on the

protection requirements. There are several WTG

configurations in commercial operation today. This discussion

focuses on the doubly fed induction generator (DFIG). Figure

1 shows a single line diagram of a typical WTG and the

location of the IED.

In this configuration a variable-pitch wind turbine is

connected through a gearbox to a wound rotor induction

machine. Back-to-back voltage-sourced converters are used to

connect the rotor circuit to the machine terminals in order to

provide variable speed control. The WTG step-up transformer

has three windings. The high voltage winding is delta

connected. Both LV windings have grounded-wye

connections. One LV winding is connected to the stator circuit,

the other to the rotor circuit. The high voltage winding of the

transformer may be connected to the grid through a circuit

breaker or through fuses.

Stator ground faults on the LV side of the WTG transformer

are not detectable by upstream protections due to the

transformer connection. The IED provides protection for these

faults using an instantaneous overcurrent element. This

element may respond to zero sequence, residual current, or

transformer neutral current. The element requires no

coordination with other protection elements, allowing it to

operate with minimal time delay. If the element is measuring

zero sequence via the phase currents or the residual current

connection, then possible CT saturation during external faults

should be considered when determining the pickup setting.

IED 1

CONTROL

IED 2

Fig. 1 WTG Single Line

The IED also provides protection for LV phase faults. An

instantaneous element will interrupt severe faults with minimal

delay. Note that the DFIG will provide a contribution to

external faults. This element should be set lower than the

minimum current expected for a phase fault at the generator

terminals and above the maximum expected generator

contribution to a fault on the network. A time overcurrent

element will detect phase faults internal to the generator.

Upstream time overcurrent protections should coordinate with

this element.

Windfarm System Protection Using Peer-to-Peer

Communications

Michael L. Reichard, , Senior Member, IEEE, Dale Finney, Senior Member, IEEE, John T. Garrity

W

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0 50 100 150 200 250 300 350 400 450 500

-6

-4

-2

0

2

4

6IstatA

IstatB

IstatC

Fig. 2. Simulation of WTG Contribution (pu) to an External Ground Fault

An IED with similar protection elements can also be applied

to the converter circuit. This IED can detect faults up to the

converter terminals but cannot detect faults in the rotor

winding.

Auxiliary protective functions are also required for the

DFIG. These protections may be embedded into the WTG

controller or alternatively may be implemented within the IED.

These include:

• Voltage unbalance

• Overheating (RTDs)

• Reverse phasing

• Poor synchronizing

• Voltage and frequency out of limits

The WTG also must be capable of isolating itself from a

fault on the feeder. Ideally, this should be done with minimal

delay. At the same time external fault protection should never

operate for faults on adjacent feeders or on adjacent WTGs.

Practically, it is not possible to achieve this level of

performance solely through measurement of local currents and

voltages. Typically, grid fault detection relies on undervoltage

and overvoltage elements. These elements are delayed to

allow upstream protection to open the feeder breaker, thereby

preventing a trip for fault on another feeder.

Finally, the WTG IED should have the abilities to capture

voltage and current waveforms and sequence-of-events data

during a fault or disturbance. These are valuable tools for fault

analysis verification of protection system performance.

III. WIND-FARM SUBSTATION PROTECTION CONSIDERATIONS

Figure 3 shows the single-line diagram of a typical wind

farm. Several feeders terminate at the collector bus. A power

transformer steps up the voltage to the transmission level. A

single HV transmission line connects the windfarm to the grid.

Protection is required for the collector bus. A high or low

impedance differential element will produce the fastest

clearing times for bus faults. If a low impedance bus

differential scheme is used, then the feeder CT should not be

paralleled. Otherwise the WTG fault contribution can produce

a false operation if CT saturation occurs during an external

fault.

TXFMR

IED

LINE

IED

FEEDER

IED

FEEDER

IED

FEEDER

IED

FEEDER

IED

BUS

IED

COLLECTOR

BUS

Fig. 3. Single Line of Typical Wind Farm

A blocking scheme can be applied as an alternative to the

bus differential. An overcurrent element in each of the feeder

IEDs sends a blocking signal to an overcurrent element located

in an IED on the transformer breaker on the occurrence of a

downstream fault. When a bus fault occurs, no blocking

signals are sent. GOOSE messaging, discussed in detail below,

over the substation LAN provides a convenient method of

exchanging the blocking signals.

Protection is also required for the power transformer. This

will take the form of a percent differential element with inrush

inhibit. If the number of feeders is low then the bus and

transformer zones may be combined using a multi-restraint

transformer differential element. This allows the transformer

breaker and CTs to be eliminated.

The windfarm may be interconnected to the grid via a two

terminal transmission line or it may be tapped onto a multi-

terminal line. In either case the protection of the transmission

line typically takes the form of line differential or distance

elements. Each scheme will require a dedicated

communications channel linking the windfarm to the remote

utility terminal(s) to provide optimum protection. A

communications channel can also be used to signal to the

utility terminal that the windfarm has been disconnected and

that reclosure is permissible. Out-of-phase reclosing onto the

windfarm will produce severe torque transients and must be

avoided.

Reclosing for ground faults can be implemented in the case

that single-pole tripping is employed. In this scheme the

windfarm remains synchronized with the grid through the

healthy phases. This will increase the availability of the

windfarm but requires protective IEDs and circuit breakers

that are capable of single-pole operation.

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0 50 100 150 200 250 300 350 400 450 500-1

0

1

2

3

4

5

6

Electrical Torque

Fig. 4. Simulation of WTG Torque due to Reclosing Out-of-Phase

IV. WIND-FARM FEEDER TOPOLOGIES

There are several types of feeder topologies currently

applied in windfarms. Radial, bifurcated radial, feeder-

subfeeder, and looped topologies are the most common types

used, each yielding their own distinct advantages and

disadvantages. These factors and other criteria such as wind

profiles, available tower placement, costs, etc. must be

considered in order when determining which topology to use.

Radial collector system topologies are comprised of a single

feeder circuit originating from the collector bus and

connecting sequentially to each WTG tower. It provides the

least complex feeder configuration, and is best suited in

applications where linear WTG placements are well defined.

It has a lower installed cost per feeder due to the low

complexity. Inter-tower cable faults or WTG faults can be

isolated to allow continued production. However, a station

circuit breaker failure or a cable fault between the station and

first tower result in complete loss of all feeder generation,

which makes it one of the least reliable.

Fig. 5. Radial Feeder

Bifurcated radial topologies are similar to the radial system

except they use one collector bus circuit breaker to switch two

collector feeders. This configuration has the lowest installed

cost base per feeder. However, it also has the lowest

reliability because a breaker failure or a cable fault between

the station and first tower result in complete loss of both

feeders’ generation.

Fig. 6. Bifurcated Radial Feeder

Feeder-subfeeder topologies are typically employed where

clusters of towers are distributed over large areas. They are

typically comprised of a single cable feeding remotely located

switchgear with several subfeeders.

Fig. 7. Feeder-Subfeeder

Looped feeder topologies provide a higher level of

availability when compared to the others. It allows continued

production in the event of single component failures. Faults in

the WTG tower or between towers can be isolated, allowing

the remaining WTGs to continue production.

Fig. 8. Looped Feeder

V. LIMITATIONS OF TYPICAL WIND-FARM TOPOLOGY

All windfarm topologies have an inherent limitation

common to the collector bus – feeder arrangement. The

windfarm topology is connected to a collector bus and stepped

up to transmission level voltage through a power transformer.

The windfarm feeders rely on the substation transformer

neutral-ground connection for a reference ground for the

medium voltage collector system. The WTGs cannot provide

a reference ground because of the WTG transformer delta

connection. A grounded WYE connection would introduce

multiple sources of ground fault current that will complicate

the ground fault protection and desensitize the IED at the

substation.

If a feeder circuit breaker opens during operation, then that

feeder and the operating WTGs will become isolated and form

an ungrounded power system. This condition is especially

troublesome if a phase-to-ground fault develops on the feeder;

a scenario that causes the unfaulted phase voltages to rise to

line voltage levels. It should be pointed out that a feeder

ground fault is the most commonly anticipated fault type for

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on-shore windfarms that use overhead lines for the feeders.

This fault can also result in severe transient overvoltages,

which can eventually result in failure of insulation and

equipment damage.

Ignoring this condition could produce eventual failure of a

cable or WTG transformer. One remedy is to design for the

ungrounded system. This results in increased costs due to the

higher voltage ratings, higher BIL, and added engineering.

Another solution is to install individual grounding

transformers on each feeder. This adds to equipment and

engineering costs and increases the substation footprint

Fig. 9. Relationship for Normal and Fault Conditions

40 60 80 100 120 140 160-60

-40

-20

0

20

40

60

Va

Vb

Vc

AG FAULT

BREAKER OPENS

OVERVOLTAGE

Fig. 10. Simulation of Feeder Overvoltage during a Ground Fault

VI. COORDINATED FAULT CLEARANCE VIA TRANSFER

TRIPPING

An alternative solution is to disconnect the WTGs

from the feeder before tripping the feeder breaker. However,

the IED protecting the feeder in the substation is the only IED

that can selectively detect feeder faults. In this case this IED

would then send a transfer trip to all WTGs on the feeder.

Once all units are disconnected, opening of the feeder breaker

results in a well-behaved collapse of the voltage. Opening of

the feeder breaker would be delayed minimally to ensure

coordinated tripping.

VII. TRANSFER TRIP IMPLEMENTATION

The proposed method for implementation of the transfer trip

solution is IEC 61850 GOOSE messaging over a fiber-optic

Ethernet network. This solution supports critical signalling to

multiple IEDs. IEDs connect directly to the network, removing

the need for expensive teleprotection equipment. Windfarms

are often designed to include an integral network of optical

fiber. Off-the-shelf Ethernet switches are available that can be

configured to the existing fiber layout and can easily

accommodate the distance between IEDs. As an added benefit,

fiber-optic media provides excellent immunity to noise or

ground potential differences.

Adoption of the IEC 61850 protocol allows the same

communication path to be utilized to transmit a variety of

additional data. Examples of this information include control

commands between devices for issuing of trip from other

substation protections, commands to preclude a device from

otherwise tripping (blocking), interlocking the control of a

device with status of another device, event and diagnostic

information (such as waveforms and event logs), and analog

information (such as current and power metering).

This protocol supports several important features that make

it an appropriate choice for this application. Any data items in

the IED that are available via 61850 are structured according

to the protocol and include standardized descriptions of the

source and type of the data. The IEC GOOSE message carries

a “user defined” dataset. The dataset can be configured with

61850-modeled data items. The methodology promotes ease-

of-configuration and interoperability between various

manufacturers IEDs.

GOOSE is a multicast message that, once transmitted can be

received by any device on the network that needs it. A feature

supported in the IEC GOOSE is the ability to restrict the flow

of data to a particular broadcast domain through the creation

of a Virtual Local Area Network or VLAN. This dataflow

restriction is achieved by adding 4 bytes to the Ethernet data

frame per the IEEE 802.1Q standard (Figure 8). A 2-byte Tag

Protocol Identifier identifies the extended data frame. The

other 2 bytes include 12 bits for a VLAN ID, 3 bits for priority

encoding of the Ethernet message, and one bit for backward

compatibility with Token Ring. Once identified as an extended

Ethernet frame, a switch in the network can decode the VLAN

ID or VID. This ID is read by the network device and

“switched” to those ports programmed with the same VLAN

ID.

Another area addressed by the IEC GOOSE is that of

Ethernet Priority. Ethernet communication has been

traditionally described as “non deterministic” in that the

possibility of collisions on the wire made it difficult to

determine the delivery time of the message. The use of Layer

Under Normal Conditions

VA=VN∠90°

VB=VN∠-30°

VC=VN∠-150°

VA

VC VB

Grounded System under A-G Fault

Conditions

VA=0

VB=VN∠-30°

VC=VN∠-150°

VA

VC VB

Isolated System under A-G Fault

Conditions

VA=0

VB=√3⋅VN∠-60°

VC=√3⋅VN∠-120°

VA

VC VB

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2, full-duplex switch technology now prevents the occurrence

of Ethernet collisions. Switches receive all messages and store

and forward them to the destination locations as required. It is

possible for a single port in the switch to have several

messages queued for delivery to a device. This would add a

certain amount of delay in the processing of a message.

Ethernet Priority, however, removes this delay. Upon receipt

of an Ethernet message with a “high priority”, the message is

moved to the front of the queue and becomes the next message

to be sent to the receiving device thereby minimizing the

transmission time of the message.

Preamble DA SA 801.1Q Type/Length Data and Pad Frame Check

8 bytes 6 bytes 6 bytes 4 bytes 2 bytes 46-1500 bytes 4 bytes

Tag

Pro toco l

Iden tifier

2 bytes 2 bytes

User Priority CFI VLAN ID

3 b its 1 b it 12 b its

Tag Contro l In fo rmation

Fig. 11. Extended Ethernet Frame

The diagram below shows how the IEC1850 network topology

would be deployed for a larger, radial feeder windfarm:

SWITCH

SW

ITC

H

WTG

IED 1

SW

ITC

H

WTG

IED 2

SW

ITC

H

WTG

IED N

SW

ITC

H

WTG

IED 1

SW

ITC

H

WTG

IED 2

SW

ITC

H

WTG

IED N

FEEDER 1 FEEDER M

Line

IED

Transformer

IED

Bus

IED

Feeder 1

IED

Feeder M

IEDSCADA

Fig. 9. Windfarm Communications Network Topology

Each wind turbine has a multifunction protection IED that

would provide electrical fault protection for the generator and

tower cable, as noted above. In addition to providing “local”

protection for wind turbine equipment, the WTG IED features

IEC61850 protocol support so as to provide the transfer trip

capabilities.

The physical arrangement of the components of the

windfarm dictates a network arranged in a ring-architecture for

each feeder. In an Ethernet network, it is not permissible to

have more than one path to a particular device. Therefore ring

topologies could not be configured with early generation

switches. However the latest generation of Ethernet switches

provides support for Rapid Spanning Tree Protocol (RSTP).

RSTP-enabled switches exchange information to ensure that

only one switch provides a path to a device. If a failure occurs

in the enabled path, the switches will automatically reconfigure

the network to re-establish a path to the device in as little as 5

milliseconds. The ring topology allows for the failure of any

one path with no loss of communications to any device. A

single switch failure results in the loss of communications to

only one device. However, its peers on the network will

quickly detect the loss of this device. This would allow the

IEDs to automatically adapt to the communications failure. For

instance The WTG IED could enable voltage tripping only in

the case that communications with the feeder IED is lost.

VIII. TRANSFER TRIP PERFORMANCE

Table 1 illustrates timing sequence for a feeder fault using

the transfer trip solution. The timing analysis above assumes a

breaker clearing time of 60 ms. The time required to process

and transmit the GOOSE message across the network is 8 ms.

Tripping of the feeder breaker by the IED is delayed by 30 ms

to ensure that all of the WTGs are disconnected prior to

clearing the fault. The Ethernet switches present a negligible

time delay and need not be included in Table 1.

TABLE 1 - TRANSFER TRIP TIMING

Event # Description Time

(ms)

1 Feeder ground fault 0

2 Feeder IED detects fault and sends transfer

trip 32

3a WTG IEDs receive transfer trip & operate

8

4a WTG breakers open

60

WTG clearing time

100

3b Feeder IED time delay

30

4b Feeder breaker opens 60

Feeder clearing time 122

Another application would be for the WTG IED to issue a

“block” command upon detection of a fault condition within

the wind turbine transformer or tower cable. If such a fault

occurs, the potential to cause nuisance tripping on the feeder

can occur. IED2, as seen in Figure 1, provides protection for

the wind tower transformer and cable, and can simultaneously

trip the MV breaker, as well as send a block command to the

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feeder IED located in the substation. This block command

allows for the feeder to stay on-line and avoids disconnecting

the remainder of the WTGs.

In addition to transfer trip and blocking commands the

network architecture also enables the windfarm operator to

take advantage of the detailed diagnostics and metering

capabilities inherent in the WTG IEDs. The current

generation of microprocessor based protective IEDs contain

detailed event logs, current/voltage waveform recorders,

metering, and other diagnostic information that prove valuable

in the diagnosis of fault and system disturbances.

IX. CONCLUSIONS

It has been demonstrated in this paper that there are

aspects of a windfarm configuration that require consideration

when designing the protective system. One important aspect is

the need to disconnect the WTGs before isolating the feeder

during a ground fault. A novel method has been presented that

achieves this, alleviating the need for a grounding source on

each feeder. This reduction in equipment translates into

increased system reliability as well as a significant cost savings

for the windfarm operator. This solution makes extensive use

of GOOSE messaging and leverages pre-existing system

components, specifically fiber Ethernet between wind turbines,

industrialized Ethernet switches, and 61850 compliant IEDs.

GOOSE messaging can also be extended to various other

protection, automation, and operational applications.

REFERENCES

[1] IEC 61400-1, August 2005, “Wind Turbines Part 1: Design

Requirements”

[2] S. Muller, M. Deicke, R.W. De Doncker, Oct. 2000, “Adjustable speed

generators for wind turbines based on doubly-fed induction machines

and 4-quadrant IGBT converters linked to the rotor”, IEEE Industry

Applications Conference, Volume 4, Pages: 2249 - 2254

[3] V. Madani, M. Adamiak, M. Thakur, Apr 2004, “ Design and

Implementation Of Wide Area Special Protection Schemes”, 57th

Annual Texas A&M University Conference for Protective Relay

Engineers, Pages: 392 - 402

[4] N.W. Miller, J.J. Sanchez-Gasca, W.W. Price, R.W. Delmerico, July

2003, “Dynamic modelling of GE 1.5 and 3.6 MW wind turbine-

generators for stability simulations”, IEEE Power Engineering Society

General Meeting, Volume 3, Pages: 1977 - 1983

[5] FEDERAL ENERGY REGULATORY COMMISSION, June 2, 2005,

Order No. 661 “Interconnection for Wind Energy”,

http://elibrary.ferc.gov/idmws/common/opennat.asp?fileID=10594521

[6] C. Abbey, G. Joos, June 2005, "Effect of Low Voltage Ride Through

(LVRT) Characteristic on Voltage Stability", Power Engineering

Society General Meeting, 2005, Pages: 2576 - 2582

[7] J. Morren, S.W.H. de Haan, June 2005, “Ridethrough of wind turbines

with doubly-fed induction generator during a voltage dip”, IEEE

Transactions on Energy Conversion, Volume 20, Issue 2, Pages: 435 –

441

[8] M. Nagpal, F. Plumptre, R. Fulton, T. Martinich, June 2006, “Dispersed

Generation Interconnection—Utility Perspective”, IEEE Transactions

On Industry Applications, Volume 42, No. 3.

Michael Reichard is currently a Principal for GE Energy’s Applications &

System Engineering group. He obtained his MBA degree from Union

College, MEng degree from Penn State University, and BS EET degree also

from Penn State. Michael is an active member of the IEEE Power Systems

Relaying Committee’ Rotating Machinery Subcommittee.

Dale Finney began his career with Ontario Hydro where he worked as a

protection and control engineer. Currently, he is employed as an applications

engineer with GE Multilin in Markham Ontario. His areas of interest include

generator protection, line protection, and substation automation. Dale has a

bachelor of engineering degree from Lakehead University and a master of

engineering degree from the University of Toronto. Dale is a registered

professional engineer in the province of Ontario, a member of the main

committee and several working groups of the IEEE PSRC, and a senior

member of the IEEE.

John Garrity is the Manager, MDS Integration at GE Multilin, a recognized

industry leader in protection, monitoring, control, and communication

solutions for generation, transmission, distribution, and industrial customers.

The focus of his responsibility is leading a team in the integration of GE

MDS’ industrial wireless solutions across GE and drive business growth

through partnerships with customers and other GE operating business units.

John has an MBA degree from Rensselaer Polytechnic Institute, Troy, NY

and a BSEE degree from Clarkson University, Potsdam, NY.

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Case Study: Design and Implementation of

IEC 61850 From Multiple Vendors

at CFE La Venta II

Victor Manuel Flores and Daniel Espinosa, Comisión Federal de Electricidad

Julian Alzate and Dave Dolezilek, Schweitzer Engineering Laboratories, Inc.

Abstract—The IEC 61850 standard provides methods of

developing best engineering practices for substation protection,

integration, control, monitoring, metering, and testing. Comisión

Federal de Electricidad (CFE) chose to build their newest

integrated transmission protection and control network with

IEC 61850 and evaluated the technology for possible future

inclusion into their design standards.

The primary IEDs chosen for protection were selected from

the devices that have been approved by the customer and that

also support IEC 61850. For the La Venta II project, the primary

focus was to include IEC 61850 devices from as many vendors as

possible rather than using traditional design criteria. In addition

to the primary protection and control equipment, the customer

invited all vendors to submit IEDs to be connected to the network

to demonstrate their ability to communicate IEC 61850.

Additional IEDs were added in an auxiliary bay because the

design constraints required that the core of the network be useful

and effective; it is not a demonstration control system but a pilot

project to gain experience with the new standard.

This system integrated 24 devices from 9 different product

platforms provided by 6 different vendors. The implementation

was completed in four months and included newly released

products from some vendors, involved staging device communi-

cations over the Internet, and relied on contributions from

engineers in seven time zones. IEC 61850 is a very large standard

with seven different protocols within it. End users implement

different combinations of the protocols and the different features

they provide. Therefore, it is important that end users not only

specify that they want to use IEC 61850, but also what parts of

the standard they want to use and, more importantly, how they

want the system to perform. Throughout the implementation of

this project, it became apparent that implementation details left

to the discretion of the vendors and not dictated by the standard

needed to be documented as requirements to attain the required

system functionality. The following is a sample of these details:

• Quantity of client/server associations to the device

• Quantity of peer-to-peer messages the device will publish

or transmit

• Quantity of peer-to-peer messages the device will

subscribe to or receive

• 8umber of characters allowed in the device name

• Run-time device diagnostics

• Configuration of the device via SCL (substation

configuration language) XML files instead of settings

I. BACKGROUND

CFE is a government-owned utility that generates,

transmits, and distributes energy to over 80 million people in

Mexico. With 174 generation plants (46,672 MW), over

45,000 km of transmission lines, 135,238 MVAs of transfor-

mation, and 8 to 9 percent annual growth, CFE is one of the

electric giants of Latin America.

CFE has been operating transmission substations remotely

for more than 25 years and has developed a well-written

specification that focuses on network topology, functionality,

and device characteristics. This specification is known as

SICLE (Spanish acronym for Information System for

Substation Local and Remote Control).

In the early 1990s CFE migrated its specification to use

DNP3 and then in 2000 moved to Ethernet as the network to

be used at the substation level. At that time CFE was looking

closely at UCA2 as an option but decided to wait until the new

IEC 61850 standard was finished in order to avoid multiple

migrations in a short period of time.

CFE has always been interested in new technologies that

allow them to reduce engineering and commissioning time as

well as overall project costs. CFE was interested in IEC 61850

because of interoperability and interchangeability.

After the release of the standard, CFE made several

attempts to gather, at one table, all manufacturers that

supported IEC 61850 in order to make a pilot project. CFE’s

goal was to prove interoperability with products from multiple

vendors, but most of the manufacturers suggested that they

preferred to build IEC 61850 systems consisting of only their

own products. The opportunity finally came with the La Venta

II project. La Venta II is an eight-phase wind farm that will

generate close to 3 GWh by 2014, becoming the biggest wind

farm in Mexico and Central America.

The bid for the first stage of the project was won by

IBERINCO (IBERDROLA Ingeniería y Construcción), a

well-known engineering firm and one of a handful with real-

life IEC 61850 experience. IBERINCO built some of the first

substations in Spain with IEC 61850. IBERINCO committed

to deliver La Venta II as an IEC 61850 substation.

II. SCOPE

The La Venta II substation is part of the associated

transmission network to Wind Farm La Venta II and in the

first stage will be a 34.5/230 kV step-up substation. One

hundred wind generators in groups of 20 will be connected to

the 34.5 kV bus. In 230 kV, a main bus/auxiliary bus

arrangement will connect the wind farm to the national grid.

The one-line diagram of the 230 kV side is displayed in Fig. 1.

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50BF

50BF

79

21PP

87L

50BF

51PHS

87T

51PHS

51NHS

51NLS

87B

RD

Fig. 1. La Venta II substation protection requirements

CFE defined the following requirements for the system to

be developed:

1. Include only protection devices that are in LAPEM 5L

(list of approved protection devices to use in electrical

substations) because this will be an operative substation.

2. Include as many vendors as possible in order to prove

interoperability between protection and control devices.

3. Comply with functionality of CFE protection specifi-

cation.

4. Comply with functionality of CFE SICLE specification

that already calls for Ethernet but not IEC 61850.

5. Consider interchangeability of main IEDs at the commu-

nications interface. Add redundant IEDs in parallel and

demonstrate their functionality in the network.

6. Connect IEC 61850 bay control and protection devices to

the Ethernet; allow no data concentrators for local

operation.

7. Perform bay control interlocks between bays using

GOOSE messages.

8. Communicate with two master stations using redundant

SCADA gateways with DNP3 and Conitel 2020.

9. Provide two local HMIs.

10. Utilize traditional wiring and GOOSE for protection

functions in order to test performance and reliability

between the two options.

III. IMPLEMENTATION

La Venta II integrates devices from SEL, ZIV, Siemens,

GE, RuggedCom, and Team ARTECHE. Other vendors were

invited to participate but either did not have IEC 61850

available or were not approved. IBERINCO provided overall

project management as well as the rules for logical devices,

logical nodes, controls, and data mapping. IBERINCO also

was responsible for defining HMI and gateway databases.

CFE defined master station databases. ZIV provided HMI

application and integration, one gateway to DNP3, one bay

control, and on-site training. SEL provided protection and

control devices, designed and built the panels, staged the

system for testing, trained CFE, and provided on-site support

for commissioning. Other vendors provided support during

testing and on-site commissioning of their devices.

IV. PROTECTION SYSTEM

As mentioned before, all protection devices were required

to be in LAPEM 5L, and all protection schemes were required

to meet CFE protection specifications. Tables I–V list the

requirements and how they were met for this project.

TABLE I

230 KV LINE PROTECTION PANEL

Description Function Device

Bay Control Local Control and

Data Acquisition ZIV-6MCV

Main Distance Protection Directional Overcurrent

21/67 SEL-421

Main Line Current

Differential Directional

Overcurrent

87L/67 GE-L90

Breaker Failure/Synchronism Check

50 BF/25/27 SEL-451

Reclosing 79 SEL-279H *

* No relays approved by CFE for this function support IEC 61850.

TABLE II 230 KV TRANSFORMER PROTECTION PANEL


Bay Control Local Control and Data Acquisition

GE-F650

Main Transformer Protection 87 GE-T60

High Side Overcurrent

Protection 50/51 HS GE-F60

Breaker Failure/Synchronism

Check 50 BF/25/27 SEL-451

Low Side Overcurrent

Protection 50/51 LS Siemens 7SJ62

Neutral Overcurrent

Protection 50/51 N Siemens 7SJ61

Tertiary Overcurrent Protection

50/51 TZ GE-F35

TABLE III

230 KV TIE BREAKER PROTECTION PANEL


Bay Control Local Control and

Data Acquisition SEL-451-4

Breaker Failure/Synchronism Check

50 BF/25/27 SEL-451

TABLE IV

230 KV BUS DIFFERENTIAL PROTECTION PANEL


Bus Differential 87B SEL-487B

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TABLE V AUXILIARY BAY PANEL


Backup Bay Control Local Control and Data Acquisition

ARTECHE-BC

Backup Line Current

Differential Backup Distance

Protection

21/87L SEL-311L

Backup Transformer Protection

87 SEL-387E

Additional panels for metering and DFR (digital fault

recorder) were part of the scope but not integrated in

IEC 61850.

V. INTEGRATED COMMUNICATIONS SYSTEM

A. ew Substation Technology: Bay Control, SCADA

Gateway, and IEC 61850

In addition to using the new IEC 61850 standard, this

design incorporates a few products that CFE has not used

before. All of the protective relays had to be independently

approved for use by CFE on their system regardless of their

support of IEC 61850 protocols. The final design relies

heavily on several relays that CFE previously approved and

used in other integration systems using other protocols that

now also support IEC 61850. Other IEDs, such as the bay

control units, were approved by CFE for use on this system.

Fig. 2 illustrates the front-panel HMI on the bay control unit

used in the 230 kV tie breaker protection panel.

Fig. 2. Front-panel HMI on the bay control unit used in the 230 kV tie

breaker protection panel

The communications integration team worked with every

IED from multiple vendors to understand and implement the

IEDs, each with different IEC 61850 capabilities, into the

communications architecture.

New work is being done by the IEC Technical Committee

(TC) Working Group (WG) 57 to extend use of the protocols

within the IEC 61850 standard to outside the substation.

Presently they are not used outside the substation, and the

designs still rely on traditional and in-service SCADA

protocols. CFE needed to support existing DNP3 links as well

as the bit-oriented Conitel 2020 protocol. A rugged computer

was deployed as a gateway to act as a client, collect and

concentrate data from the IEDs via IEC 61850 protocols,

convert these data into SCADA protocols, and serve them to

the existing SCADA consoles. Therefore, in addition to acting

as a protocol gateway, the rugged computer is a data

concentrator and a client/server. Fig. 3 illustrates an example

SCADA console similar to the ones in the project. The data

collected via IEC 61850 protocols are converted into DNP3

and Conitel 2020 and transferred over established SCADA

links. The operators are unaware of the fact that the substation

protocols are different than previous designs that used DNP3

and other protocols in the substation.

Fig. 3. Typical SCADA console user unaffected by choice of protocol

within the substation

The major impact of using IEC 61850 in this project and

then converting it into traditional and legacy protocols is the

dramatic increase in complexity of the new IEC 61850

protocols. Because some of the new IEC 61850 protocols are

more functional they have more features and attributes that do

not exist in other protocols like DNP3 and Conitel 2020.

Therefore, it is difficult to convert simple DNP3 messages to

perform actions that are more elaborate in the IEC 61850

protocols. One such example is commanded control.

IEC 61850 protocols require six or more attributes to be set

before an IED will act on it. The simple DNP3 command

structure requires only two. Therefore, there is not a one-to-

one correspondence of necessary protocol attributes to

complete client/server transactions. This eliminates the oppor-

tunity to automatically map configuration between the

protocols and creates the need for much manual configuration

of the protocol translation. This translation effort became the

most time consuming part of the system integration activity.

Additionally, commands and other message transactions via

IEC 61850 methods benefit from object-oriented data

structures; however, some of these data structures include data

types that are not available within the other protocol methods.

Therefore, not only must missing data attributes somehow be

created, existing data attributes often must be converted from

one type to another.

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B. ew Software Automatically Creates Communications

Settings and Configuration

New IEC 61850 configuration methods work in conjunc-

tion with previously existing IED application configuration

software to create and set relays and other IEDs to perform

logic, interlocks, and protection. The best practice method

mentioned in the standard relies on the creation of a config-

ured IED description (CID) file, which uses SCL to describe

all of the IEC 61850 protocol configurations, and is then

downloaded directly into the IED. When the IED starts up, it

finds the CID file and performs self-configuration. This file is

locally or remotely transferred into the IED without impacting

any other functionality in the IED. Because this configuration

is an IEC 61850 communications configuration file only, there

is no opportunity to inadvertently impact protection or

automation settings. Therefore, the communication is

configured, tested, and commissioned without impacting the

other applications within the IED. Furthermore, this CID file

is also retrieved directly from memory within the IED to

definitively verify what configuration is being used by the

IED.

Because the IEC 61850 standard does not specify a single

way to perform configuration, several vendors chose to add

IEC 61850 configuration as settings among the existing

protection and automation settings within their IED. For these

IEDs, the protection-settings software is used to create and

download all the settings into the IED. Care must be taken to

preserve, test, and commission all affected, or possibly

affected, settings. The upper portion of Fig. 4 illustrates the

relationship between IEC 61850 configurations via designs

saved as files to be distributed using traditional file transfer

means, like FTP, and directly loaded into local or remote

IEDs. The lower portion of Fig. 4 illustrates protection and

automation settings being created and the IED being set with a

separate, special-purpose software application.

Fig. 4. File configuration of IEC 61850 and protection and automation

settings configuration

For those IEDs that support the necessary SCL files,

configuration software from any vendor should be able to

view data descriptions within the SCL files that represent the

system needs and IED capabilities. This allows the designer to

visualize and logically connect data among IEDs from any

vendor.

Using the methods described in the standard, IEC 61850

configuration software allows the designer to create data

groups and reporting methods that identify what data are sent,

to whom they are sent, when they are sent, and under what

conditions.

Once the IEC 61850 configuration software imports files

representing the capabilities of IEDs, designers make use of

these capabilities to exchange data among the IEDs. After the

configuration files or settings are installed in the IEDs, they

report data to SCADA gateways, engineering workstations,

sequential events recorders (SERs), etc., as well as to each

other. Once an IED is configured to receive data from another

IED via the IEC 61850 protocol GOOSE, the IED has access

to that information as a logical status with the value of a

binary one or zero. To the IED, this is now the same as a

binary status received any other way, such as the mirror of the

state of a bit in another relay via a peer-to-peer serial protocol,

a commanded change of state via a SCADA command, a

front-panel operator command, a remote engineering console

command, or a local hardwire contact input.

In Fig. 5, the window in front illustrates combining several

IED digital logic variables into a graphical Boolean

expression. These digital logic variables are used freely

without restriction based on their source, e.g., hardwire input

contacts, GOOSE, serial peer-to-peer, or front-panel or remote

command. The window behind illustrates the association of

contents of received GOOSE messages to digital logic

variables in an IED. In this case, Logic Bits RB01 through

RB03 are received from other IEDs via GOOSE messages and

then combined. RB04 and RB05 are received from another

IED via a GOOSE message and then combined with RB06,

which can be updated from any of the possible data sources.

Fig. 5. Mapping of GOOSE contents to IED logic variables and use of these

variables within a graphical logic editor

VI. SYSTEM ARCHITECTURE

The design called for the devices to be directly connected

to the Ethernet LAN, and no data concentration was to be

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allowed for data exchange among the IEDs, local HMIs, and

protocol gateways. Vendors submitted product designs that

performed direct transmission and receipt of IEC 61850

protocols. As mentioned previously, data concentration was

initially allowed only for the SCADA gateway function that

converted IEC 61850 protocols into DNP3 and Conitel 2020.

In the end, the HMIs were served via a data concentrator and

did not communicate via the IEC 61850 protocols.

The substation LAN is configured in a ring topology with

Ethernet switches installed in each cabinet. Because of the

short distances and the fact that all the IEDs are inside one

cabinet, the bay IEDs are connected to the switch using copper

cables. Longer switch-to-switch connections between bays are

accomplished via fiber optics that support the ring topology as

seen in Fig. 6. This topology provides redundant ring

communications at the switch level; however, IED connec-

tions within the same bay cabinet do not warrant redundant

communications at the IED level based on past experience.

Also, the use of internal switches within the IEDs connected

in a ring is not allowed because it dramatically decreases

reliability and increases complexity for the sole purpose of

overcoming a cable failure.

Two local computers provide the operation HMI to the user

for local control and visualization. Redundant SCADA

protocol gateways provide the interface to the SCADA master

in DNP3 and Conitel 2020.

Router

+ Firewall

Remote HMI

RuggedCom

Fiber-Optic Ring

DNP

Conitel

SW-4

SW-5

SW-3

SW-1

SW-2

GE F650 BC

SEL-451 50BF, 25, 27

SEL-387E

GE T60 87T

GE F60 50, 51HS

GE F35 50, 51TZ

Siemens 7SJ62 50, 51LS

Siemens 7SJ61 50, 51N

SEL-451-4 BC

SEL-451 50BF, 25, 27

ZIV 6MCV BC

SEL-421 21, 67

SEL-279H 79

SEL-451 50BF, 25, 27

GE L90 87L

SEL-311L

SEL-487B 87BGPS

ZIV CPT ZIV HMI ZIV HMI

SEL-3332

SCADA Gateway

Fig. 6. Various connections to the substation fiber-optic Ethernet ring

As mentioned, each bay panel has its own Ethernet switch,

regardless of the number of IEDs. This was done for several

reasons: robust communications, ease of field installation, and

ease of future maintenance. IEDs connected in a star fashion

with the switches connected in a fiber-optic ring provide the

most reliable and dependable substation LAN. Because each

panel has its own switch, none of the bay communications

cabling needed to be disrupted or retested between factory

acceptance testing (FAT) and field installation. Each panel

was complete and tested during the FAT. Once delivered on-

site, the switches were reconnected in a ring, and the network

was quickly reconfigured, regardless of their eventual distance

from one another. Future Ethernet troubleshooting and

maintenance has been simplified by inclusion of a switch in

each bay instead of multidrop connections between IEDs or

long-distance cable runs to a distant switch.

VII. COMMUNICATIONS IMPLEMENTATION CONSIDERATIONS

The IEC 61850 standard requires timestamp resolution to the

microsecond. Therefore, the recommended best practice for

time synchronization remains IRIG-B because it is the only

method that provides this accuracy. SNTP (simple network

time protocol) can be used but will not provide the accuracy

for some applications. Future changes to the IEC 61850

standard may recommend a method over Ethernet once one is

available. The IEEE is working on a standard, referred to as

IEEE 1588, that may provide microsecond time-

synchronization accuracy over Ethernet. However, until then,

some vendors suggest that customers use SNTP, which is

convenient because it travels over Ethernet and does not

require a second connection like IRIG-B. The accuracy of

SNTP is at best several milliseconds and varies as the network

traffic varies. CFE agreed to implement time synchronization

via SNTP or IRIG-B because of different implementations

among all the vendors. CFE asked that the vendors provide

useful descriptive naming of the IEC 61850 data and groups,

such as logical node names, and avoid generic names.

However, many of the vendors used generic naming. These

generic names are conformant with the standard; however,

they are not very useful to the end user and are actually

counterproductive to creating the SCL and self-description. By

using generic naming, the vendors eliminate the ability to

perform automatic configuration and require the integrator to

refer to documentation to see which generic IEC 61850 value

represents the needed phase voltage or breaker position.

As shown in Fig. 6, each IED must serve data to six clients,

perhaps simultaneously. These six include the two dual-

primary redundant HMIs, two dual-primary redundant proto-

col gateways, one local engineering access connection, and

one remote engineering access connection. For each client

connection, the design called for separate binary-state data set

buffered reports and measurement data set unbuffered reports.

A. Match Existing Device aming Methods

CFE planned to continue using the naming convention

developed within their organization. All of the databases that

receive substation data—protocol gateway, engineering,

SCADA, HMI, and documentation—use the name of the

source IED. The CFE naming convention requires 12

characters, XXX YYYYY ZZZZ. These 12 characters

represent the aggregate name, where XXX identifies the

substation (e.g., LVD), YYYYY is the breaker identifier

associated with the device (e.g., 97010), and ZZZZ identifies

the IED function (e.g., MCAD, the acronym for bay control).

This combines to be LVD97010MCAD and represents the bay

control for tie breaker 97010 in station LVD.

Some vendors do not support 12 characters in their IED

description within their IEC 61850 configuration. Though this

is not defined by the standard, it has been common for many

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years via many protocols to provide enough characters for end

users to uniquely name each IED based on their established

internal naming conventions, and it became a problematic

“local issue.” Local issue is the term used within the standard

to refer to important implementation details that are not

addressed by the standard and must be resolved locally—

within the implementation of the IED. However, because

many of the local issues result in differences that impact

integration among vendors’ IEDs, the connotation has come to

mean issues local to the substation where the integrator must

make things work. Because character length is a local issue,

out of scope of the standard, IEDs were included that do not

support CFE’s naming convention. Discovering this local

issue so late in the project resulted in a tremendous amount of

rework and testing because each element in each database that

referred to data from these IEDs had to be changed to the

shorter name and retested. Furthermore, CFE was not able to

maintain their established naming convention.

B. Logical Devices, Functions

CFE, like other customers, would like the opportunity to

replace IEDs from one vendor with those of another vendor

that perform the same function and would like to have each

IED support the same communications interface capabilities.

This is a useful consideration, but even though communica-

tions via IEC 61850 protocols can be standardized, they can

only be standardized to the features that overlap within every

product (the lowest common denominator). Also, keep in

mind that even though IEC 61850 IEDs communicate

similarly, they do not perform protection or automation the

same, and the standard does not specify how they perform

these functions. To allow interchangeability at the communi-

cations level for this project, IEC 61850 logical devices within

the IEDs were defined for each required function. Only the

specified logical nodes were allowed to exist inside each

logical device. Examples of the logical devices include:

• CTRL1 for bay control – LVD97010MCADCTRL1

• PRO for main protection – LVD97010MCADPRO

• MET for metering – LVD97010MCADMET

The left view in Fig. 7 illustrates browser software finding

several IEDs (physical devices) on the network, including the

physical device bay control LVD97010MCAD. The right

view shows the detail within the MCAD that exposes each

logical device and the logical nodes inside the CTRL1 logical

device.

Logical

Devices

Physical Device

Fig. 7. Browsing on physical devices, logical devices, and logical nodes

C. IED Data Sets

Inside each logical device, only the logical nodes required

for the project were allowed to be communicated within the

data sets. This was accomplished by some vendors through the

use of configurable data sets that were easily modified to

support this. Also, several default logical devices and nodes

were left in the IED in case of future needs, but they were not

reported in the data sets developed for the in-service design.

CFE requested data sets for binary data states (estados),

analog measurements (medidas), and GOOSE bits (GOOSE)

as summarized in Table VI.

TABLE VI DATA SETS

8ame Association Report Type

Estados Binary Status Buffered

Medidas Measurements Unbuffered

GOOSE GOOSE Bits GOOSE Messages

The contents of the digital state and measurement data sets

are illustrated in Fig. 8.

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Fig. 8. Required IED data sets and their contents

D. ew IEC 61850 Data Objects

Based on previous design experience, IBERINCO had

recommended the use of new data objects not yet a part of the

standard. IBERINCO had already submitted a proposal to be

added to the standard so that all users could benefit from their

future use. Even though they were not yet a formal part of the

standard, some vendors were able to implement them because

the IEC 61850 standard defines the methods necessary to

extend the logical nodes and data objects to include new and

unanticipated contents.

One such data object is the open and close order activation

information, or ACT. This is a status that represents that the

IED received a control action command. The control switch

logical node, CSWI, was extended to include both an open

order ACT (CSWI\OpOpnOr) and a close order ACT

(CSWI\OpClsOr).

E. Controls Filtered by Origin

The project design also required control functionality

where the status was mandatory within the standard, but the

function was left undefined. Origin category (orCat) and other

features became local issues not expected by the vendors and

required additional development during the project. It was

determined to use orCat to filter the controls based on what

the client sent them, or the “control origin category.” This

control origin, the originator category, is illustrated in Fig. 9 in

this excerpt from the standard. As can be seen, the standard

does not address the behavior or use of this attribute.

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CFE requested that the IEDs accept or deny control

execution based on the source of control that is the orCat

attribute for circuit breakers, control switches, and section-

alizer switches. In this way, the IEDs are configured to accept

or deny control commands by comparing the origin to the

present state of permission for that client. Addressing it as a

local issue, the integration design team defined its behavior to

satisfy CFE’s requirements. As designed, an IED can be set

for remote control only and act on only commands with the

origin associated with a remote SCADA client and deny local

HMI commands. Conversely, when the IED is expected to

perform in local mode, it can filter out all remote SCADA

commands based on their origin and accept only commands

from a local HMI. This filtering is useful to assure that the

communications are configured correctly on a trusted network.

However, it should not be considered a method to satisfy

cybersecurity requirements because the origin is simply a

setting and is not authenticated in any way. The IEC 62351

standard is under development and when complete will

provide cybersecurity methods for IEC 61850 substations.

Logical node implementations for breakers, control

switches, and sectionalizer switches are filtered as listed

below:

• Breaker – XCBR\POS\origin

• Control switch – CSWI\POS\origin

• Sectionalizer switch – XSWI\POS\origin

Fig. 9. Excerpt from IEC 61850 standard defining the originator type and orCat values

VIII. MAJOR COMMUNICATIONS INTEGRATION PROJECT

CHALLENGES

A. Local Issues Undefined by the Standard

By and large, the complications encountered in this project

resulted from local issues left unresolved by the standard.

Many of these local issues cannot, and will not, be addressed

by the standard but are essential to a successful implemen-

tation. Through this process, the communications integration

team documented a list from these local issues and the chosen

solutions as a guideform specification to aid other users of the

standard. The most arduous task was actually representing

specific CFE data requirements within the noncustomer

specific international standard methods of IEC 61850.

The previously mentioned request to support CFE-specific

IED names and logical device names was not unusual.

However, it was unexpected by a few vendors. The primary

IED vendor anticipated these requests because of years of

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experience supporting UCA2, which uses all of the same

messaging specifications and data transfer methods. Thus, the

flexibility of configuration of IEDs from this vendor’s IEDs

easily supported CFE’s desires. However, several of the IEDs

from other vendors did not. In some instances product

development provided the solution; in others, the final design

was modified to match the IED capabilities.

B. Unnecessary and Unexpected Use of Generic Data

References

The choice of several vendors to use generic data

references instead of specific naming for commonly used

information was a surprise. Though not mandatory, it was

definitely expected that vendors would provide logical node

and data object names that reflected the source and purpose of

the data.

Fig. 10. Specific naming versus generic naming for a switch status

Fig. 10 illustrates an example of specific naming versus

generic naming for a switch status. In the generic example on

the left, the contents of a data set published in a GOOSE

message represent the position of an apparatus as a generic

data object (indicator, Ind) associated with a generic logical

node (single point generic process input/output, SPGGIO35).

The more descriptive example on the right shows the contents

of a data set where each of three windings are associated with

a separate circuit breaker. Winding one circuit breaker logical

node is W1XCBR1, and the position is identified as Pos rather

than a generic indication. Therefore, with a little experience, it

can be observed that W1XCBR1.Pos.stVal refers to the value

of the position of the circuit breaker associated with winding

one. It is not possible from the generic description to know

what SPGGIO35.Ind.stVal refers to.

Without specific naming within the IED, separate

documentation must be used to identify what the generic data

objects represent. This eliminates the possibility of self-

description and automatic configuration. Generic naming is

defined in the standard for use when data that cannot be

anticipated, such as results of customer and/or site-specific

logic, are incorporated in a system. This feature should be

used sparingly to improve self-description but is a useful

method to incorporate data at the time of installation that

would otherwise be unavailable. If these data are common to

other applications, they may become mapped to new or

existing logical nodes as the products evolve.

The fact that devices from nine different product

developments from six different vendors were combined for

the first time in any project was also a difficult challenge, but

this would be true regardless of the protocol chosen. Engineers

that participated in the engineering of this project were located

across seven time zones (United States, Mexico, Spain,

Germany). Several communications tests were staged over the

Internet between remotely located engineers and products so

that work could begin before all products were collected at the

site of the FAT. It quickly became evident that the vendors

were in different stages of completeness of their IEC 61850

implementations. Some development continued until the

beginning of the FAT, which in some cases allowed the

vendors to incorporate some of CFE’s local issue requests.

Time was also a concern because delivery was initially

required four months after the contract award for the team to

design, build, and test all the protection panels and integration

systems. This, in concert with the fact that some IEDs were

the result of product development completed during the design

stage, resulted in a lot of integration rework during the FAT.

IX. FACTORY ACCEPTANCE TEST

Overall, the FAT took six weeks. SEL, IBERINCO, and

ZIV were involved in the total length of the testing. Siemens

and GE were involved in the configuration and testing of their

devices. The process started with initial network setup, switch

configuration, and initial communications tests. This part of

the process went quickly but also brought to attention the

following issues:

1. Some manufacturers were not able to meet some of the

IEC 61850 requirements for the project. Below is a list

of limitations found during this process:

a. Physical device name limited to eight characters.

This made IBERINCO redefine the database

naming and meant reconfiguration of databases for

all the clients.

b. Logical device name was not configurable. This

limited the overall goal of device interchange-

ability.

c. No mapping flexibility meant that the IED did not

allow for mapping any desired IED digital value to

a specific data object in a logical node. Therefore,

the team used more generic nodes than what was

expected in the design stage.

d. Some IEDs did not support the six clients required

by the project.

Most of these limitations exist because of IED

limitations and were not possible to overcome,

requiring the design team to change databases and

naming conventions for the devices with limitations.

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2. After these problems were addressed, HMIs and

SCADA gateways were reconfigured in order to start

functional testing. During this second part of testing,

new issues were discovered:

a. Report control block names were not configurable

for some of the IEDs.

b. Writing to report control block named components

OptFlds and TrgOps was a challenge because

values defined in the design stage were not

accepted by all the IEDs.

c. Double point indication for breakers and sectional-

izers caused problems when mapped to DNP3 and

Conitel 2020.

d. Some IEDs did not support the origin attribute to

report back to the HMI. The HMI uses orCat to

discriminate from which level the control was

executed and to log the control origin.

e. IEDs must use orCat as a filter to allow controls

from different control levels.

i. Local

ii. HMI

iii. Control center

3. After status, measurements, and controls were tested,

GOOSE messages for interlocks were tested. The

following two issues were addressed:

a. Control block reference (CBR) cannot exceed 32

characters for some IEDs. CBR is configured by

adding the physical name, logical name, logical

node, and data set. Because of the naming conven-

tion used, this limitation was exceeded most of the

time in several IEDs, and the customer was not

able to use the CBR that they originally chose.

b. Configuration software from some vendors will

import SCL files from other vendors but will not

respect all the configuration parameters. As a

result, the device is not allowed to subscribe to the

GOOSE messages from the other devices.

After these issues were addressed, the testing of

interlocks between bay controls was fast and easy,

showing the real advantages of GOOSE.

4. Confirming the successful use of GOOSE messages for

protection was the last part of the FAT. CFE wanted to

perform detailed testing in order to gain confidence in

the new technology.

421

DISTANCE

93100

451

BREAKER FAILURE

93100

487B

BUS DIFFERENTIAL

DB91 = 21 TRIP A

2 = 21 TRIP B

3 = 21 TRIP C

4 = 67 TRIP

451

BREAKER FAILURE

97010

1 = 50BF TRIP

2 = RETRIP A

3 = RETRIP B

4 = RETRIP C

451

BREAKER FAILURE

92010

T60

TRANSF. DIFF

92010

F60

LS OVERCURRENT

92010

7SJ61

HS OVERCURRENT

92010

L90

LINE DIFF

931001 = 50BF TRIP

2 = 86FI 97010

3 = 86FI 92010

1 = 50BF TRIP

CCIN001 = 93100 21 TRIP A

CCIN002 = 93100 21 TRIP B

CCIN003 = 93100 21 TRIP C

CCIN004 = 93100 67 TRIP

CCIN005 = DB9 86FI

CCIN006 = 93100 87L TRIP A

CCIN007 = 93100 87L TRIP B

CCIN008 = 93100 87L TRIP C

CCIN001 = 93100 50BF TRIP



1 = 86FI 93100

Fig. 11. Breaker failure protection scheme using GOOSE

The complete breaker failure protection scheme was

implemented using both traditional wiring and GOOSE.

The operation sequence of the breaker failure scheme is

presented below. Fig. 11 illustrates the process.

a. Trip of protection relay—the relay detects the

fault, operates, and at the same time, sends a

GOOSE message to the breaker failure relay.

b. Retrip of breaker failure relay—breaker failure

relay receives the GOOSE message and sends the

retrip signal to the associated breaker.

c. Trip of breaker failure protection—in the case

when a breaker failure timer expires, a breaker

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failure trip GOOSE message is sent to the bus

differential relay to start the bus isolation.

d. Bus differential relay receives the GOOSE

message, identifies feeders connected to the bus

with the breaker failure, and sends a GOOSE

message to trip the required breakers through their

associated breaker failure scheme.

Fig. 12 shows an event report from the breaker failure relay

93100 for a retrip operation. IN101 represents the trip signal

from the distance protection relay using a hardwired contact;

CCIN001 represents the trip signal from the same relay using

GOOSE. The time difference between hardwired and GOOSE

is about 12 ms because of the time introduced by the physical

output of the distance protection relay and the debounce timer

of the breaker failure relay. Because of this delay, the retrip

operation using GOOSE was 12 ms faster than the hardwired

operation. This difference might be reduced using high-speed

output contacts.

Fig. 12. An event report from the breaker failure relay 93100 for a retrip

operation

Fig. 13 shows an event report for the breaker failure relay

97010. In this case the hardwired trip comes into IN103, and

after about 200 ms, BFTR1 represents the output contact to

the 86FI lockout relay that will distribute the trip to all

breakers in the bus. The GOOSE trip comes into CCIN003,

the same 200 ms apply, and another GOOSE (CCOUT001) is

sent to the bus differential relay that determines which

breakers to trip and sends another GOOSE message

(CCIN005). Fig. 13 shows that the GOOSE scheme is 8 ms

faster, without considering that the wiring scheme still has to

go through the lockout relay.

Additional tests were performed, increasing traffic in the

network and obtaining the same results. In this specific

project, Ethernet switches with VLAN (virtual LAN) priority

tagging and store-and-forward technology to avoid collisions

were used in order to guarantee the results.

Fig. 13. An event report for breaker failure relay 97010

X. LESSONS LEARNED

Much was learned during the project because it was the first to

integrate so many different vendor IEDs into one system and

prove interoperability. Success was possible because of the

skills and years of experience of the design team working with

the messaging and methods of the new standard. The vendor

that supplied the bulk of the IEDs has been providing this

technology for six years as UCA2 and recently upgraded their

implementation to incorporate SCL. However, most of the

lessons that can and should be taken from this paper are the

resolution of local issues documented as a guideform specifi-

cation. These local issues were not solved in the past because

other IEC 61850 system designs were created with a handful

of IEDs from the same vendor or perhaps two different

vendors. The design team for this project offers the following

list of lessons learned.

A. Design Stage

• Be aware of desired IED name length and restrictions

within the IEDs.

• As early as possible, identify optional parts of the

standard that you will require in order to increase the

likelihood that each vendor will support them. Be

prepared to compromise if your IED of choice does

not support these requirements.

• Choose IEDs that support configuration flexibility so

that any IED data available to the communications

interface can be presented and so that logical devices

and logical nodes can be extended to incorporate new

and unanticipated data.

• Choose vendors that will support your requirements

and desires to implement nonmandatory elements of

the standard as well as your selection of resolutions to

local issues.

• Test new product communications as much as possible

prior to the FAT.

• Use IRIG-B for better timestamp accuracy.

• Use substation-grade communications equipment.

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• Use Ethernet switches that support VLAN and priority

tagging.

• Preferably, use IEDs that support direct loading of

SCL configuration files over devices that require

proprietary software.

• Choose IEDs that support the required number of

clients (recommend six).

• Choose IEDs that support the appropriate GOOSE

parameters.

− GOOSE subscriptions (recommend 24)

− Logic variable associations for bay control

(recommend 128)

− Logic variable associations for protection

(recommend 16 or 128, depending on application

complexity)

− GOOSE publications (recommend eight)

B. Communications Interface Testing

• Be prepared to understand and test communications at

the manufacturing messaging specification (MMS)

level.

• Be aware that, because of the anonymity of Ethernet,

messages are interleaved from multiple sources.

− This complicates troubleshooting and eliminates

straightforward functional testing.

− One must trust software test tools rather than

hardware connections and diagnostics, such as

LEDs, to provide communications information.

• Choose IEDs that respond to commands to identify

what configuration file is loaded within the IED and in

use.

• Choose IEDs that respond to commands to identify the

status of their configured outgoing GOOSE message

publications.

• Choose IEDs that respond to commands to identify the

status of subscription to expected incoming GOOSE

message.

C. Functional Testing

• Document everything.

• Keep your Ethernet analyzer recording at all times.

You cannot troubleshoot what was not captured by an

analyzer.

• Recognize that part of the simplicity and speed in

using GOOSE is that permissive logic is done in the

relay logic rather than auxiliary relays because so

much information can be received quickly from many

sources.

D. Software

At this time, not all vendors have IEC 61850 configuration

software available. Some still edit files at the XML level. For

this project, only three vendors had an IEC 61850 configura-

tion tool available. Engineering software tools (SCL software)

that can import ICD files from the different IEDs and create

CID files for the IEDs, SCADA gateways, and HMIs will help

to reduce configuration time as well as complexity.

Fig. 14. Construction of Wind Farm La Venta II

XI. GUIDEFORM SPECIFICATION

In order to confirm that IEDs that support IEC 61850 are

successfully integrated into a substation system, the following

details also need to be met. Some of these details are not

mandatory for IEC 61850 conformance but are necessary to

satisfy integrated communications. Therefore, IEDs offered

for inclusion in a system to satisfy this specification need to be

IEC 61850 conformant and support the following itemized

functionalities:

• Each IED shall support the appropriate protocols

within the IEC 61850 standard.

− Reporting, poll response, controls, and self-

description shall be performed via MMS protocol.

− Configuration shall be performed via XML-based

SCL files.

− Peer-to-peer messaging shall be performed via

IEC 61850 GOOSE messages.

• Each IED shall have a native Ethernet port that

supports each of the IEC 61850 protocols mentioned

previously as well as essential engineering access

connections over the same Ethernet port. Specifically,

each IED Ethernet port shall support, at a minimum,

the following:

− IEC 61850 reporting via MMS

− IEC 61850 polling MMS

− IEC 61850 controls via MMS

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− IEC 61850 self-description via MMS

− IEC 61850 GOOSE messaging

− IEC 61850 configurations via XML-based SCL

files loaded directly into the IED (preferred)

− Engineering access via standard TCP/IP

mechanisms

− Event report collection via standard TCP/IP

mechanisms

− Non-IEC 61850 settings transfer via standard

TCP/IP mechanisms (e.g., protection and logic

settings)

In order to support varied future and additional

installations, each IED shall also support a SCADA protocol

in addition to IEC 61850 via the Ethernet port.

Each IED shall support the origin category (orCat) for

controls and filter permission to execute a received command

based on the command origin.

Each IED shall support the data object ACT to represent

the open and close order activation information. This status

represents that the IED received a control action command.

Each IED shall support a descriptive name of up to 16

characters in order to provide the ability for the end user to

uniquely name the IEDs within their system based on new or

established naming practices.

Each IED shall be capable of supporting six simultaneous

client-server associations. This number is necessary to support

the possible network requirement of two redundant SCADA

gateway connections, two redundant HMI connections, and

two redundant engineering access connections.

Each IED shall support six default preloaded buffered

reports and six preloaded unbuffered reports. These reports

shall be preconfigured and capable of being used without

customization. However, the IED shall also support customi-

zation of the reports and data sets.

Each IED shall have the ability to freely rename data sets,

logical devices, and logical nodes.

Each IED shall have the ability to add and remove logical

nodes to and from each logical device.

Each IED shall use specific naming for commonly used

information rather than generic data references.

Changes to data sets and reporting configuration shall be

done via ease-of-use configuration software. The resulting

SCL CID file shall be downloaded directly into the IED as

described within the standard. This is necessary to confirm

that future IEDs from multiple vendors can be used and

configured with one software tool.

Each IED shall support remote loading of the CID file via

Ethernet using standard TCP/IP mechanisms in order to

accommodate engineers designing and technicians configuring

IEDs remotely from each other because of geography and/or

time.

It is of utmost importance that the IEDs support stations

and applications with different data requirements, have the

ability to accommodate data that were not recognized to be

necessary until after contract award, and represent customer

specific data and IED logic values as appropriate IEC 61850

logical nodes and data objects. Therefore, flexible configura-

tion of data sets shall be required as well as the ability to

create new logical devices, logical nodes, and their contents.

To support this, it shall be possible to create different ICD

(IED capability description) and CID files that map any and

all available IED data for specific customer applications. In

this way, unique data sets and customer specific names shall

be supported. Modification of the IED IEC 61850 capabilities

shall be done without hardware or firmware changes to the

IED.

Each IED shall allow the user to query it directly and to

verify which IEC 61850 configuration file is active within the

IED. This function is necessary to confirm correct

configuration and identify what behavior should be expected

from the IED in order to perform effective commissioning and

troubleshooting.

In order to perform effectively in the anticipated

communications designs, the IEC 61850 GOOSE implemen-

tation in each IED shall support the following requirements:

• Each IED shall be capable of publishing eight unique

GOOSE messages.

• Each IED shall be capable of subscribing to 24 unique

GOOSE messages.

• Each IED shall be capable of monitoring GOOSE

message quality.

• Each IED shall be capable of processing incoming

data elements and their associated quality.

• Each IED shall be capable of monitoring message and

data quality as permissives prior to use of the

incoming data. At the time of configuration, the end

user can choose to ignore the possibly corrupted

data—if the data or message quality fails—to prevent

an unwanted operation.

• Each IED shall be capable of creating a GOOSE data

set that includes both Boolean values and non-Boolean

data types, such as analog values.

• Each IED shall be capable of accepting and processing

data sets from other IEDs that contain Boolean and

non-Boolean data types even though IEDs need only

map and use Boolean data types.

• Each IED shall support priority tagging of GOOSE

messages for optimizing latency through Ethernet

switches.

• Each IED shall support VLAN identifiers to facilitate

segregation of GOOSE traffic on the Ethernet

network.

• Each IED shall support a preloaded default GOOSE

message for use without custom configuration.

• Each IED shall support custom editing of the data sets

published in the GOOSE messages so the user can

send what they choose.

• Changes to data sets, GOOSE parameters, GOOSE

publication, and GOOSE subscription shall be done

via ease-of-use configuration software. The resulting

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SCL CID file shall be downloaded directly into the

IED as described within the standard. This file shall not

be converted into settings and downloaded via the

conventional settings process. This difference is

documented specifically and necessarily to confirm

that future IEDs from multiple vendors can be used and

configured with one software tool.

• The configuration software from the IED vendor shall

import CID, ICD, and substation communications

description (SCD) files in order to learn the available

GOOSE publications and data sets from other IEDs.

The software will use this information to configure the

IED to subscribe to other vendor IEDs and use the

data being broadcast.

• Each IED, while in service, shall allow the user to

query it to learn communications diagnostics as well

as status and/or error codes of GOOSE messages

being sent and received.

In order to effectively configure the IED for use within the

network, the ease-of-use configuration software provided with

the IED shall be capable of the following requirements:

• The software shall be capable of importing configura-

tion information about other IEDs from ICD, CID, or

SCD files.

• The software shall validate the imported information

to confirm that it complies with IEC 61850

parameters.

• The software shall provide error messages describing

problems detected in imported files.

• The software shall support naming IEDs with up to 16

characters.

• The software shall support review and editing of IED

data sets and report parameters.

• The software shall support review and editing of data

sets and GOOSE parameters.

• The software shall support the mapping of any

available data into the data sets.

• The software shall support the association of data

quality with data elements.

• The software shall support visible end-user warnings

to prevent incorrect data set editing as well as warning

when editing a data set that is already in use. In this

fashion, the end user can be warned not to disrupt an

existing configuration and/or create a data set too

large for its intended purpose.

• The configuration software shall support creation of

eight GOOSE publications.

• The configuration software shall present the user with

all available GOOSE messages and support up to 24

subscriptions.

• The configuration software shall support assigning

VLAN and priority tags to GOOSE messages.


the entire data set for each potential GOOSE

•

subscription and allow the user to browse for

necessary data.


the entire data set for each potential GOOSE

subscription and allow the user to map data from the

incoming data sets into the IED. When this is done,

the software automatically subscribes to the associated

GOOSE message.

• The configuration software shall allow the user to

choose message and data validation on incoming

GOOSE data set contents.

• The configuration software shall allow the user to

directly load the SCL file into the IED, or export it for

storage or remote loading.

• The configuration software shall allow importing and

exporting of SCL files without modification of the

private regions of the original.

• The configuration software shall create files in XML

format that can be modified by XML editors and tools

to help resolve conflicts or errors in badly formed

files.

IEC 61850-5 identifies several specific performance

requirements for applications operating in the IEC 61850

series environment. Unfortunately, the IEC 61850 standard

defines speed criteria that cannot be exactly measured.

Therefore, it is not presently possible to test and verify the

transmit time performance classes as described in the

standard. Instead, it is possible to measure the transfer time,

which includes the transmit time plus the time to process and

timestamp the transmitted data. This transfer time represents

the performance of communications in actual use. Data

element state changes are timestamped and logged as

sequential events records (SER). In IEDs with clocks

synchronized to the same time reference and that create

accurate timestamps, SER are used to calculate transfer time.

The transfer time is described as the difference in time

between the timestamped SER in the initiating IED and the

timestamped SER in the receiving IED. For each IED, the

measured GOOSE transfer time shall be provided with a

description of how it was measured.

IEC 61850-10 defines other metrics to be measured within

devices and documented by the vendors so that end users can

compare multiple vendors. For each IED, timestamping

accuracy will be identified and documented by providing the

two following measures:

• Maximum clock synchronization error, which

indicates the accuracy of the IED to synchronize its

clock to the time reference

• Maximum timestamp delay error, which indicates the

accuracy of the IED to timestamp the data when the

event occurs

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Product reliability metrics are essential because of the

nature of networked IEDs being used to design systems of

interoperable devices working in a coordinated fashion.

IEC 60870-4 Telecontrol Equipment and Systems Part 4:

Performance Requirements documents methods to measure

and calculate the following [1]:

• Reliability

• Availability

• Maintainability

• Security

• Data integrity

• Time parameters

• Overall accuracy

These and other device performance measures are essential

information for predicting performance, functionality, and

reliability of designs executed by networked IEDs. No specific

performance benchmarks are expected to be met; however,

verification and publication of actual performance measures is

necessary to be conformant. Using these published perfor-

mance measures, system integrators can predict the

performance of the interconnected IEDs and, thus, the per-

formance of the system. Furthermore, system integrators will

be able to identify suitable devices for specific applications.

Reliability measures should include, but not be limited to,

specific product reliability metrics and a description of how

the metrics are calculated or measured. Metrics that are

mandatory include:

• Specific device mean time between failure (MTBF)

• Product family MTBF

• Specific product mean time between removals

(MTBR)

• Product family MTBR

Reliability data should be based on the actual incidence of

field failures for a large population of installed units. If the

provided figures are based on actual data, the approximate size

of each installed population used as a basis for each value

should be indicated.

If insufficient field data are available to provide a

meaningful MTBF, base the predicted MTBF on the parts-

count procedure defined in Military Handbook, MIL-HDBK-

217F, December 1991 [2]. Manufacturing quality and design

quality can yield significantly better MTBF than predicted by

MIL-HDBK-217F. The parts-count procedure does establish a

pessimistic MTBF to support a minimum system availability

calculation.

XII. REFERENCES

[1] Telecontrol Equipment and Systems Part 4: Performance Requirements,

IEC Standard 60870-4.

[2] Military Handbook: Reliability Prediction of Electronic Equipment,

MIL-HDBK-217F, Department of Defense, Washington DC, December

1991.

[3] D. Dolezilek, “IEC 61850: What You Need to Know About

Functionality and Practical Implementation,” presented at the Western

Power Delivery Automation Conference, Spokane, WA, 2005.

XIII. BIOGRAPHIES

Victor Manuel Flores is chief of the automation department of CFE GRTSE. He is an electrical engineer from ITESM with 22 years of experience in CFE

SCADA and automation systems. His experience also includes planning,

design, implementation, commissioning, and testing of systems using DNP3, Harris 5000/6000, Conitel 2020, and Modbus®. He is a CFE-certified instruc-

tor and is actively involved in the CFE specifications group for SICLE, SIME,

and the working group to adopt IEC 61850 in CFE.

Daniel Espinosa received his B.S. in electrical engineering from the Instituto

Politécnico Nacional in 1998. He is a member of the Protection Specialists

National Committee from CFE and is involved in several aspects of electric power protection and automation systems standardization and normalization

in CFE. Since 1999 he has been responsible for preparing bid specifications

for integrated systems for distribution substations and for 13.8 kV to 400 kV power lines in the CPTT in CFE.

Julian Alzate received his B.S. in electrical engineering and telecommuni-

cations at the Universidad Nacional de Colombia in 1998. Julian joined Schweitzer Engineering Laboratories, Inc. in 1999 as an integration and

automation application engineer in the International Sales and Marketing

Division. He provided technical support to international customers on integration and control applications and relay technical training. In 2003 he

became Automation Engineering Manager for the SEL Mexico Division,

where he was involved in preparation of technical bid responses and management of international projects. In 2005 Julian became the new

technologies manager and is involved in the design, implementation, and

management of projects in which new SEL technology is involved.

Dave Dolezilek is the technology director of Schweitzer Engineering

Laboratories, Inc. He is an electrical engineer, BSEE Montana State

University, with experience in electric power protection, integration, automation, communications, control, SCADA, and EMS. He has authored

numerous technical papers and continues to research innovative technology

affecting our industry. Dolezilek is a patented inventor and participates in numerous working groups and technical committees. He is a member of the

IEEE, the IEEE Reliability Society, CIGRE working groups, and two Intern-

ational Electrotechnical Commission (IEC) technical committees tasked with global standardization and security of communications networks and systems

in substations.

Copyright © CFE / SEL 2007

(All rights reserved) 20070406

TP6271-01

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High-Speed Control Scheme to Prevent

Instability of A Large Multi-Unit Power Plant

Vahid Madani , Fellow, IEEE, Edward Taylor, Senior Member, IEEE, Davis Erwin, Anatoliy Meklin,

Mark Adamiak, Fellow, IEEE

Abstract

Unintended loss of a major power plant can cause

substantial strain on the remaining generating resources

and lead to local system instability and/or generate

oscillations with impact to the overall bulk power

system.

In the continuing quest to improve the availability of

the generation supply and in order to meet the more

stringent electric coordinating council reliability

criteria, power companies and grid operators are

focusing on System Integrity Protection Schemes

(SIPS) that can detect and react on events leading to

potentially unstable power system conditions. One

such situation occurs when severe disturbances occur

on transmission line exits from large multi-generator

power plants. Based the disturbance severity, the

typical results are intensive swings or loss of plant

synchronism which will lead into loss of the entire

generation complex either by out-of-step protection, or

unit shutdown by protective devices reacting to voltage

dips at auxiliary buses. By quickly detecting the

destabilizing conditions, preemptive actions can be

taken to preserve the plant and minimize the extent of

the disturbance and subsequent effect on the power

grid.

Such SIPS offer added advantages under normal

operating conditions for scheduled transmission line

outages, and allow full power operation with a line out

of service.

This paper discusses a control solution based on

implementation of high-speed SIPS. The control

strategy results from transient stability analysis for

various types of transmission line faults, including

delayed faults caused by complete and partial breaker

failures. Different types of faults and transmission

outlet line outage conditions for various system and

plant initial conditions are investigated and options for

mitigation are recommended. The discussion includes

stability requirements, alternative actions and

algorithms, SIPS components, the methodology for

obtaining arming settings, interaction with the existing

protection schemes, and effect of a switchyard

topology.

Technical implementation considerations such as

system design, architecture, measures for reliable and

secure operation, synchrophasor capture, event capture,

performance under missing or conflicting information,

and testing are discussed.

Introduction:

This scheme is in service at a multi-unit power plant

that is a significant generation facility on the Pacific

Gas & Electric (PG&E) system, Figure 1. At the

500kV Voltage level, the plant is connected to the

Midway substation through two lines on a common

right of way, and to the Gates 500 kV substation

through a diverse path. The recent upgrades of the two

Power Plant units has increased plant generating

capacity on average by about 6% each.. Stable

operation of the plant is essential for reliable energy

delivery not only to the PG&E system but also for the

entire Western Electricity Coordinating Council

(WECC) grid.

Figure 1 - Portion of the PG&E’s Transmission and the

WECC Grid Region

Power Plant

68



A single line overview of the critical elements

pertaining to the SIPS described in this paper is

presented in Figure 2.

Figure 2 - Power Plant Electrical System with Control

Voltage Sensing Points

Detailed unit stability studies and the plant operating

experience have not revealed any plant stability

problems with all three 500 kV lines in service or

following a loss of a single 500 kV component (a line

or a unit). However, at certain plant output levels; a

single line loss in a two-line scheme (type 1 event);

double line outages (type 2 event), and breaker failure-

caused delayed single line loss (type 3 event) may lead

to synchronous swings or to a loss of synchronism

between the plant generators and the WECC system.

Because of the high plant inertia and small system

impedance, these swings would potentially result in

widespread voltage dips with magnitudes and durations

outside the guidelines defined by the NERC/WECC

Planning Standards. These swings may also cause

operation of plant protective devices, such as out-of-

step and/or 12 kV undervoltage protection that can

result in double unit outages (DUO).

From the system perspective, DUO at peak output

could impose a significant stress on the WECC system

and increase dependence on the adequate performance

of protecting and regulating devices throughout the

system. Any failure or misoperation may result in a

cascading affect, e.g. with possible collapse and

separation at the California – Oregon Intertie (COI)1.

This intertie can also be affected by simultaneous loss

of other multiple units. For example, another SIPS has

been implemented to maintain safe operating

parameters for the loss of two Palo Verde Units [3].

1The dynamic swings at COI, following a simultaneous trip of

two Power Plant units, are supposed to be detected for

initiation of capacitor/reactor switching to prevent the

separation. However, the more realistic sequential unit trips

may produce swings at COI, which are not intensive enough

to be detected.

Loss of a large generation source at once may also

cause a definite strain on the remaining generating

resources. From the plant perspective, the most

undesirable consequence is switching to the alternative

power supply of the plant auxiliary loads. Therefore,

application of automatic remedial actions have been

studied and implemented to provide stable operation

following one of the previously described severe

disturbances.

The remedial actions considered include:

• Pulsing generator voltages upward immediately

after a critical disturbance with full utilization of

generator short-term overloading capabilities.

• Turbine main and intercept valve fast closing,

initiated by an advanced overspeed control or by a

disturbance detecting device.

• Tripping one generator immediately after

indication of a critical disturbance2.

Studies have determined that the third measure –

tripping one generator – is the only effective option

amongst the above considered remedial action

alternatives to achieve first swing suppression over the

entire range of plant operation. Studies have also

determined that for line faults with significant 500 kV

voltage dips, very high speed remedial actions are

required. System studies have shown that SIPS would

have to correctly identify the condition and issue the

appropriate plant trip signal within 100 milliseconds

(msec) following the disturbance initiation. High speed

performance relies on SIPS initiation by redundant pilot

transmission line protection for each of the plant

outlets.

A high-speed SIPS is necessary for disturbances which

are aggravated by line faults. In some no-fault cases,

delayed generator tripping has been identified as an

effective solution to prevent poorly damped oscillations

which may occur if only one 500 kV line remains in

service (Type 1 and 2 events). Figure 3 illustrates

generator trip effectiveness in the described situations.

2 A loss of one unit does not affect WECC stability and meets

the WECC reliability performance requirements.

69



Figure. 3 - Plant generator angles following a

type 2 event. Maximum plant generation with

0.975 p.u. terminal voltage: (1) – 3-ph. fault

without remedial actions; (2) – 3-ph. fault and

immediate generator trip; (3) – no fault and 3

second delayed generator trip.

Implementation Alternatives:

To distinguish various types of system conditions for

which SIPS is considered, some representative

parameters are monitored in the SIPS, and combined in

analytical or logical conditions, describing a stability

region boundary (stable without remedial actions).

If such a description includes only local parameters and

does not involve remote limitations and, therefore,

flow/voltage measurements in the remote parts of the

system – local SIPS can be used. Otherwise, remote

information should be transmitted to SIPS, or a

centralized system-wide SIPS, containing data from

different part of a system, should be used to ensure

plant stable operation.

The scheme requirements have also identified the need

for independence from other existing known remedial

action systems that may be monitoring the flow and

status of the power plant outlets because the purpose

and the performance requirements of those schemes are

different. For example, the power plant transmission

outlets are involved in the WECC Pacific AC Intertie

remedial action scheme (PACI RAS). The flows and

status of critical equipment on COI and other critical

transmission paths (e.g.: Path 15 and Path 26 on Figure

1) along with the plant are monitored, providing

remedial actions for a variety of disturbances on the

500 kV grid [4]. However, the PACI RAS provides

remedial actions for interregional transients, is not a

localized scheme near the plant facility, and in some

severe fault scenarios, may not meet the throughput

timing requirements needed for the dynamic control of

the plant.

The possibility of using local SIPS was confirmed by

obtaining adequate control conditions based on local

parameters. The SIPS triggering conditions for

disturbance “i” can be presented by the following

inequality:

Y > A0i + A1i • X1 + A2i • X2

Where:

Y – pre-disturbance plant generation

X1– pre-disturbance voltage at the 25 kV generator

terminals

X2 – minimum 500 kV bus positive sequence voltage

during a fault

A0i , A1i , A2i – disturbance specific coefficients.

The polynomials are constructed using the results of

stability calculations organized as a multi-factor

experiment [1, 2]. Each test has been conducted with

the detailed WECC model as a series of transient

stability calculations, determining critical Y for the

fixed values of X1 and X2. These values3 have been

defined in each test in accordance with the 2-level

orthogonal experimental plan [1]. The results

demonstrate that least square polynomial coefficients

are statistically significant (contributions of all included

parameters are significant) and the entire formulas are

adequate in mathematical sense (formula inaccuracy is

comparable with the “noise”). This conclusion is based

on the comparison of the formula inaccuracy with the

test inaccuracy, which has been emulated by test

replications. Each test is conducted twice with the

same values of X1 and X2 and random conditions in the

rest of the system. Randomization has been provided by

random selection of two WECC power flow cases for

each test from the variety of available cases for

different years, seasons, hours, etc. The following are

the examples of the obtained normalized4 inequalities

for the type 2 and type 3 events:

y > -0.067 + 0.912 • x1 + 0.614 • x2, (1)

y > -0.052 + 0.370 • x1 + 0.769 • x2 (2)

The second and third coefficients reflect contributions

of X1 and X2 in approaching an unstable value of Y.

3 Initial tests included some other parameters. 4 Normalized variables represent deviations from average

values in per unit of maximum deviations

70



Further analysis has shown that generator stability

conditions are often less critical than preventing

dynamic voltage dips at the auxiliary buses causing

operation of the 12 kV undervoltage protection. This

gives additional confidence that system conditions in

remote parts cannot affect SIPS triggering condition.

Therefore, the entire SIPS, including generator tripping

and disturbance detecting circuits, can be located at the

plant.

Detection of speed-critical disturbances is provided by

the direct input from the redundant transmission line

protective schemes for all the 500kV transmission

outlet lines. Demarcation from conventional line

protection is provided at the line protection trip busses

in breaker failure devices by energizing independent

auxiliary paths to the SIPS.

It is of interest to note that for the high-speed detection

portion of the plant SIPS, trip detection at Gates and

Midway is not necessary. For double line outages not

resulting from faults, such as manual or inadvertent

opening either end of the transmission line, the SIPS

response can be delayed by a few seconds. This time is

used for reliable undercurrent detection of a remote line

end. Otherwise, double line outages could be falsely

indicated during intensive swings.

The triggering conditions described above are used as a

foundation of the SIPS algorithm. Some of the

technical decisions and the arming levels are based on

the equipment location (in the 500kV switchyard). For

example, only Y and X2 parameters available at the 500

kV switchyard have been utilized and the lowest

guaranteed generator terminal voltages are used as the

fixed X1 for all three types of events. The worst case

value X2=0 (3-phase faults near the plant 500 kV bus)

was used for the type 1 and 2 events. The X2 value is

more essential for the type 3 events (breaker failure-

caused delayed single line loss). The following is the

final form of SIPS arming conditions:

for type 1 event: P > L1 (3)



for type 3 event: UV <UVs (6)

where:

P – pre-disturbance plant generation

L1-L3 – three arming levels for P

UV – minimum 500 kV bus positive sequence

voltage during a fault, and

UVs – arming level for UV.

Design Considerations & Implementations:

i. Functional Components

Based on the selected alternative, SIPS includes the

following main functional components:

• High speed initiators for fault related line trips

triggered by the same group of line protection

outputs, which energize breaker failure schemes,

see Figure 4.

• Line status indicators using local breaker circuit

status along with the “undercurrent” for security

and to indicate a remote end status change.

Initiators for the no-fault line trips are not speed-

critical and are also based on the line status

indicators.

• Four indicators of plant generation levels prior to

a disturbance

• Indicator of significant 500 kV positive sequence

voltage drop during a fault

• Indicator of a severe delayed fault using breaker

failure scheme outputs in combination with the

positive sequence drop indicators

• Generator trip decision logic including:

a) Recognition of an event type (1 or 2 or 3)

using the above described initiators and status

indicators;

b) Selection of a corresponding inequality from

(3)-(6) and use of the selected inequality to

determine a need for a generator trip

• Generator selection logic based on switchyard

topology

ii. System Architecture

In order to meet the functional requirements of high

availability, reliability, and performance, a system

architecture has been developed that encompassed

redundant components, compartmentalized

measurements, fail-safe logic, and direct sensing of

protective relay trips. The Intelligent Electronic Device

(IED) based implementation of these various

components is described below:

iii. System Availability:

Redundant hardware systems have been used to meet

the high degree of availability required by the

application. The basic redundancy of this SIPS scheme

is implemented by having two identical systems,

System “A” and System “B”, which are programmed

identically and can operate independently, Figure 5.

71



Fig. 4 – Typical SIPS Interface with Transmission Line Protection, Control, and Breaker Failure

Both “A” and “B” systems are normally in service,

however, one may be taken out of service for

maintenance, repair, or reprogramming while the other

system remains on line. For added security, a fail-safe

mode is implemented when both systems are fully

functional and operational. With both systems in

service, a veto provision is programmed, that is, if the

output of each system is different that the other, the two

systems would “veto” the trip decision of each other.

The fail-safe mode is intended to enhance the security

of the scheme and to validate the decision between the

redundant systems prior to issuing any critical plant trip

decisions. In order to address maintenance, a “cut-out”

switch was installed that opens the trip circuits from the

respective system to all unit breakers and also provide

status information of such to the other system to allow

it to operate without any delay.

iv. Physical Architecture:

System “A” and System “B” are each composed of five

identical microprocessor devices – The devices in each

system are connected together via a high-speed serial

fiber optic communications ring. The overall system is

designed so that no single point of failure will result in

the failure of the SIPS to function. Further demarcation

has been provided by physical isolation of the wiring

between units and redundant systems. All devices

connecting to Unit 1 signals or controls are located in a

separate rack from those devices connecting to Unit 2

and physical separation between Systems is effected by

placing the IEDs in different rack locations. This

physical separation is illustrated in Figure 5. Separate

DC panels and independent DC circuits are used for

each system.

Three devices in each system function as a Phasor

Measurement Units (PMUs) and compute synchronized

phasors on each unit and each line exiting the plant. At

present, the PMUs are configured to capture data based

on trigger settings; however, streaming measurements

are also available for advanced protection applications

such as dynamic line rating, wide- area out of step, and

oscillation damping as these applications become

needed. Each device, in each of the SIPS, is

synchronized to absolute time via IRIG-B time codes

from a GPS clock in the station. The IRIG-B signals

are sent in level-shift format as this format is required

to achieve the 1usec accuracy required by the

synchrophasor calculation. Requirements for the GPS

to meet the precision protection applications are further

described in [8].

Engineering and Design:

i. Input Sensing Redundancy

System “A” and System “B” are designed with

independent inputs to monitor the 500kV switchyard

bus configuration, line status, and generator power

output and other power system telemetry values. These

inputs include:

• Separate current transformer (CT) circuits from

each 500kV circuit breaker to monitor line loading

status, and generator loading.

72



1 2 3 4 5 6

7 8 9 101112

A

B

12x

6 x

8x

2x

9 x

3 x

10x

4x

1 1x

5x

7x

1x

Ethernet

A

12 x

6x

8x

2x

9x

3x

1 0x

4x

11x

5x

7x

1x

C

Figure 5 – Overall Physical Device Arrangement and Communication Topology

(Loop Communications, Ethernet, & IRIG-B)

• Three independent 3-phase voltage sources for

each system (SIPS). Two of the voltage sources

are from the 500kV side of the generator step-up

transformers (one from each unit). The third

voltage source is from one of two diverse path 500

kV lines.

• Independent breaker auxiliary contacts from the

circuit breakers to monitor breaker open/close

status of each circuit breaker. In addition, a circuit

breaker maintenance switch is provided for each

breaker. Contacts from each SIPS-applicable

breaker maintenance switch are wired in parallel

with the corresponding breaker auxiliary contact

and energize one input per system. The scheme

interprets the input as a breaker open and also

logically disables breaker trip sensing and breaker

failure logic.

ii. Output Redundancy

Redundant trip outputs are provided from each system

and wired to the redundant breaker trip coils for the unit

/ step-up transformer 500kV winding breakers.

Of note in the tripping output operation is the “fail safe”

design that ensures only one unit can be tripped by the

scheme. Specifically, a normally closed latching

contact is connected in series with the tripping contacts.

When a “trip” is issued to a unit; e.g. Unit 1, the

latching relay in series with the Unit 2 trip outputs is

locked “open” thereby blocking an inadvertent trip of

Unit 2. Likewise, if a trip is issued to Unit 2,

inadvertent trips to Unit 1 are blocked.

iii. Shared Elements Between the Redundant

Systems

Only two elements are identified as common hardware

interacting with both Systems namely:

1. Breaker maintenance switch – One switch per

circuit breaker is a common industry practice.

Separate contacts from the switch are wired to each

SIPS system providing redundancy on the breaker

status inputs. Operating procedures are in place to

assure breaker maintenance switch positions are

verified before and after switching for breaker

maintenance. The intent is to prevent accidental

incorrect positioning of the maintenance switch.

2. Each breaker is equipped with one breaker failure

device / scheme. Failure within the breaker failure

circuitry could possibly cause the SIPS not to

receive correct indication of a line protection relay

trip or breaker failure condition. The breaker

failure scheme diagnostics provide alarms to the

operators. Upon receipt of the alarms, the breaker

is switched out of service allowing the SIPS to

remain operational.

73



iv. Redundant Communications

The five devices in each system share telemetry data

and status information using peer-to-peer

communication connected in a ring configuration with

fiber cable. When data is sent from one device, it is

sent in both directions around the local ring among all

the relays in one system. As such, any single

communication failure has no effect on the

communications within a given system.

v. Local Line Status Detection (Line Outage)

As one of the detection functions is detection of a Line

outage, a logic function is developed that depends on

the following conditions:

• The local line breakers are Open or in Maintenance

• An “undercurrent” on all 3 phases of the line is

detected for a specified period of time – Note, there

is hysteresis in the measurement to minimize

continuous pickup / dropout when current value is

near the detection set point.

vi. Remote Open Detection

Local breaker status or relay trip indication is not

sufficient to determine a remote terminal open breaker

at the remote terminals of the transmission outlet lines.

A remote may be opened manually, an inadvertent trip

could be initiated by maintenance personnel, or the line

may be open simply due to the special set-up of the bus

at the remote end of the line. To detect a line open at

the remote end of the line, “Remote Open Detection”

(ROD) logic has been included. The ROD logic makes

the determination of a remote open by checking for:

i. Local line undercurrent condition on A, B, and C

phases – specifically – all 3 currents are around

line charging current levels

ii. At least one local breaker is closed

iii. The power delivered by both generators is greater

than the lowest megawatts (MW) arming threshold.

vii. Logic Design

As described earlier, the functional requirements from

system studies have identified several different “states”

of operation of the scheme – depending on pre-existing

and existing power system conditions. To succinctly

represent the functional requirements, a State Variable

approach has been taken to develop the road map prior

to programming the SIPS logic, Figure 6.

The State Diagram defines the different “states” in

which the system can reside and the state transition

variable that forces the transition from one state to the

next. Once in a given state, specific logic is executed

pertaining to the functionality required by the

respective state. Most transitions require multiple state

variables to be “True” in order to change states.

The State Diagram also enables communication with a

broader set of stakeholders and communication with

entities outside of company as the graphical

representation of the state transitions are easier to

follow.

The “states” and “state transition variables” for the state

diagram resulted from identifying the sequence of

conditions (identified in the stability analysis) that

would result (if not mitigated) in violations and

possibly in a Double Unit Outage. The potentially

“unstable” events are classified into three categories,

namely:

Category 1: Two lines are tripped / or opened within a

“short” (10 seconds) period of time

Category 2: One line has been out (greater that 10

seconds) and there is either a protective trip or an

outage on a second line

Category 3: A Breaker Failure occurs with an

accompanying “severe” undervoltage condition

There are two types of power system events that can

result in a line outage, namely, a Faulted Line

Protective Trip (Line Trip) or Line Outage (local or

remote). These two types of line out events result in 4

possible states / transitions:

• Line Trip followed by a second Line Trip

• Line Trip followed by a second Line Outage

• Line Outage followed by a second Line Trip

• Line Outage followed by a second Line

Outage5

Figure 6 shows the various states of 1 or 2 lines out and

the state variables required to “transition” from one

state to the next.

One of the state transition variables is “time”. For

example, time come into play when a line is tripped or

outaged and no other events occur in a 10 second

window since oscillations resulting from a single line

outage event will damp out over this time period. If a

second trip or outage does occur after the 10 second

time frame, the criteria for transitioning to a 2-line out

trip condition changes, specifically, the power level at

which a DUO would occur increases.

5 Generator trip for this combination of events prevents

oscillatory instability.

74



Figure 6 - Simplified State Transition Diagram

Breaker Failure - Category 3 Event:

A breaker failure action may require tripping a unit

depending on:

• The breaker that has failed (Note: a breaker failure

on a unit breaker always trips the respective unit).

• The output power level of both units

• The severity of the fault

Specifically, a close-in 3-phase fault followed by failure

of one of the 3 poles of one breaker to trip may result in

rotor acceleration and unstable generator condition. To

detect this condition, the positive sequence 500 kV

voltage is monitored and if the voltage dip is initially

below a certain level ε1 and the subsequent recovery

stays below ε2 (at least one breaker pole failed to trip),

the scheme will arm to trip a unit. As there are voltage

measurements available from each step up transformer,

if a Voltage Transformer Fuse Failure is detected on

either voltage source, that source is blocked from

providing input to the SIPS.

In order for a trip decision to be made when a breaker

failure input is received, there are several state variable

conditions that must be met, specifically

• The breaker was closed prior to receiving the

BF trip

• A breaker trip signal was received

• A Breaker Failure Trip was issued

• The output power level of both units was

greater than a specific value

• The voltage on the 500kV bus dipped below εεεε1

for at least 1 cycle and was below εεεε1 at the

time the breaker failure trip was issued

Figure 7 shows the profile for the undervoltage

condition described above.

V1 < εεεε1

V1 < εεεε2

time

1~V1

V1 < εεεε1

V1 < εεεε2

time

1~V1

Figure 7 - Breaker Failure Undervoltage Profile

75



Generator Selection Logic

A manual switch is provided for selecting which unit to

be armed for tripping. Even though a selector switch is

provided, the logic only uses the switch position as a

“recommendation” if possible when determining which

unit to trip. In reality, for a given double-line outage

scenario, there is typically only one unit that can be

tripped without automatically taking out both units.

For example, if the Gates line (breakers 622 & 722) and

the Midway3 line (breakers 632 & 732) are tripped, the

only option the system has it to trip Unit 1 as tripping

Unit 2 removes the only remaining outlet.

Use of a Karnough map (K-map) technique provides a

simple and methodical approach to ensure all outage

conditions are considered for a specific event analysis.

The results of the K-Map provide the most efficient

Boolean logic to satisfy unit tripping equations. Figure

8 shows an example of the K-map for the loss of the

Gates and Midway #3 line breakers open, the SIPS

response is based on the state of the remaining breakers

(532, 542, 642, and 742).

By considering the status of the four breakers not

affected by the line loss, a determination is made as to

which unit, (if either), will be tripped by the scheme.

The K-Map shown is rather basic and can become more

detailed when considering breaker failure scenarios.

Figure 8 – Simplified Karnough Map (K-Map) for

Equipment Outage Analysis Tool

Scheme Performance - Reliability and Security

i. System Reliability

Security and dependability are designed into the

scheme at many levels to avoid unnecessary tripping of

the generators. Various measures are incorporated in

the design, hardware, measuring elements, and the

software logic to enhance both the reliability and

dependability of the SIPS. The security measures per

systems include:

• System Topology and Demarcation of

hardware and design

• Device Error Supervision

• Redundant telemetry

• Voltage supervision

• Inter-system state comparison

• Dual trip contacts in series

• Lockout contacts in trip circuit

ii. System Topology Supervision

The implemented scheme will trip a Unit only if it

results in a benefit to the system. Many events, either

due to the type of event or the initial operational

configuration of the 500kV bus, will result in the

removal of one or both units. If the initiating event

removes one or both units, DCSPS will not issue a trip.

For example:

• If a pre-existing switching condition followed

by a line outage results in a double line trip /

outage and also disconnects one generator

from the system, there is no need to trip a

generator.

• When only one generator is on-line, there is no

need to trip a generator.

• If a breaker failure operation will result in the

separation of a unit, there is no need to trip a

generator.

iii. Critical Alarm Supervision

The system will take itself off line if any one of the five

relays in the system has a critical alarm condition.

Critical alarms can be caused by device failure (internal

relay monitoring), power supply failure or double fiber

break in the communication ring.

iv. Double Line Outage Without Trip

Generators may become unstable following a double

line outage caused by a non-relay trip if the voltage is

below a specified threshold determined by system

studies. For those double-line outage scenarios, the unit

trip decision is “supervised” by the generator 500kV

voltages and is restrained if the voltage is above a pre-

determined level.

v. “Fail-Safe / Veto Logic”

This portion of the scheme logic could be easily

described as supervisory or “Cross Blocking” logic

because each system can be blocked from tripping by

the alternate system when there is a disagreement.

System “A” and System “B” exchange information

regarding decision to trip over hard-wired connections.

76



Since the two Systems each receive independent inputs

from CTs, PTs and breaker seals, they may have

different response times to a power system event.

Therefore, there is allowance for differences in output

times due to data / calculations variances of the two

systems plus a margin for each scheme to complete its

evaluations. Also, it is possible that System “A” could

receive a different input, such as breaker status, than

System “B” and could issue a different trip command or

fail to issue a trip based on that information. The time

allowance is within the throughput timing of the

scheme for the severe system faults and is above and

beyond all other logic performance security measures.

In the worst case, a disagreement in decision to

selecting a unit to trip may arise between System “A”

and System “B”. System “A” could determine Unit #1

should trip while System “B” SIPS could determine

Unit #2 should trip. Each SIPS compares the outputs

with results from the redundant system prior to issuing

a trip, thereby significantly reducing the possibility of

un-intentionally tripping both units.

The following actions are taken based on information

received by each System. Note, these actions are

described based on System “A” logic, but similar logic

is implemented in System “B”:

a. When System “A” and System “B” agree to

trip the same unit (A=B), an immediate trip is

issued to trip the selected / armed unit.

b. When System A=Trip and System B= “No

Decision”, System “A” trips alone. For

example, if System “A” makes a decision to

trip Unit #1 but it does not immediately

receive a corresponding input from System

“B”. If there is no response from System “B”

within a preset time, then Unit #1 will be

tripped by System “A”. The time delay is

provided to allow resetting of any transient

data that may have been received by one

System alone as well as to allow the “lock-

out” function to operate.

c. When A≠B, No trip. If System “A” makes a

decision to trip Unit #1, and System “B”

makes a decision to trip Unit #2, no trip action

is taken and both systems are locked out and

alarmed. The scheme provides an alarm and

the sequential event recording will reflect the

steps leading to the disagreement between the

two systems as it pertains to the SIPS.

d. When A=Trip AND B=System critical failure

OR B=Cut Out, System “A” trips alone. If

there is a failure of one System, or one system

is cut out, the remaining system can trip

independently.

Note: There are additional plant protective devices that

would respond to abnormal system conditions if the

conditions occur. For example, out of step protection

and 12 kV undervoltage protection, both result in a

DUO. Those devices detect and operate independently,

are not part of the SIPS, but their non-operation was

used as the main condition in SIPS setting selection.

The out-of-step blocking modules of 500 kV line are

enabled to avoid line trips by distance protection before

SIPS actions achieve their effect.

In addition to the fail-safe algorithms, there are

provisions to prevent inadvertently defeating the

primary objectives of the scheme; only separating one

unit when necessary to maintain resources and system /

plant stability. The following section describes such

provisions as part of scheme dependability.

vi. Scheme Performance Security

The first system to issue a unit trip blocks any output

from the second system to prevent the SPS from

tripping both units for one event. This is accomplished

by wiring latching contacts in the trip circuits for each

system.

Figure 9 - Output Trip Logic

• System “A” latching contacts for the non-

tripping unit will open either by a System “A”

trip OR a System “B” trip.

• System “B” latching contacts for the non-

tripping unit will open either by a System “B”

trip OR a System “A” trip.

Reset Pushbutton

532 TC1 PRI (F1)

Operate

Seal-In

532 TC1 SEC (M1)

Operate

Seal-In

532_SUP_TC1 (U1)

Operate

ResetOther Unit Trip

Unit Trip

Bkr Closed

Trip 2

Trip 1

LO

Reset Pushbutton

532 TC1 PRI (F1)

Operate

Seal-In

532 TC1 SEC (M1)

Operate

Seal-In

532_SUP_TC1 (U1)

Operate

ResetOther Unit Trip

Unit Trip

Bkr Closed

Trip 2

Trip 1

LO

77



• Operator intervention is required to reset the

scheme-latched conditions. The latched

conditions require a RESET in order for the

respective System “A” to reset. System “B”

latching contacts will close only when the

System “B” is reset, Figure 9.

vii. Voting vs. Vetoing Scheme Overall

Operation

In the development of the SIPS, engineering

requirements should be carefully reviewed and the

solutions to the requirements should be carefully

evaluated.

Arguably, either a voting scheme or a vetoing scheme

would offer the same degree of dependability. Of

concern is the incorrect operation of the SIPS

associated with disagreement of the redundant SIPS

when the SIPS is called upon to activate. The vetoing

scheme mitigates the possibility of incorrect SIPS

operation due to misinterpretation of inputs and / or

data.

In addition, the vetoing scheme offers an order of

magnitude in reduced components and space, and

complexities in design, implementation, and testing

while maintaining performance reliability for this SIPS

project.

Scheme Testing

A detailed test plan is prepared as part of the overall

implementation. A combination of the Logical

Architecture, Logic Design, and the Physical

Architecture are used in preparation of the test plan.

The test plan includes the lab testing, field-testing,

study validation, and automatic and manual periodic

testing amongst other tests to satisfy performance and

reliability [6].

i. Lab Testing and Demo

Lab testing is designed to validate the overall scheme in

a controlled environment. Lab tests permit controlled

inputs from numerous sources with frequent checks of

the output at every stage of the testing process. The lab

tests ensure that the desired results are achieved in the

lab environment to minimize field debugging. Lab

testing also provides an environment for information

exchange and participation input of all stakeholders.

ii. Commission Testing

Field commissioning tests are carried out to check the

performance of the SIPS under real system conditions.

The telemetry data and the dynamics of various power

system configurations such as breaker close and bypass

contacts (such as maintenance switch) are all validated.

Total throughput time is measured to assure

implementation meets design criteria.

The possible scenarios of unavailability of devices at

the time of execution of a command signal in a given

station all need to be tested. In general, every input

point and every logic condition is validated against

expected results. Additionally, the effect of DC

transients is tested thoroughly in the field before putting

the scheme into service.

iii. Periodic Testing (Input / Output)

A proper test plan to simulate line outage are conducted

on a periodic basis to test the contingency plans and as

a learning curve for better understanding of the SIPS.

The SIPS design permits taking one system out of

service to conduct these tests.

Test Scenarios Using State Variables:

State variable approach to the logic design provides a

clearly defined suite of test cases common to all the

various test processes from lab, to commissioning, to

period maintenance.

As each state has a unique set of state variables that

have to be true to enter the given state, the ensemble of

state variable conditions defines a matrix of test cases –

each with a unique set of variables.

Note: Testing of such schemes should also include

both positive and negative state variable tests.

Conclusion

The SIPS described in this paper is designed to prevent

the loss of two generating units for well-defined system

events that could cause unstable oscillations between

the units and the WECC system. Implemented using

commercially available IEDs and configured as two

identical systems operating in parallel for redundancy,

this SIPS meets the performance requirements defined

by system studies. This project also illustrates the

choices made to create the best fit for the engineering

requirements in specific, the merits of vetoing scheme.

Although the scheme is designed for reliability, a

vetoing logic is added for security preventing the SIPS

itself from tripping two units for any system event. The

scheme is in service and has already proven valuable in

allowing the plant to run at full load of two units during

some transmission system clearances that would

otherwise have required curtailments to generation. As

the utility industry strives to improve the availability of

electric power delivery, System Integrity Protection

Schemes (SIPS) will be front and center as one means

of achieving this goal.

References and Further Reading:

1. L. B. Barrentine., An Introduction to Design of

Experiments, ASQ Quality Press, 1999.

78



2. Meklin et al., Obtaining Emergency Control

Models using Statistical Experiments on Detailed

Power System Simulator. In: Power System

Stability and Emergency Control, ВНИИЭ,

Moscow, Энергоиздат, 1982 (in Russian)

3. J. Sykes, M. Adamiak, G. Brunello;

Implementation and Operational Experience of a

Wide Area Special Protection Scheme on the SRP

System; Georgia Tech Relay Conference; April 27-

29, 2005.

4. The RAS Book. A Comprehensive Handbook for

Remedial Action Schemes. Hardware, Software,

Operations and Procedures. PG&E, December

2004.

5. V. Madani, D. Novosel, A. Apostolov, S. Corsi

Innovative Solutions for Preventing Wide Area

Disturbance Propagation, International Institute for

Research and Education in Power Systems (IREP),

August 2004.

6. CIGRE-TF.38-02-24, “Defense Plans Against

Extreme Contingencies”, August 2006

7. V. Madani, M. Adamiak, M. Thakur - Design and

Implementation of Wide-Area Special Protection

Schemes

8. Vahid Madani; Western Interconnection

Experience with Synchronized Phasor

Measurements; IEEE PSCE 2006.

Biographies:

Vahid Madani is a registered Electrical Engineer with

more than 23 years of academic and utility experience. Vahid

He has been a member of several investigative and restoration

recovery task forces including the 1989 San Francisco and

1994 Los Angeles Earthquakes and the 1994 – 1996 Western

Interconnection Disturbances.

Vahid is a Tau beta Pi member and has a MS Degree in

Power system from University of Idaho. Mr. Madani has

various technical, advisory, and leadership roles within the

North America and Internationally. He is Chair of the

Remedial Action Scheme Reliability Subcommittee in the

Western Electricity Coordinating Council (WECC), and

Chairs committees in IEEE and CIGRE.

Vahid has contributed to the development of many advance

applications in power system protection and control. He is an

invited author, panelist and speaker in system automation,

protection & controls applications, and practical wide-area

monitoring systems with advance warning and fast

restorations. He is a senior IEEE member and has over 50

refereed publications in professional journals and conferences

including:

• Blackout Prevention - McGraw Hill Yearbook of

Science and Technology 2006

• Getting a Grip on the Grid, IEEE Spectrum,

December 2005

• Shedding Lights on Blackout, IEEE Power and

Energy Magazine, January / February 2004

Ed Taylor is a registered Electrical Engineer with more

than 39 years of experience in System Protection in the utility

business covering applications from distribution protection to

500kV EHV protection. He has a MSc EE degree in Power

Engineering from Santa Clara State University. Ed is a

member of the IEEE PES, the Western protective Relay

Conference (WPRC) Planning Committee and a WECC

Relaying Working Group member. Ed is one of the original

members of the Pacific AC Intertie Remedial Action Scheme

(PACI RAS) project at PG&E. Ed has contributed to many

Guides in WECC protection applications.

Davis Erwin received his BSEE and MSEE in 1997 and

1998 respectively from New Mexico State University. Davis

is a registered professional engineer in California and has

been with PG&E system protection since 1999 primarily

supporting 500kV system projects and Special Protection

Schemes.

Anatoliy Meklin received his M.S. and Ph.D. degree in

Electrical Engineering from St. Petersburg Technical

University, Russia in 1968 and 1978, respectively. He

worked for 23 years for the Engineering and Research

Institute of High Voltage Power Systems

(Энергосетьпроект), St. Petersburg, Russia. Since 1999, Dr.

Meklin has been with Pacific Gas & Electric Company,

California and is a member of the WECC Modeling and

Validation Work Group and Load Modeling Task Force.

Anatoliy has been involved in a wide range of projects related

to power system analysis and control system development. He

is an author of many inventions and publications in the fields

of electric power system analysis and remedial action

schemes. He is a registered Professional Engineer in

California and North Carolina.

Mark Adamiak received his Bachelor of Science and

Master of Engineering degrees from Cornell University in

Electrical Engineering and an MS-EE degree from the

Polytechnic Institute of New York.

Mark started his career with American Electric Power (AEP)

in the System Protection and Control section where his

assignments included R&D in Digital Protection, relay and

fault analysis, Power Line Carrier and Fault Recorders. In

1990, Mark joined General Electric where his activities have

ranged from development, product planning, and system

integration.

Mr. Adamiak has been actively involved in developing the

framework for next generation relay communications and was

the Principle Investigator on the Integrated Energy and

Communication System Architecture, now IntelliGrid. Mark

is a Fellow IEE and past Chairman of the IEEE Relay

Communications Sub Committee, and a member of the US

team on IEC TC57 - Working Group 10 on Substation

Communication.

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Analysis of PSB and OOS relays using

COMPTRADE files Juan M Gers, PhD Jaime Ariza

GERS USA MEGGER

Weston, Florida Dallas, TX

[email protected] [email protected]

Abstract- This paper reviews the behavior of electrical

systems when they are subjected to oscillations which can

cause that one or more synchronous machines loose

synchronism with each other. The paper makes a detailed

reference to power swing blocking and out of step relays

whose operation has to assure adequate protection under

these conditions. A thorough procedure to carry out the

setting of Out of Step relays is proposed. This is illustrated

with a case study that includes transient stability runs and

a methodology to generate COMTRADE files and use

them to analyze relay performance.

I&DEX TERMS

Generator Protection, Distance Protection, Out of Step

Protection, Loss of Synchronism, Power Swing Blocking,

Transient Stability.

1. I&TRODUCTIO&

Electrical power systems are exposed to a variety of abnormal

operating conditions such as faults, loss of generators, line

tripping and other disturbances which can result in power

oscillations and consequent system instability. Under these

conditions appropriate relay setting is essential to assure proper

protection, this is, the disconnection of generators that loose

synchronism and the blocking of distance relays associated to

HV lines, whose operation is not required. This topic is

receiving especial attention after the blackout of August 14th

,

2003, that affected severely millions of users in the Midwest

and Northeast of the US Electrical system, when it was evident

that many relay schemes did not perform appropriately.

Transient stability studies are aimed to determine if the system

will remain in synchronism following major disturbances. The

nature of these problems do not allow the linearization process

to be used but the solution of nonlinear differential and

algebraic equations by direct methods or by iterative step-by-

step procedures.

Usually the time period under study is the first second

following a system fault. If the machines of the system are

found to remain in synchronism within the first second, the

system is said to be stable. Multiswing stability problems must

consider effects over an extended time period. Models of

higher sophistication must be used to reflect accurately the

machine behavior.

2. TRA&SIE&T STABILITY CO&CEPTS REVIEW

Transient stability concepts will be reviewed with a simple

lossless transmission line connecting two sources

corresponding to a generator at a location S and an equivalent

network at a location R. It is well known that the active power,

P, transferred from the generator into the network can be

expressed as:

)1(δSinX

VrxVsP =

Where Vs is the sending-end source voltage magnitude, Vr is

the receiving-end source voltage magnitude, δ is the angle

difference between the two sources, and X is the total

reactance of the transmission line that connects the two

sources.

With fixed Vs, Vr and X values, the relationship between P

and δ can be described in a power angle curve as shown in

Figure 1. Starting from δ = 0, the power transferred increases

as δ increases. The power transferred reaches the maximum

value PMAX, when δ is 90 degrees. After that point, further

increase in δ will result in a decrease of power transfer.

P

0

0

PMAX

180δ 90

δ

P

0

0

PMAX

180δ 90

δ

Figure 1 Power Angle Curve

During normal conditions, the output of electric power from

the generator produces an electric torque that balances the

mechanical torque applied to the generator rotor shaft. The

rotor therefore runs at a constant speed with this balance of

electric and mechanical torques. When a fault occurs, the

amount of power transferred is reduced and so the electric

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torque that counters the mechanical torque. If the mechanical

power is not reduced during the period of the fault, the

generator rotor will accelerate proportionally to the net surplus

of torque input.

Thorough developments of this concept, as well as the so

called equal-area criterion are explained in detail in most

power systems books and numerous papers and therefore are

not treated in this paper.

When an unstable condition exists in the power system, one

equivalent generator rotates at a speed that is different from the

other equivalent generator of the system. Such a condition is

referred to as a loss of synchronism or an out-of- step condition

of the power system.

If such a loss of synchronism occurs, it is imperative that the

generator or system areas operating asynchronously be

separated immediately using out-of-step protection systems-

OST identified as 78. On the other hand, it is important that

distance relays do not operate for oscillations of the system

which might bring the swing impedance locus to its protective

zone coverage. This is achieved with Power Swing Blocking -

PSB relays identified as 68. Setting criteria for both types of

relays will be discussed in the following sections.

3. IMPEDA&CES SEE& BY RELAYS

During power system oscillations the voltage and current

which feed the relay vary with time and, as a result, the relay

will also see an impedance that is varying with time which may

cause it to operate incorrectly. The equivalent circuit for an

analysis considering two sources VS and VR is shown in Figure

2. Vector and impedance diagrams corresponding to the system

of Figure 2, are shown in Figures 3 and 5 respectively.

A B VRVS

ZS ZRZL

A B

A B VRVS

ZS ZRZL

A B

Fig. 2 Equivalent circuit for analysis of power system

oscillations

I ZS

0

S

S

SV

I ZS L

SI

VA

V

BV

RI ZS

R

δ

RS

I ZS

0

S

S

SV

I ZS L

SI

VA

V

BV

RI ZS

R

δ

RS

Figure 3 Vector diagram for system of Figure 2

δS

S

V V

SI

SV

A

SI

0

= ZB

SI

V

I

R

S

AZS LZ

BR

R

Z

δS

S

V V

SI

SV

A

SI

0

= ZB

SI

V

I

R

S

AZS LZ

BR

R

Z

Figure 4 Impedance diagram for system of Figure 2

4. POWER SYSTEM BLOCKI&G OF DISTA&CE

RELAYS

To illustrate the situation involving a distance relay during

such oscillations, consider the equivalent circuit of the power

system shown in Figure 2. Assume that there is a transfer of

power from the source of supply, S, to the most distant load at

R. The current, IS, which flows from S towards R causes a

voltage drop in the system elements in accordance with the

vector diagram shown in Figure 3. The value of δS, the phase

difference between VS and VR, increases with the load

transferred.

The impedance measured by the distance relay situated at A is

Z = VA/IS; the expression for this impedance can be obtained

starting from the voltage VA which supplies the relay:

VA = ISZL + ISZR + VR (2)

VA/ IS = ZL + ZR + VR/IS (3)

From Figure 3, the last equation can be easily drawn by

dividing the vectors by the current IS. In this way the diagram

of system impedances, which is shown in Figure 4, is obtained

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in which all the parameters can be assumed to be constant

except IS and δS, which are variable and depend on the power

transfer. The increment of load transferred brings with it an

increase in IS and δS. This results in a reduction in the size of

the vector VA/ IS, (see Figure 4), and, if the increment of load is

sufficiently large, the impedance seen by the relay (VA/ IS) can

move into the relay operating zones, as shown in Figure 5.

Z

Increase in when

R

LZ

S

S

A

S

S

ISAV /

I

V

S

by the relayImpedance seen

O

SI

Q

ZX

R

R

B

V

S R

R

V = VS

δ

δ

Z

Increase in when

R

LZ

S

S

A

S

S

ISAV /

I

V

S

by the relayImpedance seen

O

SI

Q

ZX

R

R

B

V

S R

R

V = VS

δ

δ

Figure 5 Impedance seen by the relay during power system

oscillations

Figure 5 is obtained by constructing an R-X plane over the

locus of the relay A, and then drawing over this the relay

operating characteristic and the diagram of system impedances.

The relay at A will measure the value of the impedance ZL for

a solid fault to earth at B and continuously measure the

impedance represented by AO. If a severe oscillation occurs

then the load angle δS increases and the impedance measured

by the relay will decrease to the value AQ', which can be inside

the relay operating characteristic. The locus of the impedance

seen by the relay during oscillations is a straight line when VS

= VR, as in Figure 5. If VS > VR, the locus is a family of circles

centered on the SR axis. A typical trajectory which delineates

the impedance in the R-X plane during a power oscillation is

shown in Figure 6. Consequently, the trajectory passes inside

the relay operating characteristic, indicating that there will be a

possibility for the associated breaker to be tripped in the

presence of system oscillations.

Power oscillation

Blocking relaycharacteristic

S Rwith V > V

Load characteristic

Zone 2

Zone 3Measuring unit

Zone 1

Power oscillation

Blocking relaycharacteristic

S Rwith V > V

Load characteristic

Zone 2

Zone 3Measuring unit

Zone 1

Figure 6 Blocking characteristic to prevent relay operation

during power system oscillations here

In order to prevent the operation of the relay during

oscillations, a blocking characteristic is used (see Figure 6).

The trajectory of the swing impedance locus crosses the

characteristics of the measuring and blocking units. If the

measuring units operate within a given time, and after the

blocking unit has operated, tripping of the breaker is permitted.

On the other hand, if the measuring units have not operated

after a predetermined time delay, the breaker will not be

tripped. Thus, under fault conditions when the blocking and

measuring units operate virtually simultaneously, tripping

takes place. However, under power oscillation conditions,

when the measuring units operate some time after the blocking

unit, tripping is prevented.

To prevent operation of the relay during oscillations, a power-

swing blocking unit is added. The diameter, or reach, of its

characteristic for mho relays is generally 1.3 or more times the

diameter of the outermost zone of the relay, which is usually

zone 3. During fault conditions the displacement of the swing

impedance locus seen by a distance relay is much faster than

during power swings. This fact is used to set the power swing

blocking unit, which is then inhibited if there is a time elapse

of typically 0.1 s or less, to enable the swing impedance locus

to move from the power-swing blocking characteristic into

zone 3 or outermost relay characteristic. Manufacturers will

usually supply recommendations for setting this unit, when

provided, depending on the actual relay types being used, and

the values given above should therefore be used as general

guidelines only.

5. OUT OF STEP PROTECTIO&

The Out-of-Step function is used to protect the generator from

running under out-of-step or pole slip conditions. There are

different ways to implement Out of Step Protection. One of the

commonest types uses one set of blinders, along with a

supervisory MHO element. As shown in Figure 7.

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The pickup area is restricted to the shaded area, defined by the

inner region of the MHO circle, the region to the right of the

blinder A and the region to the left of blinder B.

Figure 7 Out of step relay with one set of blinders

The following conditions have to be satisfied for operation of

out of step relay using the blinder scheme:

• The positive sequence impedance must originate

outside either blinder A or B.

• It should swing through the pickup area and progress

to the opposite blinder from where the swing had

originated.

• The swing time should be greater than the time delay

setting

When this scenario happens, the tripping circuit is complete.

The contact will remain closed for the amount of time set by

the seal-in timer delay.

The setting of 78 elements is carried out with the procedure

presented as follows. Figure 8 helps to illustrate the

impedances calculation.

A B

D

P

M

R

Swing Locus

ELEMENTMHO

X

d

δ

C

ELEMENTSBLINDER

ELEMENTPICK-UP

ELEMENTPICK-UP

A B

1.5 X TG

2X´d

XmaxSG1SYSTEM

O

TRANSTGX

O

GENdX´

A B

D

P

M

R

Swing Locus

ELEMENTMHO

X

d

δ

C

ELEMENTSBLINDER

ELEMENTPICK-UP

ELEMENTPICK-UP

A B

1.5 X TG

2X´d

XmaxSG1SYSTEM

O

TRANSTGX

O

GENdX´

Figure 8 Procedure to set out of step relays

1. Model the overall system and carry out transient

stability runs for representative operating conditions.

The modeling of the generators should include the

voltage regulator, generator governor and PSS if

available.

2. Determine values of X’d, XTG and XmaxSG1. The

summation makes up the so called line of impedance.

3. Set the Mho unit to limit the reach to 1.5 times the

transformer impedance in the system direction. In the

generator direction the reach is typically set at twice

generator transient reactance. Therefore the diameter

of the MHO characteristic is 2X’d + 1.5XTG.

4. Determine by means of the transient stability runs, the

critical angle δ between the generator and the system.

This happens at the point where the system just gets

unstable.

5. Determine the blinder distance d, which is calculated

with the following expression:

6. Determine the time for the swing impedance locus to

travel from the position corresponding to the critical

angle to that corresponding to 180°. This time is

obtained from the rotor angle vs. time curve which is

generated by the transient stability study, for the case

just when the system experiences the first slip.

(4)

−

++= )2/90(tan

2

1max

´

δxXXX

dSGTGd

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7. With the above value times two, determine the time

taken by system to travel within the blinders. This

gives the reference to set the out of step relay.

6. CASE STUDY

Consider the power system of the Figure 10, corresponding to

the Example 14.9 from the book ‘Elements of Power System

Analysis by William D. Stevenson. This case is used to

illustrate the procedure to determine the critical clearing time

and the traveling time within the blinders of an Out of Step

relay by means of a transient stability study. The other settings

of the relay are rather straightforward as they depend on the

reactances of the elements and will not be illustrated here. The

transient stability analysis will be carried out considering a

three-phase fault over line L_45, near node 4.

Figure 10 Power system for example

6.1 CONSIDERATIONS

The considerations to analyze the example are the following:

• The fault inception will be considered at t = 0.5 s

• Clearance times starting at t = 90 ms (Approx. 5

cycles) will be analyzed in consecutive steps of 10

ms.

• For each case, the fault is removed with the

consequent outage of the line.

• The voltage regulator is IEEE type ST1 Excitation

System. This voltage regulator is of static excitation

type where the rectifiers provide enough DC current

to feed the generator field. The model represents a

system with the excitation power supplied from a

transformer fed from the generator terminals or from

the auxiliary services and is regulated by controlled

rectifiers.

• The turbine-governor is IEEE type 1 Speed

Governing Model. This model represents the system

of speed control (Mechanical-Hydraulic) and the

thermal steam turbine.

• For this machine no power system stabilizer is

available.

The models for the voltage regulator and governor are shown

in the figures 11 and 12.

Figure 11 IEEE type ST1 Excitation System

Figure 12 IEEE type 1 Speed Governing Model

6.2 CRITICAL CLEARING TIME

Determining the critical clearing time is perhaps the most

elaborate part of the entire setting process. To achieve this,

several runs of the transient stability study have to be done to

determine when the system looses synchronism or has the first

slip.

6.3 RESULTS

The transient stability analysis was made for a three-phase

fault over line L_45, near node 4. The solution was obtained by

using a software package called NEPLAN®. The results

corresponding to the load flow conditions prior to the fault are

shown graphically in Figure 13 by the software package as

follows:

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Figure 13 Load flow results

Numerous cases were run with clearing times starting at t = 90

ms with increments of 10 ms in an iterative process until

stability was lost. The results of three representative cases were

analyzed and correspond to the critical clearing times obtained

that are shown in the following table.

Several plots from the transient stability runs can be obtained

for a myriad of applications. For setting OST elements the

most important ones are those related to Rotor Angle vs Time

and R vs X . From the respective plots it is observed that in

Case 1 with a clearing time of 0.09 s the system remains in

synchronism. In Case 2, G_1 the system is still in synchronism

with a clearing time 0.18 s. For case 3, G_1 the system looses

synchronism when clearing time is 0.19 s. From the above it is

clear that the critical time to clear the fault of the generator

G_1 is equal to 180 ms after fault inception.

The rotor angles for the three cases are shown in Figure 14,

from which it can be seen that the critical angle is

approximately 140°. The time for the swing impedance locus

to travel from that critical angle to 180° is approximately 0.25

s. Therefore the traveling time within the blinders should be set

at 0.5 s.

This figure also illustrates the benefit of having voltage

regulator and voltage governor responses which are shown

with the continuous lines. Under these conditions, the

performance of the system is a lot better as those when there

are not controls.

It can be observed that when there are not controls, the

excursions of the rotor angles are higher especially from the

second oscillation upwards and also that the system tends to

stabilize faster.

Rotor Angle Generator G_1

-40

-20

0

20

40

60

80

100

120

140

160

180

200

220

240

260

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Time (s)

Angle (degree)

Case1 (tc=90 ms), with controls



Case1 (tc=90 ms), without controls



Figure 14 Rotor angle vs Time form the three cases considered

6.4 ANALYSIS OF R VS X DIAGRAMS

R vs X diagrams for the three cases show the trajectory

followed by the impedance seen by the relay during the

disturbances. When there is an oscillation in the generator

which is stable, the swing locus does not cross the line of

impedance.

When there is an Out of Step in the generator, the transient

swing crosses the line of impedance of the system each time a

slip is completed and the relay should disconnect the generator.

Figure 15a shows the diagram R vs X for cases 1, 2 and 3. In

the first two it is clear that the load point does not cross the line

of impedance of the system. For case 3, the load point crosses

the line of impedance indicating therefore that synchronism is

lost and therefore Out of Step operation must be allowed.

Figure 15b shows simultaneously the diagrams for the three

cases.

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

R (Ohm)

X (Ohm)

Generator Impedance Line

Case 1

Case Fault Clearance Time

(ms)

Case 1 90

Case 2 180

Case 3 190

Case Fault Clearance Time

(ms)

Case 1 90

Case 2 180

Case 3 190

CaseCase Fault Clearance Time

(ms)

Fault Clearance Time

(ms)

Case 1Case 1 9090

Case 2Case 2 180180

Case 3Case 3 190190

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-16.0

-14.0

-12.0

-10.0

-8.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

-10.0 -5.0 0.0 5.0 10.0

R (Ohm)

X (Ohm)


Case 2

-2.0

-1.5

-1.0

-0.5

0.0

0.5

-1.0 -0.5 0.0 0.5 1.0 1.5

R (Ohm)

X (Ohm)


Case 3

Figure 15a Diagram R vs X for cases 1, 2 and 3

-16.0

-14.0

-12.0

-10.0

-8.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

-10.0 -8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0 10.0

R (Ohm)

X (Ohm)

G1, tc=90 ms G1, tc=180 ms G1, tc=190 ms Impedance Line

Figure 15b Diagram R vs X for cases 1, 2 and 3 simultaneously

7. SIMULATIO& WITH COMTRADE FILES

The appropriate response of numerical relays under transient

swings is obviously vital to assure that the power system will

react adequately. It is then important to restrain the operation

of the distance relays with the Power Swing Blocking elements

and allow the operation of the Out of Step relays and so

remove from service those generators prone to lose

synchronism.

For this purpose it is very important the use of the IEEE

Standard Common Format for Transient Data Exchange

(COMTRADE) files. Standard IEEE Std. C37.111-1999

defines this format for files containing transient waveform and

event data collected from power systems or power system

models.

As indicated in the standard, each COMTRADE record has a

set of up to four files associated with it, as follows:

• Header (xxx.HDR)

• Configuration (xxx.CFG)

• Data (xxx.DAT)

• Information (xxx.INF)

The Header and Information files are optional and therefore are

not very critical. The Configuration file is an ASCII text file

intended to be read by computer program and therefore must

be saved in a specific format. The Data file contains the value

for each input channel for each sample in the record. Therefore

at least the Configuration and Data files have to be generated

to achieve a proper analysis of the relays.

There are many packages offering good calculations for

transient stability analysis. By exporting the results so

produced to Excel files, it is possible to generate COMTRADE

files. The procedure is simple following the guidelines of the

standard referred. It consists basically in exporting the results

given by the transient stability program into an Excel sheet as

shown in figure 16.

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Figure 16 Results in Excel format for example of case study

From here only the columns of time and the magnitudes

(voltage and current) are selected. With this information the

files with extensions .cfg and .dat are obtained. The figures 17

and 18 show the samples for the case study considered in this

paper.

Figure 17 File .cfg for example of case study

Figure 18. File .dat for example of case study

The results obtained with one of those packages, NEPLAN®

were taken to generate COMTRADE files as per IEEE Std.

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C37.111-1999. Figure 19 shows the COMTRADE file

obtained for the A Phase current of system of the case study of

Figure 11 when the fault is cleared 0.18 seconds after its

inception. As this file is in COMTRADE format, it allows

enhancing and automating the analysis, testing, evaluation and

simulation of the system and related protection schemes during

fault and disturbance conditions.

In particular the testing of Out of Step Relays with these files

can be tested to assure a proper operation under transient

swings of the system.

Figure 19 Comtrade File Corresponding to the Phase A Current

of Case Study

Modern testing equipment allows reproducing analog signals

from these files and so achieving a comprehensive relay

testing.

It is highly convenient to reproduce these analog signals at

which a relay will be submitted, in order to check its

performance with appropriate testing devices capable of

handling COMTRADE files. Analyzing relays performance

beforehand with this type of technique assures a more reliable

response.

8. CO&CLUSIO&S

This paper provides general guidelines on the application

of power swing blocking and out-of-step relaying for

generators. This protection should be installed virtually on

any generator if the electrical center of the swing passes

through the region from the high-voltage terminals of the

step-up transformer down into the generator. This

condition tends to occur in a relatively tight system or if a

low excitation condition exists on a generator. Unit out-of-

step protection should also be used if the electrical center

is out in the system and the system relays are blocked or

not capable of detecting the out-of-step condition.

Power Swing Blocking relays avoid unnecessary line

disconnection during swings. Out of Step relays are very

important and reliable to determine truly slip conditions of

synchronous generators.

From the formulation it is clear that there are ways the

protection system can mitigate the affect of the fault on the

power swing which includes: fast clearing to minimize the

time that the fault is reducing the transfer capability; use

of pilot systems to clear both ends fast; use of breaker

failure systems to reduce the worst case situation;

implement single pole tripping to allow transfer of energy

during breaker open time; implement high speed reclosing

and load shedding whenever practicable.

Transient stability studies are essential to determine the

behavior of an electrical system subjected to oscillations

following disturbances in the networks and require an

appropriate modeling of the system. Among other reasons,

transient stability studies should be conducted to properly

set out of step relays since they provide the critical angle

and the traveling time of the swing locus within the

blinders set. Ideally the result of transient stability studies

should be used also to generate COMTRADE files and

achieve a better relay testing.

-50000.000

-40000.000

-30000.000

-20000.000

-10000.000

0.000

10000.000

20000.000

30000.000

40000.000

50000.000

1 175 349 523 697 871 1045 1219 1393 1567 1741 1915 2089 2263 2437 2611 2785 2959 3133 3307 3481 3655 3829 4003 4177 4351 4525 4699 4873

Time

IAxSEN(wt)

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In particular, the modeling should include the operation of

voltage regulators, governors and power systems

stabilizers as applicable. From the example of the case

study it is clear the effect of these elements to enhance the

performance of the system under transient swings.

REFERE&CES

• BASLER ELECTRIC, Summer Relay School Notes, St. Louis,

June 2003

• BECKWITH ELECTRIC Instruction Manual Relay M-3425, Largo

FL, 2001

• Blackburn, J. I., Protective Relaying Principles and Applications,

Marcel Dekker, Inc., copyright 1987

• GEC ALSTHOM. Protective relays application guide’, Baldini and

Mansell , 1987, 3rd Edition

• IEEE Std 399-1997, IEEE Recommended Practice for Industrial

and Commercial Power Systems Analysis

• IEEE Std 242-1986, IEEE Recommended Practice for Protection

and Coordination of Industrial and Commercial Power Systems

• IEEE, Guide for AC Generator Protection IEEE Std C37.102

• IEEE, Power Swing and Out of Step Considerations on

Transmission Lines, PSRC WG D6, 2005

• NEPLAN®, User Manual, 2004.

• WESTINGHOUSE/ABB Power T&D Co., Protective Relaying

Theory and Application, Marcel Dekker, Inc., copyright 1994

• HOLMES E.J., GERS J.M., Protection of Electricity Distribution

.etworks’, IEE, 2004, 2nd Edition.

• STEVENSON, W. D.: ‘Elements of power system analysis’,

McGraw Hill, New York, 1982, 4th Edition.

• TZIOUVARAS, D.M., HOU, D., “Paper Out-of-step protection

fundamentals and advancements”, USA, 2003

89

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Backup Transmission Line Protection for

Ground Faults and Power Swing Detection

Using Synchrophasors

Armando Guzmán, Venkat Mynam, Greg Zweigle, Schweitzer Engineering Laboratories, Inc.

Abstract—This paper proposes the use of synchrophasors for

backup transmission line protection for ground faults and power

swing detection. The proposed protection approach complements

protective distance elements and is suitable for single-pole and

three-pole tripping applications. The paper presents the syn-

chrophasor-based protective element performance for challeng-

ing fault conditions such as cross-country faults with high fault

resistance. The power swing detection algorithm this paper pro-

poses uses angle difference measurements and does not require

setting traditional impedance-based out-of-step (OOS) characte-

ristics.

Keywords—!egative, Zero, Sequence, Current, Angle, Differ-

ence, Frequency, Slip, Acceleration, Swing, Out-of-Step

I. INTRODUCTION

Synchrophasors within protective relays have been availa-

ble since 2002. Typical applications of this technology are

visualization, state measurement, and system integrity protec-

tion schemes.

Relays that combine synchrophasor measurements and

programmable logic control capabilities [1] use synchrophasor

measurements from both ends of a two-terminal transmission

line to provide backup protection and power system stability

monitoring (see Fig. 1). The backup protection uses negative-

or zero-sequence current elements to detect high fault resis-

tance (RF) faults. Operating times for these elements depend

on the synchrophasor message rate and the synchrophasor

filtering process. In the present implementation, the sequence

component-based backup protection elements detect faults

with RF greater than 300 Ω within 160 ms. This current only

element RF coverage compares to negative-sequence imped-

ance-based directional elements [2], 67Q, but does not require

voltage measurements. These elements include faulted phase

identification (FPI) logic that makes them suitable for single-

pole tripping (SPT) applications.

These relays also gather positive-sequence voltage angle

measurements from two different power system buses. With

these measurements, the relays determine the angle difference

[3] between the two buses and calculate the slip frequency and

acceleration to identify power swings and OOS conditions.

GPS Rcvr

Relay 1

A

GPS Rcvr

Relay 2Synchrophasors

B

Local

Synchrophasors

Remote

Synchrophasors

Trip

Alarm

(Relay 1 Partial)

Line

Protection

Power Swing

Detection

Time

Alignment

Fig. 1. Relays Exchange Synchrophasors for Backup Line Protection and

Power System Detection in a Two-Terminal Line Application.

II. BACKUP TRANSMISSION LINE PROTECTION

Line protective relays calculate synchrophasors at specific

instants (60 times per second, for example). Communications

channels make the local and remote time-stamped currents

available to the local and remote relays. These relays time

align the local and remote currents on a per phase basis and

make them available to protective functions (see Fig. 2) such

as FPI logic, negative-sequence current directional element

(32IQ), zero-sequence current directional element (32IG),

negative-sequence current differential element (87LQ), and

zero-sequence current differential element (87LG).

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Trip

Logic

Faulted

Phase

Identification

Protection

Elements

Trip A

Trip B

Trip C

Time- Aligned Currents

Phase and

Sequence

Currents

Fig. 2. Synchrophasor-Based Protection Including Phase Currents, Sequence

Currents, Faulted Phase Identification Logic, Protection Elements, and Trip Logic.

A. Faulted Phase Identification (FPI)

The synchrophasor-based protection element includes FPI

logic that uses the total zero-sequence and total negative-

sequence fault currents [4]. The total currents are the sum of

the local and remote currents. The logic in Fig. 3 defines sec-

tors FSA, FSB, and FSC corresponding to A-phase, B-phase,

and C-phase faults respectively. The logic calculates the angle

difference between the sequence fault currents and the relative

magnitudes of the total phase-to-phase currents to identify the

faulted phase:

A-Phase Fault. The logic asserts the FSA bit

if ( ) 0T

2

T

0

06060 II ≤∠−∠<− and

),,max( IIIIT

CA

T

BC

T

AB

T

BC≠

B-Phase Fault. The logic asserts the FSB bit

if ( ) 0T

2

T

0

018060 II ≤∠−∠< and

),,max( IIIIT

CA

T

BC

T

AB

T

CA≠

C-Phase Fault. The logic asserts the FSC bit

if ( ) 0T

2

T

0

060180 II −≤∠−∠<− and

),,max( IIIIT

CA

T

BC

T

AB

T

AB≠

where

IT

0 is the total zero-sequence current phasor

IT

2 is the total negative-sequence current phasor

IT

AB is the total A-phase minus B-phase current phasor

IT

BC is the total B-phase minus C-phase current phasor

IT

CA is the total C-phase minus A-phase current phasor

The relay uses FPI logic for tripping the faulted phase in

SPT applications.

B. "egative-Sequence Current Directional Element (32IQ)

The 32IQ element compares the angle of IL

2with the angle

of IR

2 and makes the trip decision according to (1). This ele-

ment detects high-impedance faults when the negative-

sequence currents enter the transmission line at both line ends.

0•Re IIR

2

L

2>

∗

(1)

where

IL

2 is the local negative-sequence current phasor

IR

2 is the remote negative-sequence current phasor

Fig. 4 shows the basic logic for 32IQ. The Protection Ena-

ble bit, PREN, asserts when IL

2 and I

R

2exceed the element

sensitivity threshold, e.g., 0.1 • INOM, and when IL

2 is greater

than IL

1•05.0 , where I

L

1 is the local positive-sequence cur-

rent phasor. Communications channel health, data integrity,

and time synchronization also supervise this logic. The 32IQ

output asserts when all the previous conditions are valid for

two consecutive counts.

Fig. 3. Faulted Phase Identification Logic Uses Total Negative-Sequence and Zero-Sequence Fault Current.

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L2I

R2I

( )[ ] 0I•IRe R2

L2 >

∗

Fig. 4. Negative-Sequence Current Directional Element, 32IQ, With Current Magnitude, Channel Health, Data Integrity, and Time Synchronization Super-

vision.

The 32IG element operates similarly to 32IQ but uses zero-

sequence quantities.

C. "egative-Sequence Current Differential Element (87LQ)

The 87LQ element characteristic uses operating ( IOP

2) and

restraint ( IRT

2) quantities [5] according to (2) and (3).

IIIR

2

L

2

OP

2+= (2)

IIIR

2

L

2

RT

2–= (3)

The element operates when the following conditions are

met:

IIRT

2

OP

2•Slope_87> (4)

II NOM

OP

2•1.0> (5)

where 87_Slope is the slope of the 87LQ element characteris-

tic.

The relay aligns the local and remote phasors according to

their time stamps. Therefore, one advantage of using time-

stamped phasors is that channel asymmetry does not affect the

element operating and restraint quantities.

The 87LG element operates similarly to 87LQ but uses ze-

ro-sequence quantities.

III. PROTECTION ELEMENT PERFORMANCE

A. Fault Resistance Coverage

The 32IQ and 87LQ elements overcome the RF coverage

limitations of traditional phase comparison line protection

schemes [6]. Fig. 6 illustrates the RF coverage of the 67Q,

32IQ, and 87LQ elements for phase-to-ground faults at differ-

ent fault locations along the transmission line of the system in

Fig. 5. We used the Real-Time Digital Simulator (RTDS®) to

model this system. For this case, we set element sensitivities

to 0.1 • INOM. The 32IQ and 87LQ RF coverage matches the

intersection of the local and remote 67Q coverage. In a per-

missive overreaching transfer trip (POTT) scheme with for-

ward and reverse elements, the scheme must coordinate for-

ward and reverse 67Q element sensitivities. The 32IQ and

87LQ elements do not have this requirement, so we can set

them more sensitive than 67Q elements. Fig. 7 shows the ad-

ditional RF coverage of 32IQ and 87LQ with 0.05 • INOM sen-

sitivity.

Fig. 5. Power System Parameters and Operating Conditions to Analyze RF Coverage Capabilities of the 32IQ, 87LQ, and 67Q Elements.

RF()

Fig. 6. 32IQ, 87LQ, and 67Q Element RF Coverage for Phase-to-Ground

Faults at Different Line Locations.

0 0.2 0.4 0.6 0.8 1100

300

500

700

9000.05 • INOM

0.1 • INOM

Fault location (pu)

Fig. 7. 32IQ and 87LQ RF Coverage With 0.05 • INOM and 0.1 • INOM Sensi-

tivity.

B. Operating Time

The operating time of the directional elements depends on

the synchrophasor message rate, the synchrophasor filtering

process, and element sensitivity. Fig. 8 shows 32IQ element

operating time for an A-phase-to-ground-fault with

RF = 450 Ω located 30 percent from the local end (left) for the

system in Fig. 5. The local and remote relays operate in 165

ms and 158 ms, respectively. In this application, the relays

exchange synchrophasors at 20 messages per second, and the

filtering system attenuates harmonics according to C37.118

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[7]. We set the sensitivity to 0.1 • INOM. The relays exchange

IA, IB, and IC synchronized phasors along with their corres-

ponding synchronized time stamps through the use of peer-to-

peer relay communications [8] at 38400 bps. A faster message

rate and faster filtering process reduce element operating time.

Seconds

Fig. 8. FPI, 32IQ, and 67Q Operating Times for an A-Phase-to-Ground Fault Located 30 Percent From the Local End.

C. Effect of Standing Unbalance and Line Loading

Standing negative-sequence current reduces 32IQ RF cov-

erage [9]. First, consider an A-phase-to-ground fault with

RF = 350 Ω located 80 percent from the local end (left) on one

of the parallel lines of the system in Fig. 9 during balanced

prefault system operating conditions. The prefault negative-

sequence current unbalance is zero (see Table I). Fig. 10

shows the local and remote negative-sequence current phasors

for this fault. The angle difference between these phasors is

5°. The 32IQ element operates correctly for this fault.

TABLE I.

LOCAL AND REMOTE NEGATIVE-SEQUENCE CURRENTS FOR AN A-PHASE-TO-

GROUND FAULT WITH BALANCED PREFAULT CONDITIONS

Current IL

2

(Primary Amps)

IR

2

(Primary Amps)

Prefault 0 0

Fault 57∠0º 92 ∠ –5º

o000.1 ∠ o403.1 ∠

Ω∠= o8897.35Z 1S Ω∠= o8640.38Z 1L

Ω∠= o8894.71Z 0S Ω∠= o8190.146Z 0L

Ω∠= o8898.17Z 1R

Ω∠= o8897.35Z 0R

Ω∠= o8640.38Z 1L

Ω∠= o8190.146Z 0L

Fig. 9. Power System Parameters and Operating Conditions to Analyze

32IQ and 87LQ Element Performance For Balanced and Unbalanced Prefault Operating Conditions.

20

60

100

30

210

60

240

90

270

120

300

150

330

180 0

Local

Remote

Fig. 10. Local and Remote Negative-Sequence Currents for an A-Phase-to-

Ground Fault Located 80 Percent From the Local End on One of the Parallel Lines With Balanced Prefault Conditions.

Next, we apply the same fault while the A-phase of the pa-

rallel line is open. Table II shows the prefault and fault cur-

rents. The phasor diagram in Fig. 11 illustrates the load com-

ponent and the fault without load component together with the

fault current at the local and remote terminals. Note that the

angle difference between the local and remote fault currents is

108º. This angle difference increases as the load current in-

creases. The 32IQ element does not detect this fault. This ele-

ment has decreased sensitivity because of the increase in load

current for this unbalanced operating condition. In the next

subsection, we show that 87LQ and 67Q have greater sensitiv-

ity than 32IQ for these operating conditions.

TABLE II.

LOCAL AND REMOTE NEGATIVE-SEQUENCE CURRENTS FOR AN A-PHASE-TO-

GROUND WITH UNBALANCED PREFAULT CONDITIONS

Current IL

2

(Primary Amps)

IR

2

(Primary Amps)

Prefault 79 ∠ 61º 78 ∠ –119º

Fault 37 ∠ 0º 154 ∠ –108º

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40

60

30

210

60

240

90

270

120

300

150

330

180 0

Local Currents

100

150

30

210

60

240

90

270

120

300

150

330

180 0

Load

Fault Without Load

Fault

Remote Currents

Fig. 11. Local and Remote Negative-Sequence Currents for an A-Phase-to-Ground Fault Located 80 Percent From the Local End on One of the Parallel Lines

With Unbalanced Prefault Conditions.

D. Cross-Country Faults (CCFs)

Fig. 12 shows the operating times of the local and remote

relays for a CCF. The fault starts as an A-phase-to-ground

fault located 80 percent from the local terminal of the parallel

line of the system in Fig. 9. After 8 ms, a C-phase-to-ground

fault occurs on the protected line located 80 percent from the

local relay. RF equals 250 Ω for both faults. The 67LQ ele-

ments, FPI logic, and 32IQ elements detect the fault in 18 ms,

75 ms, and 125 ms respectively.

Seconds

Fig. 12. FPI, 32IQ, and 67Q Operating Times for a CCF. First, an A-Phase-

to-Ground Fault Occurs on the Parallel Line. After 8 ms, a C-Phase-to-

Ground Fault Occurs on the Protected Line. RF Equals 250 Ω for Both Faults.

Now, we increase RF to 450 Ω. The 32IQ elements do not

operate for this fault because of the first unbalanced fault. For

this reason, the 32IQ elements do not appear in Fig. 13. Table

III shows the operating times of the 67Q, FPI, and 87LQ local

and remote elements. We set 87_Slope = 0.2.

TABLE III. OPERATING TIMES OF 67Q, FPI, AND 87LQ ELEMENTS

Local (ms) Remote (ms)

67Q 83 23

FPI 96 94

87LQ 148 158

We note that for both CCFs the total current FPI provides

reliable phase selection information. The 87LQ and 67Q ele-

ments provide better RF coverage than the 32IQ element for

unbalanced prefault conditions. We also combine the 67Q

elements with the FPI logic to trip the correct phase in SPT

applications.

Seconds

Fig. 13. FPI, 87LQ, and 67Q Operating Times for a CCF. First, an A-Phase-

to-Ground Fault Occurs on the Parallel Line. After 8 ms, a C-Phase-to-

Ground Fault Occurs on the Protected Line. RF Equals 450 Ω for Both Faults.

IV. POWER SWING AND OUT-OF-STEP DETECTION

Traditional power swing and OOS detection devices use

voltage and current measurements that these devices acquire at

a particular power system location.

The Clarke Diagram [10] in Fig. 14, shows the load imped-

ance, Zλ, in a two-machine system for |EA/EB| = 1.1 and δ = 70°. The diagram also shows the trajectory of Zλ on the im-

pedance plane for |EA/EB| = 1.1. This voltage ratio and the

impedance between the two sources define the impedance

trajectory. EA and EB are the electromotive forces of the two

machines, and δ is the angle between EA and EB.

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= 1.1EA

EB

R1 ( )

Z

Fig. 14. Load Impedance Trajectory on the Impedance of Plane for |EA/EB | = 1.1.

Line relays include an OOS element that uses local infor-

mation to monitor impedance trajectory for discrimination

between power swings and fault conditions [11]. When this

OOS element detects power swing conditions, it blocks the

distance elements. The OOS element requires the apparent

impedance to enter dedicated impedance characteristics. We

want to detect power swings before the apparent impedance

enters the OOS impedance characteristic.

The Power Swing Relay [12] uses a different OOS detec-

tion method. It determines δ from positive-sequence voltages

and positive-sequence currents that the relay measures at one

location. To calculate the voltage at the remote end, the power

swing detection algorithm requires network parameter and

network topology information. This relay calculates the first

and second derivatives of the angle difference, δ, to identify unstable swing conditions.

Another approach to δ calculation is to use synchrophasors from devices located close to generators [13]. This approach

does not require network parameter and network topology

information.

We now describe a synchrophasor-based approach that cal-

culates slip frequency and acceleration to identify power

swings and OOS conditions. The change of δ with respect to time defines the slip frequency, Sf, and the change of slip fre-

quency with respect to time defines the acceleration, Af, be-

tween the two system areas.

A. Power Swing Detection (PSD)

The PSD algorithm uses the positive-sequence voltage an-

gles that relays with synchrophasor measurement capabilities

acquire at two different power system buses to calculate δ between these buses. Then, the algorithm determines Sf and Af

between the two system areas. The relay running the PSD al-

gorithm calculates the absolute values of Sf and Af at constant

intervals according to the synchrophasor message rate. Fig. 15

shows the block diagram of the PSD algorithm.

IL

M1

VL

M1

VL

A1

VR

A1

VR

M1

Fig. 15. Synchrophasor-Based Power Swing Detection Logic.

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The algorithm enables the angle difference calculation

when all of the following operating conditions exist:

• Local positive-sequence voltage magnitude, VL

M1, is

greater than 1 V secondary.

• Remote positive-sequence voltage magnitude, VR

M1 ,

is greater than 1 V secondary.

When local positive-sequence current magnitude, IL

M1, is

greater than 0.1 • INOM, |Sf| is greater than 0.2 Hz, and |Af| is

greater than 0.1 Hz/s for three cycles, the algorithm asserts the

power-swing detection bit, PSD. The PSD bit assertion indi-

cates the existence of a power swing condition. The PSD bit

deasserts when any of the following conditions occur:

• |Sf| is greater than 10 Hz

• |Af| is greater than 50 Hz/s

• |Sf| is less than or equal to 0.2 Hz and |Af| is less than

or equal to 0.1 Hz/s for three cycles

Relay engineers can modify these thresholds according to

their applications.

B. Predictive Out-of-Step Tripping (OOST)

The OOST element characteristic [12] in Fig. 16 uses (6) to

define the power system unstable region. This characteristic

identifies unstable swings before the OOS condition occurs,

allowing the system protection scheme to take immediate re-

medial actions.

Offsetff ASSlope_78A +•> (6)

OOST

Af

Sf

Sf

Af

Unstable

Region

Enable

AOffset

78_Slope

Fig. 16. OOST Characteristic Using Slip and Acceleration Information to

Detect Unstable Swings.

C. Out-of-Step Detection (OOSD)

OOSD element assertion indicates machine pole slip

events. The OOSD logic in Fig. 17 compares the absolute val-

ue of the calculated angle difference with the OOS threshold,

OOSTH. This threshold defines the Angle Difference Operat-

ing Region (ADOPR) in Fig. 18. This logic monitors whether

the Angle Difference Operating Point (ADOP) crosses this

region. When ADOP crosses the ADOPR region, the logic

asserts the OOSD bit to indicate the OOS occurrence. Note

that ADOP can cross this region from the right or from the

left. The OOSD bit feeds the OOS counter (OOSCN) to track

the number of OOS events.

Fig. 17. OOSD Logic Uses Angle Difference Information to Identify Out-of-Step Conditions.

B

A

ADOPSwing

Direction

ADOPR

| | = OOSTH

Fig. 18. Angle Difference Operating Region.

V. POWER SWING AND OUT-OF-STEP DETECTION ALGORITHM

PERFORMANCE

We used the two-machine RTDS power system model in

Fig. 19 and the MATLAB® power swing and OOS detection

algorithms running at 60 messages per second to analyze PSD,

OOST, and OOSD logic performance.

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All impedances are in per unit on a 100 MVA base

N4 (500 kV)

N5 (500 kV)

N3 (287 kV)N2 (287 kV)N1 (13.8 kV)

XS: = j0.1 XT: = j0.009

XL: = j0.17

XT: = j0.009

XL: = j0.034

XS: = j0.045

Swing Center

Relay 1

Relay 2

Fig. 19. Two-Machine Power System Model to Illustrate PSD, OOST, and

OOSD Element Performance During Power Swing and Out-of-Step Condi-

tions.

A. Power Swing Detection (PSD)

At 0.5 seconds, the system has a fault for 7.25 cycles at bus

N2. After the fault is removed, the power swing condition

begins: |Sf| is greater than 0.2 Hz, |Af| is greater than 0.1 Hz/s,

and the PSD bit asserts at 0.94 seconds (see Fig. 20). The PSD

element detects the swing condition 2.93 seconds before the

machine poles slip.

B. Predictive Out-of-Step Tripping (OOST)

The delta-slip plot in Fig. 21 shows the angle difference

and slip calculations from 0.81 to 3.87 seconds. Three seconds

after fault inception, δ is greater than 90°, and the swing be-comes unstable. The slip-acceleration plot in Fig. 22 shows

the slip and acceleration calculations from 3.39 to 4.79

seconds together with the OOST element characteristic. In this

example, we set 78_Slope = –15 and AOffset = 7. The OOST

element detects the OOS condition 3.16 seconds after fault

inception and 0.22 seconds before the machine poles slip (see

Fig. 20). An angle δ greater than 90° supervises this element

to increase scheme security. .

-200

0

200

δ (deg)

-5

0

5

Slip (Hz)

-50

0

50

Acc (Hz/sec)

0 1 2 3 4

Seconds

FAULT

PSD

OOST

OOSD

Fig. 20. Angle Difference, Slip, Acceleration, and Digital Bits for an Unstable Swing after a 7.25-Cycle Fault at Bus N2.

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C. Out-of-Step Detection (OOSD)

The OOSD bit asserts at 3.88 seconds when the OOS con-

dition occurs (see Fig. 20). The angle difference trajectory in

Fig. 23 illustrates when ADOP enters and leaves ADOR. In

this example, OOSTH = 120°.

-20 0 20 40 60 80 100 120 140 160 180-200

-100

0

100

200

300

400

500

Angle Difference δ (deg)

Slip (deg/sec)

Fig. 21. The System Becomes Unstable When δ is Greater Than 90°.

0 0.5 1 1.5 2 2.5 3 3.5 4-40

-30

-20

-10

0

10

20

30

40

Slip (Hz)

Acceleration (Hz/sec)

Fig. 22. OOST Characteristic Using Slip and Acceleration Information

Determines Unstable Swing Condition

0 50 100 150 200 250 300 3501.5

2

2.5

3

3.5

4

4.5

5

5.5

6

Angle Difference δ (deg)

Seconds

Angle DifferenceOperating region

Fig. 23. ADOP Trajectory Indicates When the OOS Condition Occurs.

VI. POWER SWING AND OUT-OF-STEP DETECTION RELAY

PERFORMANCE

The following results show performance for OOS algo-

rithms implemented in a two relay protection system using

programmable logic. Section IV describes these algorithms in

more detail.

The test system in Fig. 19 simulates swing conditions. Pro-

tective relays at bus N1 and N5 exchange synchrophasor data

(positive-sequence voltage angle) and run the OOS algorithms

20 times per second using peer-to-peer relay communications.

We applied a three-phase fault at bus N2 for 7.25 cycles to

start the power swing, as we did in Section V. Fig. 24 shows

the three-phase voltages at each bus. Note that during the

pole-slip period the voltages drop to nearly zero at buses N3

and N4. These buses are close to the swing center of the sys-

tem.

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Fig. 24. Instantaneous Three-Phase Voltages at Each Bus on the Test Sys-tem.

Fig. 25 shows the relay oscillography at bus N1 triggered

during the swing. Analog values include the three-phase vol-

tages and the three-phase currents. Digital values include PSD,

OOST, and OOSD. The PSD bit asserted 3 seconds before the

first pole slip when the OOSD bit asserted. The OOST ele-

ment detected the slip condition 0.23 seconds before the first

pole slip, providing adequate time for remedial action.

Seconds

Fig. 25. Relay Oscillography Showing the Power Swing Detection Element Response for the System Oscillations.

To illustrate the angle difference, slip, and acceleration

analog values that the relay calculated, we included the analog

values in the synchrophasor output message. We used a syn-

chrophasor visualization tool to obtain the results in Fig. 26.

These results are similar to the calculations shown in Fig. 20.

Fig. 26. Angle Difference, Slip Frequency, Acceleration Relay Calculations, and PSD, OOST, OOSD Element Operation.

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VII. CONCLUSIONS

1. Synchrophasor-based protection complements pri-

mary distance protection schemes, provides backup

protection, and does not require voltage informa-

tion. The latter capability allows the relay to protect

the line during loss-of-potential conditions.

2. Negative-sequence current directional and differen-

tial elements together with total current faulted

phase identification detect high-resistance faults

without compromising phase selectivity. These

elements have minimum communication bandwidth

requirements.

3. Negative-sequence current differential elements

provide sensitive protection with unbalanced pre-

fault conditions.

4. Communications channel asymmetry does not af-

fect the operating and restraint quantities of the

synchrophasor-based current differential element.

5. PSD, OOST, and OOSD elements do not require

power system network parameter and topology in-

formation to calculate angle difference, slip fre-

quency, and acceleration between two system

areas.

6. Synchrophasor-based protection and monitoring

require reliable communications and reliable time

information.

7. Time-aligned current and voltage measurements

acquired at different power system locations im-

prove performance of protection and power swing

detection algorithms.

VIII. REFERENCES

[1] G. Benmouyal, E. O. Schweitzer, III, A. Guzmán, “Synchronized

Phasor Measurement in Protective Relays for Protection, Control,

and Analysis of Electrical Power Systems,” in 2002 29th Annual

Western Protective Relay Conference Proceedings.

[2] E. O. Schweitzer III and J. Roberts, “Distance Relay Element De-

sign,” in 1992 19th Annual Western Protective Relay Conference

Proceedings.

[3] E. Martinez et al., “Using Synchronized Phasor Angle Difference for

Area-Wide Protection and Control,” in 2006 33rd Annual Western

Protective Relay Conference Proceedings.

[4] J. B. Roberts and D. Tziouvaras, “Fault Type Selection System for

Identifying Faults in an Electric Power System,” US Patent

6,525,543, Feb. 25, 2003.

[5] A. R. van C. Warrington, Protective Relays: Their Theory and Prac-

tice, vol. 1 London: Chapman and Hall, 1974, p. 106.

[6] F. Calero and W. A. Elmore, “Current Differential and Phase Com-

parison Relaying Schemes,” in 1992 19th Annual Western Protective

Relay Conference Proceedings.

[7] IEEE Synchrophasors for Power Systems, IEEE Standard

C37.118-2005.

[8] K. C. Behrendt, “Relay-to-Relay Digital Logic Communication for

Line Protection, Monitoring, and Control,” in 1997 51st Annual

Georgia Tech Protective Relaying Conference Proceedings.

[9] G. Benmouyal, “The Trajectories of Line Current Differential Faults

in The Alpha Plane,” in 2005 32nd Annual Western Protective Relay

Conference Proceedings.

[10] E. Clarke, Circuit Analysis of AC Power Systems, vol. II New York:

Wiley and Sons, 1950, pp. 335–343.

[11] D. Hou, A. Guzman, and J. Roberts, “Innovative Solutions Improve

Transmission Line Protection,” in 1997 24th Western Protective Re-

lay Conference Proceedings.

[12] E. O. Schweitzer III, T. T. Newton, and R. A. Baker, “Power Swing

Relay Also Records Disturbances,” in 1986 13th Annual Western

Protective Relay Conference Proceedings.

[13] V. Centeno, J. de la Ree, A. G. Phadke, G. Michel, R. J. Murphy, R.

O. Burnett, Jr., “Adaptive Out-of-Step Relaying Using Phasor Mea-

surement Techniques,” Computer Applications in Power, IEEE, Vol.

6, No. 4, pp. 12–17, Oct 1993.

IX. BIOGRAPHIES

Armando Guzmán received his BSEE with honors from Guadalajara

Autonomous University (UAG), Mexico, in 1979. He received a diploma in fiber-optics engineering from Monterrey Institute of Technology and

Advanced Studies (ITESM), Mexico, in 1990, and his MSEE from Uni-

versity of Idaho, USA, in 2002. He served as regional supervisor of the Protection Department in the Western Transmission Region of the Federal

Electricity Commission (the electrical utility company of Mexico) in

Guadalajara, Mexico for 13 years. He lectured at UAG in power system protection. Since 1993 he has been with Schweitzer Engineering Labora-

tories, Inc. in Pullman, Washington, where he is presently Research Engi-

neering Manager. He holds several patents in power system protection and metering. He is a senior member of IEEE and has authored and coauthored

several technical papers.

Mangapathirao “Venkat” Mynam received his MS in Electrical Engi-neering from the University of Idaho in 2003 and a Bachelors in Electrical

and Electronics Engineering from Andhra University College of Engineer-

ing, India, in 2000. He is presently working as a Research Engineer with Schweitzer Engineering Laboratories, Inc. He is a member of IEEE.

Greg Zweigle earned his BS in Physics and MS in Electrical Engineering

from Northwest Nazarene University and Washington State University, respectively. He is presently a Principal Research Engineer at Schweitzer

Engineering Laboratories in Pullman, Washington. He holds patents in

the areas of power systems, signal processing, and data compression and is a member of the IEEE and the ACS.

© 2007 by Schweitzer Engineering Laboratories, Inc.

All rights reserved.

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Abstract— The wide-area synchronized phasor measurement system envisioned by Comisión Federal de Electricidad (CFE) during the 1990’s and designed to increase the security and integrity of Mexico’s electric power system. This paper presents the different development stages taken for the deployment of WAMS. Details of the current state and PMU data-based application examples within CFE are also provided. CFE has a potential of more than 140 Units of Mensuration Fasorial (PMU´s) and relays protection with phasor measurement functions of different manufactures and models, installed in the three different electric power systems. The project of a Wide Area Measurement System of CFE is conformed by regional data concentrators of PMU´s, located in each Regional Management of Transmission or Control Áreas, and a Central Unit or super concentrator. In this Centrl Unit is possible to save the files for analysis post mortem. Also is possible the visualization in real time of voltage, frequency, fase angle, MW and MVAR in different points of the electric systems. During ten years of experience with sincrofasors, the CFE has developed applications for the analysis of fauls and reproduction of events. Also, with the registrations of PMU´s regulators, stabilizers and underfrequency load shedding schems have been adjusted. At the moment, in CFE are working in the development of applications for the Automatic Generation Shedding Schemes (AGSSs) using Phasor Measurement and Control Units PMCU´s. Index Terms— Phasor Measurement Unit (PMU), Wide Area

Measurement Systems (WAMS), Real-Time Power System State Visualization.

I. INTRODUCTION

HIS paper reports on the development of a Wide-Area

Measurement System in Mexico, It has been designed to

increase the security and integrity of National Electric

Power System. Current synchrophasor activities in Mexico

include some regional PDCs for visualization of system in real

time. Developed applications include model validation,

computation of operation and performance curves of

generators and relays, automatic generation shedding scheme

and CCVT monitoring.

The remainder of this paper is organized as follows. Section

II gives a description of WAMS and the initial deployment

stage of the system. Section III discusses the structure of the

Mexican National Electrical System. In Section IV, the main

applications that have been deployed and considerations for

the deployment of future applications are presented. In Section

V, the architecture of CFE project is presented. Section VI

discusses the different hierarchy and application levels of

E. Martínez Martínez is with Comisión Federal de Electricidad (CFE),

México (e-mail: [email protected]).

WAMS. Information security aspects are discussed in Section

VII.

II. SYNCHROPHASORS AND WAMS IN CFE

During the 1990’s Mexico’s Federal Electricity Commission

(Comisión Federal de Electricidad, CFE) envisioned a project

that consisted of the deployment of a synchronized phasor

measurement system for contingency analysis, and

visualization of the operational state of the National Electrical

System. The initial stage of this project consisted of the

installation of fifteen Phasor Measurement Units (PMUs) in

two of the four subsystems that comprise the National

Electrical System. The installation criteria for the PMUs

considered included largest generation complexes, major load

points, and critical power transfer interfaces. In the initial stage

post-fault analysis and model validation of power system

simulator models have been of primary interest. In the second

stage, a synchronized phasor measurement system for the

security and integrity of Mexico’s electric power system, has

been proposed[1].

WAMS in CFE includes visualization and real-time

decision applications whose main aim is to guarantee

reliability and security for the National Electrical System.

The WAMS architecture developed by CFE allows the

inclusion of a phasor data concentrator (PDC) at eight

transmission regions giving rise to regional wide-area

measurement systems at very low cost. Also, it allows the

integration of PMUs from different manufacturers and models,

and to take advantage of the PMU functions implemented in

digital relays within discrete control schemes and substation

control modules.

III. NATIONAL ELECTRICAL SYSTEM OF MEXICO

As of November 2007, the National Electrical System of

Mexico is formed by three main electric power systems that

operate independently (see Fig. 1):

1. National Interconnected Power System

2. North Baja California Electric Power System

3. South Baja California Electric Power System

Based on the topology of the National Electrical System

three phasor data concentrators were installed, one for each

independent power system. The number of PMUs in each

concentrator will depend on the information requirements from

each substation and each system, and also on the use of the

phasor measurement data which may be used by protection

specialists, analysts, system operators, etc.

Wide Area Measurement & Control System in

Mexico Enrique Martínez Martínez, Member, IEEE

T

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Fig. 1 Three independent systems in the National Electric Network of Mexico

Fig. 2 Frequency in the North-West and Interconnected systems during a test

of synchronization of systems in march 2004. Record of PMUs.

IV. MAIN APPLICATIONS OF PMUS IN CFE

For off-line analysis, the installation of GPS-synchronized

PMUs represents 90% of the project. Meanwhile, for real-time

visualization and real-time decisions in the power system, the

communications infrastructure can surpass the 95% of the

same project. The main reason is that to obtain reliable angle

measurements in the PDC, information has to be transmitted in

a pre-defined bandwidth that allows synchronization of PMUs

with minimum delay and continuous flow. CFE has established

as short- and mid-term goals to enable the following four

applications within PMUs:

1. Post-fault off-line analysis

2. Real-time Wide-Area Measurement System

3. Wide-Area Protection and Control Schemes

4. PMU-based Power System State Estimator/Visualizer

A. Off-line Analysis

Off-line analysis at CFE was the first application of PMUs.

Frequency and voltage triggers were implemented to

simultaneously record disturbance data in the PMUs installed

in different substations. Later, the recordings where

synchronized by using the GPS time tags, and the phase angle

was calculated. [2]-[4]. This information has been proven

valuable for model validation and for updating power system

simulator databases. It has also been used to obtain R-X, P-f,

Q-V, and PV curves that provide insight on the behavior of

machines, regulators, stabilizers, and protection relays during

disturbances [10]. Also, this information was very important to

interconnection of North-West and National systems in 2005.

For example, the fig. 2 shows the frequency of the two

systems during one of the first synchronization intents in 2004,

the increment of the oscillations for a negative effect of the

PSS, the behavior of the most important generators in both

systems (fig. 3) and the risk of trip by power oscillation in

transmission line of 230 kV that united the systems Fig. 4

Fig. 3 P-F curves during test of synchronization of systems in march 2004

Fig. 4. Off-line analysis example: PMU recording analysis of power

oscillations in a transmission line and protection characteristic during the

disturbance.

Currently data recording no longer requires triggering, and

is done continuously, with all the information sent to regional

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PDCs. A sampling frequency of 20 samples per second is used

for all the PMUs installed within the National Interconnected

Power System, and 30 samples per second is used for the

PMUs at the North Baja California Electric Power System.

The sampling rate at North Baja California was selected to

share the same sampling rate as the one proposed by NASPI

(North America SynchroPhasor Initiative) that will coordinate

all the phasor measurement from all North American utilities

by NERC (North American Electric Reliability Corporation).

In the fig 5, we observe the behavior of the frequency captured

by PMUs of Mexico during the generation loss in Canada. A

same sampling frequency will allow us exchange of

information in the WECC, it will be possible the analysis of

the speed of propagation of flaults in the system of the three

countries to establish preventive actions.

Fig.5 Frequency in Baja California Norte during trip of 2535 MW of

generation in Canada.

For off-line data analysis and applications it is important to

have a sufficiently high sampling frequency, reliable data

capture, and precise signal processing. These requirements

intrinsically depend on the technology of the PMUs. For these

local applications, the communications infrastructure does not

affect the reliability of the analyses.

B. Real-Time Wide-Area Measurement System

For this application, it is important to have high-quality

PMUs and a reliable and secure communications system,

preferably based on fiber optic links, interfaces and routers

with sufficient bandwidth.

To provide operators with adequate signals for corrective or

preventive actions, system state visualization requires high

speed data transmission because computation of angle

differences is done in real-time as the samples of each PMU

reach the PDCs.

Sampling frequency is determined by the requirements of

each specific real-time application, dynamic or transient,

however, we consider that the information for analysis of

transitory can be obtained by trigger of relay or PMU. In other

countries there are applications that use two samples per cycle

requiring high bandwidth from the communication channels

and larger memory capacity of PDCs for data storage.

Fig. 6. Regional PDCs and their integration into the single PDC of the

National Electrical System.

C. Wide-Area Protection and Control Schemes

To implement PMU-based control schemes there are two

options currently available in the market:

a) Integrating PMU functionalities in protective relays

b) Integrating protection and control functionalities in

PMUs

Currently, programmable logic controllers (PLCs) are used by

the power industry to take control actions through dedicated

communication channels that make decision based on the pre-

programmed logic. These control actions enable automatic

generation shedding, load shedding, or transmission line

switching. However, with this method when the system is

separated through opening of tie lines the system operator

loses control and visibility of isolated areas making the event

analysis and resynchronization process complex and slow

because of the existence of difference time stamps and

references[6].

Recently, some relay manufacturers have implemented

phasor measurements in distance and overcurrent protective

schemes. This prototype schemes can take control actions, but

they are not ready to operate as special protection and control

schemes. This is mostly because the IEEE C37.118 protocol

has to be the same for WAMS applications[5]. Also, this

scheme should not be completely dependent on the GPS signal

to make correct decisions. When the GPS signal from one or

more PMUs is lost, the decisions on control actions should not

be affected as in a future “Angular Difference Protection

Scheme”, where the local measurements are sent to the

WAMS and at the same time enabling automatic generation

shedding, automatic load shedding, or automatic line shedding.

Currently these prototype schemes use Phasor Measurement

and Control Units (PMCUs) for the assignment of logical

variables in devices.

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Fig. 7 Schematic diagram of Automatic Generation Shedding Schemes using

PMCUs

As shown in several studies [11], wide area monitoring,

protection, and control systems (WAMPAC) are required to

measure, evaluate the measurement, and return the control

action commands. This process requires high reliability and

speed in the communications system to take control actions

when needed, or to detect false triggers. Thus measurement,

protection and control concepts need to be integrated within

these systems.

CFE plans to build a WAMS in each transmission region

(Gerencia de Transmisión), in which the state of the discrete

control schemes can be observed, while maintaining the

control and protection actions independent of the PDC and the

WAMS. The control actions will be taken from one or several

PMCUs based on local tuning and on previous studies. This

philosophy optimizes for operation times, facilitates

supervisory functions for safer and more reliable actions, and

reduces the dependency on communication channels when

facing disturbances that would require immediate action. In

applications deployed by CFE operation department, time

delays less than 90 ms have been obtained, including

verification of V, P, Q, f, phase angle, and breaker states.

D. PMU-based Power System State Estimator/Visualizer

In the future a super PDC will support a power system state

estimator or visualizer to integrate all the information available

at CFE. It has been a primary concern to develop an interface

between the PDC containing the phasor measurements from all

the installed PMUs in the National Electrical System and the

current control system in operation in the National Energy

Control Center (Centro -acional de Control de Energía).

Such application would allow CFE to perform contingency

simulations based on a database directly compiled from phasor

measurement data. The research and development for this

application has not been considered in this stage of the

proyect.

V. SYSTEM ARCHITECTURE OF CFE´S PROJECT

WAMS of CFE has been designed to satisfy the

requirements from each phasor measurement data user or

potential client. This has been done to cater for the speed,

quantity, and type of information needs of each client

depending on their responsibility area and security.

Fig. 8 shows pyramidal architecture. The base is formed by

the network entities that manage local data, i.e. substations and

generation stations. At this level the local data transfer speed

requirements to PDCs are lower than local data management

requirements. At the highest level less local PMU information

is required for obtaining a broader visibility of the overall

system, this requires a higher information transfer speed than

at the lower levels.

SIN

Gerencia

Regional de

Tarea de Cont rol

Enlaces Interareas

Subestaciones

Centrales Eléct ricasInformación

Velocidad

Fig. 8. Data management structure. SIN: National Interconnected Power

System (Sistema Interconectado -acional, SIN), Regional Control Task

Manager (Gerencia Regional de Tarea de Control), Interarea Ties (Enlaces

interareas), Substations (Subestaciones), Generation Stations (Centrales

Eléctricas), Velocity (Velocidad), Information (Información).

VI. HIERARCHICAL AND APPLICATION LEVELS

A. First Level: Substations and Generation Stations

At this level data transfer speed is not of primary concern

and applications are unlimited. Applications are local and

independent; however, it is possible to send a lower amount of

information with higher speed to PDCs to enable the

functioning of a Real-Time WAMS. At CFE we have seen that

at this level the use of PMUs or disturbance recorders with

PMU functions has shown more advantages over digital relays

with PMU functionalities. The main current and voltage

phasors being monitored in a substation will share the same

time tags, which is important when analyzing the response of

machine clusters, automatic voltage regulators, stabilizers, and

the AGC. Common monitored variables from PMUs at this

level are frequency, voltage, phase angle, active and reactive

power. These variables have been used to compute R-X, P-f,

Q-V, and PV curves. [7]-[10]

B. Second Level: Inter-area Ties

This level is important for the analysis of the behavior of

critical intearea ties which have shown small signal oscillations

or power flow inversions that have impact on transmission line

protection schemes.

At CFE, one of the dilemmas that protection engineers have

ΣP=P1+P2

OTE OTE

RS-232 RS-232

150 MW

ΣP=P1+P2

OPTIC FIBER

CONDICIONES PARA

ARMAR EL DAG

• VOLTAJE

• FRECUENCIA

• 10 ≤ ΣP ≥ -800

• POS. INT

• ANG=α-β

V1

F1

P1, Q1

P2

, Q2

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V2

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POWER FLOW

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faced is on how protection schemes are enabled or disabled

when power oscillations appear. Triggering of protection

schemes requires monitoring of the magnitude, speed, and

frequency of oscillation of the modes involved.

This permits maintaining stability and load-generation

balance when large disturbances occur in the system.

Currently CFE is developing an adaptive protection scheme

based on the angular difference between subsystems. CFE is

also performing field test data analysis on the behavior of a

prototype generation shedding scheme which assesses the

transmission capability among two hydro generation stations.

The scheme has a decision logic that uses signals from the

active power flow, voltage, frequency, breaker state, and

angular difference between the two stations. Both the adaptive

protection and generation shedding schemes are fully

independent from the WAMS with regards of decision making

for maintaining stability in the system. Nevertheless, phasor

information is continuously sent to the WAMS providing

visibility of isolated areas in case of islanding.

CFE has observed that for this type of applications digital

relays with PMU and PLC functionalities are more advantage

to PMUs that do not have protection and PLC functionalities.

C. Third Level: Regional PDCs

At this level the main goal is to guarantee efficient

information management and to provide appropriate

maintenance to the PMUs and PDCs installed by each

Regional Transmission Manager (Gerencia Regional de

Transmisión). These are shown in Fig. 6

CFE has considered using the wealth of available

information for real-time visualization of each regional area

independently and to apply it in transformer bank and

transmission line loading studies, energy interchange, power

quality, and the behavior of protection and relief schemes.

D. Fourth Level: Central PDC

CFE has designed to integrate all the information from the

regional PDCs and from strategically placed PMUs into a

single PDC.

This PDC will hold the most selective information from a

large number of PMUs allowing it to synchronize frequency

and voltage phasor measurements with ease and to calculate

phase angles accurately, giving the operator a broader view of

the system state from the measurements from each selected

location. To enable a state estimator it is also needed to have

active and reactive power measurements from the networks,

PMUs can provide this information.

As shown in Fig. 9, depending on the user needs and

application plans in WAMS or WAMPAC systems, the

selection of PMUs or PMCUs can lead to complex and costly

structures within a substation.

Fig. 9. Substation monitoring with eight current and two voltage phasors

using a single PMU (left) and multiple digital protective relays (right)

VII. INFORMATION SECURITY

To safeguard information, CFE has developed a

communications project that comprehends a Virtual Local

Area Network (ViLAN) with fiber optics. It has large

bandwidth capability and TCP/IP access guaranteeing

reliability, speed, and security in data transmission from each

PMU to the regional PDCs, and later to the central PDC .

VIII. CONCLUSIONS

As described in this paper, the architecture of CFE project

presents an alternative solution for the integration of different

models of PMUs and different manufacturers under the IEEE

C37.118 protocol [5]. The architecture is based on PDCs that

synchronizes and integrate phasor measurements through

software providing a low cost alternative without limiting the

integration of additional PMUs.

CFE has also considered the application of PMUs in

monitoring of wind energy farms which are being introduced

in Mexico. Continuous monitoring will improve CFE’s

knowledge of wind farm dynamics and will aid in the

elaboration of the Network Code of the Electrical System.

CFE has not yet worked with special protection schemes

that use digital relays simultaneously providing PMU

functionalities and protective actions. The drawbacks are

limitations on logical variable assignments in the prototype

PMCUs and strong dependency of the GPS signal of each

device that can affect the calculation of angular differences.

In angular instability triggered-based automatic generation

or load shedding applications the PMCUs must take control

actions independently from the GPS signal, similarly as done

in differential protection schemes. This new special protection

scheme, called “Angular Difference Protection Scheme”,

should be able to operate as a discrete control scheme and at

the same time to transmit measurements at the same sampling

frequency and under the IEEE 37.118 protocol. This is only

feasible if there is a fiber optic link sending the computed

angular difference of two measurement points between the

PMCUs.

Another application in use at CFE is monitoring of CCVTs.

Some regions in Mexico experience extreme heat and humidity

conditions. CFE has observed that under these conditions

CCVTs may explode. Voltage differences in the CCVT are

monitored in real-time. When abnormal conditions are

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detected an alarm will enable and the equipment is taken out of

service to protect the device, the installation, and the

personnel.

Currently CFE has deployed six out of a total of ten regional

PDCs and several special applications. Short- and mid-term

goals in the future development include the integration of all

the regional PDCs into a single central PDC.

IX. REFERENCES

[1] E. Martinez M. “Proyecto de Medición Sincronizada de Fasores de

CFE: Fase I” Subdirección de Transmisión, Transformación y Control.

México D.F. 1999

[2] E. Martinez M. and J.J. López M. “Application of Phasor Measurement

Units in the Adaptive Protection of Interconnected Systems”, Power

Systems and Communication Systems Infrastructures For the Future,

Beijing, People’s Republic of China, September 23–27, 2002.

[3] S. H. Horowitz, A. G. Phadke, and J. S. Thorp, “Adaptive Transmission

System Relaying” Paper N° 87 SM 625-77, in Proc. IEEE PES Summer

Meeting, San Francisco, CA, July 1987.

[4] R. J. Murphy and R. O. Burnett, “Phasor measurement hardware and

application” Proceedings of the Georgia Tech Protective Relay

Conference, Atlanta, GA, 1994.

[5] IEEE Synchrophasors for Power Systems, IEEE Standard

C37.118-2005.

[6] Enrique Martínez, Nicolás Juárez, Armando Guzmán, Greg Zweigle,

and Jean León, “Using Synchronized Phasor Angle Difference for Wide-

Area Protection and Control” WPRC, Spokane, WA, USA 2006

[7] J.J. Sanchez-Gasca and J.H. Chow “Performance comparison of three

identification methods for the analysis of electromechanical

oscillations,” IEEE Transactions on Power Systems, vol.14, no.3,

pp.995-1002, Aug 1999.

[8] J.S. Thorp, A.G. Phadke, S. H. Horowitz, and M.M. Begovic, “Some

Applications of Phasor Measurements to Adaptive Protection”

Proceedings of the Fifteenth IEEE PICA Conference, Montreal,

Canada, 1987.

[9] V. Centeno, J. De La Ree, A. G. Phadke, G. Michel, R. J. Murphy, and

R. Burnett, “Adaptive out-of-step relaying using phasor measurement

techniques” Memoria Técnica del Segundo Simposio Iberoamericano

sobre Protección de Sistemas Eléctricos de Potencia, Monterrey, N. L.,

México, 14 al 19 de Noviembre de 1993.

[10] E. Mart í nez Martínez “Analysis of Contingencies with PMUs, Causes

and Effects in Power Systems and Their Components” CRIS, Third

International Conference on Critical Infrastructures, Alexandria, VA,

September 2006.

[11] Daniel Karlsson and Xavier Waymel “System Protection Schemes in

Power Networks” Task Force 38.02.19 CIGRE, June 2001.

X. BIOGRAPHIES

Enrique Martínez Martínez (M) graduated from the Power Department of

the Polytechnic Institute of Belarus in 1986. Since 1986 he has worked in

Comisión Federal de Electricidad (CFE), initially in the Special Engineering

Unit as an engineer specializing in electric network projects and analysis.

From 1995 to 1998 he served as a specialist of transmission lines and

substation protection methods in the Coordination of Transmission and

Transformation Projects. From 1998 to 2005 he was head of the Stability

Studies Department of the National Agency for Protection. Currently he

serves as Sub-manager of Network Analysis at CFE. He is a member of IEEE

and CIGRE.

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Abstract—Synchrophasors open opportunities for improving

power system operation. Even though today’s installations are

limited in coverage and speed of connectivity, and the high level

applications are being formulated, it is clear the technology will

mature very quickly yielding significant gains.

Widespread deployment of the Phasor Measurement

Units (PMUs) providing for both coverage and

redundancy is an important factor. Such widespread

deployment can be achieved when integrating the PMU

function on modern microprocessor-based relays, similarly

to integrating metering, fault recording or sequence of

event recording capabilities.

Implementation of PMU functions, however, imposes

new requirements on protection platforms. In a nutshell

PMUs require correlation of the waveform samples with

the absolute (GPS) time, and reporting the phasors with

reference to this absolute time. Traditional relay

implementations sample asynchronously and derive

measurements as quickly as possible for the speed of

response, rather than in relation to any external process.

In addition, processing requirements are increased in

order to measure, communicate and record the PMU data.

All this raises concerns with respect to integrating PMU

functions on protective relays. Whether on new platforms

or as a part of an upgrade of an existing product, changes

to the traditional well-tested data acquisition system of the

relay in order to accommodate synchrophasors can have

serious consequences for all the other functions of the

relay, protection in particular.

This paper reviews the basic aspects of synchrophasor

implementations integrated with protective relays. It

presents the key technical challenges, and discusses

solutions that eliminate the risk of impacting the core

protection functionality of the relay. The paper offers

simple tests that can be applied to gauge impact of an

integrated PMU on the overall performance of a given

relay.

The overall goal of this paper is to educate the user and

allow for more rational decision making with respect to

deploying integrated versus standalone PMUs.

Index Terms—Data acquisition, Phasor Measurement Units,

PMU functions in microprocessor relays, synchrophasors

I. INTRODUCTION

ynchronized phasor measurements have come a long way

since their conception [1]-[3]. Many potential applications

have been identified [2], including improved state estimation,

frequency estimation, instability prediction, adaptive relaying,

and wide area control, for example. The recently published

IEEE Standard C37.118 [3] will assure that compliant phasor

measurement units will all report phasors using the same

convention for measuring phase angle, particularly when the

underlying power system frequency is off-nominal.

Even though today’s installations of Phasor Measurement

Units (PMUs) are limited in coverage and enterprise

communication performance, it is clear the technology will

advance quickly yielding significant benefits.

Widespread deployment of the PMUs providing for both

appropriate penetration and redundancy of synchronized

measurements is a key factor. Such widespread deployment

can be achieved when integrating the PMU function within

modern microprocessor-based relays - similar to the relay

integration trend seen with metering, fault recording, and

sequence of event recording capabilities.

Implementation of PMU functions, however, imposes new

requirements on protection platforms. Most importantly PMUs

require correlation of the waveform samples with the absolute

time driven by the Global Positioning System (GPS), and

reporting the measured phasors with reference to such absolute

time. Traditional relay implementations sample their input

voltages and currents asynchronously from any external

process such as the GPS time, and derive measurements as

quickly as possible for speed of response.

Additional processing requirements are presented for the

relay to measure, communicate and record the PMU data in

addition to providing for their core protection functionality.

All this raises potential concerns with respect to integrating

PMU functions in protective relays. Whether on new platforms

or as a part of an upgrade of an existing product, changes to

the existing or commonly deployed data acquisition system of

a relay in order to accommodate synchrophasors can have

serious consequences for all the other functions of the relay-

protection in particular.

This paper reviews the basic aspects of synchrophasor

Implementation and Performance of

Synchrophasor Function within Microprocessor

Based Relays

Bogdan Kasztenny, Fellow, IEEE, Mark Adamiak, Fellow, IEEE

S

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implementations integrated with protective relay functionality.

It presents the key technical challenges, and discusses

solutions that eliminate the risk of impacting the core

protection functionality of the relay. The paper offers simple

tests that can be applied to gauge the impact of an integrated

PMU on the overall performance of a given relay.

The overall goal of this paper is to educate the user and

allow for more rational decision making with respect to

deploying integrated PMUs versus standalone PMUs.

II. ISSUES WHEN IMPLEMENTING SYNCHROPHASORS ON

PROTECTION PLATFORMS

It is self evident that wide penetration of PMUs facilitating

both faster accumulation of experience in preparation for

advanced applications, and redundancy of measurements

required for the future critical applications of synchrophasors,

can be naturally achieved by integrating PMU functions with

protection and control platforms. Successful integration of

sequence-of-events (SOE) and digital-fault-recorder (DFR)

capabilities with protective relays is a historical lesson to

follow when considering cost-efficient and widespread

deployment of PMUs.

Modern protection platforms are capable of supporting

synchrophasor measurements, local recording and reporting.

This relates to internal architectures, time synchronization,

metering accuracy, communication capabilities, and

processing power required to comply with the C37.118

requirements.

However, microprocessor-based protection relays have

been designed historically without regard to the notion of

absolute time. Time stamping for SOE and DFR recording is

probably the only instance of reference to an absolute time in

protective relaying. Sampling and synchronization, even in

critical and high performance systems such as the line current

differential protection, is typically achieved without reference

to the absolute time. This is a prudent protection approach as it

limits exposure of mission-critical protection functions to

availability and misbehavior other devices such as the GPS

system and associated receivers/clocks.

Predominantly protection relays sample asynchronously

with respect to the absolute time, but in synch with power

system frequency. The latter is to keep the digitally

implemented measurements accurate should the power

frequency depart from its nominal value.

The following sections provide some insight on

implementation of synchrophasors on a typical

microprocessor-based relay [4]. It presents some solutions, and

highlights certain aspects that need to be understood and

evaluated by a protection engineer to make sure the extra

functionality put on a relay does not jeopardize the core

protection task of the device.

III. DESIGN PRINCIPLES WHEN IMPLEMENTING

SYNCHROPHASORS ON EXISTING PLATFORMS

It is prudent to follow these design principles when

implementing synchrophasor measurements on existing or new

protection platforms:

1. The underlying sampling process of the relay shall not be

altered. Sampling and data collection potentially affects

all other functions of the relay. To minimize the risk, this

area shall not be modified. Sampling in synchronism with

the absolute time is not only unnecessary; it actually yields

a substandard solution from the point of view of metering

accuracy as shown later in this paper.

2. The synchrophasor calculations shall be added in parallel

to the existing protection, control and metering functions

to minimize the risk of affecting these critical functions.

3. Hardware modifications shall be minimized for the reason

of stability of the design.

4. Calculations shall be organized in a way that the extra

processing power is optimally distributed and can be

accommodated by existing platforms with appropriate

security margin, even under fault conditions and other

periods of increased activity of an IED.

The key design areas for implementation are: timing

accuracy; sampling and correlating input signals with the

absolute time, algorithms for accurate measurement of the

phasors, data storage, recording and streaming.

IV. TIMING ACCURACY

Accuracy of synchrophasors as measured by the C37.118 is

defined as a Total Vector Error (TVE) being the percentage

magnitude of a vectorial difference between the measured and

actual phasors treated as vectors.

As such the TVE has three major components: magnitude

error, angle error as related to the input signals, and angle

error as related to the measurement of the absolute time.

It is enlightening to think of time as a quantity that needs to

be “measured” by a given device based on a standard physical

input, such as the 1 pulse per second (1pps) marker embedded

in the standard IRIG-B input. Assuming 1% TVE target as per

the C37.118, and budgeting accordingly for the three sources

of error, leaves up to 5-8 microseconds for the total timing

error.

Not only does a given device needs to synch with the 1pps

signal but between the pulses, the device must internally

maintain a very precise notion of time so that each of the

synchrophasor reference points (referred in this paper as

“synchrophasor interrupts”) occurring within the period of the

full second is maintained with an error not larger than few

microseconds.

Figure 1 illustrates this process. In one particular

implementation a precise phase lock loop is run with the

objective to null out the positional error between the 1pps

signal and the last synchrophasor interrupt that ought to occur

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exactly at the top of the second. This phase lock loop

compensates for the natural drift of the internal IED oscillator,

and the finite resolution of the latter.

For example, a given oscillator could have an error of say

25 parts per million as specified by the component

manufacturer. This means it could drift up to 25 microseconds

over a period of 1,000,000 microseconds (1 second). This

value would prevent successful implementation of

synchrophasors. Moreover, the error can change with

temperature and between different articles (samples) of the

oscillator. The drift, however, is easily measurable with the aid

of the 1pps signal. When measured, validated, and averaged,

the drift of the oscillator is an input to the phase lock loop

making the internal time keeping mechanism extremely

accurate.

IRIG-B 1pps signal

ts

ts

ts

ts

Ideal

Actual:

Definition of Errors

E0

E1

E2

EN-1

E0

( ),...,,...,,max 0110 EEEEE −=

Fig. 1. Defining synchrophasor interrupts and timing errors.

The compensation process works as follows. The

algorithm, using a precise hardware-implemented interrupt

service, captures the local relay time (oscillator value) at the

exact moment of the 1pps reference pulse. If the internal relay

oscillator is perfect, the captured value should be exactly

1,000,000 microseconds from the last 1pps pulse. A reading of

1,000,015 microseconds, for example, means the oscillator is

15 microseconds / second too fast; while the reading of

999,994 microseconds means the oscillator is 6 microseconds /

second too slow.

The value of the second-over-second drift is checked for

validity, and averaged over longer periods of time. The secure

and smoothed out value is now used to control the oscillator or

as a correction in the algorithm generating the synchrophasor

interrupts. Our solution uses the measured drift of the internal

oscillator to discipline the synchrophasor interrupt generator

rather than control the oscillator [4]. This avoids changes to

the relay and thus following the design goals outlined in

section 3 above.

Another issue is the required resolution of the internal

oscillator. Assuming 60 synchrophasors are produced per

second, the synchrophasor interrupts are to be generated every

1,666.66(6) microseconds. When this number is rounded to a

practical oscillating frequency, an error would accumulate

making the last synchrophasor interrupts in a given second

inaccurate. For example assume an implementation using 0.25-

microsecond resolution that is generating synchrophasor

interrupts every 1,666.50 microseconds. The 1,666.50

microsecond interval is off only by 0.166(6) microseconds

from the ideal value. However, after 1 full second when this

error adds up 59 times, the last interrupt within the second will

come after 60*1,666.50 = 999,990 microseconds that is a 10

microsecond error from the required time.

In addition, assume the oscillator is too slow by 12

microseconds in each second (example). To compensate for

the drift each synchrophasor interrupt will have to be adjusted

by 12/60 = 0.2 microsecond, while a practical resolution of the

oscillator can be in the range of a quarter of a microsecond.

The 0.25 – 0.20 = 0.05 microsecond error repeated 60 times

within each second would yield 3 microseconds of error eating

away from the tight timing error budget required by

synchrophasors.

To minimize this error, a dithering algorithm is applied

yielding a high accuracy of timing for the synchrophasor

interrupts. An internal variable is used to count the time with a

nanosecond accuracy, while the interrupts are generated with a

0.25 microsecond resolution. The device keeps track of the

error accumulated due to the finite resolution of the oscillator.

Once the error reaches half the resolution period, the

synchrophasor interrupt is moved by one resolution period. In

this way the error is kept below half the period of the

oscillator, and never accumulates.

The discussion on timing presented in this section is an

excellent illustration of issues and challenges faced when

implementing synchrophasors on existing relay platforms or

traditionally designed new relay platforms. The solutions

outlined in this section are elegant and avoid any changes to

the existing relay hardware, thus minimizing the risk and

avoiding expensive internal oscillator upgrades. The “time

keeping” is implemented in software based a on carefully

crafted algorithm.

V. SAMPLING FOR PROTECTION AND SYNCHROPHASORS

Protective relays typically do not sample synchronously

with respect to the absolute time. Instead, they sample based

on a free-running sample and hold timer and often apply

frequency tracking or compensation so that the measurement

calculations retain accuracy even if the system frequency

departs from the nominal value. It is a common misconception

that measuring synchrophasors requires sampling

synchronously to absolute time.

Some applications force the data acquisition system (A/D

converter) to take samples at precise pre-defined points in time

with respect to absolute time. This, however, results in

unnecessarily complicated designs, and is not required. In

order to measure synchrophasors one needs to know the

absolute time of each sample taken by the A/D, but these

samples can be taken at any point in time. They do not have to

be “hard-synched” to the GPS clock.

Relays and other devices measuring sine waves apply

frequency tracking. These devices calculate features of sine-

waves (magnitude, for example) using their measuring

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algorithms such as the Fourier Transform. These algorithms

assume typically a constant pre-defined number of samples

taken in each period of the waveform. If the system frequency

changes, the period changes, and the number of samples in a

period would change as well if using a constant sampling rate.

This would yield certain finite measurement error. In order to

eliminate this error either the sampling rate is made variable to

follow the system frequency, or a numerical compensation is

programmed in the device.

The first approach is typically more popular and referred to

as “frequency tracking”. Effectively, frequency tracking varies

the length of the data window used for digital measurements to

follow the length of the signal period as it varies under off-

nominal frequencies and power swings.

Another misconception is that staying in synchronism with

the system frequency (for accuracy) and staying in

synchronism with the absolute time (for phase reference) are

contradicting targets, and require convoluted solutions such as

measuring the magnitude and angle using different algorithms.

The former is about adjusting the length of the data

window so that it covers pre-selected multiplies of power

cycles; the latter is about positioning of this data window so

that the measurement complies with the C37.118 angle

convention.

Both can be controlled independently with no major

obstacles. One may think about these two processes as having

two controllers: one positions the center of the data window to

align it precisely with the synchrophasor interrupts; the other

controls the sampling rate to keep the length of the data

window in relation to the slightly changing system frequency.

Although the samples must be correlate-able to absolute

time, they can be taken at any time instant. Figure 2 presents a

solution in which the samples are collected asynchronously

with respect to absolute time. The platform applies frequency

tracking to keep the number of samples constant in the actual

period of the waveform as the period changes [4]. When the

synchrophasor interrupt is asserted, the device locks the

sample index and collects half its data window from the

samples that follow the interrupt and half – from the samples

preceding the interrupt. In this way, without altering the

sampling process the device gets a data window that is placed

very closely with respect to the required reporting point in

time.

Synchrophasor Interrupt

DSP time

x

(1)

(2)

(3)

(31)

(32)

....

(-1)

(-2)

(-31)

(-32)

x(k)

t(k)

a sample immediately after

the synchrophasor interrupt is

labeled (1)

a sample immediately before

the synchrophasor interrupt is

labeled (-1)

t0

Fig. 2. Data window based on asynchronously taken samples.

Note that in this approach:

• The length of the data window is already correct and

adequate as the sampling period is controlled by the

frequency tracking mechanism;

• The position of the window is within half of the sampling

period from the required position as per the synchrophasor

convention.

• It is trivial for the device to calculate the offset between

the center of such “best-placed” window and the required

position of the window. Calculate of this difference does

not require referring to absolute time. This time difference

is used to compensate the synchrophasor measurements as

explained below.

The device calculates the center of the window by

averaging the time stamps of the samples within the window.

This averaging is done using any time reference, not

necessarily the absolute time reference. In our implementation

a free running microsecond counter is used to calculate the

position of the center of the data window. The same free

running counter is used to capture the time of the

synchrophasor interrupt asserted based on the true absolute

time. Even though the free running microsecond counter is not

a true time, the time difference between the synchrophasor

interrupt (point when the center of the window should be), and

the calculated center of the window (point when the data

window actually is) is precise and can be used for

compensation.

Following the window selection procedure illustrated in

Figure 2 the DSP places the window to within few degrees to

the synchrophasor interrupt. The inherent displacement is

precisely measured and is used for very precise compensation

of the calculated phasor (an angular rotation of 2-3 degrees as

described later in this paper).

This approach is ideal for typical relay architectures:

samples are taken by data acquisition systems typically

incorporating an A/D converter and a Digital Signal Processor

(DSP). These data acquisition subsystems typically do not

have a notion of absolute time. In our approach a very simple

solution is adopted. In this architecture (Figure 3) the Central

Processing Unit (CPU) of the IED synchronizes to the 1pps

signal and executes the phase lock loop that generates precise

synchrophasor interrupts. These interrupts are captured by the

DSP using a “local DSP time” in the form of a free running

counter. The interrupt triggers calculations for the

synchrophasor instant and allows the DSP to obtain the notion

of time, and produce the phasor precisely aligned with the time

mark as driven by the interrupt.

VI. POST-PROCESSING AND EXTRA FILTERING

As depicted in Figure 4, our device uses “best-placed”

windows for synchrophasor measurement without altering the

sampling process (windows X). It measures the small shift

between the required and actual positions of such windows and

compensates for the difference by a simple phasor rotation.

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This yields synchronized full-cycle Fourier windows (windows

Y).

C P U(notion of absolute time, asserts

synchrophasor interrupts)

D S P(local time; samples

asynchronously)

measured

input

IRIG-B / 1pps

input

synchrophasor interrupt =

= position of the window

sampling frequency =

= length of the window DATA

I E D

Fig. 3. CPU & DSP architecture for synchrophasor implementation.

time

X(-3) X(-2) X(-1) X(1) X(2)

Y(-3) Y(-2) Y(-1) Y(0) Y(1) Y(2)

P(-3) P(-2) P(-1) P(0) P(1) P(2)

S(-3) S(-2) S(-1) S(0) S(1) S(2)

X(0)

1/fREPORT

1/fREPORT

1/fREPORT

1/fREPORT

1/fREPORT

Example: 5-point symmetric post-filter used

"best-placed" windows of

asynchronous samples

one-cycle synchronized

Fourier

4-parameter GE model

Post-filtered, final

synchrophasor

Fig. 4. Processing of best-placed raw data windows into synchrophasor

values.

The X and Y windows are produced at nominal system

frequency regardless of the recording or reporting rates set for

the PMU function. A pair of Y windows (the present and past

windows) is used to implement the four-parameter signal

estimator as described later in this paper. As a result a new,

more accurate estimate of the phasor is calculated at the rate of

nominal system frequency (windows P in Figure 4). The P-

values are calculated assuming the phasor may change in time,

and as such are extensions of the C37.118 synchrophasor

standard, aimed at future dynamic applications of

synchrophasors.

In order to control the balance between speed and accuracy

of the measurement, the device further implements user

selectable post-filtering, that is, a number of P-measurements

can be combined into the filtered synchrophasor output, S,

effectively extending the estimation window. The post-filtering

is not a straight average, but takes into account the value and

rotation speed of each of the used P-values as described later

in this paper.

VII. COMPENSATING FOR ANALOG ERRORS

Synchrophasor implementation calls for accuracy above a

typical protection accuracy or metering accuracy as typically

provided on protective relays. When implemented on a

protection platform, synchrophasors may need correcting for

errors of the IED’s input transformers.

Figure 5 shows a correcting function for the current inputs:

the correction is small – in the order of 0.2 – 1.8 degrees – and

depends on both the magnitude and frequency of the signal. In

particular at very low signal levels and lower frequencies the

excitation current of the input transformers starts causing some

angular errors, and the device applies higher correction for the

measured angle for the current inputs.

Fig. 5. Correction of current input transformers.

Figure 6 shows the correction applied to the voltage inputs.

The required angle shift to keep the measurements accurate is

smaller (up to 0.2 degrees), and again depends on the

magnitude and frequency of a given voltage input.

Fig. 6. Correction of voltage input transformers.

Analog filters, necessary in any digital measuring system to

deal with aliasing of samples, introduce a phase shift, which

also needs to be compensated. When the analog filter is set

relatively high, the phase shift for the frequency band around

the nominal is very linear, and can be easily compensated.

Figure 7 shows the measured (red dots) and applied (blue line)

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correcting angles accounting for the impact of analog filters in

the solution [4].

20 30 40 50 60 70 80-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

Frequency, Hz

Angle Correction, deg

Fig. 7. Correction for the Analog Filter.

The few implementation details outlined above are meant to

direct attention to the way synchrophasors are implemented on

protective relays, and the potential impact on the existing

mission-critical protection functionality. In the outlined

implementation minor hardware changes were required to

provide synchrophasor interrupts from the central processing

unit, having the notion of the absolute time (from the IRIG-B

input), to the digital signal processor, which is responsible for

the majority of the calculations but has no direct relationship

with absolute time. All the other aspects of the synchrophasor

implementation have been accommodated in software, in

subroutines completely detached from the key protection

functions. This minimizes the risk and allows claiming a very

secure implementation [4].

VIII. IMPLEMENTATION OF THE DATA COMMUNICATIONS

PROTOCOL

An important part of the C37.118 synchrophasor standard

is the interoperable data communication protocol. The

C37.118 protocol is a low-overhead “lean” protocol well

suited for real-time data communication. The communication

is organized around 4 types of frames:

• Configuration frames describing either present or

maximum device configuration are sent to the higher

order system (Phasor Data Concentrator, PDC) on

demand or automatically upon configuration change of the

PMU. These frames are therefore sent only exceptionally

and are intended for the PDCs.

• Header frame is similar to the configuration frames but is

not standardized and contain human-readable information

about the PMU.

• Command frame is sent by a PDC and received by the

PMU (relay when integrated). Commands are sent to stop

and resume data transmission, request configuration data,

or execute actual commands by sending data that could be

used to close/open an output and execute other user-

programmable actions.

• Data frames are sent continuously by the PMU (relay) at

regular and C37.118 standardized time intervals.

Streaming data frames is of primary concern when

considering integrating PMUs with microprocessor-based

relays. The standard specifies 30 frames per second as the

fastest reporting rate, but some implementations support up to

60 frames/second. Data content may vary from a single phasor

(typically the positive-sequence voltage) to several sets of

three-phase voltages and currents (frequency and rate-of-

change of frequency are always sent).

Assume sending 6 phasors (3 currents and 3 voltages) each

represented by 2 numbers (real and imaginary or magnitude

and angle); with each number encoded on 2 bytes and reported

at 30 frames a second. Ignoring the overhead one gets the bit

rate of:

6 (phasors) x 2 (real, imaginary) x 2 (bytes) x 8 (bits) x 30

(frames / second) ≈ 5.76kbps

Even when accounting for the protocol overhead and

doubling the reporting rate, as increasing the packet size by

including frequency, rate of change of frequency, etc. one

stays within the DS0 level of 64kbps.

Modern protection relays are built to comfortably serve

64kbps real-time traffic. Such channels are used for

teleprotection or in line current differential applications.

In addition, multi-function relays have been used for years

to support SCADA and automation functions by providing for

server functionalities of typical SCADA protocols (DNP,

Modbus, UCA and IEC61850). Compared with these protocols

the C37.118 synchrophasor protocol is neither complex nor

demanding and can be safely implemented on a modern

microprocessor-based relay.

IX. IMPLEMENTATION OF THE RECORDING FUNCTIONALITY

Typically PMUs provide for data recording functions.

These are useful in applications when no real-time

communication is provided between the PMUs and the PDC,

or in cases when the communication fails or is temporarily

unavailable. Because system events are of interest, the time

horizon for practical recorders is in the range of minutes or

tens of minutes. This calls for mega-bytes of storage space.

Assume again the 5.67kbps data rate from the previous

example, and consider a system event recorded for 10 minutes.

The required storage space is in the range of:

10 (minutes) x 60 (seconds / min) x 5.67kbps ≈ 3402kb, or 3.402/8 MB ≈ 0.42MB.

Modern relay may provide for tens of MB of data storage,

allowing records as long as few tens of minutes even at very

high recording rates.

Proper engineering of the recording function needs to allow

for the following:

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• Safe recording for tens of minutes during which faults and

other events can occur.

• Safe power down when recording – the control power can

be removed when the PMU function is recording and

producing massive records. No data corruption or other

unexpected deficiencies should take place under such

circumstances.

• Safe retrieval of stored data. When using a slow

communication media to access the relay, it may take

minutes to download the stored records. During this time

faults, system events, or new records may occur. The relay

needs to respond accordingly always giving priority to the

protection functions.

Recording capabilities are standard on modern relays. The

above problems exist today, and have been solved. The only

difference between an existing fault recorder and an added

PMU recorder is the amount of data and duration of recording

or extracting the record from the device.

X. REQUIREMENTS FOR THE EXTRA PROCESSING POWER

Measuring (calculating) synchrophasors including: precise

timing, data collection and data processing, and various

required corrections as described earlier; communicating the

measured data as well as serving requests from the PDC; and

performing local triggering and recording require extra

processing power.

Modern relays use multiple processors for data processing,

logic engines, and communications. As a result it is achievable

and safe to integrate the PMU function, assuming a prudent

approach is taken with respect to the architecture.

In our solution each set of 8 analog signals (ac voltage and

currents) is given a separate DSP to process the associated

data. This results in a scalable architecture when adding more

inputs to a given relay does not put more requirements on the

DSP. This is no different with the synchrophasor calculations.

When interrupted by the synchrophasor time tag, a DSP

gathers a data window, calculates the full-cycle Fourier phasor,

calculates the center of the window and the offset of the center

with respect to the synchrophasor interrupt, compensates

(rotates) the phase to account for the small offset, and

compensates for the errors of VTs, CTs and the impact of

analog filtering. These operations are very lean and account

for only a small portion of the full set of typical DSP

calculations required.

The rest of the process of calculating synchrophasors runs

only at 60 times a second, and is relatively simple (Figure 4).

The communication protocol runs at up to 60 times a

second, and therefore is relatively lean as well. The same

applies to the integrated PMU recorder.

In our approach, the processing power required to provide

for the PMU function even when reporting at the rate of 60

phasors a second, is at the level similar to calculations required

to run one zone of distance protection. We consider it

moderate and acceptable. No protection functions are

suspended or delayed as a result of synchrophasor

activities/calculations. No synchrophasor functions are

suspended or delayed as a result of protection events or

activities.

XI. TVE ACCURACY ACHIEVABLE WHEN INTEGRATING

PMU’S ON PROTECTION PLATFORMS

The following summarizes the steady state performance as

tested on the IED hardware [4]:

• TVE for voltages, frequency range 45-70Hz < 0.30%

• TVE for currents, frequency range 45-70Hz < 0.40%

• TVE at 10% of THD, nominal frequency < 0.45%

Figure 8 presents results of the interfering frequency test

when reporting at 60 times per second, and using a user-

selectable 7-point post-filtering algorithm.

Interfering Frequency Test

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%

5 10 15 20 25 30

Added Frequency (10% of magnitude)

TVE, %

Fig. 8. TVE under interfering frequency tests

(reporting at 60/second, 7-point post-filter applied).

The described implementation details, and the test results

prove that when carefully engineered, modern P&C platforms

allow for both secure and accurate implementation of

synchrophasor measurement, recording and reporting. When

integrated with protection platforms the PMU functionality is

provided universally with wide coverage of the metering

points, at a fraction of the cost of stand-alone PMU solutions.

XII. EXAMPLES OF SYNCHROPHASOR MEASUREMENTS UNDER

FAULT CONDITIONS

This section presents few examples of synchrophasor

measurements under simulated fault conditions.

Figure 9 shows a case of a reverse ABG fault as recorded

by a line current differential relay. During the fault the system

frequency was 59Hz, and the relay frequency tracking

mechanism was intentionally disabled in order to test the

response of both protection and PMU functions under

frequency errors.

The top three traces show current waveform recorded by

the relay. The next three traces are voltages, with the A and B

voltages dropping to zero during the fault.

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The last trace shown in Figure 9 is the operand of the 87L

function. As expected, the integrity of this key function is not

jeopardized by either the external fault, off nominal frequency,

or PMU function operational on the same IED platform.

Similarly other protection functions respond correctly. For

example, the neutral directional reverse-looking overcurrent

element picks up during the fault and stays operated for the

entire duration of the fault.

Fig. 9. Sample record of a line-current differential relay containing both

oscillography data (samples) and PMU data (synchrophasors).

The “PMU1 Va Mag” trace shows the magnitude of the

phase A voltage as measured by the synchrophasor algorithm.

The value is steady and accurate regardless of the off nominal

frequency (signal at 59Hz, relay sampling at 60Hz). The

“PMU 1 Va Angle” trace is the angle measurement. This value

is recorded at 60 times / second and makes one full revolution

every second. This is expected as the signal is at 59Hz, thus

recorded 60 times a second it changes at (60-59)*360deg/sec.

For comparison the “3403 Vag Mag” trace is the voltage

magnitude as measured for protection purposes. The

synchrophasor version (PMU1 Va Mag) and the relaying

version (3403 Vag Mag) are better shown in Figure 10. The

synchrophasor measurement is implemented using an

algorithm optimized for accuracy. As such this trace does not

show the ripple distinctive for the off nominal frequency

situation, and is accurate to within 1% of TVE. The protection

measurement is affected by the off nominal frequency (visible

ripple and the average value slightly off). This is because the

relay was configured with frequency tracking disabled for the

purpose of the test. Even with tracking disabled this particular

relay shows only 2-3% of error in voltage for every Hz of

frequency difference.

Figure 10 also illustrates that the synchrophasor values are

recorded every 1/60th of a cycle (user setting), while the

protection values are refreshed 8 times a cycle or every 1/480th

of a second. Also, having less filtering and being optimized for

speed rather than accuracy, the protection version of the

voltage measurement responds much quicker to the voltage

changes, exhibiting a short lasting overshoot when the voltage

recovers after clearing this external fault. At the same time the

synchrophasor measurement is very well controlled showing

no overshoot or other problems.

Fig. 10. Synchrophasor and protection measurements on the same

voltage signal in the record of Fig. 9.

Figure 11 shows and internal fault occurring under off

nominal frequency (59Hz while the relay intentionally tracked

to 60Hz). The fault is cleared by the 87L function as expected.

Other protection, such as zone 2 shown in the Figure, operate

as expected and stay picked up for the entire duration of the

fault.

This test was done as a closed loop test resulting in opening

the breaker. Once the breaker opened, the line-side VTs

measure the voltage oscillating between the line capacitance

and shunt reactors. The phase C voltage decays exponentially

and the frequency measured by the relay changes from 59Hz in

the pre- and fault periods, to about 50.3Hz being the

resonating frequency between the line and its shunt reactors

(Figure 12).

Fig. 11. Sample record of a line-current differential relay containing both

oscillography data (samples) and PMU data (synchrophasors).

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Fig. 12. Phase C voltage decays after the breaker opens. The PMU

measurement tracks the dynamic of this signal. The measured frequency

registers the actual 50.3Hz resonant frequency between the line and its shunt

reactors.

The phase A voltage registers small values coupled via the

shunt reactors after the breaker is opened and the fault

removed. It is worth observing the phase angle of this voltage

as measured via the synchrophasor algorithm. Figure 13

displays the phase A voltage angle. Before the fault the angle

changes at the rate of 360deg/sec because it is reported at 60

times a second while the signal is of 59Hz ((60-

59)*360deg/sec). When the voltage is driven by the 50.3Hz

resonant frequency on the disconnected line, the angle changes

much faster at (60-50.3)*360deg/sec = 3500deg/sec, or one

full revolution every in less than 100ms.

Fig. 13. Phase A voltage coupled after the breaker opens. The PMU

measurement reflects the frequency of this signal (seen as the rotating phase

position of the voltage vector).

Examples presented in this section demonstrate the power

of synchronized measurements to post-mortem analysis,

including faults. Also, they depict secure co-existence of

protection and PMU functions on the same IED platform.

XIII. TESTING RECOMMENDATIONS FOR PMU’S INTEGRATED

WITH PROTECTIVE RELAYS

Protection and control platforms integrating PMU

functions should be tested in both protection and PMU modes

of operation.

The protection functionality shall be tested given specific

evaluation and approval philosophy for protection and control

relays. During those tests the PMU functions should be

enabled and configured in a way representative for a typical or

worst-case future application. Similarly, the PMU functionality

should be tested with a set of protection functions enabled and

configured to reflect typical or worst-case future applications.

Having both sets of functions enabled and configured

allows identifying any natural or unintended interactions

between the two functionalities.

While the above general rules are followed, a few specific

tests are worth recommending as follows:

• Speed of response of key protection function shall be

checked during PMU-related activities. This includes

normal PMU operation and extra activities such as

coincidence of a system fault with a PMU command

issued towards the IED from the PDC, local recording

being initiated or in progress, retrieval of local records,

and so on.

• Accuracy and integrity of key protection functions shall be

checked during increased PMU activity.

• Accuracy and speed of response of key protection

functions shall be checked during off-nominal

frequencies. This includes steady state frequency

deviations as well as frequency ramps. Modern protective

relays are typically designed to retain full functionality

under steady state off nominal frequencies, and exhibit

only slightly degraded performance under frequency

ramps, with the extent of degradation depending on the

rate of frequency change. Increased demand on PMU

accuracy under abnormal frequency conditions may result

in shifting the design targets - potentially impacting

performance of the core protection functions of the

device.

• PMU functionality shall be checked under fault

conditions. This includes any impact on accuracy after the

fault is cleared, as well as integrity during the fault

condition. For example, are all data frames produced

during the fault or some of them may be lost? Is the post-

fault steady state accuracy as expected or is the

disturbance is having a long lasting impact on the

accuracy of subsequent measurements?

• Integrity of both protection and PMU functions shall be

checked under periods of simultaneous activity. For

example, a command frame can be issued toward the IED

just before a fault is applied – response to the fault should

be checked as well as response to the command frame.

• Integrity of protection functions should be checked under

impairments of IRIG-B input signal. Having to correlate

measurements with the absolute time, IEDs implementing

PMU functions may become affected by impairments of

the IRIG-B timing signal. Adding noise, particularily to

generate spurious 1pps patterns, or invalidating the time

and date code is a meaningful check when overlaid on

fault conditions. Step changes in time and date generated

at the IRIG-B clock, or leap seconds, are good tests as

well. Overall integrity of protection – both speed and

selectivity – should be verified under such abnormal

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activities of the IRIG-B input.

• Communication impairments related to the PMU-PDC

data exchange should be tested with respect to integrity of

key protection functions. Classical channel impairments

such as bit error rates corrupting the packets, multiple

requests, invalid requests, etc. should be placed

simultaneously with fault conditions. Selectivity and speed

of protection should not be compromised.

• Dynamic response of the synchrophasor measurements

under fault conditions should be tested and understood.

The C37.118 standard does not mandate any specific

performance under dynamic conditions, such as during

system faults. However, PMU records will be a valuable

source of information for post-mortem fault analysis.

Response of a particular synchrophasor algorithm under

fault condition needs to be tested and understood before

the records can be used for fault analysis.

XIV. SYNCHROPHASOR MEASUREMENT ALGORITHM

This paper describes implementation of synchrophasors on

modern relay platforms. Our particular implementation uses an

optimized algorithm aimed at measurements under dynamic

conditions.

Under steady-state operation of a power system at a

constant known frequency, the appropriate definition of a

synchrophasor is intuitive and obvious, and is the one

specified by the C37.118 standard [3]. However, during

dynamic conditions, it is not as clear what the definition

should be. Also it is well known that off-nominal frequency

operation [5] or power swings [6] can cause issues in the

accuracy of the results of a classical phasor computation. For

example, a power swing is actually equivalent to at least two

closely spaced, distinct power frequencies with comparable

amplitudes. Which one should be reported? Our

implementation uses a multi-parameter model that resolves

these issues, as well as matching the classical model under

steady state operation at a single frequency.

Under steady-state conditions, a synchrophasor is the

cosine and sine projections of a power system signal, at

whatever frequency the power system is operating [3]. It is not

necessary or likely for the power system to be operating

exactly at the nominal frequency. The phase angle of a

synchrophasor is defined to be the angle between the reporting

time-tag and the peak of the signal, at the actual frequency [3],

so the issue of steady state off-nominal frequency does not

arise in the definition of synchrophasors, only in their

implementation [5].

The question arises how to define a synchrophasor during

changing conditions? A logical approach is to define the

power system signals to be projections of phasors that

themselves are changing in time:

( )

phasor varyingtime)(

time

or voltagecurrent ousinstantane)(

)(2)(2

=

=

=

⋅⋅≈ ⋅⋅

t

t

tx

etRealtxtfj

X

Xπ

(1)

Definition (1) encompasses both changes in phase angle as

well as changes in amplitude, so it models both the off-

nominal frequency case, as well as power swings. The value of

a phasor at a time-tag is simply the value of the time varying

phasor in (1) when the time is equal to the value of the time-

tag of the reported synchrophasor.

It is well known that the classical algorithms for computing

phasors on a per-phase basis from sequences of samples incur

errors during off-nominal frequency operation [5], [7] or

during power swings [6]. Most of the errors cancel out in

positive sequence phasors that are computed from per-phase

phasors, provided that the negative sequence value is equal to

zero. If there is some negative sequence, the errors in per-

phase phasors do not exactly cancel, so there is residual error

in the positive sequence phasor.

It is impossible in principle to tell the difference between

off-nominal frequency operation and a constant time rate of

change of the phase angle of the phasor. In either case, if the

sampling rate is not matched to the power system frequency,

errors arise [5], [7] in the classical algorithms. For constant

amplitude and phase angle signals, the computed per-phase

phasors trace an elliptical trajectory [7]. The eccentricity of the

ellipse can be predicted from the frequency. If the frequency is

known, the errors in the per-phase phasors can be exactly

compensated, though there will still be an issue of incomplete

harmonic rejection. Two other solutions to the off-nominal

issue include frequency tracking and re-sampling.

The off-nominal frequency effect is equivalent to a

backward rotating error [6]. If the underlying phase signals are

balanced, the backward rotating errors cancel in the positive

and zero sequence phasors computed from phase values,

although there will be an apparent negative sequence

component. If the phase signals are not balanced, there is

trouble in general.

The power swing case has been analyzed in [6], and one

method for greatly improving the accuracy using a raised

cosine windowing function has been described.

Another method, described here, uses a Taylor’s series

expansion to represent a time varying phasor to address both

the off-nominal frequency effects as well as power swing

issues with a simple extension of the classical algorithms for

computing phasors.

To solve this problem our implementation assumes both the

magnitude and “phase” of a phasor to be linear function of

time, and estimates such varying phasors to fit them best to the

measured waveforms. As a result our model gives much better

response under dynamic system conditions.

Annexes A and B describe our algorithm in detail.

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XV. CONCLUSIONS

This paper discusses various implementation issues related

to integration of synchrophasor measurements and PMU

functionalities on microprocessor-based relay platforms.

The paper alerts prospective users to possible pitfalls of the

integration and allows making a more informed decision based

on the understanding of both the synchrophasor and relay

technologies.

The paper discusses sample tests that could be used to

probe the robustness of the integrated PMU/relay

implementation.

We presented one particular way of implementing

synchrophasors that calls for practically no changes to the

underlying relay architecture. The sampling, frequency

tracking, data collection and manipulation processes have been

preserved with no changes. All the synchrophasor related

calculations and operations are kept completely separated

within a framework of object-oriented programming. The only

change is the addition of one new interrupt between the CPU

and DSP. This interrupt is not used at all by any of the

protection functions, thus minimizing any danger of

unintended changes.

The presented implementation is based on a novel multi-

parameter algorithm for estimating synchrophasors under

dynamic system conditions. The approach assumes slow

transients in the estimated phasors and solves the assumed

multi-parameter signal model accordingly to provide for both

accurate and fast synchrophasor measurements.

Test and simulation results prove equivalency with classical

algorithms under steady states, and superior performance

under system transients.

Test results on the actual hardware allow claiming accuracy

of approximately twice as good as the most stringent

requirements of the IEEE Std. C37.118.

It is justified to assume that synchrophasors will follow

SOEs, DFRs, RTU and metering functions and become

universally integrated on modern relay platforms. This is not

only possible with future new platforms, but also within

existing presently used relays. Careful engineering allows safe

implementations and the accuracy equal if not better than

standalone PMUs.

Integrated PMUs will allow wider penetration of this new

technology, faster learning curve, and cost savings related to

purchasing, installing and operating the equipment.

ANNEX A – FOUR-PARAMETER SYNCHROPHAOSR ESTIMATOR

A.1. Signal Representation

One way of representing raw current and voltage signals that

we are trying to compute phasors from is in the form of the

real part of Taylor’s expansion according to (2).

( )( )

frequency systempower nominal

phasor theof derivativefirst

phasor theof portionconstant

time

or voltagecurrent ousinstantane)(

2)(2

=

=

=

=

=

⋅⋅+⋅≈ ⋅⋅

f

t

tx

etRealtxtfj

X

X

XX

&

& π

(2)

We call this a four-parameter model, because the

specification of the constant portion of the phasor and its first

derivative with respect to time requires a total of four real

parameters to specify the model. In this model, the phasor is

meant to be a stationary value. If the actual power system

frequency is equal to the nominal value and the power system

is in steady state, X is a stationary value, and X&is identically

equal to zero. The goal is to accurately determineX in the face

of non-zero values of X&.

It is also possible to represent a time varying phasor with a

Taylor’s expansion in polar coordinates rather than Cartesian

coordinates. While this would be a better fit for the off-

nominal frequency situation, the mathematics would become

more complicated. For a one-cycle window, there would not

be much difference between an expansion in polar coordinates

and an expansion in Cartesian coordinates.

Equation (2) is applied over a limited time window in which

the expansion is approximately true, on the order of a few

cycles, in which the frequency and other parameters of the

representation can be considered constant. Of course, the same

model can be applied in a piecewise fashion over all cycles, by

selecting the appropriate parameters for each cycle.

It is convenient to (2) in terms of phasors and their complex

conjugates to eliminate the Real operator as follows:

( )( )( )( )tfj

tfj

et

ettx

⋅⋅−

⋅⋅

⋅⋅++

⋅⋅+≈

π

π

2**

2

2

2

2

2)(

XX

XX

&

&

(3)

The derivative term in (2) or (3) can be used to approximate

either slightly off-nominal frequency or power swings. In the

case of slightly off-nominal frequency operation, there is a

phasor derivative that is perpendicular to the phasor. In the

case of a power swing, there is a phasor derivative that is

parallel to the phasor.

A.2. Error analysis

Before proceeding to a four-parameter solution, it is useful

to examine the error introduced by a classical computation

when currents and voltages are given by (3). Suppose a phasor

is computed from samples of current and voltage with a

variation of the classical algorithm, using the one-cycle, N-

sample, centered “Boxcar” algorithm specified by (4).

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[ ]

[ ]

⋅+

=

⋅=+−

−

−=

∑

f

nxnx

enx

nj

n

2/1

22)2/1(

12

2

π

Y

(4)

We prefer the use of window that is centered on the time

reference for the phasor, because some types of errors exactly

cancel that way. N is assumed to be an even number. The

combination of even N and the centered window leads to a

shift in the sampling time equal to ½ of the sampling period.

Substituting (3) into (4), it can be shown that the computed

one-cycle phasor produced by (4) for the signal model given

by (3) is given exactly by (5).

⋅⋅⋅+=

f

jπ2

sin2

*XXY

&

(5)

The detailed steps in deriving (5) are not given here because

of space limitations. The derivation is not difficult: the

principal goal is reducing sums of powers of complex

exponential expressions to simpler forms. The summation

identities given in the Annex B are useful for that purpose as

well as analyzing other phasor algorithms, and the interested

reader is encouraged to use them to verify (5).

Under steady-state conditions with the actual power system

frequency exactly matching the nominal value, the derivative

term vanishes, and (5) indicates that the classical algorithm

recovers the correct value, X . However, if there is an off-

nominal frequency condition, or a power swing, or other

transient condition, there is a non-vanishing first derivative of

the phasor, and there is a backward rotating error phasor given

by the second term in (5). If we could somehow determine the

actual value of the derivative, we could compensate for the

error.

It can be shown that a positive sequence phasor computed

from per-phase phasors computed by equation (4) is related to

positive- and negative-sequence quantities as follows:

⋅⋅⋅+=

f

jneg

pospos π2sin2

*X

XY

&

(6)

This means that if the negative-sequence component is zero,

and if the positive-sequence phasor moves in a straight-line

trajectory in the complex plane, the classical algorithm will

produce the correct value for the positive-sequence phasor. For

the case of slightly off-nominal frequency operation or gradual

power swings, the trajectory can be approximated as a

gradually changing straight-line trajectory, so that we can

conclude that a classical algorithm will produce an

approximately correct estimate of positive-sequence quantities,

provided that the negative-sequence component is zero. If

there is a negative-sequence component, (6) indicates that off-

nominal frequency operation will produce an error in positive-

sequence quantities computed using the classical algorithm.

A.3. Estimating the time derivative of a phasor

Before proceeding to developing an algorithm for correcting

the error in the classical algorithm that is generated by a

changing phasor, we will need an estimate of the time

derivative of a phasor. One approach is to examine the

sequence of phasors computed by the classical algorithm.

Examination of (5) reveals that the error in a sequence of

computed phasors is the same for each phasor in the sequence,

provided the derivative of the sequence is approximately

constant. Therefore, the derivative can be estimated simply by

taking the differences of pairs of computed phasors in the

sequence.

For example, suppose that a phasor value is computed once

for each power system cycle, at the nominal, fixed, power

system frequency. Furthermore, suppose that the phasor

derivative over a few cycles is approximately constant. Then,

the phasor derivative at cycle M can be estimated from the

classically computed phasors at cycle M and cycle M-1 using

(7). Note that it is convenient to compute the ratio of the

derivative to the nominal power system frequency.

( )( ) ( )1−−≈ MM

M

fYY

X&

(7)

Equation (7) is exact for a phasor trajectory that is a straight

line in the complex plane. It is approximately true for off-

nominal frequency operation when the classically computed

phasors trace an elliptical trajectory in the complex plane.

A.4. Estimating the true value of the phasor

By substituting (7) into (5) and rearranging, it is possible to

derive (8), which is a simple formula for the corrected

estimates of phasors, starting with the classical algorithm and a

“Boxcar” window.

( ) ( )( ) ( )( )

−⋅−≈ −

jMM

MM π2sin2

1**

YYYP (8)

Equation (8) corrects classically computed phasors for the

error generated by the derivative of the phasors, provided the

phasors are computed using (4). It is also possible to derive

similar formulas for other variations of the classical phasor

computation by first computing the error introduced by the

derivative of the phasor.

Equation (8) is not difficult to implement in practice. The

constant denominator of the second term can be pre-computed,

and the division can be replaced by a multiplication by the

reciprocal of a constant. The effect of combining the

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multiplication by j with the conjugate operator can be achieved

by suitable sign changes and the swapping of real and

imaginary components.

The accuracy of (8) will depend on how well the actual

conditions are described by the assumed Taylor’s expansion.

For slight frequency deviations and for power swings, a first

order Taylor’s expansion is a reasonable approximation.

A.5. Performance of the Four-Parameter Estimator

A comparison of the performance of (8) with the classical

algorithm using a one-cycle window is shown in Figures A.1-

A.12. Figure A.1 is the theoretical performance during off-

nominal frequency for a 1 per unit phasor input. Total Vector

Error (TVE) as specified under the C37.118 Standard is

plotted versus frequency for a nominal frequency of 60Hz.

This is the same as the magnitude error, and approximately

equal to the angle error in radians. TVE for the four-parameter

algorithm is less than 1% over the range of 55 Hz to 65 Hz,

while the TVE for the classical algorithm exceeds 4%. This

translates to an angle error of less than 0.6 degrees for the

four-parameter algorithm, and more than 2.4 degrees for the

classical algorithm. Note that typical implementation apply

frequency tracking to eliminate the off-nominal frequency

errors. However, the tracking algorithms can lag intentionally

the actual system frequency, or become slightly inaccurate

during dynamic system conditions. Therefore, it is beneficial

to implement a phasor estimator algorithm that is naturally

immune to off-nominal frequencies.

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

50 55 60 65 70

Frequency, Hz

Angle error in radians, or magnitude

error

c lassicalFourier

4 parametermodel

Fig. A.1. Maximum error due to off-nominal frequency.

The theoretical TVE of the classical algorithm during a

linear ramp as the phasor crosses 1 per unit is shown in Figure

A.2. For a ramp rate exceeding 8 per unit per second, the error

exceeds 1 percent. The theoretical TVE of the four-parameter

algorithm is zero.

The results of a 5 simulation cases are shown in figures A.3-

A.12. For each case, there is a pair of time plots. The first plot

is the actual real and imaginary phasor components. The

second plot is a comparison of the total vector error for the

classical and four-parameter algorithms. Sampling rate is 64

samples per cycle. Nominal frequency is 60 Hz. Phasors and

TVE are computed for each sample.

Figure A.3, a simple linear ramp, is a rough approximation

of the current through a transmission line during a power

swing that results in a power reversal, where the voltages at the

opposite ends of the transmission line are swinging in opposite

directions. The plot of the TVE in Figure A.4 shows that there

is zero TVE for the four-parameter algorithm during most of

the swing. This is expected, because the approximations made

by the four-parameter algorithm are exact during a linear ramp.

The similar response of both algorithms at the start and the end

of the ramp is due to the discontinuity at those points.

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0 2 4 6 8 10 12

Ramp rate, per unit per second

Magnitude erro,r or radian phase angle

error

Fig. A.2. Classical error due to a linear ramp rate.

0 50 100 150 200 250-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time, milliseconds

Real, imaginary phasor

Actual phasor

RealImaginary

Fig. A.3. A linear ramp example.

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0 50 100 150 200 2500

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Time, milliseconds

Total vector error

Classical and 4-parameter TVE

Classical4-parameter

Fig. A.4. Classical and 4-parameter TVE response to a linear ramp.

The TVE for the classical algorithm climbs to a maximum

of 8%. The reason it climbs so high is due in part to the way

that TVE is defined as the ratio of the vector error divided by

the magnitude of the actual phasor. Because in this example

the magnitude temporarily approaches a small value, the TVE

for the classical algorithm surges. The point is, during a

reversing power swing, the four-parameter algorithm provides

superior performance.

The discontinuities at the start and the end of the power

swing in Figure A.3 are not encountered in practice. A more

realistic example is shown in Figures A.5 and A.6. In this case,

instead of a linear ramp, there is a cosine ramp, which is a

better approximation to actual behavior of a power swing. In

this case, there is less of a disturbance in TVE at the start and

the end of the swing. TVE for the four-parameter algorithm is

no longer identically zero, because the model is an

approximation. However, the TVE for the four-parameter

algorithm is less than 1% during the entire duration of the

swing, while the TVE for the classical algorithm climbs to

over 12%. The peak TVE for the classical algorithm depends

on how close the magnitude of the phasor approaches zero

during the swing. In this example, the minimum magnitude is

0.2 per unit.

0 50 100 150 200 250-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time, milliseconds


Actual phasor

RealImaginary

Fig. A.5. A cosine ramp example.

0 50 100 150 200 2500

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Time, milliseconds

Total vector error



Fig. A.6. Classical and 4-parameter TVE response to a cosine ramp.

A phase angle rotation example is shown in Figures A.7 and

A.8. The phase angle is a clockwise cosine ramp rotation

between minus 180 degrees and 0 degrees. For this example

the TVE of the classical algorithm exceeds 5%, while the four-

parameter algorithm is below 2%.

0 50 100 150 200 250-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time, milliseconds

Real, imaginary phasorActual phasor

RealImaginary

Fig. A.7. A phasor rotation example.

0 50 100 150 200 2500

0.01

0.02

0.03

0.04

0.05

0.06

Time, milliseconds

Total vector error



Fig. A.8. Classical and 4-parameter TVE response to a phasor rotation.

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Figures A.9 and A.10 show an off-nominal frequency

example, which is equivalent to a continuous angle rotation,

for a 58Hz actual frequency, 60Hz nominal frequency. The

TVE for the simulations agree with the theoretically predicted

values shown in Figure A.1.

0 50 100 150 200 250-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time, milliseconds


Actual phasor

RealImaginary

Fig. A.9. A 58/60 Hz off-nominal frequency example.

0 50 100 150 200 2500

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

Time, milliseconds

Total vector error



Fig. A.10. Classical and 4-parameter TVE response to off-nominal

frequency.

Finally, a combination of off-nominal frequency and a

magnitude shift is shown in Figures A.11 and A.12. TVE for

the classical algorithm approaches 70%. Our four-parameter

estimator provides for 3-4 times better performance.

0 50 100 150 200 250-1

-0.5

0

0.5

Time, milliseconds


Actual phasor

RealImaginary

Fig. A.11. A combination magnitude shift and off-nominal frequency

example.

0 50 100 150 200 2500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Time, milliseconds

Total vector error



Fig. A.12. Classical and 4-parameter TVE response to Figure A.11.

Keep in mind that for the examples shown in Figures A.3-

A.12, the calculation is over a single cycle. Multi-cycle

calculations of the new method may further reduce the TVE.

The window length is a user setting in our implementation.

Also, all cases were based on fixed sampling rate. It is possible

to greatly reduce errors due to off-nominal frequency effects

by adjusting the sampling rate in accordance with the

measured power system frequency. Our implementation allows

for tracking frequency in the range better than ±10Hz from

nominal, and rates of change up to 10Hz/sec.

A.6. Multi-parameter Taylor’s Expansion

It is possible to extend the model to include even more

terms in the Taylor’s expansion, using steps similar to those

given in the previous section. For example, a six-parameter,

second order model is developed as follows.

Extend the representation to a second order Taylor’s

expansion:

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( )( )

phasor theof derivative second

phasor theof derivativefirst

phasor theof portionconstant

2/2)( 22

=

=

=

⋅⋅+⋅+⋅≈ ⋅⋅

X

X

X

XXX

&&

&

&&& tfjettRealtx π

(9)

A sequence of phasors computed from the classical one-

cycle phasor algorithm given by (4) is assumed.

By substituting (9) into (4), it can be shown that the

computed one-cycle phasor produced by (4) for the signal

model given by (9) is given exactly by (10).

2

2

222

sin2

2cos

24

1

2sin2

+

−

+

⋅⋅⋅+=

f

f

f

j

π

π

π

*

*

XX

XXY

&&&&

&

(10)

The approach for estimating the first derivative of the

phasor for the four-parameter model is easily extended to

estimate the first and second derivative from differences in

phasors from a three-cycle sequence, given by (11).

( )( ) ( ) ( )

( )( ) ( ) ( )212

21

2

2

12

2

3

−−

−−

+−≈

+−≈

MMM

M

MMM

M

f

f

YYYX

YYYX

&&

&

(11)

By substituting (11) into (10) and rearranging, it is possible

to derive (12), which is another simple formula for the

corrected estimates of phasors, starting with the classical

algorithm and a “Boxcar” window.

( ) ( )( ) ( ) ( )

( ) ( ) ( )( )

( ) ( ) ( )( )***

***

21

21

YYY

YYY

YYY

YP

−−

−−

+−⋅

−

+−⋅−

−

+−⋅−≈

−−

MMM

MMM

j

MMM

MM

22

sin2

2cos

224

11

2sin2

2

12

2

3

2

2

21

π

π

π

(12)

Equation (12) is more accurate than (8), particularly for

significant deviations of the actual power system frequency

from the nominal value.

Simulations have shown us that the four-parameter model is

accurate enough to meet the requirements of the phasor

standard, so we have elected to use it to implement a phasor

measurement unit.

A.7. Asynchronous Sampling

So far, the analysis has assumed synchronous, fixed rate

sampling. That is, samples are taken at a fixed sampling rate

with sampling instants that align with times that are defined by

the proposed synchrophasor standard. In that case,

synchrophasors can be computed directly from (8) or (12).

In some applications it may be useful to compute

synchrophasors asynchronously. Typically, the situation arises

when frequency tracking is employed. The sampling rate is

continually adjusted to match the power system frequency. The

advantage of frequency tracking is that phasors computed from

the samples using a classical algorithm are nearly free of off-

nominal frequency effects. This simplifies the problem of

correcting for power swings or angle shifts. Also, protection

platforms apply typically frequency tracking. Successful

integration of synchrophasors with protection must minimize

the risk of causing problems for the mission-critical protection

functions, and therefore shall be adapted to the existing

method of sampling, rather then vice versa.

With frequency tracking, the sampling times are well

known, but no effort is made to force synchronization with

predefined times. Therefore the actual time associated with a

phasor will not line up with a desired reporting time tag. The

models developed in the previous sections may be

conveniently used to adjust for the difference between the

desired time and the actual time. Suppose that it is desired to

compute a phasor with respect to a predefined, synchronous

time tag, and that phasor model parameters are available for a

time window whose center time is not too far from the time

tag, but not exactly aligned. The two times are defined by (13).

window theofcenter theof timeactual

tag timessynchronou ,predefined

=

=

Window

Tag

t

t (13)

Then, the computed phasors can be explicitly adjusted to the

synchronous the time tag. Equation (14) is the algorithm for

the first order Taylor’s expansion. The procedure is to first

compute the phasor and its derivative, and then to use (14) to

make the adjustment.

( )

( ) θ

πθ

πθ

∆⋅⋅

⋅

∆+≈

−⋅⋅=∆

jTag

WindowTag

ef

t

ttf

XXX

&

2

2

(14)

There are two effects in the adjustment. The first effect is

due to the fact that the phasor is changing, and is simply the

value of the phasor at the time tag, computed by the Taylor’s

expansion. The second effect is a simple rotation that corrects

for the fact that the proposed synchrophasor standard defines

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the angle of a phasor in relation to the time tag, while (8) and

(12) are equivalent to defining the angle of the phasor in

relation to the center of the sampling window.

There is another, related issue that must be considered

during an asynchronous implementation of synchrophasors.

How should the samples be selected and assigned to particular

time slots? There are at least two viable strategies. One

strategy is to group every N samples in sequence and compute

phasors using a multi-parameter model. A second process is

then needed to bridge the mismatch between the sampling

frequency and the reporting rate. This can be done by taking

the synchrophasor in the asynchronous frame of reference that

is closest in time to the desired time tag, and use (14) to make

the adjustment between the time frames. This approach has the

advantage of maintaining a simple implementation of the

computation of the derivative in a frame of reference where the

phasors are not rotating very rapidly. The disadvantage is that

the adjustment could be as large as ½ cycle.

Another approach is to select N samples approximately

centered on the time tag. In this approach, some samples may

be used in more than one reported synchrophasor, or some

samples may not be used at all, depending on whether the

actual sampling frequency is less than or greater than the

nominal value. One advantage of this approach compared to

the previous is a smaller correction to bridge the gap between

the actual center of the time window and the time tag, at worst

½ of a sample period. The disadvantage of this approach is

that, in order to compute the derivative, which should be

measured in the sampling time frame of reference, the phasors

computed in the reporting time frame of reference must be

rotated. This is done by replacing (7) with the following:

( )( ) ( )

( ) ( )

frequency reporting

1 Mcyclefor frequency tracking

1

1

*

12

1

1

12

1

1

1

=

−=

⋅−⋅

−+

⋅−≈

−

−⋅⋅⋅

−−

−⋅⋅⋅

−

−

−

f

f

ef

f

ef

M

f

fj

MM

M

f

fj

MM

M

M

M

π

π

YY

YYX&

(15)

There is also an effect in (8), which becomes:

( ) ( )( )

⋅

⋅⋅−≈

−

ff

fj

M

M

MM π2sin2

1

1

XYP

&

(16)

A.8. Post-processing and Filtering

The previous sections described how to use a multi-

parameter model to compute synchrophasors on a once per

cycle basis, based on a one-cycle window. In order to attenuate

interfering frequencies and/or improve accuracy, it is useful to

have the option to compute synchrophasors over a time

window that is wider than one cycle. This can be done in a

post-processing step by extending multi-parameter concepts to

the problem of combining several phasors measured over a

multi-cycle window into a best estimate at a given time-tag in

the window.

The approach is to use an n-th order Taylor expansion in

either Cartesian or polar coordinates, using a multi-parameter

regression technique. The parameters of the expansion are

determined from the phasors in the post-processing window.

The expansion is evaluated at the desired time-tag. We will

give a few examples to illustrate the technique.

One issue that must be addressed is that during off-nominal

frequency operation there may be significant rotation of the

phasors from one end of the post-processing window to the

other. This would cause an error in a simple four parameter

Taylor’s expansion in Cartesian coordinates that would

manifest itself as a contraction in the apparent magnitude of

the phasor. There are three approaches that we can use to

compensate for rotation:

1. Use a four parameter model expressed in polar

coordinates. This would eliminate the contraction effect

during off-nominal frequency operation.

2. Use a six parameter Taylor’s expansion in Cartesian

coordinates. This would accommodate the curvature

due to off-nominal frequency operation.

3. Use a four parameter Taylor’s expansion, but rotate the

phasors to the time-tag before fitting them to the model.

In a previous section we discussed the fact that when there

is no negative-sequence, the classical algorithm works fairly

well for positive-sequence quantities, except for a small

contraction in amplitude that occurs during off-nominal

frequency operation. The contraction effect is proportional to

the square of the width of the window so that although the

error is negligible for a one-cycle window, it becomes

significant during post-processing.

For the examples to follow, we assume a post-processing

window that is centered on the reporting time-tag, with an odd

number of phasors in the window, equal to 2N+1. The

techniques can be extended to asymmetric windows and/or

even numbers of phasors.

With a four-parameter model in polar coordinates, post-

processing proceeds as follows:

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( )( ) ( )( )( )

( )

( )

( ) ( )

( ) phasor processedpost the

12

12

1

to

,

=

⋅+

=

≤Ψ−Ψ≤−

Ψ−Ψ⋅+

+Ψ=

≤Ψ≤−

+−=

=Ψ

∑

∑

+

−=

⋅

+

−=

M

M

Mn

n

j

M

Mn

M

Mn

MnMM

n

nnn

e

MMn

ImagRealatan2

M

S

YS

YY

θ

ππ

θ

ππ

(17)

That is, the magnitude of the post-processed phasor is the

average of the individual phasors, and its angle is the average

of the angles. The reason that the average angle is computed as

the angle for the phasor in the center of the window plus the

average of the deviation angles for all of the other phasors is to

avoid an implementation issue that arises because of the wrap

around of phase angles.

An advantage of this option is that it perfectly compensates

for the magnitude contraction effect during off-nominal

frequency operation. Also, it works well enough with a narrow

post-processing window such as 3 phasors. A disadvantage is

that it requires several trigonometric calculations. Another

disadvantage is that it does not compensate well for straight

line trajectories in the complex plane that pass close to the

origin, such as for a power swing.

The second option is to use a six parameter Taylor’s expansion

over the window. In that case, the best estimate of the phasor

at the time tag at the center of the window is given by:

( ) ( )

( )

( ) ( ) ( )

( ) phasor processedpost the

311404816

13215

311404816

1331323

220

2456

2

2

2456

22

0

=

⋅+=

−−++

++⋅−=

−−++

−+⋅++⋅=

∑+

−=

M

M

Mn

nM nAA

A

A

S

YS

(18)

Although the coefficients look rather complicated, they can

be pre-computed. Implementation then reduces to simply

multiply each contributing phasor by the appropriate

coefficient, and add. For example, lets take the case of N=1,

the formula for the best fit is:

( ) ( )MM

A

A

YS =

−=

=

1

1

2

0

(19)

In other words, for a three-phasor window with a six-

parameter model, the best fit is to simply take the phasor in the

center of the window. This will not provide much attenuation

of interfering frequencies, so we will need to use more points.

For N=2, the formula for the best fit is:

( ) ( ) ( )

( ) ( ) ( )21

12

2

0

35

3

35

12

35

17

35

12

35

3

35

5

35

17

++

−−

⋅−⋅+⋅+

⋅+⋅−=

−=

=

MMM

MMM

A

A

YYY

YYS

(20)

An advantage of the second option is its computational

simplicity and its good (though not perfect) compensation for

magnitude contraction during off-nominal frequency

operation. A disadvantage is that it needs at least 5 phasors to

achieve any attenuation of interfering frequencies, leading to

reporting latency.

The third option can be used if frequency measurements are

also available. The concept is to rotate individual phasors to

the reporting time tag and then apply a four-parameter model,

which amounts to a simple average over the window:

( ) ∑

∑

∑

−=+

Ψ⋅

+

=+

−

=+

⋅⋅+

=

=

+=

=⋅=Ψ

−−=⋅=Ψ

p

pM

j

M

nM

p

n

nMp

pn

nMp

pe

f

f

pff

pff

YS21

1

frequency reporting

n Mcyclefor frequency tracking

...1 2

1.. 2

1

1

π

π

(21)

An advantage of the third option is its perfect compensation

for magnitude contraction during off-nominal frequency

operation. Also, it will work well enough with as little as three

phasors. Its disadvantage is that it needs estimates of the actual

frequency of the power system.

A.9. Efficient Computations

The algorithms in the previous sections are presented as

equations involving complex numbers, arranged for elegance

and understanding. Direct implementation of the equations as

shown is not necessarily computationally efficient. It is

possible to restructure them for computational efficiency.

For example, consider (15) and (16), which are used to

compute phasors with frequency tracking using samples in a

window that is approximately centered on the reporting time

tag. Both equations are executed once per cycle for each input

channel of a phasor measurement unit. A little thought will

show that (16) can be implemented with four real

multiplications and two real additions. It is not immediately

clear how best to implement (15), which involves a

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trigonometric function and several real and complex

multiplications and additions. The following is the most

computationally efficient approach.

First, pre-compute the following scale factor as a compile-

time activity:

=

bπ2

sin2

1 (22)

Next, compute a measure of the deviation of frequency from

nominal:

11 −= −

f

fW M (23)

Compute the following two factors:

( )( )12

12

+⋅=

+=

WEF

W

bE

(24)

Perform two trigonometric table lookups:

)2sin(

)2cos(

WH

WG

⋅⋅=

⋅⋅=

ππ

(25)

Finally, use the following two equations to compute the real

and imaginary components of the synchrophasor from the real

and imaginary components of the classical computation:

( )

( ))1()1()(

)()(

)1()1()(

)()(

−−

−−

⋅+⋅−⋅−

=

⋅−⋅−⋅−

=

MIMAGMREALMREAL

MIMAGMIMAG

MIMAGMREALMIMAG

MREALMREAL

YHYGYE

YP

YGYHYF

YP

(26)

These equations involve 4 multipliers, and call for 6

additions and 6 multiplications. The 12 operations are per each

physical channel measured. The 4 multipliers depend on

tracking and reporting frequencies only, and therefore are

common for all channels.

It is assumed W, E and F are calculated in real time. G and

H are look up tables. W, E and F require 3 additions, 5

multiplications and 1 bit shift.

ANNEX B – PHASOR SUMMATION IDENTITY

This is a summary of some identities that are useful in

analyzing any phasor model with any number of parameters.

Sums of powers of complex exponentials appear in the

analysis. The following sum is typical:

( ) ∑−

−=

⋅+⋅=

12

2

)2/1(0

n

nje φφΣ (B1)

The subscript 0 was selected deliberately in anticipation of a

family of summations. The variable φ is typically some

parameter divided by N.

Since the right side of (B1) involves complex numbers, the

left side is shown as a complex number that will be a function

of φ . As will be demonstrated, the combination of a centered

window and the ½ sample offset will lead to a real number for

( )φ0Σ .

It is useful to factor out the ½ sample rotation:

( ) ∑−

−=

⋅⋅⋅

=

12

2

20

n

nj

j

ee φφ

φΣ (B2)

Next, multiply (B2) by a 1-sample rotation, and re-express

in terms of a summation index that has a range that is shifted

by 1:

( ) ∑+−=

⋅⋅⋅

⋅ =⋅2

12

20

n

nj

j

j eee φφ

φ φΣ (B3)

Subtract (B2) from (B3). Most of the terms in the

summations cancel out, leaving the first term from (B2) and

the last term from (B3):

( ) ( ) ( )2/2/201 jj

j

j eeee ⋅⋅−⋅⋅⋅

⋅ −=⋅− φφφ

φ φΣ (B4)

Dividing (B4) by 1−φje yields:

( )22

2/2/

0 φφ

φφ

φ⋅−⋅

⋅⋅−⋅⋅

−

−=

jj

jj

ee

eeΣ (B5)

It is then a simple matter to expand the complex

exponentials in terms of trigonometric functions and simplify

to show that:

( )

=

2sin

2sin

0 φ

φ

φ

Σ (B6)

The next higher order summation that appears in the

analysis is:

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( ) ∑−

−=

⋅+⋅⋅+=

12

2

)2/1(1 )2/1(

n

njen φφΣ (B7)

We can build on the analysis of ( )φ0Σ by noting that ( )φ0Σ

and ( )φ1Σ are related by a derivative operator. Since we are

dealing with finite sums, the derivative of the sum (B1) is

equal to the sum of the derivatives, and we find:

( )∑

−

−=

⋅+⋅+=

12

2

)2/1(0 )2/1(

n

njenjd

d φ

φφΣ

(B8)

Therefore, ( )φ1Σ can be computed from the derivative of

( )φ0Σ :

( ) ( )φ

φφ

d

dj 0

1

ΣΣ −= (B9)

In fact, there is a family of functions that arise from sums of

complex exponentials. The k’th function can be expressed as:

( )k

kk

n

njkk

d

dj

en

φφ

φ φ

)(

)2/1()(

0

12

2

)2/1(

Σ

Σ

⋅−=

+= ∑−

−=

⋅+⋅

(B10)

The functions described by (B10) are useful in performing

an analysis of arbitrarily high order Taylor’s expansion phasor

models.

REFERENCES

[1] A.G. Phadke, J.S. Thorp, M. Adamiak, “A New Measurement

Technique for Tracking Voltage Phasors, Local System Frequency,

and Rate of Change of Frequency,” IEEE Transactions on PAS, May

1983.

[2] A.G. Phadke, “Synchronized Phasor Measurements,” IEEE Computer

Applications in Power, April 1993.

[3] IEEE Std. C37.118, IEEE Standard for Synchrophasors for Power

Systems, 2005.

[4] D60 Line Distance Protection System, Instruction Manual, GE

Publication GEK-113270. Available at www.multilin.com.

[5] T. Funaki, S. Tanaka, “Error Estimation and Correction of DFT in

Synchronized Phasor Measurement,” Transmission and Distribution

Conference and Exhibition 2002: Asia Pacific. IEEE/PES Volume 1,

6-10 October 2002, pages: 448-453.

[6] J. A. de la O Serna, K.E.Martin, “Improving Phasor Measurements

Under Power System Oscillations,” IEEE Transactions on Power

Systems, February 2003.

[7] M. Adamiak, B. Kasztenny, W. Premerlani, “Synchrophasors:

Definition, Measurement, and Application”, Proceedings of the 59th

Annual Georgia Tech Protective Relaying, Atlanta, GA, April 27-29,

2005.

Bogdan Kasztenny holds the position of Protection and System Engineering

Manager for the protective relaying business of General Electric. Prior to

joining GE in 1999, Dr.Kasztenny conducted research and taught protection

and control at Wroclaw University of Technology, Texas A&M University,

and Southern Illinois University. Between 2000 and 2004 Bogdan was

heavily involved in the development of the Universal RelayTM series of

protective IEDs. He authored more than 160 papers, is the inventor of several

patents, Senior Member of the IEEE, and the Main Committee of the PSRC.

Dr.Kasztenny is a registered professional engineer in the province of Ontario.

In 1997, he was awarded a prestigious Senior Fulbright Fellowship. In 2004

Bogdan received GE’s Thomas Edison Award for innovation.

Mark Adamiak received his B.S. and M.E. degrees from Cornell University

in Electrical Engineering and an MS-EE degree from the Polytechnic Institute

of New York. He started his career with American Electric Power (AEP) in

the System Protection and Control section where his assignments included

R&D in Digital Protection, relay and fault analysis, power line carrier, and

fault recorders. In 1990, Mark joined General Electric where is activities have

ranged from development, product planning, and system integration. In

addition, he has been actively involved in developing the framework for next

generation relay communications and was the Principal Investigator on the

Integrated Energy and Communication System Architecture (IECSA) project.

He is a Senior Member of IEEE, past Chairman of the IEEE Relay

Communications Subcommittee, and a member of the US team on IEC TC57

- Working Group 10 on Substation Communications.

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Aplicaciones de la medición de sincrofasores por el operador del sistema eléctrico español

S. López J. Gómez R. Cimadevilla

Red eléctrica de España Red Eléctrica de España ZIV P + C

Resumen-Este artículo describe algunas de las aplicaciones que el Operador del Sistema Eléctrico Español (Red Eléctrica de España) ha pensado para los equipos de medición de sincrofasores (PM Us), tales como el cálculo de las impedancias de secuencia de una línea, la localización de faltas en líneas mixtas y la monitorización del comportamiento dinámico del sistema. Para cada aplicación se explica la problemática asociada a los algoritmos tradicionales, empleados hasta ahora, y se describen las ventajas ofrecidas por los nuevos algoritmos, basados en la medida de sincrofasores, incluyendo resultados obtenidos a partir de datos reales.

I. INTRODUCCIÓN

Los sistemas eléctricos de hoy en día se encuentran cada vez más debilitados y sobrecargados, lo que ha reducido los márgenes de estabilidad. Las restricciones medioambientales están limitando la expansión de la red de transporte, a la vez que, alejan, cada vez más, la generación del consumo final. Por otra parte, la gran presión del mercado eléctrico fuerza a las compañías eléctricas a aprovechar al máximo sus activos. Por ello, y dada la mayor calidad del suministro eléctrico exigida hoy en día, es necesario operar el sistema de una manera más eficiente. Los equipos de medición de sincrofasores (PMUs) presentan un importante número de aplicaciones que permiten aumentar la eficacia de la red. Este artículo describe algunas de las aplicaciones Red Eléctrica de España (REE) ha pensado para dichos equipos, pudiendo destacar, entre ellas, las siguientes:

- Cálculo de las impedancias de secuencia de una línea: los cálculos tradicionales, efectuados a partir de las constantes de la línea, pueden dar lugar a errores considerables, sobre todo por lo que respecta a la impedancia de secuencia cero, con el consecuente tarado erróneo de los relés de distancia, localizadores de faltas, etc. El cálculo efectuado a partir de las medidas de dos PMUs situadas a ambos extremos de la línea permite, de una forma sencilla, obtener resultados más exactos. - Localización de faltas en líneas mixtas: la variación de la impedancia homopolar de los cables reduce, en gran medida, la eficacia de los localizadores de faltas tradicionales. La localización de faltas basada en las medidas de dos PMUs situadas a ambos extremos de la línea mixta ofrece resultados mucho más precisos. - Monitorización de comportamiento dinámico del sistema:, la extensión de los sistemas eléctricos está dando lugar, hoy en día, a oscilaciones de pequeña señal. Dada la reducción en los márgenes de estabilidad, el conocimiento del comportamiento dinámico del sistema es de vital importancia para su correcta operación. Mediante las

medidas de PMUs instaladas en diferentes puntos del sistema, se pueden caracterizar las posibles oscilaciones, lo cual permite tomar medidas para aumentar su amortiguamiento y establecer planes de defensa ante oscilaciones inestables.

II. CÁLCULO DE LAS IMPEDANCIAS DE UNA LÍNEA

Las compañías eléctricas suelen calcular las impedancias de secuencia de las líneas de transporte en base a las características geométricas y eléctricas de sus conductores. Dicho método puede dar lugar a errores considerables, sobre todo por lo que respecta a la impedancia de secuencia cero, con el consecuente tarado erróneo de los relés de distancia, localizadores de faltas, etc.

Los datos empleados para el cálculo de la impedancia de

secuencia directa son, por una parte, las constantes de permeabilidad tanto de los conductores como del medio, las cuales se consideran iguales (42 x 10-7 H/m) al suponer que el material de los conductores es totalmente paramagnético (incluso aunque se trate de conductores de material ferromagnético como es caso de los conductores ACSR (aluminium core steel reinforced) se efectúa dicha aproximación, dado que la variación de la permeabilidad se considera pequeña). Por otra parte también se requiere la resistencia de los conductores y una serie de parámetros geométricos asociados a éstos, tales como el radio y la distancia entre ellos (a partir de los cuales se obtiene el GMR y el GMD), además de su longitud. Si la línea presenta uno o varios cables de guarda, también es necesario conocer la resistencia y la disposición geométrica de dichos cables[2].Analicemos las fuentes de error que presentan los parámetros anteriores:

- Resistencia de los conductores: su valor varía con la temperatura ambiente y el flujo de potencia a través de ellos. Algunas líneas presentan secciones con diferentes tipos de conductor y, por lo tanto, con distinta resistencia por unidad de longitud. El uso de un único valor de resistencia en los programas de cálculo de impedancias supone, evidentemente, un error. - Parámetros geométricos: pueden variar de un vano a otro (variación en la configuración de las torres o en su disposición con respecto a la torre anterior), por lo que se suele considerar un valor medio, con el consecuente error que ello supone. Cabe destacar, por otra parte, que en muchas ocasiones no se conoce con exactitud la longitud de los conductores.

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Por lo que respecta al cálculo de la impedancia de secuencia cero, además de los parámetros anteriores, de la distancia de los conductores a la tierra, parámetro geométrico también mediado, y de la resistencia de la tierra (evaluada de forma empírica por Carson en función de la frecuencia), es necesario, tener en cuenta la resistividad del terreno[2], dato difícil de estimar de forma precisa, dada la no homogeneidad del camino de retorno. La resistividad del terreno se ve muy afectada por la composición del mismo, que puede variar a lo largo de la línea, por la humedad y por la temperatura (por debajo de 0º C se congela el agua del terreno lo que reduce enormemente su humedad). Por ello varía con las condiciones meteorológicas. Por otra parte, el estudio de la composición del terreno, no tiene en cuenta elementos metálicos que pudieran estar enterrados, como tuberías, cables, etc.

En el caso de dobles circuitos, también suele interesar conocer el valor de la impedancia mútua de secuencia cero, cuyo cálculo requiere datos comunes a los empleados en el cálculo de la impedancia de secuencia cero de cada circuito por separado, tales como la resistencia y la resistividad del terreno.

En general cabe destacar que el cálculo de las impedancias de secuencia depende de un número elevado de parámetros, lo cual incrementa las fuentes de error.

El cálculo de las impedancias de secuencia efectuado a partir de las medidas, sincronizadas, de dos PM Us situadas a ambos extremos de la línea permite, de una forma sencilla, obtener resultados más exactos. La impedancia de secuencia directa puede ser calculada, en cualquier momento, a partir de las medidas de tensión e intensidad de secuencia directa a ambos lados de la línea. La impedancia de secuencia cero requiere las medidas de tensión e intensidad de secuencia cero y, obviamente, solo podrá ser calculada cuando exista un flujo de secuencia cero a través de la línea. Éste se generará ante faltas a tierra o faltas serie (una o dos fases abiertas, desequilibrios en las impedancias, etc). En el caso de dobles circuitos, las medidas de tensión e intensidad de secuencia cero a ambos extremos de la línea paralela permiten medir, además, la impedancia mutua de secuencia cero.

Los resultados obtenidos a partir de las medidas de las

PMUs en un determinado momento pueden utilizarse para ajustar todos los equipos basados en la medida de impedancia. No obstante, dado que las impedancias de secuencia pueden variar con las condiciones meteorológicas y el flujo de potencia en la línea se pueden efectuar cálculos cada cierto tiempo: de forma programada para la impedancia de secuencia directa y cuando se produzcan faltas a tierra para la impedancia de secuencia cero. Si los valores calculados difieren bastante de los valores ajustados, se podría efectuar un cambio de tabla de ajuste en los relés de distancia o localizadores de faltas, que se adapte mejor a los valores medidos en el momento. No obstante, la creación de las distintas tablas de ajuste requiere un estudio previo, una vez que se han registrado valores de impedancia durante un determinado periodo de tiempo.

2.1 Cálculo de impedancias de secuencia directa La figura 1 representa el equivalente PI de secuencia directa de una línea de transporte. Las ecuaciones que relacionan las tensiones e intensidades de secuencia directa a ambos extremos de la línea son las siguientes:

A partir de (2) se puede calcular . Sustituyendo en (1) se obtiene

El cálculo anterior es válido tanto para líneas aéreas como

para cables. Para líneas largas (aproximadamente con una longitud mayor de 200 km para líneas aéreas y de 30 km para cables) se debe utilizar un circuito de parámetros distribuidos, en el que la tensión y la intensidad de secuencia directa, u1 y i1, respectivamente, en un punto de la línea situado a x km del extremo local, cumplirán las siguientes ecuaciones diferenciales parciales en función del tiempo:

donde R1, L1, C1 y G1 representan la resistencia, inductancia, capacidad y conductancia, por unidad de longitud, de secuencia directa de la línea, respectivamente.

Resolviendo las anteriores ecuaciones en el dominio de la frecuencia se obtiene:

donde: y

representan la constante de

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propagación e impedancia característica de secuencia directa de la línea, respectivamente. V1x y I1x representan la tensión e intensidad de secuencia directa, ya como fasores, a una distancia x del extremo local (para x=L, V1x=V1R y I1x=I1R).

En ese caso, la impedancia y admitancia de secuencia directa reales de la línea (Z1=z1*L y Y1=y1*L respectivamente) se pueden calcular a partir de las ecuaciones anteriores.

Resolviendo se obtiene:

Otra posibilidad sería la de, una vez obtenidos los parámetros del equivalente PI (Z1’ y Y1’), emplear las ecuaciones siguientes [1]:

Cabe destacar que la impedancia de secuencia directa que

requiere REE para la mayoría de las aplicaciones (relés de distancia, localizadores de falta basados en las medidas en un único extremo de la línea, cálculos de cortocircuito), será la del equivalente PI (Z1’) puesto que dichas aplicaciones, generalmente, no consideran la capacidad de la línea. No obstante, la instalación de PMUs en la red está incentivando al uso de localizadores de falta basados en circuitos de parámetros distribuidos, como el que se describe en el apartado 3, los cuales deberán utilizar la impedancia y admitancia de secuencia directa reales de la línea. 2.2 Cálculo de impedancias de secuencia cero El cálculo de la impedancia de secuencia cero se efectuará cuando se produzca una falta a tierra. Dicha falta puede ser tanto interna como externa a la línea. Si la falta es interna, es necesario calcular, en primer lugar, la distancia a la falta, para lo cual se podría utilizar la red de secuencia directa con un circuito similar al empleado en el apartado 3 pero más simplificado, al no tratarse de una línea mixta. Una vez conocido este valor, recurriendo a la red de secuencia cero, se puede calcular la impedancia de secuencia cero. No obstante, se descarta el cálculo de dicha impedancia para faltas internas a la línea porque se ha comprobado que el valor de la impedancia de secuencia cero se ve muy afectado por la precisión en el cálculo de la distancia a la falta, de forma que pequeños errores en este primer cálculo dan lugar a grandes errores en el segundo cálculo. Si la falta es externa a la línea no es necesario calcular la distancia a la falta. Por otra parte hay que tener en cuenta que, generalmente, se producirá un mayor número de faltas externas que de faltas internas. En la figura 2 se representa el equivalente PI de secuencia cero de una línea para una falta externa a la misma.

Con fórmulas similares a las incluidas en el apartado anterior,

se pueden calcular la impedancia y la admitancia de secuencia cero:

El cálculo anterior será válido tanto para líneas aéreas como

para cables, aunque para estos últimos el resultado variará dependiendo del camino de retorno de la intensidad (por la pantalla, por tierra o por ambas). En el caso de líneas largas, se podrán obtener, de forma similar a la descrita en el apartado anterior, la impedancia y admitancia de secuencia cero reales de la línea.

En dobles circuitos, se puede calcular, además, la impedancia mutua de secuencia cero. En la figura 3 se muestra la red de secuencia cero asociadas a un doble circuito. Dado que se han considerado equivalentes PI de cada línea, la admitancia mutua de secuencia cero se supone también concentrada a ambos extremos de las dos líneas. En dicho circuito se cumplirán las siguientes ecuaciones:

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Dado que existen 4 ecuaciones y 6 incógnitas (Y0, Y0’, Y0M , Z0, Z0’ y Z0M ), será necesario registrar medidas de secuencia cero en dos instantes de tiempo diferentes (dos faltas a tierra distintas) con el fin de duplicar el número de ecuaciones.

En el caso de dobles circuitos largos, el acoplamiento que existe entre las redes de secuencia cero no permite una resolución directa de las ecuaciones diferenciales asociadas a los dos circuitos. La mejor forma de obtener la impedancia mútua sería en base a la transformada de Clarke para dobles circuitos que permite un desacoplamiento entre todos los modos [13]. No obstante, para las actuales aplicaciones de REE, el cálculo basado en un circuito de parámetros concentrados se considera válido.

En el caso de líneas no transpuestas, si se requiere una mayor precisión en el cálculo de las impedancias de secuencia, se pueden resolver las 9 incógnitas de la matriz de impedancias de secuencia con las 3 ecuaciones que proporcionan las tres redes de secuencia, tomando medidas en tres instantes diferentes. En este caso no hay que esperar a que se produzca una falta para calcular la impedancia de secuencia cero, sino que los desequilibrios de la línea ya generan un flujo de secuencia cero. Si las líneas, además de no estar transpuestas, son largas, los cálculos se complicarían bastante, puesto que sería necesario resolver las ecuaciones diferenciales que utilizan las matrices de impedancias y admitancias de fase, acopladas entre sí. El desacoplo de las ecuaciones anteriores se efectúa mediante la teoría modal, transformando las magnitudes de fase a magnitudes modales [13]. Para ello se debe determinar la matriz transformadora (matriz de vectores propios), cuyos valores no son constantes, sino que dependen de las matrices antes citadas. El problema reside en que los valores de las matrices de impedancias y admitancias de fase son, en este caso, incógnitas. 2.3 Simulación Con el fin de probar los algoritmos antes descritos, se simulan, mediante un RTDS (Real Time Digital Simulator), dos líneas de 220 kV de longitudes 50 y 300 km y un doble circuito, de la misma tensión, con una longitud de 100 km. Se introducen diferentes condiciones: distintas impedancias de fuente, flujos de carga y, para el cálculo de la impedancia de secuencia cero, diferentes tipos de falta a tierra con diferentes resistencias de falta.

Las medidas a ambos extremos de la línea se registraron con relés de distancia de ZIV que incorporan la funcionalidad de PM U. Dichos equipos calculan 50 sincrofasores por segundo a la frecuencia nominal de 50 Hz, empleando una transformada de Fourier recursiva de un ciclo, con 32 muestras por ciclo. Con el fin de mantener la precisión en la medida a frecuencias diferentes a la nominal, los instantes de muestreo se calculan en función de la frecuencia de la red medida [12]. Al no efectuarse un muestreo síncrono con la señal que entrega el reloj de GPS (PPS - Pulso por Segundo), para obtener el ángulo del sincrofasor, se compensa el desfase existente entre la onda coseno que emplea la transformada de Fourier (onda definida por los coeficientes coseno, cuyo máximo coincide

con el coeficiente nº 0) y la onda coseno que define el GPS

(máximo coincidiendo con el PPS). De esa forma se consigue un TVE (Total Vector Error) menor que el 1% para rangos de 40 a 70 Hz.

Con el fin de eliminar la componente exponencial de la intensidad de falta, las PMUs efectúan un filtrado digital antes de que las muestras sean procesadas por la transformada de Fourier. Dicho filtro limita en un 3% el sobrealcance transitorio, introduciendo un retardo inferior a ³ ciclo.

Las PMUs disponen de filtros digitales antialiasing con el fin de eliminar señales de interferencia que puedan ocasionar fenómenos aliasing para la frecuencia de cálculo de 50 sincrofasores/sg. Dado que dichos filtros consideran ventanas de cálculo mayores de un ciclo para esta aplicación se deshabilitan, con el fin de poder registrar valores de falta adecuados.

El registro de los valores de falta, requeridos para la medida de la impedancia de secuencia cero, se efectúa en base a una unidad de detección de falta, muy sensible, basada en variaciones en las intensidades de secuencia. Si el tiempo desde la activación de dicha unidad hasta la primera fracción de segundo que aparece es menor que medio ciclo se guardará el sincrofasor asociado a la siguiente fracción de segundo. Si el tiempo anterior es mayor que medio ciclo se guardará el sincrofasor asociado a esa primera fracción de segundo. De esa forma y teniendo en cuenta que los sincrofasores se calculan medio ciclo después de la fracción de segundo, con el fin de centrar en ella la ventana de cálculo, los valores de falta se tomarán de 1 a 2 ciclos después de la activación del detector de falta.

2.3.1 Resultados sin errores externos Las tablas 2, 3 y 4 muestran los resultados obtenidos en el cálculo de las impedancias de secuencia directa y cero, sin tener en cuenta errores externos a las PMUs y sin haber considerado, para las faltas, componente de continua. Como se puede observar, los errores en el cálculo de la reactancia, parámetro que mayores fuentes de error presenta empleando el método tradicional, son menores que el 3%.

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2.3.2 Resultados con errores externos Se incluyen, a continuación, los resultados para el cálculo de

las impedancias de secuencia de las líneas 1 y 2, teniendo en cuenta una de las condiciones antes simuladas (carga de 1.5 A, impedancia de fuente de 20 ohmios y tipo de falta BCG para el cálculo de la secuencia cero), incluyendo, esta vez, errores en la sincronización entre extremos y en los transformadores de medida. Por otra parte, se analiza la influencia de la componente de continua en las faltas. 2.3.2.1 Influencia de la sincronización entre extremos En la tabla 5 se pueden ver los errores adicionales en la medida de resistencia, reactancia y admitancia de secuencia directa y secuencia cero cuando se añade un desfase de 10º entre las intensidades medidas por las dos PMUs. La tabla 6 incluye los errores cuando el desfase de 10º se introduce entre las tensiones.

Los grandes errores registrados en la medida de la reactancia de secuencia directa muestran la necesidad de una precisa sincronización entre extremos, la cual vendrá asegurada por el uso de los relojes GPS. Es importante comprobar que los sincrofasores empleados para los cálculos de las impedancias incluyen una indicación de la calidad del tiempo adecuada. La influencia del error de sincronización entre las tensiones de ambos extremos de la línea es mayor cuanto más elevada sea la tensión. Por ello los errores en la medida de la reactancia de secuencia directa se reducirán si ésta se calcula en una situación de falta (conjuntamente con la impedancia de secuencia cero) en lugar de en una situación de carga. No obstante, en situación de falta, los errores se redujeron muy poco puesto que se inyectaron faltas muy resistivas, que generaron una tensión de falta cercana a la nominal. Ante este tipo de faltas el método más adecuado para calcular la reactancia de secuencia directa es el basado en las magnitudes de secuencia directa de falta pura. La tabla 6b representa los errores en la resistencia, reactancia y admitancia para un cálculo de la impedancia de secuencia directa, efectuado a partir de magnitudes de falta pura, con las medidas registradas para el cálculo de la impedancia cero.

Como se puede observar, ante un desfase de 10º entre las tensiones, dichos errores son muy pequeños.

Tabla 6b. Influencia de un error de sincronización entre tensiones de 10º para

un cálculo efectuado a partir de magnitudes de falta pura

2.3.2.2 Influencia de los transformadores de medida REE utiliza los siguientes transformadores de medida: - Transformadores de intensidad 5P20: según la norma CEI 44-1, presentan errores límites en módulo y ángulo de 1% y 60 minutos, respectivamente, a la intensidad nominal; a una intensidad de 20 veces la nominal el error compuesto debe ser menor que el 5%.

- Transformadores de tensión 3P: según la norma CEI 60044-2, presentan errores límites en módulo y ángulo del 3% y 120 minutos, respectivamente, al 5% de la tensión nominal y al producto de la tensión nominal por el factor de tensión (1,2; 1,5 ó 1,9). Con el fin de tener en cuenta los errores introducidos por los transformadores de medida, tanto a las intensidades como a las tensiones medidas por las PMUs se les añaden errores en módulo y en ángulo del3% y 2º respectivamente. Tanto para el cálculo de la impedancia como para el cálculo de la admitancia se ha considerado la combinación más desfavorable: a) +3% en Ilocal / +3% en Iremot y +2º en Ilocal / +2º

en Iremota para el cálculo de la impedancia b) +3% en Ilocal / -3% en Iremot y +2º en Ilocal / -2º

en Iremot para el cálculo de la admitancia c) +3% en Vlocal/ +3% en Vremot y +2º en Vlocal / +2º en Vremota para el cálculo de la admitancia d) +3% en Vlocal / -3% en Vremot y +2º en Vlocal / -2º en Vremota para el cálculo de la admitancia

Dichos errores se han introducido directamente en las

medidas de secuencia directa y cero, considerando que el error en las magnitudes de fase es igual. Sin embargo, diferentes

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errores en las magnitudes de fase pueden generar errores muchos mayores en las magnitudes de secuencia cero, sobre todo en la tensión. El uso de magnitudes de secuencia cero de falta pura elimina prácticamente los errores que existan en las tensiones siempre que éstos no varíen mucho de las condiciones de prefalta a las condiciones de falta, es decir si las curvas de error de los transformadores de tensión no presentan mucha dispersión en todo el rango de medida.

Las tablas 7, 8, 9 y 10 representan los errores adicionales en la medida de resistencia, reactancia y admitancia cuando se

introducen los errores indicados en las combinaciones anteriores. Los resultados muestran la necesidad de calibrar las PMUs, en base a las curvas de error de los transformadores, con el fin de poder calcular adecuadamente las impedancias de la línea, principalmente la de secuencia directa.

Cabe destacar que el cálculo de los parámetros de secuencia directa basado en magnitudes de falta o de falta pura (dependiendo del valor de la tensión de falta) reduce mucho los errores anteriores.

2.3.2.3 Influencia del ángulo de incidencia

En el caso más desfavorable (intensidades tomadas 1 ciclo después de la activación del detector de falta y máxima componente exponencial), el error introducido en la intensidad es de un 1% en módulo y de 3º en ángulo. Si las intensidades de ambos extremos presentan el mismo error, los errores adicionales en la medida de la resistencia y reactancia de secuencia cero serán de 21.66% y 2.30%, respectivamente,

para la línea 1 y de 21.48% y œ2.26%, respectivamente, para la línea 2 y. Si ese error lo presenta uno solo de los extremos, el error en el cálculo de la admitancia de secuencia cero será de 10.24% para la línea 1 y de 2.46% para la línea 2. Con el fin de reducir los errores anteriores, será necesario esperar más tiempo, desde la activación del detector de falta, para registrar las magnitudes de falta. Ésto será posible si lo permite el tiempo de despeje de las faltas. Para ello será necesario estudiar los tiempos de operación tanto de los relés de

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protección como de los interruptores instalados en las líneas adyacentes.

III. LOCALIZACIÓN DE FALTAS EN LÍNEAS MIXTAS

El gran crecimiento de las áreas urbanas ha provocado un importante aumento de los soterramientos parciales en España, lo que ha incrementado el número de líneas mixtas propiedad de REE. Dichas líneas mixtas presentan un tramo subterráneo bastante más corto que el tramo aéreo (menos de un 15-20% de la longitud de la sección aérea) por lo que se utiliza la función de reenganche, con el fin de que opere para faltas en el tramo aéreo. Las faltas en el cable, sin embargo, no deben reengancharse, en primer lugar, como medida de seguridad pública, puesto que bastantes faltas son causadas por personas trabajando con máquinas cerca del cable. Por otra parte hay que tener en cuenta que la inmensa mayoría de las faltas que se producen en el cable son permanentes, en cuyo caso el reenganche lo único que provocaría es un mayor daño en éste.

Con el fin de detectar cual es el tramo en falta, el subterráneo o el aéreo, la solución, aplicada en principio a todas las líneas mixtas, fue la de instalar dos relés diferenciales de línea a ambos extremos del cable, cuya operación enviaba, por comunicaciones, una orden de bloqueo a los reenganchadores situados a ambos extremos de la línea mixta. Dicha solución presenta el inconveniente de requerir transformadores de intensidad, alimentación de continua, etc a ambos extremos del cable lo que incrementa mucho el coste tanto de instalación como de mantenimiento. Otra solución, empleada hoy en día, es la de instalar relés de distancia a ambos lados de la línea mixta con una zona específica para detectar faltas en el tramo aéreo. El reenganche queda, en ese caso, supeditado a la operación de alguna de esas dos zonas de distancia. Esta segunda solución es mucho más barata que la anterior, puesto que no hay necesidad de instalar protecciones en los extremos del cable, sin embargo las zonas de distancia empleadas para detectar faltas en los tramos aéreos no pueden cubrir el 100% de cada tramo dado el posible efecto de sobrealcance, como consecuencia de los siguientes factores: el carácter mixto del lazo en falta cuando el defecto se produce en el cable o en el siguiente tramo aéreo (se usa un factor de compensación homopolar característico del tramo aéreo, muy diferente al correspondiente a un cable), la no consideración de las capacidades de la línea, las imprecisiones en el valor de la impedancia de secuencia cero del tramo aéreo, la no homogeneidad del sistema y el flujo de carga en la línea cuando la falta es resistiva, posibles errores en la selección del tipo de falta, etc. El alcance de las zonas de distancia que se suele utilizar es de un 85-90% el valor de la impedancia de secuencia directa del tramo aéreo. Por ello muchas de las faltas que se produzcan en el tramo aéreo no cubierto no van a ser detectadas por la zonas de distancia, por lo que no se van a reenganchar. Incluso faltas que se produzcan en el porcentaje del tramo aéreo cubierto tampoco van a ser detectadas por las zonas de distancia si existen efectos de subalcance, los cuales siempre se producirán ante faltas muy resistivas.

La operación de las zonas de distancia que cubren el tramo

aéreo puede ser complementada con un localizador de faltas que, aunque requiera más tiempo para efectuar sus cálculos, discrimine cual es el tramo en falta. Esa información puede ser enviada al centro de control para que, en el caso de que la falta se produzca en la parte del tramo aéreo no cubierto por las zonas de distancia, se pueda efectuar un cierre manual en poco tiempo. No obstante, REE pretende que la discriminación del tramo en falta esté basada únicamente en el localizador de faltas, el cual debe efectuar sus cálculos antes de que finalice el ciclo de reenganche con el fin de poder abortarlo si la falta se produce en el cable. Con esta última solución todos los disparos instantáneos iniciarían el ciclo de reenganche. Los localizadores de faltas basados en las medidas de uno de los extremos de la línea mixta no dan buenos resultados, dado que sus algoritmos requieren usar la impedancia de secuencia cero del cable, la cual varía dependiendo del camino de retorno de la intensidad ante una falta a tierra. La localización de faltas basada en las medidas de dos PMUs situadas a ambos extremos de la línea mixta puede basarse únicamente en la red de secuencia directa, lo que elimina el problema anterior. Como la red de secuencia directa se utiliza para todas las faltas no hay necesidad de determinar el tipo de falta. Por otra parte, el algoritmo no se ve afectado por la resistencia de falta, flujo de carga y no homogeneidad del sistema.

Dada la variación de la impedancia de secuencia directa de la línea, principalmente de los tramos aéreos al tramo subterráneo, el algoritmo de localización de faltas deberá emplear diferentes circuitos en función del tramo en falta. Las figuras 4 y 5 muestran los circuitos a considerar para faltas en el primer tramo aéreo y en el cable respectivamente.

Las ecuaciones asociadas a los circuitos anteriores se incluyen a continuación. Con el fin de tener en cuenta las capacidades tanto del cable como de los tramos aéreos, se han considerado circuitos de parámetros distribuidos. 3.1.1.1.1 Falta en primer tramo aéreo

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Falta en cable

γL1

, γL2 γC - constantes de propagación para tramos aéreos 1 y 2 y cable respectivamente ZCL1

, ZCL2, ZCC - impedancias características para tramos

aéreos 1 y 2 y cable respectivamente LL1, LL2, LC - longitudes de tramos aéreos 1 y 2 y cable respectivamente

El circuito considerado por el algoritmo del localizador de faltas para una falta situada en el segundo tramo aéreo es similar al considerado para la falta en el primer tramo aéreo.

El algoritmo de localización de faltas debe determinar, en primer lugar, el tramo en falta con el fin de elegir el circuito correcto. La referencia [8] describe un localizador de faltas para una línea aérea que se ha dividido en varias secciones. La sección en falta se determina efectuando el cálculo desde uno de los extremos y analizando el valor de la distancia a la falta obtenido. Por otra parte, existen algoritmos de localización de faltas que determinan la sección en falta en líneas de tres terminales [4], [5] y [6] o en redes de distribución con cargas intermedias [7], suponiendo una hipotética localización de la falta. Para una línea mixta se puede determinar la sección en falta de forma simil . Como lo primero que se quiere saber es si la falta se encuentra en el cable, con el fin de decidir si se aborta o no el ciclo de reenganche, se efectuará el cálculo de la distancia a la falta (d: contada ésta desde uno de los extremos del cable œ ver figura 5) suponiendo que ésta se encuentra en el tramo subterráneo. Si el resultado obtenido se encuentra entre 0 y 1, se confirma la anterior suposición y se genera la orden de bloqueo del reenganchador. Si el resultado es

negativo o mayor que 1, se deja que finalice el ciclo de reenganche y se efectúa el cálculo considerando el siguiente tramo aéreo en falta: - Aéreo 1 si d<0: la caída de tensión en las impedancia d*Z1C representada en el circuito de la figura 5 sería negativa, lo que indica que la intensidad I1L1 debería tener el sentido contrario alrepresentado.

- Aéreo 2 si d>1: la caída de tensión en las impedancia (1-d)*Z1C representada en el circuito de la figura 5 sería negativa, lo que indica que la intensidad I1L2 debería tener el sentido contrario al representado.

No obstante, teniendo en cuenta los errores que puede presentar el localizador de faltas antes descrito, la falta se considerará fuera del cable cuando d>1*K1 y cuando d<K2. Las constantes K1 y K2 se determinarán tras efectuar simulaciones para cada línea mixta a proteger. Se consideran en un principio dos algoritmos, que utilizan las magnitudes de secuencia directa de falta (algoritmo 1) y de falta pura (algoritmo 2), es decir una vez restada la componente de prefalta. Los valores de prefalta se registrarán uno o dos ciclos antes de la activación del detector de falta descrito en el apartado 2.3. 3.1 Simulación

Se simula, mediante RTDS, una línea mixta de 220 kV, cuyas características se incluyen en la tabla 11. Se introducen diferentes tipos de faltas, con distinta resistencia de falta y ángulo de incidencia. Las tensiones e intensidades de secuencia directa a ambos extremos de la línea mixta se obtienen a partir de dos PM Us similares a las descritas en el apartado 2.3.

3.1.2 Resultados sin errores externos

En las tablas 12, 13 y 14 se pueden observar algunos de los resultados obtenidos sin tener en cuenta parámetros externos a las PMUs y considerando las faltas sin componente de continua. El máximo error registrado para faltas en el primer tramo aéreo es de 0.373%. Debido a la reducida impedancia por unidad de longitud del cable (del orden de 3 veces menor que la correspondiente a los tramos aéreos) y a la longitud de éste, la precisión del localizador de faltas empeora bastante para defectos en el tramo subterráneo. Los resultados incluidos en la tabla 1, para faltas en el cable, se han obtenido a partir de las medidas registradas 1 o 2 ciclos después de la activación del detector de falta (tal y como se comenta en el apartado 2.3). No obstante, efectuando los cálculos a partir de las medidas tomadas en otro instante de tiempo, se han llegado a registrar errores en torno al 11%, lo que hace que el algoritmo no sea muy adecuado para localizar la falta en dicho tramo. De todos

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modos hay que tener en cuenta que un error del 11% relativo a la impedancia del cable equivale a un error del 0.239% y del 1.289% con respecto a la impedancia de los tramos aéreos 1 y 2 respectivamente, lo que hace que el algoritmo permita localizar, con buena precisión, faltas en toda la línea mixta. A pesar de que se han simulado más faltas en el cable de las consideradas en el artículo, no se incluyen sus resultados dada la gran dispersión que presentó el error al tomar medidas en diferentes instantes de tiempo. En cualquier caso los errores obtenidos, relativos a la impedancia del primer tramo aéreo fueron siempre del orden de los errores incluidos en las tablas para faltas en dicho tramo aéreo.

Tabla 12. Influencia de la localización de falta (tipo de falta: AG, resistencia

de falta: 10 ohmios)

Tabla 13. Influencia del tipo de falta (Resistencia de falta: 10 ohmios)

Tabla 14. Influencia de la resistencia de falta

3.1.3 Resultados con errores externos Para faltas en distintos porcentajes del primer tramo aéreo, se analiza el efecto de algunos factores externos a las PMUs tales como: la incertidumbre en los parámetros de la línea, posibles errores en la sincronización entre extremos y los errores los transformadores de medida. También se tiene en cuenta la influencia de la componente de continua.

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3.1.3.1 Influencia de los parámetros de la línea La tabla 15 representa los errores adicionales que introducen los algoritmos 1 y 2 cuando se modifica un 10% la impedancia de secuencia directa de cada tramo. Se ha considerado la combinación más desfavorable, la cual resulta ser la siguiente: Ztramo_aéreo1*1.1 / Zcable*0.9 /Ztramo_aéreo2*0.9.

Tabla 15. Influencia de un error del 10% en las impedancias de la línea

3.1.3.2 Influencia de la sincronización entre extremos En la tabla 16.a) se pueden observar los errores adicionales

que introduce el algoritmo 1 cuando se añade un desfase de 10º entre las intensidades medidas por las dos PM Us. La tabla 16.b) incluye los errores cuando el desfase de 10º se introduce en las tensiones. Como se puede ver, en este último caso, para falta al 20% el error adicional es de un 16.245%, intolerable para esta aplicación. Dicho error es debido al elevado valor que presenta la tensión de falta, dado que las faltas inyectadas son muy resistivas. Por ello el algoritmo 2, basado en magnitudes de falta pura, prácticamente no introduce ningún error adicional.

Hay que tener en cuenta que el uso del GPS reduciría a valores mínimos (teóricamente 1 us) los errores de sincronización. No obstante, cabe destacar que el algoritmo 2 (elegido para las faltas inyectadas) no requiere el uso de relojes de GPS de alta precisión.

16.a) Error de sincronización entre intensidades 16.b) error de

sincronización entre tensiones Tabla 16. Influencia de un error de sincronización entre extremos de 10º

3.1.3.3 Influencia de los transformadores de intensidad La tabla 17 representa los errores adicionales que introduce el algoritmo 1 cuando se añaden a las intensidades medidas por las PMUs, errores del 3% y de 2º, respectivamente. Se han considerado los casos más desfavorables, que son aquellos en los que ambas intensidades local y remota presentan errores en módulo de signos contrarios (+3% en Ilocal

/ -3% en Iremota) y errores en ángulo del mismo signo (+2º en Ilocal

/ +2º en Iremota).

17.a) error en módulo del 3% 17.b) error en ángulo de 2º

Tabla 17. Influencia de los transformadores de intensidad

3.1.3.4 Influencia de los transformadores de tensión La tabla 18 representa los errores adicionales que introduce el algoritmo 1 cuando se añaden a las tensiones medidas por las PM Us, errores del 3% y de 2º, respectivamente. Se han considerado los casos más desfavorables, que son aquellos en los que ambas tensiones local y remota presentan errores de signos contrarios, ya sea en módulo (+3% en Vlocal

/ -3% en Vremota) o en ángulo (+2º en Vremota)

18.a) error en módulo del 3% 18.b) error en ángulo de 2º

Tabla 18. Influencia de los transformadores de tensión

En vista de los resultados anteriores, es necesario compensar

los errores introducidos por los transformadores de tensión. Lo más adecuado sería efectuar una calibración de las PMUs en base a las curvas que presenten dichos transformadores. No obstante cabe destacar que, para las faltas inyectadas, el algoritmo 2 reduciría bastante los errores anteriores. 3.1.3.5 Influencia del ángulo de incidencia

En el caso más desfavorable (intensidades tomadas 1 ciclo después de la activación del detector de falta y con máximo offset), el error introducido en la intensidad es de un 1% en módulo y de 3º en ángulo, lo que da lugar a un error adicional máximo en la localización de faltas de 0.383%, para faltas al 80% del tramo aéreo 1. Los resultados anteriores, considerando que las PMUs se van a calibrar según las curvas de error de los transformadores de medida (principalmente los de tensión), implican una mejora importante con respecto a la opción basada en zonas de distancia.

IV. MOTORIZACIÓN DEL COMPORTAMIENTO DINÁMICO

El crecimiento y la cada vez mayor interconexión de los sistemas eléctricos tienen un impacto sobre la estabilidad de dichos sistemas. Por un lado se producen oscilaciones en el sistema UCTE en el rango de los 0.2 Hz que plantean problemas como:

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Flujos de energía no planificados a través de la red de

la UCTE Incertidumbre en el comportamiento dinámico del

sistema ante oscilaciones mal amortiguadas, Por otra parte el rápido crecimiento de la generación eólica en el sistema eléctrico peninsular introduce mayor incertidumbre en el comportamiento dinámico del sistema. Un contingente importante de generadores convencionales equipados con PSS, se ve desplazado por generación eólica, lo que puede implicar un cambio en el comportamiento dinámico del sistema. Se hace pues necesario ante esta nueva situación mejorar el conocimiento del comportamiento dinámico del sistema

mediante la observación directa adicionalmente al análi s del sistema mediante modelos. Para este fin se va a desarrollar un proyecto pil o en el que se van a utilizar equipos de medida fasorial (PM U) para almentar una aplicación que determine las siguientes características modales de la interconexión España-M arruecos:

Frecuencia modal Amplitud del los diferentes modos Amortiguamiento del modo de oscilación Fase del modo

La figura 6 muestra los principales componentes funcionales del sistema.

Figura 6 Sistema de monitorización de la dinámica de la red.

Los equipos de medición serán PMU. Se van a instalar dos unidades PMU en una subestación de 400 kV que estarán monitorizando la corriente y tensión de un doble circuito de 400 kV de manera continua. La frecuencia de escaneo será 50 fasores por segundo.

Estos equipos estarán sincronizados mediante un reloj GPS directamente conectado al equipo con una precisión de al menos 100 us.

Las medidas de estos equipos se enviarán a través de la red de comunicación de REE de modo continuo a un servidor donde residirá la aplicación que procesará los datos fasoriales. La figura 7 muestra la arquitectura de comunicación que se desarrollará para este proyecto.

A partir de este sistema y mediante la utilización de PMUs REE estará en disposición de: Investigar potenciales problemas de amortiguamiento en el

sistema, identificando modos de oscilación local e interarea, mediante la monitorización continua de la

amplitud de los modos de oscilación y su mortiguamiento. Reajuste de los PSS de las centrales. La observación del

amortiguamiento de los diferentes modos de oscilación será util para el reajuste de los PSS de las centrales de generación

Validación de modelos. La medida continua de la dinámica del sistema proporcionará información para la validación de los modelos para las diferentes condiciones de explotación del sistema.

Mejora de la seguridad del sistema. A través del análisis de los datos será posible establecer planes de defensa ante oscilaciones inestables.

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CO/CLUSIÓ/

Este artículo ha descrito las aplicaciones que REE ha pensado para las PM Us a corto plazo. El cálculo de las impedancias de una línea basado en la medidas de las PM Us permie obtener resultados más exactos que a partir de los métodos tradicionales. No obstante las PM Us requieren una alta precisión en la sincronización y requieren ser calibradas con las curvas de error de los transformadores de medida. El cálculo de la impedancia de secuencia directa con magnitudes de falta o de falta pura mejora mucho los resultados cuando existen errores de sincronización entre tensiones o errores derivados de los transformadores de tensión. El localizador de faltas para líneas mixtas, basado en PM Us, descrio en este artículo permite que el esquema de protección para dichas líneas no requiera relés instalados a ambos lados del cable. Para las faltas inyectadas, el algoritmo basado en magnitudes de falta pura tolera mayores errores de sincronización entre tensiones y mayores errores derivados de los transformadores de tensión. Por último, la instalación de PM Us en puntos estratégicos de la red permitirá detectar y caracterizar posibles oscilaciones de pequeña señal, con el fin de incrementar su amortiguamiento y establecer planes de defensa.

BIBLIOGRAFÍA

[1] Líneas de Transporte de Energía œ L. M . Checa, M arcombo S.A. 01/01/1988 [2] Analysis of Faulted Power Systems œ Paul M . Anderson IEEE Press Power Systems Engineering Series [3] Handbook of Power System Engineering œ Yoshihide Hase, W ILEY 2007 [4] A New Fault Location Technique for Two- and Three-Terminal Lines“- Girgis, A.A.; Hart, D.G.;Peterson, W .L.- IEEE Transactons on Power Delivery, Volume 7, Issue 1, Jan 1992 Page(s):98 œ 107 [5] A Practical Approach to Accurate Fault Location on Extra Highvoltage Teed Feeders“ - Aggarwal, R.K.; Coury, D.V.; Johns, A.T.; Kalam, A.- IEEE Transactions on Power Delivery, Volume 8, Issue 3, Jul 1993 Page(s):874 œ 883 [6] Development of a new faultocation system for multi erminal single transmission lines“ - Abe, M .; Otsuzuki, N.; Emura, T.; Takeuchi, M . - IEEE Transactons on Power Delivery, Volume 10, Issue 1, Jan 1995 Page(s):159 œ 168 [7] Fault location method for M V cable network“ - Saha, M .M .; Provoost, F.; Rosolowski, E. Developments in Power System Protection, 2001, Seventh International Conference on (IEE) Volume , Issue , 2001 Page(s):323 œ 326 [8] Development of an advanced transmission line faultocation system.II. Algorithm development and simulation“ - Lawrence, D.J.; Cabeza, L.Z.; Hochberg, L.T. - IEEE Transactions on Power Delivery, Volume 7, Issue 4, Oct 1992 Page(s):1972 œ 1983 [9] Evaluation and development of transmission line fault ocating techniques which use sinusoidal steady-state information,“ - E.O. Schweitzer III Ninth Annual Western Protective Relay Conference, Spokane, W ashington, Oct. 1982. [10] Challenges and Solutions in the Protection of a Long Line in the Furnas System“ œ R. Abboud, W . Ferreira, F.Goldman - W estern Protective Relay Conference, Spokane, W A, October, 2005 [11] Protective Relaying Considerations for Transmission Lines W ih High Voltage AC Cables“ - Working Group D12 of the Line Protection Subcommittee, PSRC - IEEE Trans. Power Delivery, vol. 12, No. 1, pp. 83œ 96, Jan. 1997 [12] Adapting Protection to Frequency Changes“ œ R. Cimadevilla, R. Quintanilla, S. W ard - W estern Protective Relay Conference, Spokane, W A, October, 2005 [13] EMTP Theory Book œ H. W . Dommel œ BPA 1987

IX SIMPOSIO IBEROAMERICANO SOBRE PROTECCIÓN DE SISTEMAS ELÉCTRICOS DE POTENCIA, SIPSEP-04-28. www.uanl-die.net 1

Estimando el Fasor Dinámico con DiferenciadoresMáximamente Lisos

Miguel Ángel Platas Garza, José Antonio de la O Serna, Senior Member, IEEE

Resumen— Estimaciones del fasor dinámico y sus derivadas seobtienen usando la solución de mínimos cuadrados ponderadospara la aproximación de Taylor, usando ventanas clásicas comofactores de ponderación. Se demuestra que la solución demínimos cuadrados simultáneamente aproxima con polinomiosde Taylor la función temporal y sus espectro respectivamente, yesta doble solución, a su vez, equivale a aproximar las respuestasen frecuencia ideales de diferenciadores en una banda de paso,la cual se puede centrar en una frecuencia deseada. Por estarazón los diferenciadores son máximamente lisos en la banda depaso. Los filtros (diferenciadores) diseñados con las ventanas deHamming y Kaiser se muestran como ejemplos de diferenciadorespasabanda y pasabajas.

Palabras Clave— Fasor dinámico, envolvente compleja, vec-tor de estados fasoriales, estimación fasorial, ajuste espectral,diferenciadores digitales, filtros máximamente lisos, ventanas,interpolación, transformada digital Taylor-Fourier

I. INTRODUCCIÓN

La estimación del fasor en condiciones dinámicas se en-cuentra en la mera base de las técnicas de monitoreo ycontrol de sistemas eléctricos de potencia. La regulaciónde intercambios de energía en redes de área amplia y laestabilidad de la red dependen de la exactitud y retraso de lasmediciones fasoriales. Además, los serios apagones recientesestán demandando mejor análisis de disturbios, y estimaciónde estados con las recientes mediciones de sincrofasores.

Aun cuando exista ya una norma para las medición de sin-crofasores [1], existen numerosos malentendidos con respectoal error de las estimaciones fasoriales [2], y discrepanciasentre las unidades de medición fasorial (Phasor MeasurementUnits, PMU) de diferentes fabricantes han sido reportadas[3], especialmente cuando operan fuera de las condicionesde operación nominal en frecuencia. Estas discordancias sedeben principalmente a la suposición tan restringente de quela amplitud y fase son constantes durante el intervalo deestimación en la oscilación. Otra idea fuertemente enraizadaes la disociación entre la medición fasorial y la frecuencial.Normalmente, se supone que la estimación de la frecuenciase hace después de que los fasores han sido estimados [4]. Espor esta razón que el uso de diferenciadores digitales basadosen diferencias finitas de las estimaciones de fase producenmediciones fasoriales muy ruidosas [5], [6], [7]. Es sabido queestos diferenciadores son filtros pasa altas con altas gananciasen la banda de altas frecuencias. La metodología propuesta

Este trabajo fue financiado por la UANL, mediante el Proyecto PAICYTCA-1615-07: "Diseño de Filtros Ultraplanos para Estimación Fasorial".

M. Platas es estudiante de la maestría en Ingeniería Eléctrica. El Dr.de la O trabaja en la Universidad Autónoma de Nuevo León, Mé[email protected].

en este artículo ofrece estimaciones de la frecuencia y susderivadas junto con las del fasor en cada toma estimadora.Los diferenciadores obtenidos son limitados en banda conganancias decrecientes hacia las altas frecuencias. El métodose basa en la aproximación de polinomios de Taylor al fasordinámico en intervalos de corta duración.

En [8] se propuso el concepto de fasor dinámico comola envolvente compleja de una señal pasabanda ampliamenteconocida en sistemas de trasmisión digital. Se sugirieroninteresantes estimadores y se ilustraron las respuestas enfrecuencia de los filtros. Se demostró que los estimados songenerados por filtros digitales con ganancias constante, linealy cuadrática en la banda lateral superior, y rechazo perfecto enla banda lateral inferior. Lo cual corresponde a las gananciasideales de diferenciadores digitales en la banda de paso yrechazo perfecto de la componente de frecuencia negativa.Sin embargo, una de las preocupaciones de esos filtros fue sualto nivel de lóbulos laterales fuera de banda, pues los hacesensibles al ruido.

En este artículo se extiende nuestro método de estimación,usando ventanas clásicas para ponderar los errores de la solu-ción de mínimos cuadrados. Presentamos los filtros obtenidoscon la ventana de Hamming, e ilustramos las opciones dediseño que proporciona la ventana de Kaiser, la cual permitecontrolar el ancho de la banda de paso y reducir el nivelde los lóbulos laterales en la banda de paro. Este métodono corresponde al método de diseño clásico de filtros derespuesta impulsional finita (FIR) usando ventanas. En vez dereconfigurar solamente la respuesta impulsional mediante elenventaneado, la solución de mínimos cuadrados ponderadostambién reconfigura los vectores de la base vectorial, y portanto la matriz de Gram. Se demuestra que este método ajustasimultáneamente el modelo de señal temporal y espectral ala señal de entrada y su espectro respectivamente, y a suvez adapta las funciones de transferencia de los filtros a lasrespuestas en frecuencia de los diferenciadores ideales, juntoa la frecuencia fundamental, logrando ganancias nulas juntoa la fundamental negativa, lo que asegura el rechazo de esacomponente obligatorio en toda medición fasorial.

Las interesantes estructuras espectrales ofrecidas por lasolución de mínimos cuadrados ponderados en las señalespasabanda nos persuadieron de aplicar la misma técnica parael diseño de filtros pasabajas. En esta aplicación se hacemás palpable que las respuestas en frecuencia de los filtrosson combinaciones lineales del espectro de la ventana ysus derivadas. Esto explica la reducción del nivel de lóbu-los laterales y el efecto ensanchador de la banda de pasocuando se aplica una ventana distinta a la rectangular. Y


sκ(−Nh)

...sκ(−n)

...sκ(0)

...sκ(n)

...sκ(Nh)

`

=

(−Nh)κe jNhω1 (−Nh)κ−1ejNhω1 · · · ejNhω1 e−jNhω1 · · · (−Nh)κ−1e−jNhω1 (−Nh)κe−jNhω1

......

......

......

......

(−n)κejnω1 (−n)κ−1ejnω1 · · · ejnω1 e−jnω1 · · · (−n)κ−1e−jnω1 (−n)κe−jnω1

......

......

......

......

0 0 · · · 1 1 · · · 0 0

......

......

......

......

nκe−jnω1 nκ−1e−jnω1 · · · e−jnω1 ejnω1 · · · nκ−1ejnω1 nκejnω1

......

......

......

......

Nκh e−jNhω1 Nκ−1

h e−jNhω1 · · · e−jNhω1 ejNhω1 · · · Nκ−1h ejNhω1 Nκ

h ejNhω1

1

2

pκ

pκ−1

...p0p0

...pκ−1pκ

`

(5)

se demuestra que esta técnica produce filtros máximamentelisos (maximally flat filters) [9], i. e. cuyas respuestas enfrecuencia maximizan el número de derivadas nulas en elcentro del intervalo. En nuestro método las derivadas sonestimadas mediante el algoritmo de mínimos cuadrados enel centro del intervalo temporal aproximando polinomios deTaylor. A partir de un cierto orden, estos polinomios sonsuficientemente precisos en intervalos cortos de señal, dondeel error queda restringido bajo un techo definido para señalescon ancho de banda inferior a la banda de paso de los filtros.Filtros máximamente lisos fueron también propuestos en [10]pero usando interpolación de Newton hacia atrás para estimarlas derivadas con el operador de diferencias hacia atrás. Esteoperador es ampliamente utilizado en análisis numérico, peroes extremadamente sensible al ruido.

Con respecto a los diferenciadores digitales obtenidos connuestro método, se puede afirmar que son de banda angosta,con una aproximación a la respuesta en frecuencia ideal enel intervalo centrado en la frecuencia fundamental. Al serobtenidos esencialmente por una aproximación de polinomiosde Taylor, la diferencia de la aproximación es máximamenteplana (como todo error de Taylor), alrededor de la frecuenciafundamental, y por tanto todos ellos son máximamente lisos enla banda de paso [11], [12]. Otros diferenciadores obtenidosen la literatura mediante mínimos cuadrados son de bandacompleta y equirizados [13], [14], los obtenidos usando seriesde Taylor, estiman las derivadas con aproximaciones de difer-encia central [15], las cuales son esencialmente ecuacionesde diferencias finitas,en las cuales los estimados se hacen alcentro del intervalo intermuestra. Finalmente, los obtenidosen [16] son de respuesta impulsional infinita (Infinite ImpulseResponse, IIR) con retraso de grupo variable, tienen respuestasen magnitud lineal en bandas más anchas, y su gananciaregresa suavemente a cero a la mitad de la frecuencia demuestreo.

El artículo se desarrolla como sigue. En la primera sección,se formula la solución de mínimos cuadrados ponderadospara la aproximación de polinomios de Taylor. Enseguida,se diseñan filtros pasabanda utilizando ventanas clásicas deprocesamiento de señales como ponderación, y se ilustransus respuestas en frecuencia. Se compara el filtro Cosenolevantado (Raised Cosine, RC) con los diseños anteriores.Entonces el diseño de filtros pasabajas es abordado en el casocontinuo para demostrar que la solución de mínimos cuadradosconstituye una doble aproximación tiempo-frecuencia, y que

los diferenciadores obtenidos son máximamente lisos en labanda base. Finalmente, se ilustran las respuestas en frecuenciade los diferenciadores pasabajas obtenidos con las ventanasrectangular y de Hamming.

II. SOLUCIÓN DE MÍNIMOS CUADRADOS PONDERADOS

El concepto de fasor dinámico fue propuesto en [8] como laenvolvente compleja de una señal pasabanda s(t) que modelaadecuadamente las oscilaciones de un sistema de potencia:

s(t) = Rep(t)ej2πf1t, (1)

en la cual f1 es la frecuencia fundamental, p(t) = a(t)ejϕ(t) esel fasor dinámico, del cual a(t) y ϕ(t) son las modulacionesen amplitud y fase en s(t). Un modelo de señal suficiente-mente completo puede obtenerse aproximando un polinomiode Taylor de orden κ

pκ(t) = p(0) + p′(0)t + p′′(0)t2

2!+ · · ·+ p(κ)(0)

tκ

κ!,

para− T

2≤ t ≤ T

2, (2)

al fasor dinámico sobre un intervalo corto de tiempo, losuficientemente corto como para contener el error bajo unacota determinada. Entonces, es posible obtener un estimadosuficientemente exacto del fasor dinámico y sus derivadas enel centro del intervalo aplicando el algoritmo de mínimoscuadrados, dado que el polinomio de Taylor es suficientementepreciso en ese intervalo, como para formar una base vectorialcompleta.

Si la aproximación de orden κ es de la forma

sκ(t) = Repκ(t)ej2πf1t, (3)

entonces, tendremos en el `ésimo intervalo

sκ,` = Bκpκ,` (4)

como se muestra en (5). Asumiendo que la señal es muestreadaa N1 muestras por ciclo T1 = 1/f1, N muestras de señalcorresponderán al intervalo de Taylor de duración T , conN = [(T/T1)N1], donde el operador [ ] toma el número imparmás cercano a (T/T1)N1, de tal manera que N = 2Nh + 1,para asegurarnos de que una de las muestras correspondaal instante t = 0. Note que las columnas de Bκ son dela forma ejnω1 , nejnω1 , . . . , nκ−1ejnω1 , nκejnω1 , y sus con-jugados complejos, n ∈ [−Nh, . . . , 0, . . . , Nh], donde ω1 =


2π/N1 es la frecuencia fundamental angular. Note finalmenteque los coeficientes pk corresponden a las derivadas del fasordinámico pk = p(k)(0)/(k!(N1f1)k), para k = 0, 1, . . . , κ. Elerror de la κésima aproximación es dado por:

eκ = s−Bκpκ (6)

Y los mejores estimados de pκ en el sentido de mínimoscuadrados son dados por

pκ = (BHκ Bκ)−1BH

κ s (7)

donde H es el operador hermitiano. Para un intervalo temporaldado, el error de Taylor se puede reducir aumentando el ordenκ del polinomio. También es sabido que para un orden κ dadoel error de Taylor es expansivo, i.e. su magnitud aumenta hacialos extremos del intervalo. Por lo tanto, una manera efectivade reducir el error en los extremos del intervalo es atenuarlocon una ventana temporal. Entonces (6) se convierte en

W eκ = W s−WBκpκ (8)

donde

W =

w1 0 · · · 00 w2

.... . .

...0 · · · wN

(9)

La solución de mínimos cuadrados ponderados de (8) seráentonces [17]:

pκWLS = (BHκ W HWBκ)−1BH

κ W HWs (10)

Note que (7) es el caso particular (W = I) de (10), y quela matriz W HW permite ponderar el error de Taylor de laaproximación en ese intervalo. Note en (10) que la soluciónde mínimos cuadrados consiste en modificar tanto la basevectorial como la señal con los pesos de la matriz W . Lasolución minimiza el siguiente criterio de error:

JW = eHκ W HW eκ (11)

si y solo siBH

κ W HWBκ > 0. (12)

Pero si W HW es definida positiva, la condición anterior serelaja a:

BHκ Bκ > 0. (13)

Como sabemos de [18], si una señal analítica es aproximadapor un polinomio de Taylor de κésimo orden, la aproximaciónes buena mientras esté dentro del vecindario cercano al puntoen el cual la señal es aproximada, en el cual predominan lostérminos de bajo orden. Por tanto, al dar más ponderación a loserrores cercanos al centro, mejorarán las estimaciones de loscoeficientes de orden más bajo. O inversamente, al despreciarlos errores de los extremos del intervalo, empeorarán losestimados de alto orden, pero eso no importa porque son losdescartados del modelo.

Aun cuando en lo que sigue los pesos cuadráticos ω2n en

W HW van a ser definidos por ventanas clásicas de proce-samiento de señales, es importante enfatizar que la soluciónen (10) no es la misma que el tradicional método de diseño

de filtros FIR mediante ventanas [19, p. 664]. Si la matrizpseudoinversa B+

κ = (BHκ Bκ)−1BH

κ contiene la respuestaimpulsional de los filtros originales, los filtros enventaneadosen [19] serán dados por B+

κ W HW , la cual no correspondecon la de (10), porque en esta última la gramiana es tambiénmodificada por los pesos cuadráticos (BH

κ W HWBκ).Finalmente, considerando la carga computacional, note en

(10) que las respuestas impulsionales de los diferenciadorespueden calcularse una única vez en la matriz 2(κ + 1) × N ,(BH

κ W HWBκ)−1BHκ W HW , ya que ésta depende exclu-

sivamente del modelo de señal y la ventana aplicada. Y losvalores de la matriz se almacenan en memoria. Además,dada la simetría hermitiana de los parámetros estimados paraseñales reales, se requiere únicamente la mitad (κ + 1) delos filtros FIR. Y más aún, las operaciones de filtrado puedencalcularse con transformada rápida de Fourier (Fast FourierTransform, FFT) para reducir el número total de productosrequeridos en cada toma de estimados.

A. Respuesta en Frecuencia

La respuesta en frecuencia de los filtros estimadores esmuy útil para evaluar su comportamiento en términos delcontenido frecuencial de la señal de entrada, en particular susensibilidad al ruido. Se encuentra estimando los parámetrosde la señal s(n) = e−jωnn=−Nh,...,Nh

con π < ω < π.La Fig 1 muestra la respuesta en frecuencia del estimadorde p4th

0 obtenido con los algoritmos WLS (Weigthed Least-Squares) y LS (Least-Squares), aplicando un filtro de cuatrociclos y una aproximación de cuarto orden. Se aplicó laventana de Hamming como ponderación de error. Es palpableque la ponderación preserva la ganancia plana junto a lafrecuencia fundamental, amplía la banda de paso, y reduce loslóbulos laterales en la banda de paro del filtro. La ponderacióndel error también mejora el rechazo de la componente defrecuencia fundamental negativa, logrando una ganancia nulaen la vecindad de dicha frecuencia f = −f1. Finalmente, noteque la solución tradicional de filtro FIR enventaneado (líneapunteada) no preserva la ganancia plana. La Fig. 2 muestralas respuestas en magnitud de los filtros diferenciadores deprimero y segundo orden. Note nuevamente que la ponderaciónensancha el lóbulo principal y reduce los lóbulos laterales.Este efecto ensanchador de la banda de paso también se notaen el vecindario junto a la frecuencia fundamental, donde seobtiene la ganancia lineal y cuadrática de los diferenciadoresideales sobre un intervalo más grande de frecuencias. Notetambién que la descomposición de Taylor del fasor dinámico,se realiza pasando la señal pasabanda s(t) a través de un bancode filtros, cuyas ganancias junto a la frecuencia fundamentalson las potencias sucesivas de las series de Taylor (u − 1)n

para n = 0, 1, 2, . . .: constante, lineal, cuadrática, etc. Como seasume que el espectro de la señal pasabanda es restringido, losestimados estarán libres de error cuando la cota frecuencial dela señal se encuentre bajo la ganancia constante. Finalmente,note que la solución tradicional de enventaneo no trabajaadecuadamente para el diferenciador de segundo orden puesno pasa por cero en la frecuencia nula.


−3 −2 −1 0 1 2 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Normalized frequency u=f/f1

Mag

nitu

de

Frequency Response (4th Approximation, 4~)

WLS

LS

Windowed

Fig. 1. Respuesta en frecuencia del estimador p4th0 de cuatro ciclos, WLS

(Línea continua), LS (línea a rayas), y el tradicional diseño de filtros FIRenventaneados (línea punteada).

−2 −1.5 −1 −0.5 0 0.5 1 1.5 20

0.01

0.02

0.03

Firs

t−D

iffer

entia

tor

Magnitude Response (4th Approximtation, 4~)

WLS

LS

Windowed

−2 −1.5 −1 −0.5 0 0.5 1 1.5 20

2

4

6x 10

−4


Sec

ond−

Diff

eren

tiato

r

WLS

LS

Windowed

Fig. 2. Respuesta en frecuencia de los estimadores de la primera y segundaderivada p4th

1 y p4th2 de cuatro ciclos, WLS (línea continua), LS (línea a

rayas), y el tradicional diseño de filtros FIR enventaneados (línea punteada).

B. Ventanas de Kaiser

El rol principal de la ventana es ponderar más los pun-tos cercanos al centro del intervalo que los alejados. Laúnica condición para la ventana es que las muestras seanpositivas. La ventana de Hamming no permite controlar elensanchamiento del lóbulo principal o la reducción de loslóbulos laterales como lo hacen las de Kaiser. Éstas son dadaspor

wn =I0

[α√

(N−12 )2 − (n− N−1

2 )2]

I0[α(N−12 )]

(14)

donde I0 es la función de Bessel de orden cero de primertipo, y α es un parámetro real nonegativo que puede ajustarsepara hacer un balance entre ancho del lóbulo principal y nivelde lóbulos laterales. Cuando α = 0 la ventana de Kaiser esidéntica a la rectangular, y al aumentar α las ventanas son másselectivas en el centro del intervalo temporal como se puedeapreciar en la Fig. 3, la cual muestra las ventanas de Kaiserpara α = 2, 4, y 8. En nuestra aplicación, α no debe ser muygrande, porque en ese caso las muestras en los extremos de laventana pueden alcanzar valores nulos y la matriz gramiana

−0.5 0 0.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Normalized time u=t/T1

Am

plitu

de

Kaiser Windows

α=2α=4α=8

Fig. 3. Ventanas de Kaiser para α = 2, 4, y 8.

−6 −4 −2 0 2 4 6−80

−70

−60

−50

−40

−30

−20

−10

0


Mag

nitu

de (

dB)

Frequency Response (4th Approximation, 4~)

LS, α=0WLS, α=4WLS, α=8

Fig. 4. Respuesta en frecuencia de los estimadores fasoriales p4th0 obtenidos

con LS y WLS, con α = 4, y 8.

(BHκ W HWBκ) no se puede invertir.La Fig. 4 muestra la reducción de lóbulos laterales en la

respuesta en frecuencia del estimador p4th0 del fasor dinámico

cuando el error es ponderado por ventanas de Kaiser conα = 4, y 8. Como puede apreciarse, la reducción de lóbuloslaterales puede ser muy alta. El efecto ensanchador de labanda de paso puede corregirse mediante dilatación temporalo reduciendo κ. Un aspecto interesante de la respuesta enfrecuencia del diferenciador Taylor-Fourier es la ganancia nulaobtenida en el vecindario de frecuencia junto a u = −1. Laganancia (en dB) exhibe la respuesta logarítmica típica delresto de Lagrange junto a u = −1 dada por la desigualdad deTaylor:

|Rn(u)| ≤ M

(n + 1)!|u + 1|n+1 (15)

La ganancia nula se obtiene en todos los diferenciadorespasabanda, como se puede apreciar en las Figs. 1 y 2.

III. FILTRO COSENO ELEVADO Y ESTIMADOSTAYLOR-FOURIER

El filtro Coseno Elevado (Raised Cosine, RC) es ampli-amente usado en telecomunicaciones. Se diseña para imple-mentar una aproximación al filtro ideal relajando sus bandas


−6 −4 −2 0 2 4 6−160

−140

−120

−100

−80

−60

−40

−20

0


Mag

nitu

de (

dB)

Frequency Response (Quadratic Approximation, 4~)

RC 4~WLS 4~, Kaiser α=12

Fig. 5. Respuesta en frecuencia del filtro RC y el estimador cuadrático WLSp2nd0 , obtenido con la ventana de Kaiser, con α = 12, ambos filtros de cuatro

ciclos.

de transición con la parte izquierda y derecha de la funcióncoseno elevado, tal como se expresa en la siguiente ecuación:

V (f) =

T |f | < 1−β2Ts

T cos2(

πT2β (f − 1−β

2T ))

1−β2T ≤ |f | ≤ 1+β

2T

0 |f | > 1+β2T

(16)donde β es el factor de redondeado roll-off factor, un indicadordel exceso de banda sobre la frecuencia de Nyquist 1/2T . Surespuesta impulsional infinita es dada por:

v(t) =π

4sinc(

t

T)(

sinc(βt

T− 1

2) + sinc(

βt

T+

12))

(17)

donde sinc(x) es la función seno cardenal sinc(x) = sin πxπx .

La Fig. 5 muestra la respuesta en frecuencia de un filtro RC,de cuatro ciclos, con β = 0.7 comparada con el estimadordel fasor dinámico cuadrático p2nd

0 usando la ventana deKaiser, con α = 12. Note que se requiere un alto valor deα para reducir el nivel de lóbulos laterales del filtro RC.Al incrementar ese valor se obtendrán niveles inferiores perocon una banda de paso más amplia. La principal ventaja delestimador con errores ponderados es su baja sensibilidad a lacomponente de frecuencia negativa (u = −1). Este estimadorse asocia además con el de velocidad y aceleración, quemiden, junto con el fasor, la frecuencia y su derivada tan útilespara la estimación de estados en sistemas de potencia y paramonitorizar el flujo de energía en una red de área amplia [5].

IV. DISEÑO DE FILTROS PASABAJAS

Los anteriores resultados merecen una explicación. ¿Porquéla aproximación por mínimos cuadrados del modelo de señalde Taylor logra estructuras espectrales tan interesantes comolas ilustradas en la sección anterior? Una propiedad interesantedel algoritmo de mínimos cuadrados es que la aproximacióna la función temporal es simultáneamente una aproximacióna la función espectral. Esto significa que mientras el modelotemporal de señal es aproximado a la señal de entrada, elespectro del modelo también es aproximado al espectro dela señal. En nuestro caso, el modelo temporal es dado porel polinomio de Taylor de orden κ. La única diferencia en

la aproximación es que la aproximación temporal se realiza,por el recorte de la ventana, en un intervalo corto; mientrasque la aproximación espectral se realiza en todo el dominiofrecuencial. Este resultado es conocido [20] en estimaciónespectral con modelos autoregresivos y de promedio móvil(Autoregresive and Moving Average models, ARMA). Unartículo reciente con numerosas referencias puede encontrarseen [21]. En lo que sigue, se ofrece la prueba para nuestraaplicación determinística.

El polinomio de Taylor de orden κ es dado por:

fκ(t) = (f(0)+f ′(0)t+f ′′(0)t2

2!+· · ·+f (κ)(0)

tκ

κ!)v(t) (18)

donde v(t) es cualquier ventana definida en el intervalotemporal (−T

2 , T2 ). Si V (ω) es la transformada de Fourier de

v(t), v(t) F←→ V (ω), entonces [22]:

tkv(t) F←→ jkV (k)(ω). (19)

La transformada de Fourier de fκ(t) es entonces

Fκ(ω) = f(0)V (ω) + f ′(0)jV ′(ω) + f ′′(0)j2 V ′′(ω)2!

+ · · ·

+ f (κ)(0)jκ V (κ)(ω)κ!

(20)

El error ponderado para la función temporal es equivalente alde (8), y es

v(t)e(t) = v(t)f(t)− fκ(t), (21)

consecuentemente la solución de mínimos cuadrados aplicadaa la función temporal en (18) es dada por

φ = (T HT )−1T Hf (22)

donde φ = [f(0) f ′(0) f ′′(0) · · · f (κ)(0)]T y los elementos dela matriz de Gram T HT se obtienen utilizando la definiciónde producto punto en el tiempo:

gr,c =∫ T/2

−T/2

tr+c

r!c!v2(t)dt, r, c = 0, 1, ..., κ (23)

y los del vector T Hf

γr =∫ T/2

−T/2

tr

r!v2(t)f(t)dt, r = 0, 1, ..., κ. (24)

por otra parte, el error espectral ponderado es la transformadade Fourier de (21)

V (ω) ∗ E(ω) = V (ω) ∗ F (ω)− Fκ(ω), (25)

donde ∗ es el operador de convolución. Por lo que la soluciónde mínimos cuadrados a la aproximación espectral en (20) será

φ = (VHV)−1VHF . (26)

Aplicando la definición de producto punto complejo en fre-cuencia, se obtienen los elementos de la matriz gramianaVHV como sigue

υr,c =∫ ∞

−∞jc−r V (c)(ω)V

(r)(ω)

r!c!dω, r, c = 0, 1, ..., κ

(27)


y los del vector VHF :

δr =∫ ∞

−∞j−r V

(r)(ω)

r!V (ω) ∗ F (ω)dω, r = 0, 1, ..., κ

(28)donde V

(r)(ω) es el conjugado complejo de V (r)(ω).

Primero se demuestra que δr = γr. Sustituyendo j−r V(r)

(ω)r!

por su transformada inversa en (28)

δr =∫ ∞

−∞

(−t)r

r!v(−t)

∫ ∞

−∞V (ω) ∗ F (ω)e−jtωdωdt,

r = 0, 1, ..., κ (29)

y resolviendo la transformada inversa de Fourier (con -t)

δr =∫ ∞

−∞

(−t)r

r!v2(−t)f(−t)dt, r = 0, 1, ..., κ (30)

que de acuerdo con la regla de sustitución en integrales esigual a la integral en (24), y dado que v(t) es restringida entiempo, se tiene necesariamente que δr = γr.

Ahora se prueba que gr,c = υr,c, siguiendo el mismoprocedimiento en (27). Se tiene

υr,c =∫ ∞

−∞

(−t)r

r!v(−t)

∫ ∞

−∞jc V (c)(ω)

c!e−jtωdωdt

r, c = 0, 1, ..., κ (31)

y aplicando transformada inversa de Fourier (ver (19))

υr,c =∫ ∞

−∞

(−t)r+c

r!c!v2(−t)dt r, c = 0, 1, ..., κ (32)

que de acuerdo a la regla de sustitución en integrales es lamisma integral que en (23), por tanto υr,c = gr,c. Note quelos productos punto en (27) y (28) se definen sobre todoel intervalo de frecuencia, y que las funciones espectralesajustadas son el espectro de la ventana V (ω) y sus derivadasjkV (k)(ω)/k! tal como aparecen en (20).

A. Ajuste Espectral

La respuesta en frecuencia de cada filtro diferenciador en(22) es una combinación lineal de las respuestas en frecuenciade los parámetros γr, r = 0, 1, . . . , κ obtenidos de (24) cuandola aproximación es aplicada en el instante t0:

γr(t0) =∫ T/2

−T/2

tr

r!v2(t)f(t + t0)dt, r = 0, 1, ..., κ (33)

con f(t) = ejωt. Esto es

γr(t0) = jr V(r)

(ω)r!

ejωt0 (34)

y consecuentemente las respuestas en frecuencia de losparámetros γr, son

Γr(ω) = jr V(r)

(ω)r!

, r = 0, 1, ..., κ (35)

El vector del lado derecho de las ecuaciones normales (22)será de la forma

Γ(ω) =

V (ω)jV

′(ω)

j2 V′′(ω)

2!...

jκ V(κ)

(ω)κ!

, (36)

el cual será igualado a las funciones de transferencia del ladoizquierdo (T HT )φ(t0):

m0 m1 m2 · · · mκ

m1 m2 m3 · · · mκ+1m22!

m32!

m42! · · · mκ+2

2!...

......

. . ....

mκ

κ!mκ+1

κ!mκ+2

κ! · · · m2κ

κ!

1jω

(jω)2

2!...

(jω)κ

κ!

(37)

en las cuales mn es el n-ésimo momento de v2(t) en (23),con n = r + c, ver Apéndice V, o [22]. Las funciones detransferencia en (37) corresponden a los primeros κ términosde la serie de Taylor (junto a ω = 0, ver Apéndice V) de loselementos en (36); y por tanto, la solución de las ecuacionesnormales aproxima el polinomio de Taylor de orden κ alespectro de la ventana, y las derivadas del polinomio a lasderivadas del espectro de la ventana en (36). Esta es la formade las ecuaciones normales que explica el ajuste simultáneotiempo-frecuencia de la solución de mínimos cuadrados. Note,de paso, que los momentos impares son nulos.

B. Diferenciadores Máximamente Lisos

Al reescribir las ecuaciones anteriores para las gananciasideales de los diferenciadores, obtenemos la interpretación dela solución de mínimos cuadrados ponderados como operaciónde filtrado, o método de aproximación a las respuestas enfrecuencia ideales de los diferenciadores. Se obtiene junto aω = 0:

1jω

(jω)2...

(jω)κ

= (T HT )−1Γ(ω) (38)

Entonces, las ganancias ideales de los diferenciadores sonaproximadas por κ combinaciones lineales del espectro dela ventana y sus derivadas en (36). En la banda base defrecuencias, donde la aproximación de mínimos cuadradoscorresponde esencialmente a una aproximación de Taylor(error de mínimos cuadrados nulo), existe una diferenciamáximamente lisa (error de Taylor) entre las ganancias idealesde los diferenciadores y la alcanzada en el lado derecho de(38); y por tanto, en la respuesta en frecuencia del n-ésimodiferenciador, hasta la κ+n derivadas valen cero en ω = 0 deacuerdo a los polinomios de Taylor en (37). Por tanto, todoslos diferenciadores son máximamente lisos [9] en el vecindariojunto a ω = 0.


−5 −4 −3 −2 −1 0 1 2 3 4 5−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Normalized frequency u=fT

Am

plitu

de

Spectrum of Rectangular Window and its Derivatives

Sinc(u)Sinc’(u)Sinc’’(u)

Fig. 6. Espectro de la ventana rectangular V (u) (línea continua) y su primera(línea a rayas) y segunda (línea a rayas delgadas) derivadas.

−5 0 5−0.4

−0.2

0

0.2

0.4

0.6

0.8

1


Am

plitu

de

Frequency Response of Differentiators

ff’f’’

Fig. 7. Respuestas en frecuencia de los derivadores de orden cero (líneacontinua), uno (línea a rayas), y dos (línea a rayas delgadas) obtenidos conla ventana rectangular.

C. Ventana Rectangular

La ventana implícita en la solución de mínimos cuadradoses la rectangular. Su espectro, primera y segunda derivada semuestran en la Fig. 6. Note que las derivadas pueden aprox-imarse con bastante exactitud con polinomios de Taylor desegundo orden, en los cuales los términos predominantes son elconstante y cuadrático para el espectro y su segunda derivada,y el término lineal para la primera derivada. Por lo que lasolución de mínimos cuadrados también está aproximandoun polinomio de Taylor al espectro de la señal de entrada.La Fig. 7 muestra las respuestas en frecuencia de los filtros

diferenciadores obtenidas con la ventana rectangular. Note queen la banda base |u| < 0.3, se logran las ganancias constante,lineal y cuadrática, correspondientes a las ganancias idealesde los primeros tres diferenciadores. Si el espectro de la señalde entrada se encuentra dentro de la banda de paso, entoncesel error de los estimados será insignificante, lo que significaque el segmento temporal de señal es aproximado con bastanteprecisión con un polinomio de Taylor de segundo orden.

−5 0 5−0.1

0

0.1

0.2

0.3

0.4

0.5


Am

plitu

de

Spectrum of Hamming Window and its Derivatives

H(u)H’(u)H’’(u)

Fig. 8. Espectro de la ventana de Hamming V (u) (línea continua) y suprimera (línea a rayas) y segunda (línea a rayas delgadas) derivadas.

−5 0 5−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1


Am

plitu

de

Frequency Response of Differentiators with Hamming Window

ff’f’’

Fig. 9. Respuestas en frecuencia de los derivadores de orden cero (líneacontinua), uno (línea a rayas), y dos (línea a rayas delgadas) obtenidos conla ventana de Hamming.

D. Ventana de Hamming

El espectro de la ventana de Hamming y sus primeras dosderivadas se ilustra en la Fig. 8. Lóbulos centrales más anchosy laterales más pequeños son patentes, comparados con losde la ventana rectangular. Por otra parte, las respuestas enfrecuencia de los filtros diferenciadores mediante la soluciónde mínimos cuadrados ponderados utilizando la ventana deHamming se ilustran en la Fig. 9. Una banda de paso másamplia es obtenida pero con lóbulos laterales más pequeños.De nuevo, las ganancias en el intervalo centrado en cero sonconstante, lineal y cuadráticos como las de los diferenciadoresideales.

Finalmente, se ilustran los errores de aproximación a laganancia unitaria (H(u) = 1) y lineal (H(u) = 2πu)obtenidas en el diferenciador de orden cero y uno, usando lasventanas rectangular y de Hamming en la Fig. 10. Note queambas diferencias corresponden a la forma logarítmica típicadel Resto de Lagrange en una aproximación de Taylor.

V. CONCLUSIONES

Se presentó un método general para diseñar diferenciadoresmáximamente lisos. Proviene de la solución de mínimos


−5 0 510

−10

10−5

100

105

|1−

Gai

n|

Approximation to Unitary and Linear Gains

−5 0 510

−10

10−5

100

105


|2π

u−Γ 1(u

)|

Rectangular Window

Hamming Window

Rectangular Window

Hamming Window

Fig. 10. Diferencia de aproximación a las ganancias ideales de los derivadoresde orden cero y uno con ventana rectangular y de Hamming

cuadrados ponderados en la aproximación de polinomios deTaylor a la señal de entrada. La solución aproxima simultánea-mente las representación temporal y espectral de la señal.Y a su vez aproxima polinomios (términos) de Taylor a lasganancias ideales de los diferenciadores en la banda de paso.Las estimaciones de las derivadas son exactas (mediciones)cuando el espectro de la señal de entrada se encuentra dentrode la banda de paso. Además, la sensibilidad al ruido se reducesignificativamente si se les compara con los diferenciadoresbasados en diferencia finita utilizados ampliamente en difer-enciación numérico, los cuales tienen altas ganancias en lasfrecuencias más altas. El método propuesto estima el fasorcon sus primeras κ derivadas de un solo golpe, incluyendo laestimación de la frecuencia y sus derivadas, tan importantespara el monitoreo sistemas de potencia.

APÉNDICEPOLINOMIOS DE TAYLOR EN FRECUENCIA

La expansión de Taylor de una respuesta en frecuenciaH(ω) alrededor de ω = 0 es dada por

H0(ω) = H(0)+H ′(0)ω+H ′′(0)ω2

2!+· · ·+H(κ)(0)

ωκ

κ!(39)

Para H(ω) se tiene

H(k)(0) = (−j)kmk (40)

donde mk es el k-ésimo momento de h(t):

mk =∫ ∞

−∞tkh(t)dt, (41)

por lo que, en término de momentos h(t), también se tiene:

H0(ω) = m0 + m1(−jω) + m2(−jω)2

2!+ · · ·+ mκ

(−jω)κ

κ!,

(42)y por tanto:

H0(ω) = m0 +m1(jω)+m2(jω)2

2!+ · · ·+mκ

(jω)κ

κ!. (43)

REFERENCIAS

[1] IEEE Standard for Synchrophasors for Power Systems. IEEE Std.C37.118-2005, 2006.

[2] M. Donolo and V. Centeno, “A fast quality assessment algorithm forphasor measurements,” IEEE Trans. Power Del., vol. 20, no. 4, pp. 2407–2413, Oct. 2005.

[3] J. Depablos, V. Centeno, A. G. Phadke, and M. Ingram, “Comparativetesting of synchronized phasor measurement units,” PES General Meet-ing, 2004, vol. 1, pp. 948–954, 6-10 June 2004.

[4] D. Fan and V. Centeno, “Phasor-based synchronized frequency measure-ment in power systems,” IEEE Trans. Power Del., vol. 22, no. 4, pp.2010–20 016, Oct. 2007.

[5] Z. Z. J. Zuo, R. M. Gardner, H. Zhang, and Y. Liu., “Off-line event filterfor the wide area frequency measurements,” PES General Meeting, 2006,vol. 1, p. 6pp, 18-22 June 2006.

[6] J. Wang, R. M. Gardner, and Y. Liu, “Analysis of system oscillationsusing wide-area measurements,” PES General Meeting, 2006, vol. 1, p.6pp, 18-22 June 2006.

[7] S. Tsai, Z. Zhong, J. Zuo, and Y. Liu, “Analysis of wide-area frequencymeasurement of bulk power systems,” PES General Meeting, 2006,vol. 1, p. 8pp, 18-22 June 2006.

[8] J. A. de la O, “Dynamic phasor estimates for power system oscillations,”IEEE Trans. Instrum. Meas., vol. 56, no. 5, pp. 1648–1657, Oct 2007.

[9] S. Samadi, H. Iwakura, and A. Nishihara, “Multiplierless and hierarchi-cal structures for maximally flat half-band filters,” IEEE Trans. CircuitsSyst. II, vol. 46, no. 9, pp. 1225–1230, Sept. 1999, p. 1226.

[10] S. Samadi, O. Ahmad, and M. Swamy, “Complete characterization ofsystems for simultaneous lagrangian upsampling and fractional-sampledelaying,” IEEE Trans. Circuits Syst. I, vol. 52, no. 3, pp. 656–667, Mar.2005, p. 658.

[11] I. Selesnick, “Maximally flat low-pass digital differentiators,” IEEETrans. Circuits Syst. II, vol. 49, no. 3, pp. 219–223, Mar. 2002, p. 219.

[12] I. R. Khan and M. Okuda, “Finite-impulse-response digital differentia-tors for midband frequencies based on maximal linearity constraints,”IEEE Trans. Circuits Syst. II, vol. 54, no. 3, pp. 242–246, Mar. 2007,p. 243.

[13] Y. Jou, “Least-squares design of digital differentiators using neuralnetworks with closed-form derivations,” IEEE Trans. Signal Process.,vol. 12, no. 11, pp. 760–763, Nov 2005, p. 760.

[14] S. Sunder and R. Ramchandran, “Design of equiripple nonrecursivedigital differentiators and Hilbert transformers using a weighted least-squares techinque,” IEEE Trans. Signal Process., vol. 42, no. 9, pp.2504–2509, Sep 1994.

[15] I. Khan, M. Okuda, and R. Ohba, “Higher degree FIR digital differen-tiators based on Taylor series,” The 2004 47th Midwest Symposium onCircuits and Systems, vol. 2, pp. 57–60, Jul. 2004.

[16] M. A. Al-Alaoui, “Linear phase low-pass IIR digital differentiators,”IEEE Trans. Signal Process., vol. 2, pp. 697–706, Feb. 2007.

[17] D. C. Lay, Linear Algebra and its Applications. New York: AdisonWesley, 2006, ch. 6.8.

[18] H. K. Khalil, Nonlinear Systems, 2nd ed. Prentice Hall, 1996.[19] J. G. Proakis and D. G. Manolakis, Digital Signal Processing, 4th ed.

New Jersey: Prentice Hall, 2007.[20] M. H. Hayes, Statistical Digital Signal Processing and Modeling. New

Jersey: Wiley, 1996, ch. 4, Sections 7.2-4.[21] M. Jachan, G. Matz, and F. Hlawatsch, “Time-frequency arma models

and parameter estimators for underspreas nonstationary random pro-cess,” IEEE Trans. Signal Process., vol. 55, no. 9, pp. 4366–4381, Sept.2007.

[22] A. Papoulis, Signal Analysis. New York: McGraw Hill, 1977, p 62.

147

IIXX SS iimmppooss iioo IIbbeerrooaammeerr ii ccaannoo ssoobbrree PPrrootteecc cc iióónn ddee SS ii ss tteemmaass EE lléécc tt rr ii ccooss ddee PPoo tteenncc iiaa


Ing. Luis Sánchez Pantoja

Sección Mantenimiento Distribución

EDELOR S.A.A., Perú

Ing. José Luis Mamani Quenta

Sección ormalización de la Red

EDELOR S.A.A., Perú

Resumen - Los alimentadores de las redes de distribución en

Edelnor son de topología radial, con régimen de operación Delta

y Neutro Aislado en 10 kV. En su gran mayoría, al interior de

los alimentadores, se encuentran pequeñas subestaciones

denominadas convencionales de cuyas derivaciones se

extienden circuitos laterales destinados a la carga de la red. Tradicionalmente, para cada uno de los circuitos laterales, se

tenía previsto la instalación de un interruptor y un relé de

protección que permita el corte del servicio eléctrico ante alguna

contingencia. Se propuso la instalación de un seccionador-

fusible de potencia de apertura tripolar asociado a un relé de falla a tierra que reemplace a la combinación Interruptor-Relé,

considerando que la magnitud de las corrientes de falla a tierra

están en el orden de los 2 A a 150 A y que el seccionador-

fusible permite apertura bajo carga a una capacidad nominal de

630 A. La implementación del equipamiento se efectúa en las

celdas de salida de circuito lateral y celda hacia clientes en media tensión en la zona de concesión. Los resultados obtenidos

son la disminución de costos en el equipamiento de maniobra y

protección y actuación confiable ante defectos de fallas a tierra

y cortocircuitos.

I. SISTEMAS DE DISTRIBUCIÓ DELTA Y EUTRO AISLADO

Los Sistemas de Distribución en delta y/o Neutro Aislado

se encuentran sin conexión intencional a tierra. En la fig. 1,

se muestra un sistema típico de distribución de la red de

Edelnor, donde el transformador de potencia de la

subestación tiene el lado de alta con el neutro puesto a tierra

y el lado de baja en conexión delta o estrella con el neutro

libre (60/10 kV). Los primarios de los transformadores de

distribución dentro de los alimentadores se encuentran en

conexión delta, por lo que el sistema en 10 kV se encuentra

con el neutro flotante. La red de baja tensión se encuentra

en régimen de neutro aislado.

Fig. 1 Sistema típico de distribución delta y/o neutro

aislado

Para estos sistemas, la distribución de energía se efectúa

por tres conductores. Los transformadores de distribución

trifásicos y monofásicos se encuentran conectados

directamente entre las fases.

En la fig 2, se muestra la localización de las

subestaciones convencionales al interior de los

alimentadores de la red, las subestaciones son del tipo

superficie o subterráneo. Los seccionadores fusible de

potencia se encuentran instalados en las derivaciones de

la subestación, en las celdas de salida para circuito lateral

y celda para clientes en media tensión.

10 kV

60 kV

Dyn5

10 / 0.23 kVTransformador de

Distribución

Transformador

de Potencia

Ynd5

Ynyn0

10 kV

60 kV

Dyn5

10 / 0.23 kVTransformador de

Distribución

Transformador

de Potencia

Ynd5

Ynyn0

APLICACIÓN DE SECCIONADORES FUSIBLE

DE POTENCIA CON RELÉS DE FALLA A

TIERRA EN REDES DE DISTRIBUCIÓN DE

MEDIA TENSIÓN CON NEUTRO AISLADO Y/O

DELTA

148

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Fig. 2 Subestaciones convencionales

En la figura 3 se muestra la disposición típica de las

celdas en una subestación convencional

Fig. 3 Celdas en subestación Convencional tipo FMG

II. SECCIOADOR FUSIBLE DE POTECIA

Para las especificaciones, los seccionadores fusibles de

potencia cumplen las normas IEC 60265-1 y IEC 62271-

5.

El seccionador cuenta con cuchillas tripolares de apertura

y cuchillas de puesta a tierra, ambas cuentan con mandos

independientes enclavados mecánicamente para seguridad

del operador. Los mandos pueden ser instalados en el

extremo derecho o izquierdo según sea más conveniente

para la maniobra. En la figura 4, se ilustra el

equipamiento.

Fig. 4 Seccionador fusible de potencia

El seccionador cuenta con una bobina de desconexión a

220 A AC, 60 hertz, la cual, por medio de una bornera se

encuentra conectado a un mando local ubicado en un

tablero de control, permitiendo la apertura a distancia. El

equipo también puede tener un motor para permitir la

operación de cierre y apertura.

Número de operaciones

Si bien es cierto que la norma IEC ro. XXXX define

como mínimo 100 operaciones de apertura y cierre a

corriente nominal del equipo, a valores menores de

corriente el número de operaciones se incrementa

considerablemente (ver fig. 5), es decir, si consideramos

por ejemplo una corriente del orden de 100 A, tendríamos

un valor cercano a las 1000 operaciones.

Fig. 5 Corriente de corte vs Número de operaciones del

seccionador 12kV – 630 A

En los cuadros N°2 y N°3, se aprecian las características

técnicas del seccionador fusible de potencia y

seccionador de puesta a tierra.

60 kV

Ynd5

Registrador V e I

10 KV

Subestación de Distribución Convencional (SED)

Relé

Subestación Aérea de transformación (SAB)

1ra SED Relé

Relé

cutout

SAB 1

SAB 2

SecionadorFusible con Reléde falla a tierra

SAB 3

Alimentador 2

Alimentador 3

Alimentador 1

Relé

Relé

2ra SED

Subestación de Transformación

Relé

Alimentador n

60 kV

Ynd5

Registrador V e I

10 KV

Subestación de Distribución Convencional (SED)

Relé

Subestación Aérea de transformación (SAB)

1ra SED Relé

Relé

cutout

SAB 1

SAB 2

SecionadorFusible con Reléde falla a tierra

SAB 3

Alimentador 2

Alimentador 3

Alimentador 1

Relé

Relé

2ra SED

Subestación de Transformación

Relé

Alimentador n

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Cuadro °1

Descripción Unidad ValoresVoltaje Nominal kV 12

Capacidad de corriente nominal (In) A 400

Corriente pico (Idyn) kA pico 75

kA eff 30 (1seg)

kA eff 20 (3seg)

A 1600

Tamaño máximo de fusible (In) A 125

Voltaje de impulso 1,2/50 us kV 75

Dsitancia entre fases mm 210

Tiempo de apertura del seccionador ms 40-60

En corriente nominal

En cortocircuito, clase E1

Corriente de cortocircuito corta

duración (Ith)

Capacidad apertura de falla a tierra,

según IEC 265, Fig 6

Característcias técnicas del seccionador fusible de potencia

kA pico 67

Corriente de apertura máxima para

coordinación con fusibles

Cantidad de ciclo de opraciones

100

3

Número de operaciones

Capacidad de cierre en cortocircuito

(Ima)

A 150

Condición de trabajo

Cuadro °2

Descripción Unidad ValoresVoltaje Nominal (Un) kV 12

Corriente pico (Idyn) kA pico 75

kA eff 30 (1seg)

kA eff 20 (3seg)

Voltaje de impulso 1,2/50 us kV 75

Dsitancia entre fases mm 210

Corriente de cortocircuito corta

duración (Ith)

Capacidad de cierre en cortocircuito

(Ima)

Características técnicas del seccionador de puesta a tierra del seccionador de potencia

kA pico 67

III. PROTECCIÓ DE FALLA A TIERRA

Los criterios para despejar fallas por contacto de una

línea viva con tierra, son los siguientes: Sistema de

detección de la falla, análisis de la distribución de las

corrientes capacitivas en la red, tipo de relé de protección

y pruebas primarias de campo con actuación del equipo

de maniobra:

Permanentemente se monitorea la contribución total de

las 3 corrientes de carga capacitiva del circuito a proteger

a través de un transformador del tipo toroidal, el cual

confina a las tres fases. Se muestran las aplicaciones para

los cables empleados en media tensión tipo NKY y

N2XSY del Standard IEEE 242 (fig. 6 y 7)

Fig. 6 Aplicación de transformadores toroidales

El transformador toroidal se instala en la parte inferior,

debajo del seccionador fusible de potencia. Es del tipo

interior, de núcleo partido para permitir el montaje fácil,

con clase de precisión de medida debido a los valores

bajos de corriente de falla que se presentan en estos

sistemas.

Fig 7, Instalación de transformador toroidal

En el cuadro N°3, se aprecia las características técnicas

del transformador toroidal. En la figura 8 se muestran los

respectivos de una subestación convencional con

derivaciones.

S1

S2

S3

Pozo M.T.

Pozo M.T.

Terminal de cable

Cable MT

3Io

Pozo B.T.

Relé SEF – 51N

Carga

CABLE TIPO NKY

S1

S2

S3

Pozo M.T.

3Io

Pozo B.T.

Relé 50N – 51N

CABLE SECO TIPO N2XSY

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Cuadro °3

Descripción Unidad ValoresVoltaje Nominal kV 0,72

Voltaje de diseño KV 3kV

Corriente nominal secundario A 1

A 1,2 In

A 100 In

Frecuencia Hz 60

Presición clase 1

Diámetro interno mm 150

Diámetro interno mm 150

Potencia VA 2

100/200-1

Sobnrecarga continua

permanente

Sobnrecarga continua

permanente

Características del transformador toroidal

Capacidad de corriente del lado

primario A

Fig. 8 Transformadores toroidales para circuitos laterales

y clientes en subestación convencional

Esquemáticamente el sistema de detección de falla por

transformador toroidal, se ubica en el punto de medición

IR ubicado al inicio del circuito que se supervisa, ver la

fig. 9.

Fig. 9 Localización del transformador toroidal

Bajo condiciones normales del servicio, la contribución

resultante IR será nula, (IR = 0), esto, debido, a que las

corrientes capacitivas Iag, Ibg, Icg se encuentran

desfasadas a 120 grados y se anulan entre si.

Fig. 10 Corrientes de carga capacitivas fase a tierra.

IR es la contribución total de corrientes de Carga

Capacitiva y se define:

IR = Iag + Ibg + Icg

Para verificar el contacto de la parte viva de alguna fase

con tierra, el criterio IR≠0, confirma la existencia de

fallas monofásicas a tierra. Se muestra en la figura 11 la

distribución de corriente de carga capacitiva, para una

falla monofásica a tierra en la fase A de una red de

distribución de 4 alimentadores. El alimentador elegido

tiene 2 subestaciones convencionales y el punto de falla

se localiza en un lateral de la segunda subestación

convencional:

Ibg

Icg

Ca

Cb

Cc

Iag

IR

A

B

C

I I

Ca

Cb

Cc

I

IR

A

B

C

= 0

Iag

Ibg

Icg

Vag

Vcg

Vbg

N = g

Iag

Ibg

Icg

Vag

Vcg

Vbg

N = g

151

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Fig. 11 Distribución simplificada de corriente de falla en la red de distribución

IBg1IAg1

IBg2IAg2

IBg3IAg3

IBg4IAg4

IBgIAg

IBgIAg

IBgIAg

IBgIAg

Ibg’Iag’

IF

Iha

Ihb

Ihc

Ihd

Ihe

IH3

IH4

IH2

IH1

Ihd

+he

+ I

IR

IR 4

IR

IR b

IR

IR e

IBg1IAg1IAg1

IBg2IAg2IAg2

IBg3IAg3IAg3

IBg4IAg4IAg4

IBgIAgIAg

IBgIAgIAg

IBgIAgIAg

IBgIAgIAg

Ibg’Iag’Iag’

IF

Iha

Ihb

Ihc

Ihd

Ihe

IH3

IH4

IH2

IH1

Ihd

+he

+ I

IR

IR 4

IR

IR 4

IR

IR b

IR

IR b

IR

IR e

IR

IR e

152

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Las corrientes IH1, IH2, IH3 e IH4 son las

corrientes de retorno de falla a tierra registradas

en cada alimentador. El sensor IR4 a la salida del

alimentador con falla registra:

IR4 = IH1 + IH2 + IH3

En el punto de falla se tendrá la distribución

mostrada en la figura 12, donde la corriente de

falla regresa a los circuitos de los alimentadores a

través de la capacitancia distribuida de la red.

Fig.12 Corriente de falla registrada en el

transformador toroidal de la subestación

convencional

El sensor registra la contribución resultante que

ocasiona el disparo del rele de protección.

IR = IH1 + IH2 + IH3 + IH4 - Ihe

Se implementa la coordinación de las

protecciones por tiempos (tiempo definido), para

permitir el despeje adecuado.

Es importante hacer notar que todas las

protecciones operan bajo el principio de que

exista la corriente de falla a tierra, luego del cual

el relé estaría en condiciones de detectar y

despejar la falla. Asimismo, el sistema de

detección es aplicable a redes de distribución de

más de dos alimentadores, debido a que en

sistemas delta de un solo alimentador el resultado

es nulo para ambas condiciones normal y de falla.

Las funciones de protección activadas en los

reles de falla a tierra de los circuitos parciales se

dan en el cuadro N°4:

Cuadro °4

La función sensitiva SEF permite despejar fallas a

partir de los 2 A. Este valor se determina según los

cálculos de corriente de distribución capacitiva para

las condiciones de falla de alta impedancia en zonas

de alta resistividad del terreno y con redes de pocos

alimentadores y/o redes aéreas. Ajustes típicos de la

protección son los siguientes:

• Io > = 2 A , to > = 1 s

• Io >> = 30 A, to >> = 0.5 s

Los relés deben despejar las fallas para los casos de

cierre sobre falla y recierre aguas arriba de los

mismos.

En la fig. 13 se aprecia el conexionado eléctrico de

circuito de apertura del seccionador fusible de

potencia.

Fig.13 Esquema simplificado del circuito de

apertura y alimentación auxiliar

En el cuadro N°5 se aprecian las características de

los relés microprocesados de falla a tierra

considerados en la implementación.

Cuadro °5 Características técnicas del relé de falla a tierra

Descripción Unidad Valores Tensión nominal V 220

Corriente nominal A 1

Frecuencia hz 60

Prueba voltaje

dieléctrico (1 min) KV 2

Prueba de voltaje de

impulso (1,2/50us) kV 5

Con puerto frontal de comunicación RS232,

Display y opción de oscilografía, registro de

corriente, fecha y hora de falla.

Para las pruebas de campo de fallas a tierra,

previamente se efectúa la verificación del

conexionado según lo indicado en la figura 6, la

medición de resistencia de puesta a tierra los

pozos, alimentación auxiliar al tablero de control

(rele–bobina de desconexión del seccionador) y la

confirmación de la programación de ajustes en el

rele. Se efectúa una prueba de inyección de

corriente primaria según el esquema indicado en

la figura 14.

Número ANSI IEEE C37-02

SEF / 51N

Símbolo IEC 60617

Io >, Io >>

Descripción

Protección no direccional de falla a tierra sensitiva

Bobina de disparo de seccionador

Fuente 220 VAC, 60 HZ (En Perú)

Pulsador de apertura local

Pozo B.T.

Relé de falla a tierra SEF - 51N

Ibg ’

Icg ’

Ca

Cb

Cc

Iag ’

IR

A

B

C

IF

I’

I’

Ca

Cb

Cc

I’

IR

A

B

C

≠ 0

IF

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Fig.14 Prueba de inyección de corriente primaria

La corriente se aplica directamente a través del

transformador toroidal (Pruebas primarias). Las

conexiones de medición para el registro de tiempo

de disparo se efectúan en los extremos finales de

una de las fases del seccionador. Los valores

registrados de corriente de disparo y tiempo de

apertura del conjunto relé-seccionador verifican la

sensibilidad de corriente y tiempos de actuación

previstos para la coordinación de las protecciones

del alimentador con relés aguas arriba.

IV. PROTECCIÓ DE CORTOCIRCUITO

La liberación de las fallas entre fases es posible

por la acción de los fusibles limitadores de

corriente tipo respaldo (backup) que se instalan en

el seccionador fusible de potencia, los cuales

accionan un percutor de disparo que golpea las

lengüetas del seccionador produciéndose la

apertura tripolar del mismo.

Los fusibles de respaldo interrumpen de forma

segura todos los niveles de corriente desde el

poder de corte (3In a 5In) hasta la intensidad

mínima de corte I3. Los fusibles limitadores de

corriente cumplen la norma IEC 60282 y tienen

las siguientes características que se indican en el

cuadro N°6

Cuadro ° 6

Características técnicas del fusible limitador de corriente

Descripción Unidad Valores Voltaje Nominal (Un) kV 12

Corriente nominal (In) A 100 125

Poder corte (I1) kA 63

Intensidad mínima de corte

(I3) A 320 390

Longitud del fusible mm 292

Fuerza de disparo del percutor N 80

El diseño de la capacidad de los fusibles

limitadores de corriente, considera la sobrecarga

de los circuitos a fin de tener operaciones sobre la

capacidad minima de corte.

Coordinación seccionador – fusible

Para la selección de la capacidad máxima de los

fusibles limitadores de corriente, se emplea el

criterio de coordinación de apertura del

seccionador con la operación del fusible limitador

de corriente, para esto se toma en cuenta la

corriente de apertura máxima del seccionador

dada por el fabricante (1600 A según el cuadro N°

1) y las curvas tiempo-corriente de la familia de

fusibles limitadores. La figura N°15 muestra la

coordinación mencionada, verificándose la

coordinación hasta fusibles de 125A.

Figura 15, Coordinación entre corriente de

apertura máxima del seccionador al 90% de su

tiempo nominal de apertura y los fusibles

limitadores de corriente.

Para las pruebas de campo de la operatividad del

mecanismo, se emplea un simulador mecánico de

fusible que mantenga la misma fuerza de disparo

en el seccionador (test fuse link).

900A 1600A

54ms

CARGA

FUENTE

FUSIBLES LIMITADORES

DE CORRIENTE

DISPARO

51N

RELE DE FALLA A TIERRA EN TIEMPO DEFINIDO

Seccionador

unipolar de cable

Seccionador unipolar de barra

SECCIONADOR BAJO CARGA

Equipo de prueba de Reles

MEDICIÓN DE CORRIENTE DE DISPARO Y TIEMPO DE APERTURA

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V. COCLUSIOES

• Se ha verificado la correcta actuación del

seccionador fusible de potencia asociado a un

relé de protección de falla a tierra, habiendo

constituido un equipamiento confiable de

protección y maniobra ante defectos de falla

a tierra y cortocircuitos.

• La alternativa rele - seccionador fusible de

potencia, resulta mucho más económica que

la opción de interruptor-rele que resulta por

encima de 3 veces más costoso.

• Los equipos se instalan tanto en celdas

modulares como en celdas abiertas, en

circuitos de hasta 1.5 MVA de potencia, para

los valores por encima de ésta, se instalan

interruptores. • El equipo requiere mantenimiento

programado del seccionador, según

especificaciones del fabricante.

• Las fallas a tierra evolutivas pueden restarle

tiempo de vida al equipo, por esta razón en el

ajuste del relé no se considera tiempo

instantáneos.

• Actualmente se tienen instalados 215

unidades.

• En la definición de la topología de la

expansión de la red y en los proyectos de

reforma de redes, se encuentra considerado la

instalación de los Seccionadores fusible de

potencia para los circuitos laterales de red y

de clientes

VI. Agradecimiento

Se agradece a los Subgerencias de Mantenimiento

Distribución, Ingeniería y Obras de la Gerencia

Técnica de Edelnor que colaboraron en la

realización de la prueba de caída de conductores

cuyo objetivo fue verificar la operación del

seccionador de potencia ante fallas a tierra.

VII. Referencias • “Selección de la Protección de Fallas a Tierra

con Altas Resistencia en las Redes de Media

Tensión". I Seminario sobre Sistemas de

Distribución y Utilización de Energía

Eléctrica, Ica, Perú, octubre 1996.

• IEEE Std 242, “IEEE Recommended Practice

for Protection and Coordination of Industrial

and Commercial Power Systems”, 2001

• “Protective Relaying: Principles and

Applications”, Third Edition, J. Lewis

Blackburn, CRC Press, Taylor & Francis

Group, 2007.

• “Arcing fault current and the criteria for

setting ground fault relays in solidly-

grounded low voltage systems”, K. Malmedal

& P.K. Sen

(http://www.neiengineering.com)

• Standard IEC 60265-1 “Switches for rated

voltages above 1 kV and less than 52 kV”,

1998

• Standard IEC 62271-105 “High-voltage

switchgear and controlgear – Alternating

current switch-fuse combinations”, 2002

• IEEE Std C37.48.1 IEEE “Guide for the

Operation, Classification, Application, and

Coordination of Current-Limiting Fuses with

Rated Voltages 1–38 kV”, 2002

• Standard IEC 60282-1 “High-voltage fuses -

Part 1 Current-limiting fuses”, 2002

• “Problemática de Fusibles Limitadores,

Gerencia de Distribución” – Ing. Orestes

Castañeda, ELECTROLIMA 1985

• “Manual de Seccionador fusible de potencia

NAL/NALF para uso interior” – ABB

• Video Técnico: “Prueba de caída de

conductores en redes de media tensión”,

Edelnor, Setiembre 2007.

VIII. Biografías

José Luis Mamani Quenta Se gradúo de Ingeniero

Electricista en la Universidad Nacional de Ingeniería XXXX. Labora desde el año XXXX en la empresa

Edelnor Endesa con sede en Perú, en el área de

Normalización de la Red. Puede ser contactado en el

email [email protected]

Luis Sánchez Pantoja Se gradúo

de Ingeniero Electricista en la Universidad Nacional de

Ingeniería 1998. Labora desde el año 2002 en la

empresa Edelnor Endesa con sede en Perú, en el área de Protecciones de Redes de Distribución. Actualmente es

miembro del IEE, IEEE y CIGRE. Su área de

investigación es la protección, operación y control de

sistemas eléctricos de potencia. Puede ser contactado

en el email [email protected]

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Detection of High-Impedance Faults in Power

Distribution Systems

Daqing Hou, Schweitzer Engineering Laboratories, Inc.

Abstract—When overhead power lines in solid or low-

impedance grounded systems lose supports and fall on poorly

conductive surfaces, they generate high-impedance faults (HIFs).

These faults are a great public safety concern because the fault

currents are generally too small for detection by conventional

overcurrent relays. This concern has generated great interest in

the detection of downed conductor-related HIFs at the substation

level. In this paper, we present an HIF detection algorithm that

uses traditional relay logic. The algorithm is easier to understand

and simpler to implement than many black-box detection me-

thods such as neural networks. We discuss such key aspects of

algorithm design as input quantity selection, generation of a reli-

able reference, adaptation to feeder ambient load noises, and

decision logic based on trending and memories. We use real-

world data collected from staged HIF tests and noisy substation

loads to validate detection results.

I. INTRODUCTION

In power distribution systems with voltages ranging from

4 kV to 34.5 kV, high-impedance faults (HIFs) have chal-

lenged utilities and researchers for years. HIFs are those faults

on distribution feeders with fault currents below traditional

overcurrent relay pickups. Fallen power conductors on poorly

conductive surfaces, tree branches brushing against power

lines, and dirty insulators are all potential causes of HIFs. Re-

searchers in many studies of staged HIFs on grounded distri-

bution systems have recorded fault current magnitudes that

vary anywhere from zero to less than 100 amperes.

HIFs have such small fault currents that they generally do

not affect power distribution system operation. However, HIFs

caused by downed power conductors are major public safety

concerns. Without timely correction, these faults can be ha-

zardous to human lives and property. There have been a num-

ber of documented cases of costly litigation as a result of

damages from undetected downed power conductors.

HIFs on multigrounded distribution systems are difficult to

detect at the substation level. Single-phase loads and the mul-

tipath returns of unbalanced currents are several factors con-

tributing to the difficulty in detecting these faults [1]. A

grounded system can be quite unbalanced when a major sin-

gle-phase lateral is out of service. Beyond ensuring coordina-

tion with downstream devices and fuses and avoiding pickup

on cold loads and transformer inrushes, one must avoid false

tripping by setting conventional ground overcurrent protection

above the maximum foreseeable unbalance. Thus, overcurrent

protections that use the fundamental component or root-mean-

square (rms) of currents are ineffective in detecting HIFs.

Some HIFs, such as those resulting from downed power con-

ductors on asphalt or dry sand, generate virtually no fault cur-

rent. No substation-based devices can detect these HIFs or

down-conductor situations. An early IEEE Power Engineering

Society (PES) publication [2] documented specifics on why

fallen power lines cannot always be detected.

HIFs are random and dynamic. A downed power conductor

can lie idle on a surface for some time and then conduct once

insulation breaks down. An arcing conductor may not lie still

on a ground surface, but may move around as a result of elec-

tromagnetic force. Fault current magnitudes and contents

change as ground surface moisture escapes from fault-

generated heat, and/or as ground silicon materials burn into

glasses. Soils during different seasons of a year and from dif-

ferent geological regions also produce different fault current

contents.

Despite these challenges, researchers remain optimistic that

they will find a cost-effective substation-based detection algo-

rithm for HIFs. Perplexed by undetected breakdowns of cross-

linked polyethylene (XLP)-covered conductors in the early

1970s, Pennsylvania Power and Light Company (PP&L) in-

itiated several staged HIF tests by dropping XLP conductors

on different ground surfaces [3]. EPRI and CEA directed re-

search in the late 1970s and early 1980s that resulted in sever-

al research reports [4]–[7]. Since then, researchers have stu-

died and applied many existing and emerging techniques to

HIF detection. These include statistical hypothesis tests [8],

inductive reasoning and expert systems [9], neural networks

[10] [11], third harmonic angle of fault currents [12], wavelet

decomposition [13] [14], decision trees [15], fuzzy logic [16],

and others. The IEEE PES and Power System Relaying Com-

mittee (PSRC) have followed the developments closely and

have offered a tutorial course [17] and published committee

reports [18]–[20].

As indicated by a lengthy history of on-going research and

the number of technologies researchers have studied and ap-

plied, one can obtain a sense of the difficulty and complexity

involved in designing an HIF detection algorithm that is both

fairly dependable and 100 percent secure against false alarms.

While it is relatively easy to design an algorithm that de-

tects certain HIFs, it is challenging to make the same algo-

rithm secure. The objective of HIF protection is to remove

hazards to the public. When an HIF detection device indicates

a fault, utilities must make tripping decisions based on a num-

ber of circumstances to ensure a trip will not cause more ha-

zardous situations. Utilities cannot tolerate false alarms from

HIF detection devices. It can be more dangerous and costly,

for example, to trip out a busy traffic intersection, hospital, or

an airport load.

In this paper, we present another HIF detection algorithm.

In Section II, we identify and introduce the key areas of de-

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signing effective detection algorithms. These include input

quantity selection, generation of a reliable reference, adapta-

tion to individual feeder ambient conditions, a trending and

memory function, and decision logic that uses simple, tradi-

tional relay logics. In Section III, we present the test results

we obtained with the algorithm, using data from staged HIF

tests. We also verify algorithm security through the use of

representative noisy substation loads.

II. DESIGN OF HIGH-IMPEDANCE DETECTION

From our research and study of the subject, we identify the

following as key elements to successful design of an HIF de-

tection algorithm:

• An informative quantity that reveals HIF signatures as

much as possible without being affected by loads and

other system operation conditions.

• A running average of the quantity that provides a sta-

ble prefault reference. The average is preferably avail-

able at all times, even during an HIF condition. For

this purpose, the running average must not follow the

large fault quantity quickly during a fault event.

• An adaptive tuning feature that learns and tunes out

feeder ambient noise conditions. Preferably, the tuning

is active whenever the algorithm does not detect an

HIF condition on the system.

• An effective decision logic to differentiate an HIF

condition from other system conditions such as

switching operations and noisy loads.

The HIF detection algorithm we propose centers on these

key elements but contains other supplementary function

blocks. Fig. 1 shows the block diagram of the algorithm for

the A-phase current. The same processing also applies to the

B-phase, C-phase, and residual currents.

Sum of Difference

Current (SDI)

IIR Limiting Averager

Trending and Memory

Adaptive Tuning

Blocking Conditions

Decision Logic

IA ArcingIA

Fig. 1. Block diagram of high-impedance detection

The first function block calculates a signal quantity upon

which the algorithm bases its HIF detection. This quantity is

called the Sum of Difference Current, or SDI. An Infinite-

Impulse-Response (IIR) Limiting Averager establishes a sta-

ble reference for SDI. The Trending and Memory block com-

pares SDI with the SDI average and memorizes the time and a

ratio if SDI is a set threshold above the SDI average. The De-

cision Logic uses the results from the Trending and Memory

block to determine the existence of HIF on the processed

phase. The Adaptive Tuning block monitors feeder back-

ground noise during normal system operations and establishes

a comparison threshold for the Trending and Memory block.

The IIR Limiting Averager also uses this threshold to prevent

the averager input magnitude from becoming too large.

The following text provides details of major functions in

Fig. 1.

A. Sum of Difference Current (SDI)

Because HIFs generated low current magnitudes, people

realized from the beginning that they would have to search for

signal quantities other than the rms and fundamental frequen-

cy component of currents for HIF detection.

HIFs typically involve arcing and conduction through

ground surfaces. Both arcing and soil conduction present non-

linear resistance to current flow and therefore generate har-

monics [4]. On the other hand, normal nonlinear loads such as

motor centers, power inverters, and arc furnaces also generate

significant harmonics, especially odd harmonics. What we

want are signal quantities that reveal mostly the signatures of

HIFs but vanish under normal system operation conditions.

Initially, people used the sequence components of the fun-

damental frequency, third and fifth harmonics, third-harmonic

phase and magnitude changes, and high-frequency compo-

nents between 2 kHz to 10 kHz [5]–[7]. Each of the compo-

nents has its mysteries and limits. Eventually, people dis-

cussed and applied such large types of signals as current dif-

ferences [11] [22], even, odd and nonharmonics [9], and ener-

gies of special frequency bands from wavelet decomposition

[13] [14]. One reference [21] has suggested using the combi-

nation of different signals.

In our design, we chose to use an SDI, shown in Fig. 2, as

the fault detection input. The system tracks power system fre-

quency and samples feeder currents (Ik) at an integer number

(Nspc) of samples per system cycle. The system uses a simple

one-cycle difference filter [22] to calculate difference current

(DIk) and obtains SDI by accumulating the absolute values of

the difference current during several power cycles (Ns).

1-cycle memory Ns-cycle memory

DIk-1 DIk-NsNspc + 1

SDIkIk

Ik-Nspc

I-IDIk

M1 M2

Nspck,...,1k II −− 1NsNspck,...,1k DIDI +−−

Fig. 2. Calculation of Sum of Difference Current (SDI)

Fig. 3 illustrates the SDI calculation in time domain with

the current waveform from an HIF sampled at 32 samples per

Icycle. For ideal sinusoidal waveforms, the one-cycle differ-

ence calculation would result in an output of all zero values.

With the arcing current of an HIF, however, the one-cycle

difference of the current reveals the activity of the rather ran-

dom arcing process.

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IkIk-32

0 1 2

Cycle

Ik-1Ik-33

1-cycle

1-cycle

∑=

−

−

−

=

•••

−=

−=

a

0n

nkk

33k1-k1-k

32kkk

DISDI

|II|DI

|II|DI

Fig. 3. Time domain illustration of SDI calculation

Fig. 4 shows the magnitude portion of the frequency re-

sponse of the one-cycle difference calculation to the fourth

harmonic. Note that the magnitude response has a zero at

every harmonic frequency, and that this includes the dc and

the fundamental frequency. All harmonic components, includ-

ing the dc and the fundamental of the current, are therefore

removed after the difference calculation. The frequency con-

tents of the difference current contain only nonharmonics. SDI

represents an average measure of the total nonharmonic con-

tent of a current over an Ns-cycle window, making SDI a val-

uable tool for HIF detection.

Harmonic

Gain

0.2

0

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.5 1 1.5 2 2.5 3 3.5 4

Fig. 4. Frequency magnitude response of the one-cycle difference filter

B. IIR Limiting Averager

When an HIF occurs, the SDI quantity increases. The

amount of increase can be appreciated only by comparing the

quantity with its history. Providing a reliable reference is the

function of the IIR Limiting Averager, and the quality of this

reference is important to the success of the detection algo-

rithm.

We chose to use an infinite-impulse-response (IIR) type of

averaging with a fixed time constant, because we can achieve

long-time memory effects efficiently with relatively few cal-

culations and memory units. One must choose a time constant

large enough to provide a stable reference during faults. On

the other hand, a small time constant is good for allowing a

rapid tracking of the input average during no fault conditions.

To strike a balance between these conflicting requirements

and to prevent the average from following quickly the large

SDI spikes, the input to the averager is limited when the SDI

value is above a threshold. One other possibility for stabilizing

the average output in case of high input spikes is to increase

the time constant. Some distance relays use this method, de-

scribed in US patent 5,790,418 [23], in the memory filter for

the polarizing quantity.

Fig. 5 shows the details of the IIR Input Limiting Aver-

ager. The averager output, SDI_REFk, follows the general first

order IIR equation (1)

( ) 1kink REF_SDI•x•1REF_SDI −α+α−= (1)

where α relates to the time constant and xin can take two pos-

sible values according to the output of comparator C1. The

input to the positive polarity of the comparator C1 is SDIk, and

the input to the negative polarity of the comparator C1 is

GIIR1d + SDI_REFk-1. The Adaptive Tuning section introduces

the variable d. Treat this variable here as a constant. The com-

parator output is a logical 1 if SDIk > GIIR1d + SDI_REFk-1,

and a logical 0 otherwise. When the comparator output is a

logical 0, the switch SW is in its position 1 and xin therefore

equals SDIk. When the comparator output is a logical 1, the

switch SW is in its position 2 and xin therefore equals

GIIR2d + SDI_REFk-1. We can then calculate the averager out-

put, SDI_REFk, from (2).

1k2IIR

1kkk

1kIIR1k

SDI_REFd•G•α)1(otherwise

SDI_REF•αSDI•α)1(SDI_REFthen

SDI_REFd•GSDIif

−

−

−

+−=

+−=

+<

(2)

Fig. 5. IIR Input Limiting Averager

When conditions other than HIFs occur, the freeze input,

RFRZ_MCLR, is a logical 1 and the IIR limiting average cal-

culation is suspended. These non-HIF conditions include large

changes in phase currents and changes in line voltages.

C. Trending and Memory

Once the algorithm establishes detection quantity SDI and

its average SDI_REF, the algorithm must extract HIF signa-

tures from these quantities. The Trending and Memory func-

tion records unusual SDI changes related to system HIF and

memorize these changes for the decision logic. The Trending

and Memory function provides information regarding how

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often and by how much SDI departs from SDI_REF plus a

margin.

Fig. 6 shows the details of the Trending and Memory func-

tion. The part of the logic before the comparator C runs at the

rate of every SDI update. The remaining portion of the logic

runs whenever the output of C is a logical 1.

kREF_SDI

kSDIkdSDI

kkk d/dSDIrd =

n21 t,...,t,t

n21 rd,...,rd,rd

Fig. 6. Trending and Memory function

The absolute value of the difference between SDI and

SDI_REF, or dSDI, goes to the positive input of the compara-

tor C. The negative input of the comparator connects to a vari-

able d. The Adaptive Tuning section introduces variable d.

When dSDI exceeds d, the comparator output is a logical 1,

Otherwise, the comparator output is a logical 0. A logical 1

from comparator C closes the switch SW1, and the algorithm

records in a memory, M3, the time at which SW1 closes. This

memory has enough units to save the maximum possible

number of tk within NTM seconds.

At the beginning of each NTM-second segment, if previous

set t1, t2, …, tn is not zero, the last time value, tn, moves to a

single memory unit, M5, as told. If the set t1, t2, …, tn has no

members, M5 retains its previous value as told.

The Trending and Memory function provides t, rd, and

told, to the decision logic to determine the existence of an HIF.

The function also provides the value n, the number of times

SDI departs from the threshold of SDI_REF plus d in previous

NTM seconds, to the adaptive tuning logic. The algorithm uses

the same blocking conditions as those in the IIR Limiting

Averager, RFRZ_MCLR, for this Trending and Memory func-

tion to clear memorized t and rd in case of system condi-

tions other than HIFs.

D. Adaptive Tuning

When setting traditional overcurrent relays, one uses a

short circuit study program to calculate the fault current under

different system operation conditions. The fault current satis-

fies Ohm’s law, so the settings calculation process is

straightforward with known system topologies and parame-

ters.

For HIF detection, however, the situation is different. HIF

detection uses nontraditional quantities. Nonlinear and dynam-

ic feeder loads influence these quantities in different ways. For

example, if the HIF detection algorithm uses the fifth harmon-

ic of currents, detection settings would be different for feeders

with six-pole power inverters than for feeders that have only

relatively quiet residential loads. Given the vast variety of

distribution loads, it would be impractical for users to study

the loads of each feeder and determine the effects these loads

have on the detection algorithm they choose to use.

The purpose of the Adaptive Tuning function is for the al-

gorithm to automatically characterize the detection quantity of

a feeder for its normal loads. The function learns a margin

above the SDI average into which the SDI value may fall as a

result of normal system operations. Both the IIR Limiting

Averager and Trending and Memory functions use this mar-

gin, labeled as variable d.

Fig. 7 shows details of the Adaptive Tuning function.

There are two inputs, n and nAT, on the right side of Fig. 7.

The input, n, is the number of times that SDI departed its av-

erage plus the margin d within the previous NTM seconds, as

this paper explained previously. An accumulator adds all n

values for as long as NAT minutes and produces an output nAT,

the number of times that SDI departs its average plus the mar-

gin d within the previous NAT minutes.

k1AT1kk REF_SDI•Gdd −= −

1kk dd −=

k2AT1kk REF_SDI•Gdd += −

kREF_SDI

Fig. 7. Adaptive Tuning function

The first comparator of the logic, C1, compares the value

of nAT to a threshold PU1. If nAT is less than PU1, the output of

C1 is a logical 1. Otherwise, the output of C1 is a logical 0. If

the output of comparator C1 is logical 1 for a consecutive pe-

riod of Dpu1 minutes, as the timer T1 determines, the timer T1

produces an output of logical 1. This logical 1 output enables

the upper row d update calculation and at the same time caus-

es the AND gate to force its output to a logical 0. In other

words, if SDI does not depart its average plus a margin d for

more than PU2 times for Dpu1 minutes, the algorithm considers

the margin d too large and decreases the corresponding update

calculation by GAT1 percent of the average, as in (3).

k1ATkk REF_SDI•Gdd −= (3)

The second comparator of the logic, C2, compares the val-

ue of n to a pickup threshold PU2. If n is greater than PU2, the

output of C2 is a logical 1. Otherwise, the output of C2 is a

logical 0. If the output of comparator C2 is a logical 1 for a

consecutive period of Dpu2 seconds, as the timer T2 deter-

mines, the timer T2 produces an output of logical 1. This logi-

cal 1 output enables the bottom row d update calculation and

at the same time causes the AND gate to force its output to a

logical 0. In other words, if SDI departs its average plus a

margin d for more than PU2 times in NTM seconds, and if the

condition lasts for Dpu2 seconds, the algorithm considers the

margin d too small and increases the corresponding update

calculation by GAT2 percent of the average, as in (4).

k2ATkk REF_SDI•Gdd += (4)

If both outputs of T1 and T2 are logical 0, the AND gate

produces a logical 1 output, which enables the middle row

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update calculation for d. The new d value does not differ from

the previous value.

The enable input of Fig. 7, AT_Enable, determines when

the d update occurs. Some distribution loads, such as a rail

train system, have daily cycles, and other loads such as motor

pumps for farms have seasonal cycles. Ideally, the tuning

process should be continuous as long as there are no HIFs on

the system. The tuning should also remain for a certain period

of time after a breaker closure and load current detection.

E. Decision Logic

The Trending and Memory function provides rich informa-

tion regarding how often and by how much SDI departs from

its reference plus a learned margin. The value of n represents

the number of times SDI departed its threshold within the pre-

vious NTM seconds, while the set of ratios, rd, represents the

information concerning the amount by which SDI exceeded its

threshold. The first block of the decision logic in Fig. 8 calcu-

lates a set of time differences, dt, through the use of the set

of time, t, and told from the Trending and Memory function.

The time difference can provide the temporal characteristic of

randomness signature of the HIFs. It is possible to use some

artificial intelligence methods of classification and pattern

recognition, such as neural network or decision trees, to deci-

pher this information for the detection of HIFs. We chose,

instead, to use relatively simple comparators and counters for

the decision logic.

Counting

Scheme

NF

Occurrence

rd

t

NA

Occurrence

Fault

Alarm

_+

_

+

PUF

C1

C2

TF

TA

Fault counts

Alarm counts

Calc. dtdt

told

DL_Clear

PUA

Fig. 8. Block diagram of decision logic

The decision logic has two counters for separate HIF

alarms and trip. Counter TF is for HIF detection, and Counter

TA is for HIF alarms. For each pair of rd,dt in the previous

NTM-second segment, a counting scheme determines whether

to count or not count and the number of counts for a fault or

alarm. For each NTM-second segment, if the number of counts

for an HIF exceeds PUF, as comparator C1 determines, the

comparator produces a logical 1 output. Counter TF accumu-

lates the number of logical 1 assertions from comparator C1.

If NF occurrences accumulate within a fault decision time,

counter TF produces a logical 1 output to indicate detection of

an HIF. The algorithm uses a similar method for deriving an

alarm for an HIF through comparator C2 and counter TA, but

it uses different detection thresholds, as Fig. 8 indicates.

Fig. 9 shows an rd-dt plane. The entire plane is divided into

three regions: Fault Count, Alarm Count, and No Count. The

dt axis has a unit of Ns-cycle, the interval over which SDI

accumulates. If a rd,dt pair falls into the no-count region,

the algorithm generates no counts for either alarm or fault. If a

rd,dt pair falls into the alarm-count region, the algorithm

generates counts only for HIF alarms. If a rd,dt pair falls

into the fault-count region, the algorithm generates counts for

both fault and alarm conditions of HIFs.

rd

2

No Count Region

1

dt

3

1 654320

0

Alarm Count Region

Fault Count Region

Fig. 9. Counting regions for alarm and fault conditions

This counting scheme on the rd-dt plane is much like the

percentage restraint current differential characteristic, with dt

similar to the restraining quantity and rd similar to the operat-

ing quantity. Sporadic and isolated high SDI values can arise

from system switching such as turning capacitor banks on and

off or moving load tap changers up and down. Such values

can also result from lightning strikes during storm seasons.

We can discount these SDI events because they are associated

with large dt values. On the other hand, intense and active

arcing events from HIFs tend to produce high SDI values clus-

tered in a short period of time, so the related rd,dt pairs

would be more likely to reside in the operating region of the

counting scheme.

Fig. 10 shows how the algorithm generates the number of

counts as a function of the ratio, rd, for each rd,dt pair that

the counting scheme shown in Fig. 9 determines to be counta-

ble. For example, if the rd value in a rd,dt pair is 4, and the

pair falls into the Fault Count region, then the algorithm gene-

rates not one but two fault and alarm counts for this pair of

rd,dt. Studies of staged HIF data indicate that the SDI value

generally correlates to the relevance of an event to HIFs. By

making the number of counts proportional to the ratio, rd, the

algorithm considers not only the event that SDI overcomes its

threshold, but also the amount of SDI increase, in determining

the existence of a fault.

rd

# count

1 2 3 4 5 6

1

2

3

Fig. 10. Number of counts as a function of rd

Several system conditions disable the decision logic as in-

dicated by the DL_Clear input. Some of these conditions in-

clude large phase current and some voltage changes. The algo-

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rithm also detects and uses events that occur in all three phas-

es to disable the decision logic, because we assume that these

events are highly unlikely HIFs.

III. SIMULATION TEST WITH STAGED FAULT AND

SUBSTATION LOAD DATA

A. High-Impedance Fault Simulation

In early HIF studies, researchers performed and recorded

many staged faults [6] [7]. Test data from these studies have

provided valuable information toward understanding and cha-

racterizing HIFs. These data provided the foundation for the

design of many early detection devices.

Over time, researchers constructed various HIF models for

the purpose of designing and testing fault detection algo-

rithms. These models ranged from simple diodes and dc

sources connected in series to variable resistances that one

could control through the relationship between the voltage and

current of some typical HIFs [24].

Nevertheless, HIFs are complicated processes that include

many nondeterministic variables yet to be understood. As ref-

erence [25] explains, the impedance of these faults includes

those of arcs, ground surface, earth return, and the interface

between ground surfaces and downed conductors. Researchers

have conducted extensive studies on some impedance, such as

that of arc, but the results probably cannot be applied directly

in HIF situations because of the voltage level, length of arc,

and multiple paths of arc. Some other impedance such as that

of earth return has a well-established formula; but it is difficult

to determine some necessary parameters used in the formula-

tion. Many other variables, such as conductor types, the way a

conductor contacts the ground surface, surface types, ground

moisture content, and return earth compositions, can all

change in too many ways to be accurately accounted for in

simulations.

It is therefore our belief that HIF simulations can provide

initial data for preliminary research, but ultimate fault detec-

tion algorithm design and verification should rely on staged

fault tests that cover fairly broad geographical terrains, cli-

mates, and ground surface types.

B. Data Acquisition Device

To prepare for staged fault test data collection, we assem-

bled two identical data acquisition systems. The data acquisi-

tion devices we used are Daqbook/2005® devices from IOtech.

These devices can sample as many as 16 analog channels at a

sampling frequency as great as 20 kHz. The Daqbook/2005

device communicates with computers through an Ethernet port

and saves acquired data directly onto the computers. To inter-

face with Daqbook/2005 devices, we made signal interface

modules that include CT/PT and analog low-pass filter circui-

tries typical of microprocessor relays. The cutoff frequency of

a two-stage RC low-pass filter is at about 5.8 kHz. We also

used a wireless router in the system to provide isolation be-

tween the personal computer and the substation secondary

circuits. The router also allows flexible placement of a data

acquisition device in a substation and test site. As the field

setup photo in Fig. 11 shows, every component of the system

fits in a briefcase.

Fig. 11. Data acquisition device used in staged high-impedance fault tests

C. Staged High-Impedance Fault Tests

We staged four HIF tests at three different locations in

2005. In all tests, we collected voltages and currents at both

the test site and the substation. Test site data allow us to study

the way that HIF signatures propagate back to the substation.

We use the substation data for detection algorithm design and

test.

The first test was on Feeder 1503 from the South Nacog-

doches substation of TXU Electric Delivery. This is a

138 kV/12.5 kV substation. We staged the HIFs at two differ-

ent locations on the feeder. One site was about 2 miles from

the substation, and the other site was 12.7 miles from the subs-

tation. The ground surfaces we used in both tests included

concrete blocks, grassy earth, dry and wet gravels, dry and wet

sands, asphalt, tree limbs, and a car tire. At the end of the

tests, we also turned on and off two feeder capacitor banks and

raised and lowered the tap of a transformer load-tap changer to

record normal system switching events.

Fig. 12(a) and Fig. 12(b) show the currents of a TXU earth

fault at the test site and the substation, respectively. The time

scales of the two plots are not synchronized. We staged the

fault by dropping a conductor on dampened, grassy earth. The

peak fault current of about 30 amperes shows quite clearly in

the substation measurement.

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0 10 20 30 40 50 60 70-60

-40

-20

0

20

40

60

Seconds

Fig. 12(a). TXU earth fault current at test site

0 10 20 30 40 50 60 70-500

-400

-300

-200

-100

0

100

200

300

400

500

Seconds

Fig. 12(b). TXU earth fault current at substation

The second test was on Feeder CDAL0017 from the Clo-

verdale 138 kv/12.5 kV substation of Idaho Power Company.

The test site is about one mile from the substation. The test

surfaces included a concrete block, earth, mixture of sand and

gravels, dry and wet asphalt, dry and wet railroad gravel, a car

tire, and maple and juniper trees.

Fig. 13(a) and Fig. 13(b) show the currents of an IPC gra-

vel/earth fault at the test site and substation, respectively.

Again, the time scales of the two plots are not synchronized.

We staged the fault by dropping a conductor on a six-inch-

thick mixture of gravel and dirt. It is virtually impossible to

see any sign of this approximately three-ampere fault current

in the substation measurement.

Amps

Fig. 13(a). IPC gravel/earth fault current at test site

0 10 20 30 40 50 60 70 80 90-500

-400

-300

-200

-100

0

100

200

300

400

500

Seconds

Fig. 13(b). IPC gravel/earth fault current at substation

We staged the last two tests on Feeder 4040 from the Patz-

cuaro 115 kV/13.8 kV substation of CFE in central Mexico.

The test location is on farmland about eight miles from the

substation. We performed the first test in June of 2005, during

the dry season for the area. The ground surface was fine

powder dirt with some dry plant stems. We began the test by

dropping a covered conductor on the dirt. We then progressed

with stripping about one meter of cover off the conductor,

watering the ground, and installing a one-meter ground rod.

We used no protection fuse at the test site. We performed the

second test in September of 2005, during the rainy season for

the area, at exactly the same location. We went through a

similar test sequence of dropping a covered conductor, laying

a stripped bare conductor on the ground, and installing as

many as three grounding rods. The fault current we obtained

for the second test is generally several times larger than the

current we recorded in the first test.

Fig. 14(a) and Fig. 14(b) show currents from a second CFE

fault test at the test site and substation, respectively. The time

scales of the two plots are not synchronized. We staged the

fault by dropping a covered conductor and then forcing the tip

of the conductor to touch a ground rod. The fault current is

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about 10 amperes. The substation measurement shows many

large changes in the current envelope that are unrelated to the

fault; these changes exist also on the unfaulted phase.

Amps

Fig. 14(a). CFE earth fault current at test site

Fig. 14(b). CFE earth fault current at substation

D. Simulation Results of Detection Algorithm

We used Matlab® programming language in a graphical us-

er interface (GUI) setup to fully simulate the detection algo-

rithm we described previously. We can use the setup to handle

data loading, channel assignments, settings change, and selec-

tion of plot quantities. We saved all collected fault data in

COMTRADE format at different sampling frequencies for

further investigation. Because of the limited length of prefault

data, several functions of the fault detection algorithm needed

special treatments under the simulation environment. These

functions included IIR Limiting Averager and Adaptive Tun-

ing. We used a fast charge process to move the simulation

process quickly into the prefault state. Through use of the

COMTRADE format, we could easily extend the prefault por-

tion of each fault event.

Fig. 15 shows the detection simulation results for the

staged TXU fault event the paper illustrates in Fig. 12. The

lower analog portion of the plot shows the SDI quantity for

the event. This portion of the plot also shows in a dashed line

the tuned threshold plus the IIR averager output, or

d + SDI_REF. Whenever SDI exceeds this threshold, the algo-

rithm records the time and calculates a ratio, which the Trend-

ing and Memory function saves for later investigation. One

can see that the SDI value increases after the fault is applied at

approximately 8 seconds. Also note that the SDI shows many

large spikes that are typical for HIFs. The upper portion of the

plot shows four digital elements named, from bottom to top,

A-SDI, B-SDI, C-SDI, and G-SDI. These are fault detection

outputs for, respectively, phases A, B, C, and the residual cur-

rent channel. A thick bar on the digital plot indicates a fault

detection with an “F” marking the starting point of a detection.

For this event, one can see that the detection algorithm is able

to detect the fault correctly in the faulted B phase. The pickup

in the residual channel also indicates fault detection.

0 10 20 30 40 50 600

1

2

3

4

5

F

FG-SDIC-SDIB-SDIA-SDI

Seconds

Fig. 15. Fault detection simulation results for TXU earth fault

Fig. 16 shows the detection simulation results for the IPC

event the paper illustrates in Fig. 13. As we might expect be-

cause of the small fault current, the arcing activity reflected in

the SDI quantity is insufficient to cause pickup of the fault

detection element. It is possible to fine-tune settings to detect

this fault event, but we have established overall settings to

retain high security for the algorithm. Any attempt to make the

detection more sensitive would inadvertently sacrifice securi-

ty.

Fig. 16. Fault detection simulation results for IPC gravel/earth fault

Fig. 17 shows the detection simulation results for the CFE

event the paper illustrates in Fig. 14. The strong SDI activity

makes this event easy for the HIF detection algorithm to

detect.

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Amps

Fig. 17. Fault detection simulation results for CFE earth fault test

E. Security Test With ,oisy Substation Loads

As previous studies pointed out, it is difficult to design an

HIF detection algorithm that is totally immune to false alarms.

It is also a great challenge to test the security aspect of a de-

tection algorithm. Collecting all foreseeable system events or

operation conditions that can cause security problems for a

detection algorithm takes time and is an on-going task.

After testing the algorithm with system-switching events

including such devices as capacitors and load-tap changers,

we identified feeders with extremely noisy loads and col-

lected voltages and currents from these loads for as long as 24

hours to further test the security aspect of the detection algo-

rithm. The loads we collected included those of a cheese man-

ufacturer, motor pumps, a foundry, car crushers, and a metro-

politan rail transit system.

Fig. 18 shows the cheese manufacturer load during a

five-minute period. The upper plot is the A-phase current. The

bottom plot contains the total harmonic distortion in the upper

trace and the SDI quantity in the lower trace. The total har-

monic distortion and the SDI are shown in percentage to the

fundamental frequency component. The load consists mostly

of motor drives. Total harmonic distortion is close to 28 per-

cent, of which most is fifth harmonic (26 percent) and third

harmonic (8 percent). It is a very noisy load in terms of the

harmonic contents. However, the load is quiet in the sense that

it does not generate and change the SDI quantity that the de-

tection algorithm uses.

Fig. 18. Five-minute cheese manufacture load–A phase (secondary)

Fig. 19 shows in its upper plot the A-phase current of the

metropolitan rail transit system load. The bottom plot shows

the total harmonic distortion (upper trace) and the SDI quanti-

ty (lower trace). Although the percentage total harmonic dis-

tortion of this load is not large, the rail load is noisy in that it

causes large variations in rms value, harmonic contents, and

the SDI quantity of the currents. The load is not always as

noisy as shown in Fig. 19. In the early morning, when the

trains are not operating, the load is as quiet as typical residen-

tial and commercial loads.

The detection algorithm “learns” this load noise through

the use of the adaptive tuning feature and retains its security

even in such an extremely noisy load environment. HIFs must

present strong fault signatures before the algorithm indicates

fault detection. Because the load characteristics encroach

those of HIF signatures, security is guaranteed while the de-

pendability of fault detection is compromised.

Amps (secondary)

Total Harm

onic Distortion

Fig. 19. Five-minute rail transportation load–A phase (secondary)

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Fig. 20 shows the plots of the same quantities as those in

Fig. 18 and Fig. 19 for a car crusher load during working

hours. While the envelope of the A-phase current resembles

those of some HIFs, its harmonic contents and the SDI quanti-

ty show few changes pertaining to HIFs. This type of load

causes no detection security concern and results in no com-

promise in the dependability of fault detections.

Fig. 20. Five-minute car crusher load–A phase (secondary)

IV. CONCLUSIONS

HIFs resulting from downed conductors create public safe-

ty concerns. Depending on ground surface materials and con-

ditions, some HIFs generate little or no fault currents. It is

therefore impossible to design a substation-based detection

device to detect all HIFs and downed conductor conditions.

Nevertheless, it is possible to detect many HIFs through the

use of some signatures of HIFs contained in signal quantities

other than current rms or fundamental frequency components.

We have introduced in this paper an HIF detection algo-

rithm that is simple to understand and economical to imple-

ment. The algorithm uses an SDI quantity that reveals signa-

tures of HIFs while remaining generally free of contamination

by distribution loads. Through the use of an adaptive tuning

process, the algorithm can “learn” the ambient noise profile of

distribution feeders and therefore increase the security of fault

detections. A novel IIR Limiting Averager provides a stable

reference for SDI during switching and fault conditions. The

detection logic uses operating and restraining quantities and

counts both temporal and amplitude characteristics of an HIF.

Tests of the detection algorithm used data from real-world

HIFs that included large geological regions, a wide range of

climates, and many foreseeable types of ground surfaces. The

algorithm has proven capabilities beyond those of traditional

overcurrent relays for detecting large portions of HIFs.

Real-world data also verify the security of the algorithm.

These data come from tests that include system-switching

conditions and as long as 24-hour noisy feeder loads such as

car crushers, foundries, rail transportation systems, and motor

pumps and centers.

When a distribution feeder contains noisy loads that en-

croach on the signature of HIFs, the adaptive tuning function

of the detection algorithm automatically tunes to enhance se-

curity. In the classical tradeoff between security and dependa-

bility, such situations cause an inadvertent negative impact on

fault detection dependability.

V. ACKNOWLEDGMENT

We would like to thank TXU Electric Delivery, Idaho

Power Corporation, and Comision Federal de Electricidad for

their support of this research. We are also grateful to Ray-

mond F. Hoad, Dave Angell, Nabucodonosor Solis Ramos,

and Alberto Avalos for their enthusiasm and dedication in

staging HIF and searching for solutions to HIF detections.

VI. REFERENCES

[1] D. Hou and N. Fischer, “Deterministic High-Impedance Fault Detection

and Phase Selection on Ungrounded Distribution Systems,” in 2005

32nd Annual Western Protective Relay Conference Proceedings.

[2] IEEE Power Engineering Society, Downed Power Lines: Why They

Can’t Always Be Detected, New York: IEEE, 1989.

[3] PP&L, “Report of Distribution Conductor Staged Fault Tests,” Oct.

1973.

[4] J. Carr, G. L. Hood, “High Impedance Fault Detection on Primary Dis-

tribution Systems,” CEA Final Report, Project No. 78–75, Nov. 1979.

[5] I. Lee, “High Impedance Fault Detection Using Third Harmonic Cur-

rent,” EPRI Final Report, EPRI EL-2430, June 1982.

[6] S. J. Balser, K. A. Clements, E. Kallaur, “Detection of High Impedance

Faults,” EPRI Final Report, EPRI EL-2413, June 1982.

[7] B. D. Russell, B. M. Aucoin, T. J. Talley, “Detection of Arcing Faults

on Distribution Feeders,” EPRI Final Report, EPRI EL-2757, Dec. 1982.

[8] S. J. Balser, K. A. Clements, D. J. Lawrence, “A Microprocessor-Based

Technique for Detection of High Impedance Faults,” IEEE Trans. Pow-

er Delivery, vol. 3, pp. 252–258, July 1986.

[9] C. J. Kim, B. D. Russell, “Classification of Faults and Switching Events

by Inductive Reasoning and Expert System Methodology,” IEEE Trans.

Power Delivery, vol.. 3, pp. 1631–1637, July 1989.

[10] S. Ebron, D. L. Lubkeman, M. White, “A Neural Network Approach to

The Detection of Incipient Faults on Power Distribution Feeders,” IEEE

Trans. Power Delivery, vol. 2, pp. 905–914, April 1990.

[11] A. P. Apostolov, J. Bronfeld, C. H. M. Saylor, P. B. Snow, “An Artifi-

cial Neural Network Approach to the Detection of High Impedance

Faults,” in 1993 International Conference on Expert System Applica-

tions for the Electrical Power Industry Proceedings.

[12] D. I. Jeerings, J. R. Linders, “A Practical Protective Relay For Down-

Conductor Faults,” IEEE Trans. Power Delivery, vol. 2, pp. 565–574,

April 1991.

[13] J. Liang, S. Elangovan, J. B. X. Devotta, “A Wavelet Multiresolution

Analysis Approach to Fault Detection and Classification in Transmis-

sion Lines,” International Journal of Electrical Power and Energy Sys-

tems, vol. 20, Issue 5, pp. 327–332, June 1998.

[14] T. M. Lai, L. A. Snider, E. Lo, “Wavelet Transformation Based Algo-

rithm for the Detection of Stochastic High Impedance Faults,” in Proc.

International Conference on Power System Transients (IPST 2003),

New Orleans, LA, September 2003.

[15] Y. Sheng and S. M. Rovnyak, “Decision Tree-Based Methodology For

High Impedance Fault Detection,” IEEE Trans. Power Delivery, vol. 2,

pp. 533–536, April 2004.

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[16] F. G. Jota and P. R. S. Jota, “High-Impedance Fault Identification Using

a Fuzzy Reasoning System,” IEE Proceedings – Generation, Transmis-

sion and Distribution, vol. 145, Issue 6, pp. 656–661, Nov. 1998.

[17] Detection of Downed Conductors on Utility Distribution Systems, IEEE

PES Tutorial Course, 90EH0310-3-PWR, Piscataway, NJ: IEEE, 1989.

[18] “The Interruption of Downed Conductors on Low Voltage Distribution

Systems,” Report prepared by the IEEE Power System Relaying Com-

mittee for the Electric Power Research Institute, Oct. 1976.

[19] J. T. Tengdin, E. E. Baker, J. J. Burke, B. D. Russell, R. H. Jones, and

T. E. Wiedman, “Application of High Impedance Fault Detectors: a

Summary of the Panel Session Held at the 1995 IEEE PES Summer

Meeting” in Proc. Transmission and Distribution Conference, Los An-

geles, CA, Sept. 1996.

[20] “High Impedance Fault Detection Technology,” Report of IEEE PSRC

Working Group D15, March 1996. [Online] Available:

http://grouper.ieee.org/groups/td/dist/documents/highz.pdf.

[21] H. J. Songster, “High Impedance Fault Detection,” in 1980 7th Annual

Western Protective Relay Conference Proceedings.

[22] J. J. Zuercher and C. J. Tennies, “Arc Detection Using Current Varia-

tion,” U.S. Patent 5,452,223, Sept. 19, 1995.

[23] J. B. Roberts and D. Hou, “Adaptive Polarizing Memory Voltage Time

Constant,” U.S. Patent 5,790,418, Aug. 4, 1998.

[24] S. R. Nam, J. K. Park, Y. C. Kang, and T. H. Kim, “A Modeling Method

of a High Impedance Fault in a Distribution System Using Two Series

Time-Varying Resistances in EMTP,” in IEEE Power Engineering So-

ciety Summer Meeting, vol. 2, pp. 1175–1180, July 2001.

[25] D. I. Jeerings, J. R. Linders, “Ground Resistance – Revisited,” IEEE

Trans. Power Delivery, vol. 2, pp. 949–956, April 1989.

VII. BIOGRAPHY

Daqing Hou received B.S. and M.S. degrees in Electrical Engineering at the Northeast University, China, in 1981 and 1984, respectively. He received his

Ph.D. in Electrical and Computer Engineering at Washington State University

in 1991. Since 1990, he has been with Schweitzer Engineering Laboratories, Inc., Pullman, Washington, USA, where he has held numerous positions in-

cluding development engineer, application engineer, and R&D manager. He is currently a principal research engineer. His work includes system modeling,

simulation, and signal processing for power systems and digital protective

relays. His research interests include multivariable linear systems, system identification, and signal processing. He holds multiple patents and has au-

thored or co-authored many technical papers. He is a Senior Member of IEEE.

Copyright © SEL 2006


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167



Experiencias con protecciones diferenciales de bus digitales

Ing. Bladimir Hernández Acosta, Ing. Eduardo O. Mora Alcaraz CFE Gerencia Regional de Transmisión Oriente

Resumen

Se analizan dos casos en los que operaron las protecciones diferenciales de bus digitales y las medidas correctivas recomendadas para brindar mayor confiabilidad al desempeño de este tipo de esquemas.

Introducción

CFE cuenta con más dos décadas de experiencia en la aplicación de relevadores digitales de protección, mayormente en protección de líneas y transformadores. Las protecciones diferenciales de buses son los esquemas en los que se ha ido incursionando más recientemente.

Los nuevos esquemas para protección de buses tienen todas las ventajas que conocemos de la tecnología digital: multifunción, medición en línea, registro de eventos, registro secuencial, autosupervisión, etc. Sin embargo, también ofrecen cambios que reducen el espacio físico que ocupaban los antiguos esquemas estáticos, como son la eliminación de los transformadores auxiliares de acoplamiento, los relevadores auxiliares de posición de cuchillas, los relevadores de disparo y bloqueo sostenido utilizando disparos directos desde la protección.

Estos cambios que debieran simplificar la aplicación de los equipos de nueva tecnología tienen detalles que a diferencia de los esquemas estáticos requieren ser verificados con ojo crítico para visualizar cómo afectan el desempeño de la protección. Como veremos en los casos de estudio del presente artículo, se debe tener cuidado en la aplicación de los nuevos modos de configuración que acompañan a los equipos de tecnología digital.

Caso 1. S.E. Minatitlán II 115 kV

La S.E. Minatitlán II (MID) en 115 kV tiene 14 bahías (alimentadores) con arreglo de dos buses con bus de transferencia:

- dos bancos de transformadores 400/115 kV - nueve líneas de transmisión - un banco de capacitores paralelo - interruptor de amarre de barras

- interruptor de transferencia

75010T1400 / 115 kV

T2400 / 115 kV

77010 79120

73050CTS

73110CLO

73120CLO

73130CTS

73310CHM

73860RMN

73870CVN

73880MAS

73890NDD

GERENCIA REGIONAL DE TRANSMISIÓN ORIENTE

S.E. MINATITLÁN II 115 KV

FEBRERO 2008

Fig 1. Diagrama unifilar MID-115 En 2005 entró en servicio el banco de capacitores paralelo y se requirió la sustitución de la protección diferencial de barras tecnología estática de 115 kV, instalando un esquema digital programable de 2 zonas. Por el arreglo de la subestación la protección requiere la señalización de las cuchillas de bus de cada bahía para su operación y se puso en servicio conectando exclusivamente contactos “a” de los interruptores y las cuchillas. El esquema se configuró con 2 zonas de pro-tección. Los alimentadores se integran a la zona 1 cuando la cuchilla de bus 1 está cerrada; y a la zona 2 cuando la cuchilla de bus 2 está cerrada (figura 2).

168



Fig 2. Configuración de las zonas de protección El interruptor de amarre de buses 79120 se integra a ambas zonas; por lo que siempre se dispara este interruptor cuando opera la protección diferencial en cualquiera de sus 2 zonas. El 3 de Noviembre de 2007 a las 5:09 horas se desprendió el hilo de guarda de la línea MID 73310 RFP, provocando una falla de fase “A” a tierra a 1.9 km de MID con una aportación de 15.3 kA y una duración de 5 ciclos. A las 5:10 horas se hizo una prueba C/D sobre el interruptor MID 73310 presentándose una falla de tres fases a tierra a 1.9 km de MID con un aportación de 16.5 kA y una duración de 5 ciclos. La línea 73310 se encontraba conectada al bus 1 de MID-115. Durante la segunda falla operó la fase “A” de la protección diferencial de bus 2 de MID-115, disparando sólo 3 de los 7 interruptores conectados a ese bus: 73050, 73860 y 79120. En el registro secuencial de la protección diferencial se observa que antes de la operación de la protección se perdió la indicación de cuchillas e interruptores de todas las bahías (figura 3); esas mismas indicaciones se recuperaron en un lapso de 24 ms.

Fig 3. Registro secuencial de la protección Este transitorio en las señalizaciones hizo que la protección midiera parcialmente y operara sobre los primeros alimentadores que reconoció nuevamente en servicio: el 73050 y el 73860, además del interruptor 79120 (figura 4).

Fig 4. Disparo de interruptores La indicación de cuchillas e interruptores se perdió debido a que la alimentación de CD disminuyó en el momento de la falla. La figura 5 muestra el

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oscilograma de la protección diferencial donde se observa el abatimiento de la alimentación y la pérdida de la señalización. La alimentación de CD se abatió desde 250 V hasta 172 V.

Fig 5. Abatimiento en la alimentación de CD. El mismo día de la falla se probó la sensibilidad de las entradas digitales de la protección, encontrando que el voltaje de operación mínimo se encuentra en 178 VCD. Finalmente se encontró que el banco de baterías estaba desconectado y que el cargador estaba alimentando directamente a los servicios propios. Al ocurrir la falla la variación se reflejó en la respuesta del cargador. Caso 2. S.E. Puerto Altamira 115 kV La S.E. Puerto Altamira en 115 kV tiene 6 bahías (alimentadores) con arreglo de dos buses con interruptor comodín: - un banco de transformadores 400/115 - cuatro líneas de transmisión - interruptor comodín

T1400 / 115 kV

77010

73130TPC

73140PUO

73210RMA

73410LDC

GERENCIA REGIONAL DE TRANSMISIÓN ORIENTE

S.E. PUERTO ALTAMIRA 115 KV

FEBRERO 2008

Fig 6. Diagrama unifilar PAE-115

Por el arreglo de la subestación la protección requiere la señalización de las cuchillas de bus de cada bahía para su operación y se puso en servicio conectando exclusivamente contactos “a” de los interruptores y las cuchillas. El esquema se configuró con 2 zonas de protección. Los alimentadores se integran a la zona 1 cuando el interruptor y la cuchilla de bus 1 están cerrados; y a la zona 2 cuando la cuchilla de bus 2 o de transferencia están cerradas (figura 7).

Fig 2. Configuración de las zonas de protección El interruptor comodín 77010 se integra a ambas zonas; por lo que siempre se dispara este interruptor cuando opera la protección diferencial en cualquiera de las 2 zonas. El 24 de noviembre de 2007 se estaban realizando maniobras para librar el banco de transformadores PAE-T1. Al ejecutar un mando de apertura sobre el interruptor 72010 opera la protección diferencial disparando todos los interruptores conectados al bus. En el oscilograma de la protección (figura 8) se observa un cambio en las corrientes de operación y de restricción de la función diferencial sin que se hayan producido variaciones en las corrientes de fase de los alimentadores.

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Fig 8. Oscilograma PAE-115 Previo al disparo la protección estaba midiendo las corrientes de tres alimentadores (banco y dos líneas, las otras dos líneas estaban fuera de servicio) y se encontraba estable. El relevador recibió la señal de cambio de estado del interruptor 72010 antes de que los contactos principales hubieran abierto. En ese momento la protección eliminó del algoritmo diferencial las corrientes de la bahía del transformador y en consecuencia se desbalanceó y disparó. Conclusiones Para la configuración de las zonas de protección no se deben utilizar las señales de estado de los interruptores. Utilizar doble contacto (“a” y “b”) para la señalización de las cuchillas de bus y activar la lógica de supervisión de cuchillas (figura 9).

Fig 9. Lógica de supervisión de cuchillas Si se utiliza un solo contacto para la señalización de cuchillas, es preferible utilizar contactos tipo “b”. Con esta lógica invertida, al fallar la señalización por fallas en la alimentación de CD la protección se pasa el modo de buses interconectados y el esquema protege a toda la subestación como una sola barra. Utilizar la lógica de supervisión de zonas; esta lógica requiere que se configure una tercera zona

de operación la cuál integra a todos los alimentadores menos el interruptor de amarre y funciona como permisivo de las zonas de operación tradicionales (figuras 10, 11 y 12).

Fig 10. Zona de supervisión.

Fig 11. Configuración de la zona de supervisión.

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Fig 12. Habilitación de la zona de supervisión. Por último se recomienda activar las funciones de monitoreo de la alimentación de CD; como se vió en este artículo la información proporcionada por esta función nos ayudó a detectar la causa del disparo ocurrido en MID-115. Bibliografía Werner G. Doehner et al. “Esquemas de Protección Eléctrica”. Comisión Federal de Electricidad, México. S. H. Horowitz, A. G. Phadke. “Power System Relaying”. Research Studies Press, Gran Bretaña, 1993. A. G. Phadke, J. S. Thorp. “Computer Relaying for Power Systems”. Research Studies Press, Gran Bretaña, 1994. Currículum Bladimir Hernández Acosta nació en 1972 en Arenal, Ver. En 1994 concluye sus estudios de Ingeniería Industrial en Eléctrica en el Instituto Tecnológico de Veracruz. En 1996 ingresa a la Comisión Federal de Electricidad en el departamento de protecciones de la subárea de transmisión Veracruz de la Gerencia Regional de Transmisión Oriente. Desde 1998 labora en el departamento de protecciones de la subárea de transmisión Coatzacoalcos. Eduardo Octavio Mora Alcaraz nació en 1964 en Xalapa, Ver. En 1988 concluye sus estudios de Ingeniería en Electrónica en la Universidad Autónoma Metropolitana de México, D.F. Desde

1988 ingresa a la Comisión Federal de Electricidad desempeñando puestos de jefe de oficina y jefe de departamento de protecciones en la subárea Poza Rica. Desde 1995 ocupa el puesto de jefe de oficina en la subgerencia de protección y medición de la Gerencia Regional de Transmisión Oriente.

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Abstract—The role of capacitor banks increased recently in the

light of blackout prevention activities, and widening penetration

of distributed generation, wind farms in particular, which add

generation without addressing the problem of reactive power

support.

Capacitor banks are valuable assets that must be available

for the daily demands of system operation and must provide

reliable operation through abnormal power system scenarios.

From the protective relaying perspective, however, capacitor

banks are historically considered a relatively low-volume market,

and therefore, did not encourage development of advanced

protective relays dedicated to capacitor banks. Quite often

protection for capacitor banks is provided by general-purpose

multi-function relays, with only a very few solutions on the

market offering protection functions specifically tailored to

capacitor bank protection. The utility relay engineer has

generally needed to combine the functionality of multiple relays

and customize their programming to provide the necessary

protective system that will avoid false tripping for system

disturbances and obtain the sensitivity for detecting capacitor can

faults and minimizing damage.

Sensitivity is paramount for protection of transmission level

capacitor banks. Typically to meet the sensitivity requirements

capacitor protection methods responding to voltage or current are

based on detecting a change in the capacitor unbalance – either

between phases or between parallel banks, and incorporate some

degree of self-adjustment in order to compensate for instrument

transformer errors, and inherent (pre-existing) bank unbalance.

This paper shows that a common approach of responding to

delta changes in the operating signals is not optimal. The paper

derives and explains accurate operating equations for capacitor

bank protection that work under simultaneous inherent capacitor

bank unbalance and system unbalance. The latter is critical, as

the ultra-sensitive protection functions must remain secure during

major system disturbances when the capacitor banks are need

most.

The presented methods also facilitate auto-setting and self-

tuning applications. Auto-setting is an operation of calculating

new accurate relay constants to account for the inherent bank

unbalances following the bank repair, and is performed in

response to the user’s request and under user supervision. Self-

tuning is an operation of constantly self-adjusting the balancing

constants in the protection equations in order to maintain

optimum sensitivity of protection when the bank reactances

change slowly in response to seasonal temperature variations and

other conditions.

The paper analyses sensitivity of the developed methods and

derives practical equations for the amount of the operating

signals given the size of the failure in the protected bank. Also,

impact of instrumentation errors (instrument transformers and

relays) is analyzed quantitatively allowing one to optimize the

secondary system design, and select settings based on data.

Index Terms—Adaptive capacitor bank protection, inherent

unbalance compensation, shunt capacitor banks.

I. INTRODUCTION

hunt Capacitor Banks (SCB) are installed to provide

capacitive reactive compensation and power factor

correction. The use of SCBs has increased because they

are relatively inexpensive, easy and quick to install, and can be

deployed virtually anywhere in the grid. SCB installations

have other beneficial effects on the system such as

improvement of the voltage profile, better voltage regulation

(if they were adequately designed), reduction of losses and

reduction or postponement of investments in the transmission

and generation capacity.

The role of SCBs increased recently in the light of blackout

prevention activities, and increasing penetration of distributed

generation, wind farms in particular, which add generation

without addressing the problem of reactive power support.

Moreover, capacitor banks are valuable assets that must be

available for the daily demands of system operation and must

provide reliable operation through abnormal power system

scenarios.

From the protective relaying perspective, however, capacitor

banks are historically considered a relatively low-volume

market, and therefore, did not encourage development of

advanced protective relays dedicated to capacitor banks. Quite

often protection for SCBs is provided by general-purpose

multi-function relays, with only a very few products on the

market offering protection functions specifically tailored to

capacitor bank protection. The utility relay engineer has

generally needed to combine the functionality of multiple

relays and customize their programming to provide the

necessary protective system that will avoid false tripping for

system disturbances and obtain the sensitivity for detecting

capacitor can faults and minimizing damage.

The SCBs are assembled out of individual cans that are

highly repairable. The need for advanced protection functions

is particularily visible when SCBs are operated under

conditions where one or more capacitor cans are temporarily

removed but the bank is returned to service pending

completion of repairs. However, continuous operation and

repairs if needed can be done only if the bank is protected by a

reliable and sensitive relay. This in turn, can be accomplished

by deploying protection principles that are developed

assuming an inherent unbalance in the protected bank.

Fundamentals of Adaptive Protection of Large

Capacitor Banks

Bogdan Kasztenny, Fellow, IEEE, Joe Schaefer, Ed Clark , Member, IEEE

S

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Presently, in many custom applications or even dedicated

capacitor bank protection products, compensation for inherent

unbalance is based on subtracting historical values from the

operating quantities, and thus making the relay respond to

incremental, “delta” signals.

This paper will show that such simplified approaches are not

optimal. Instead this paper derives technically accurate

operating equations for capacitor bank protection that are

derived assuming both inherent capacitor bank and system

unbalance.

It is important that the relay is capable of dynamically

compensating for unbalances between the power system phase

voltages. These differences are constantly changing and may

be on the order of 2 percent or more under normal conditions,

and tens of percent during major system events such as close-

in faults. The presented protection methods allow

compensating simultaneously for the bank inherent unbalance

and system unbalance increasing both sensitivity and security

of protection.

The presented methods also facilitate auto-setting and self-

tuning applications. Auto-setting is an operation of calculating

new accurate relay constants to account for the inherent bank

unbalances following the bank repair, and is performed in

response to the user’s request and under user supervision. Self-

tuning is an operation of constantly self-adjusting the

balancing constants in order to maintain optimum sensitivity of

protection when the bank reactances change slowly in response

to seasonal temperature variations and other conditions. The

self-tuning applications require monitoring the total changes in

the balancing constants in order to detect slow failure modes,

and account for a series of small changes that do not trigger

alarms on their own.

II. CAPACITORS

Protection engineering for shunt capacitor banks requires

knowledge of the capabilities and limitations of the capacitor

unit and associated electrical equipment including individual

capacitor unit, bank switching devices, fuses, location and type

of voltage and current instrument transformers.

A capacitor unit, Figure 1, is the building block of any SCB.

The capacitor unit is made up of individual capacitor elements,

arranged in parallel/series connected groups, within a steel

enclosure. The internal discharge device is a resistor that

reduces the unit residual voltage allowing switching the banks

back after removing it from service. Capacitor units are

available in a variety of voltage ratings (240V to 25kV) and

sizes (2.5kVAr to about 1000kVAr).

The capacitor unit protection is based on the capacitor

element failing in a shorted mode. A failure in the capacitor

element dielectric causes the foils to weld together and short

circuits the other capacitor elements connected in parallel in

the same group, refer to Figure 1. The remaining series

capacitor elements in the unit remain in service with a higher

voltage across each of them and an increased capacitor can

current. If a second element fails the process repeats itself

resulting in an even higher voltage for the remaining elements.

There are generally four types of the capacitor unit designs

to consider.

Internal Discharge

Device

Bushing

Element

Case

Group of

Elements

Fig.1. Capacitor unit.

A. Externally fused capacitors

An individual fuse, externally mounted between the

capacitor unit and the capacitor bank fuse bus, protects each

capacitor unit. The capacitor unit can be designed for a

relatively high voltage because the external fuse is capable of

interrupting a high-voltage fault. However, the kilovar rating

of the individual capacitor unit is usually smaller because a

minimum number of parallel units are required to allow the

bank to remain in service with a capacitor can out of service.

A SCB using fused capacitors is configured using one or more

series groups of parallel-connected capacitor units per phase,

as shown in Figure 2.

phase A

phase B

phase C

Fig.2. Externally fused shunt capacitor bank and capacitor unit.

B. Internally fused capacitors

Each capacitor element is fused inside the capacitor unit. A

“simplified” fuse is a piece of wire sized to melt under the

fault current, and encapsulated in a wrapper able to withstand

the heat produced by the arc during the current interruption.

Upon the capacitor failure, the fuse removes the affected

element only. The other elements, connected in parallel in the

same group, remain in service but with a slightly higher

voltage across them.

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Figure 3 illustrates a typical capacitor bank utilizing

internally fused capacitor units. In general, banks employing

internally fused capacitor units are configured with fewer

capacitor units in parallel, and more series groups of units than

are used in banks employing externally fused capacitor units.

The capacitor units are built larger because the entire unit is

not expected to fail.

phase A

phase B

phase C

Fig.3. Internally fused shunt capacitor bank and capacitor unit.

C. Fuseless capacitors

Fuseless Capacitor Bank designs are typically the most

prevalent designs in modern day. The capacitor units for

fuseless capacitor banks are connected in series strings

between phase and neutral, as shown in Figure 4. The higher

the voltage for the bank, the more capacitor elements in series.

The expected failure of the capacitor unit element is a short

circuit, where the remaining capacitor elements will absorb the

additional voltage. For example, if there are 6 capacitor units

in series and each unit has 8 element groups in series there is a

total of 48 element groups in the string. If one capacitor

element fails, this element is shorted and the voltage across the

remaining elements is 48/47 of the previous value, or about

2% higher. The capacitor bank remains in service; however,

successive failures of elements would aggravate the problem

and eventually lead to the removal of the bank.

The fuseless design is usually applied for applications at or

above 34.5kV where each string has more than 10 elements in

series to ensure the remaining elements do not exceed 110%

rating if an element in the string shorts.

Fig.4. Fuseless shunt capacitor bank and series string.

D. Unfused capacitors

Contrary to the fuseless configuration, where the units are

connected in series, the unfused shunt capacitor bank uses a

series/parallel connection of the capacitor units. The unfused

approach would normally be used on banks below 34.5kV,

where series strings of capacitor units are not practical, or on

higher voltage banks with modest parallel energy. This design

does not require as many capacitor units in parallel as an

externally fused bank.

III. CONFIGURATIONS OF SHUNT CAPACITOR BANKS

Protection of shunt capacitor banks requires an

understanding of the basics of capacitor bank design and

capacitor unit connections. As a general rule, the minimum

number of units connected in parallel is such that isolation of

one capacitor unit in a group should not cause a voltage

unbalance sufficient to place more than 110% of rated voltage

on the remaining capacitors of the group. Equally, the

minimum number of series connected groups is that in which

the complete bypass of the group does not subject the other

capacitors remaining in service to a permanent overvoltage of

more than 110%. The value of 110% is the maximum

continuous overvoltage capability of capacitor units as per

IEEE Std 18-1992.

The maximum number of capacitor units that may be placed

in parallel per group is governed by a different consideration.

When a capacitor bank unit fails, other capacitors in the same

parallel group contain some amount of charge. This charge

will drain off as a high frequency transient current that flows

through the failed capacitor unit. The capacitor can fuse

holder, when used, and the failed capacitor unit must withstand

this discharge transient.

The discharge transient from a large number of paralleled

capacitors can be severe enough to rupture the failed capacitor

unit or explode a fuse holder, which may damage adjacent

units and even cause a major bus fault within the bank. To

minimize the probability of failure of the explosion of the fuse

holder, or rupture of the capacitor case, or both, the standards

impose a limit to the total maximum energy stored in a

parallel-connected group to 4650 kVAr. In order not to violate

this limit, more capacitor groups of a lower voltage rating

connected in series (with fewer units in parallel per group)

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may be a suitable solution. However, this may reduce

sensitivity of applied unbalance detection schemes. Splitting

the bank into two sections as a double wye may be the

preferred solution, and may allow for better unbalance

detection scheme.

Two prevalent designs of SCBs are the externally fused

bank and the fuseless bank. There are advantages to each

design.

Externally fused banks typically have a higher unbalance

current when a unit fails which is used to operate a fused

disconnect device. This design typically results in a simpler

bank configuration and provides an easy method for field

identification of a failed unit. A fused design also requires less

sensitive unbalance protection since the fuse is the principal

method used for isolating a can failure. However, this style of

bank has a higher initial cost and usually higher maintenance

costs. Since the fused element is exposed to the environment,

the fuses become less reliable and require more maintenance to

ensure correct operation. As a result, fuseless capacitor banks

have become increasingly popular. Elimination of the fused

connection results in a lower initial cost, reduced maintenance

costs, smaller bank footprint, and fewer losses. Also, this bank

design typically makes catastrophic can rupture less likely

since the discharge energy of a failed element will be small.

However, the fuseless bank design has two main

disadvantages that increase the emphasis on requiring sensitive

relaying protection. One, the elimination of the external fuse

means that visual indication of the failed capacitor has been

lost. In addition, an element failure results in an overvoltage

condition of the remaining elements, stressing them. Without

a fuse as a means of isolating the failed can, the protective

relay must now be sensitive enough to detect a failed element

and alarm before additional elements fail causing a higher

overvoltage condition on the remaining units. Because of

these two factors, it is especially important to utilize a

sensitive protective relay which can correctly isolate a bank for

a failed element. Also, the use of faulted phase identification

assists field personnel in locating a failed capacitor can

without having to test the entire bank.

The optimum connection for a SCB depends on the best

utilization of the available voltage ratings of capacitor units,

fusing, and protective relaying. Virtually all HV and EHV

banks are connected in one of the two wye configurations

listed below [1,2]. Distribution capacitor banks, however, may

be connected in wye or delta. Some banks may use an H

configuration on each of the phases with a current transformer

in the connecting branch to detect the unbalance.

A. Grounded wye-connected banks

Grounded wye capacitor banks are composed of series and

parallel-connected capacitor units per phase and provide a low

impedance path to ground. This offers some protection from

surge overvoltages and transient overcurrents.

When a capacitor bank becomes too large, making the

parallel energy of a series group too high for the capacitor

units or fuses (above 4650kVAr), the bank may be split into

two wye sections. The characteristics of the grounded double

wye are similar to a grounded single wye bank. The two

neutrals should be directly connected with a single path to

ground.

The double wye design facilitates better protection methods.

Even with inherent unbalances the two banks will respond

similarly to system events, and therefore, methods based on

comparing one split-phase versus the other are more sensitive

and less prone to system events (phase current balance

technique, for example).

B. Ungrounded wye-connected banks

Ungrounded wye banks do not permit zero sequence

currents, third harmonic currents, or large capacitor discharge

currents during system ground faults (phase-to-phase faults

may still occur and will result in large discharge currents).

Another advantage is that overvoltages appearing at the CT

secondaries are not as high as in the case of grounded banks.

However, the neutral should be insulated for full line voltage

because it is momentarily at phase potential when the bank is

switched or when one capacitor unit fails in a bank configured

with a single group of units.

C. Delta-connected banks

Delta-connected banks are generally used only at

distribution voltages and are configured with a single series

group of capacitors rated at line-to-line voltage. With only one

series group of units no overvoltage occurs across the

remaining capacitor units from the isolation of a faulted

capacitor unit.

D. H-configuration

Some larger banks use an H configuration in each phase

with a current transformer connected between the two legs to

compare the current down each leg. As long as all capacitors

are balanced, no current will flow through the current

transformer. If a capacitor fuse operates, some current will

flow through the current transformer. This bridge connection

facilitates very sensitive protection. The H arrangement is used

on large banks with many capacitor units in parallel.

IV. SENSITIVE CAPACITOR BANK PROTECTION METHODS

A. Voltage differential (87V)

With reference to Figure 5, this function is based on a

voltage divider principle – a healthy capacitor string has a

constant and known division ratio between its full tap

(typically the bus voltage) and an auxiliary tap used by the

protection. The principle could be used on both grounded

(Figure 5a) and ungrounded (Figure 5b) banks. In the latter

case the neutral point voltage (VX) must be measured by the

relay, and used to derive the voltage across the string.

The function uses the following operating signal:

AAAAOP VkVV 21)( ⋅−= (1a)

for grounded banks, and

( )121)( −⋅+⋅−= AXAAAAOP kVVkVV (1b)

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for ungrounded banks., where kA is a division ratio for the A-

phase of the bank.

Identical relations apply to phases B and C.

Note that equations (1) can be implemented using either

phasors or magnitudes. During no-fault conditions and under

small bank unbalances caused by internal bank failures, the

two voltages will be almost in phase, suggesting the phasors

and magnitude versions would yield similar results. However,

the function is set very sensitive and given possible angular

errors of the used VTs, there will be differences in

performance between the two possible versions. The

performance depends on the type of security measures used to

deal with errors of instrument transformers. More information

is provided in one of the following sections.

Typically, the method is used on grounded banks and

equation (1a) is used. In theory, the algorithm could be applied

on ungrounded banks using equation (1b), but it requires both

the neutral voltage and the tap voltages to be measured. Such

arrangements may not be practical (the tap voltages not

measured on ungrounded banks). If the tap voltages are

measured, one could apply multiple overlapping protection

zones to the ungrounded bank as long as the applied relay(-s)

support the required number of inputs and associated

protection functions. Specifically, equation (1b) can be used

for voltage differential; and two neutral voltage unbalance

protection elements can be used – one balancing the bus

voltages with the neutral voltage, and another balancing the tap

voltages against the neutral voltage.

V2A

V1A

ABC(a)

V2A

V1A

ABC(b)

VX

Fig.5. Voltage differential application to grounded (a) and ungrounded (b)

banks.

Equations (1) apply to primary voltages, and as such they

incorporate the voltage-dividing ratio of the capacitor, but

ignore the ratios of applied instrument transformers. In

secondary voltages, the operating voltage is:

A

VT

VTAAAOP V

n

nkVV 2

1

21)( ⋅⋅−= (1c)

for grounded banks, and

( )11

2

1

21)( −⋅⋅+⋅⋅−= A

VT

VTXXA

VT

VTAAAOP k

n

nVV

n

nkVV (1d)

for ungrounded banks, where the operating signal is in

secondary volts of the bus VT, and the nVT1, nVT2 and nVTX

stand for ratios of the bus, tap, and neutral voltage

transformers, respectively.

Normally the VT ratios are selected so that the secondary

voltages for the bus and tap voltages are similar under nominal

system voltage. This leads to the effective matching factor for

the secondary voltages being close to unity:

11

2 ≈⋅VT

VTA

n

nk (1e)

Voltage-based capacitor protection functions are set

sensitive. Given the format of equations (1) both the bus and

tap voltages shall be measured accurately in order to gain

sensitivity of protection. As a result the VT ratios shall be

selected so that the resultant secondary voltages fall in the

region of maximum relay accuracy, and the two VTs work

within their maximum class accuracy under nominal system

voltage. The latter is ensured for the bus voltage; selection of

the VT for the tap voltage shall be done carefully to minimize

VT and relay errors for the tap voltage. Relay setting range for

the ratio-matching factor is another condition that may limit

selection of this VT ratio.

The following characteristics apply to the voltage

differential function [3]:

• The element shall support individual per-phase settings to

cope with different unbalances between the phases

(repairs and shorted units).

• The element is capable of indicating the affected phase,

and potentially the number of faulted capacitor elements,

to aid troubleshooting and repairs of the bank.

• The function shall apply appropriate security measures for

sensitive but secure operation: appropriate restraint signal

could be developed to accompany the operating signal (1).

Setting range shall allow disabling the restraint if desired

so.

• Several independent pickup thresholds shall be provided

for alarming and tripping.

• The voltage matching coefficients (k) shall be individually

set-able per phase.

• Both auto-setting and self-tuning applications of this

method are possible. Provision could be made to calculate

the matching factors k automatically under manual

supervision of the user, either locally or remotely (auto-

setting), or calculate the factor constantly in a slow

adjusting loop (self-tuning).

The process of finding the constant balancing a given phase

of protection is based on the following simple equation:

A

AA

V

Vk

2

1ˆ = (under no-fault conditions) (2)

The voltage differential method can be used in a number of

configurations as long as the relay allows wide range of ratio

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matching for the compared voltages: tap voltage can be

compared with the bus voltage; two taps can be compared on

the same bank; two taps can be compared between two parallel

banks, etc

.

B. Compensated bank neutral voltage unbalance (591U)

With reference to Figure 6 this function is applicable to

ungrounded banks, and is based on the Kirchhoff’s currents

law for the neutral node of the bank:

0=−

+−

+−

C

XC

B

XB

A

XA

Z

VV

Z

VV

Z

VV (3a)

The above expression can be rearranged as follows:

0111

=+++

++⋅−

C

C

B

B

A

A

CBA

XZ

V

Z

V

Z

V

ZZZV (3b)

and further to an equivalent form of:

0111

=−+−++++

++⋅−

A

C

C

C

A

B

B

B

A

C

A

B

A

A

CBA

XZ

V

Z

V

Z

V

Z

V

Z

V

Z

V

Z

V

ZZZV

(3c)

which is identical with:

( ) 011111111

=

−⋅+

−⋅+++⋅+

++⋅−

AC

C

AB

BCBA

ACBA

XZZ

VZZ

VVVVZZZZ

V (3d)

Multiplying both sides by AZ− and substituting the sum of the

phase voltages by 03 V⋅

01131 0 =

−⋅+

−⋅+⋅−

++⋅

C

AC

B

AB

C

A

B

AX

Z

ZV

Z

ZVV

Z

Z

Z

ZV

(3e)

Introducing the following matching k-values to reflect the

inherent bank unbalance:

B

A

B

AAB

X

X

Z

Zk ≈= ,

C

A

C

AAC

X

X

Z

Zk ≈= (4)

allows re-writing the balance equation (3e) into the

following operating signal:

( ) ( ) ( )ACCABBxACABOP kVkVVVkkV −⋅+−⋅+⋅−⋅++= 11313

10

(5)

Equation (5) involves phasors, not magnitudes, i.e. the

vectorial sum of the voltages is created by the protection

function implementing the method.

Note that the ratios of the capacitor impedances between

phase A and the two other phases are close to unity, and

therefore the correcting factors for the B and C-phase voltages

are small numbers, while the coefficient in front of the VX

voltage is close to 3.

Equation (5) while following relations (4) is a proper neutral

overvoltage function compensated for both the system

unbalance (V0), and the bank unbalance (kAB, kAC). To

understand it better assume the bank is perfectly balanced (kAB

= 1, kAC = 1). If so, the precise operating equation takes a

familiar simplified form [1]:

0VVV XOP −= (6)

Equation (5) identifies the source of the inherent bank

unbalance, and therefore allows for proper compensation. In

addition, this key equation allows analyzing the impact of

imperfect compensation and/or errors of instrument

transformers on sensitivity of protection as explained later in

this paper.

Equation (5) can be implemented using either derived

neutral component in the bus voltages (vectorial sum of the

phase voltages calculated by the relay), or directly measured

neutral voltage component (open-delta VT voltage). Slightly

different errors would occur in these two approaches.

When deriving the 03 V⋅ internally the relay is presented

with near-nominal voltages under internal failures that require

high protection sensitivity, typically has maximum accuracy of

voltage measurement under such conditions, and calculates the

vectorial voltage sum with relatively high accuracy.

When measuring the 03 V⋅ directly the relay is presented

with a very small signal under internal failures that require

high protection sensitivity. In order to keep high accuracy a

high-sensitivity voltage relay input shall be used. At the same

time, this voltage could reach as high as system nominal

voltage during external faults. Therefore, the input range shall

be high enough to measure this voltage correctly and balance it

accurately against the VX signal.

The VX voltage, in turn, is relatively small under internal

failures that require high protection sensitivity. Therefore

either the relay shall be equipped with a high-sensitivity

voltage input, or the VT ratio is selected to create this signal

and improve measuring accuracy of this signal, or both. In any

case, the ratio must be selected such as the input voltage does

not exceed the conversion range of a given relay. Sometimes

this requirement may be relaxed allowing saturation of the

relay input – the function shall be blocked in this case under

external faults either by time delay or explicit logic in order to

cope with the spurious unbalance caused by saturation of the

VX measurement. In any case, one shall observe the thermal

withstand rating of the relay input when selecting relatively

low-ratio VT for the measurement of the VX signal.

When written for secondary voltages the key operating

equation becomes:

• When measuring the 03 V⋅ internally and expressing the

operating signal in secondary volts of the bus voltage:

( ) ( ) ( )ACCABBxACAB

VT

VTXOP kVkVVVkk

n

nV −⋅+−⋅+⋅−⋅++= 1131

3

10

(7a)

• When measuring the 03 V⋅ from an open-delta VT and

expressing the operating signal in secondary volts of the

bus voltage:

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( ) ( ) ( )ACCABB

VT

VTxACAB

VT

VTXOP kVkVV

n

nVkk

n

nV −⋅+−⋅+⋅−⋅++= 1131

3

10

0 (7b)

VA - VX

VA

ABC

VX

IC

IB

IA

IA + I

B + I

C = 0

Fig.6. Compensated bank neutral overvoltage application.

The following characteristics apply to the compensated bank

neutral voltage unbalance function [3]:

• The single element function does not indicate explicitly

the effected phase. It could, however, aid troubleshooting

and repairs by reporting the k-factors (pre-fault and fault

values).



could be used with the operating signal (5). Disabling the

restraint should be allowed if desired so.

• Several independent pickup thresholds shall be provided

for alarming and tripping.

• The inherent bank unbalance constants (k-values) shall be

settable.

• Both auto-setting and self-tuning applications are possible

as long as the neutral point voltage is non-zero and is

measured with adequate accuracy. Provision could be

made to calculate factors k automatically under manual

supervision of the user, either locally or remotely (auto-

setting), or continuously in a slow adjusting loop (self-

tuning).

The process of finding the two unknown constants is based

on the following principle. When the bank is healthy, equation

(5) is perfectly balanced, and therefore it can be zero-ed out.

Writing the real and imaginary parts of the equation separately

one obtains two equations for two unknowns:

( ) ( ) ( ) 01131Re 0 =−⋅+−⋅+⋅−⋅++ ACCABBXACAB kVkVVVkk (8a)

( ) ( ) ( ) 01131Im 0 =−⋅+−⋅+⋅−⋅++ ACCABBXACAB kVkVVVkk (8b)

The above is now solved for the two unknowns kAB and kAC

while treating the involved voltages as knowns (the k-values

are treated as real numbers per equations (4)). The method

works as long as the Vx voltage is above the measuring error

level. The procedure does not call for the system to be

unbalanced (V0 can be zero) as the unknowns (k) do not appear

as multipliers for the V0 value in equations (8).

C. Phase current balance (60P)

With reference to Figure 7, this function is based on the

balance between phase currents of the two parallel banks, and

is applicable to both grounded and ungrounded arrangements.

Higher sensitivity can be achieved when using a window CT

(compared with the two individual CTs summated

electrically). With the two banks slightly different, a

circulating current flows, and shall be compensated for in

order to increase sensitivity of the function. This protection

element is founded on the following theory.

Both parallel banks work under identical voltage, and

therefore:

A

VBANK

IA1

IA2

IA

IDIF(A)

IA

IA1

IA2

IA = I

A1 + I

A2

window CT

grounded or

ungrounded

Fig.7. Phase current balance application.

AA

AAABA1KADIF

ZZ

ZZVI

21

21)()( ⋅

−= (9a)

AA

AA

ABA1KAZZ

ZZVI

21

21

)( ⋅

+= (9b)

Utilizing the fact the voltage is the same in expressions (9a)

and (9b) one writes:

AA

AAA

AA

AAADIFABA1K

ZZ

ZZI

ZZ

ZZIV

21

21

21

21)()( +

⋅⋅=

−⋅

⋅= (9c)

creating the following balance equation:

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021

21

21

21)( =

+⋅

−−⋅

AA

AAA

AA

AAADIF

ZZ

ZZI

ZZ

ZZI (9d)

Dividing both sides by the coefficient next to the differential

current gives:

021

21)( =

+−

−AA

AAAADIF

ZZ

ZZII (9e)

Introducing the inherent unbalance compensating factor, k:

AA

AA

AA

AAA

XX

XX

ZZ

ZZk

21

21

21

21

+−

≈+−

= (10)

yields the following operating signal of the phase current

balance protection:

AAADIFAOP IkII ⋅−= )()( (11)

Identical relations apply to phases B and C. The operating signal (11) implements proper compensation

for the inherent unbalance of the bank. The equation identifies

that the error is proportional to the amount of the total phase

current (IA) and the difference between the impedances of the

two banks (kA). When not compensated, the straight

differential current would display a non-zero value “leaking”

from the phase current. Subtracting the historical value of such

leakage current, often applied today, improves sensitivity but it

is not a correct way of compensating this functions. More

discussion follows in section 5 of this paper.

Note that equation (11) is a vectorial difference between the

two signals. However, as the k-factor is a real number (very

small or zero imaginary part), the two currents are in phase

and their magnitudes, not phasors, could be used as well.

Typically CTs used to measure the total phase current and

the differential current would have drastically different ratios.

The differential CT might have much lower ratio in order to

increase magnitude of the secondary current under internal

bank failures requiring high sensitivity of protection. During

external fault conditions, the differential current remains low

further promoting the usage of low-ratio CT. On the relay side,

a sensitive ground current input shall be used for better

sensitivity and accuracy.

When written in secondary terms, the key equation (11)

when expressed in secondary amperes of the differential CT

becomes:

A

DIFCT

CTAADIFAOP I

n

nkII ⋅⋅−= )()( (12)

The following characteristics apply to the phase current

balance function [3]:

• The element shall support individual per-phase settings.

• The function indicates the effected phase, as well as

reports the change in the current division ratio, k (pre-fault

and fault values) to aid troubleshooting and repairs of the

bank.

• The element shall apply appropriate security measures for


could be provided to accompany the operating signal (11).

Disabling the restraint shall be possible if desired so.

• Several independent thresholds shall be provided per

phase for alarming and tripping.

• The current dividers (k) are individually set per phase.

• Both auto-setting and self-tuning applications of this

method are possible. Provision could be made to calculate

factors k automatically under manual supervision of the

user, either locally or remotely (auto-setting), or

constantly in a slow adjusting loop (self-setting).

The process of finding the balancing constants for each

phase of protection is based on the following simple equation:

A

ADIF

AI

Ik

)(ˆ = (under no-fault conditions) (13)

D 1eutral current balance (601)

With reference to Figure 8, this function is based on the

balance between interconnected neutral currents of two

parallel banks, and is applicable to both grounded and

ungrounded installations. A window CT measuring the

vectorial difference between the two neutral currents allows

for better accuracy/sensitivity.

With the two banks possibly slightly different, a circulating

zero-sequence current may be present and shall be

compensated for in order to increase sensitivity of the

function.

Proper inherent unbalance compensation is founded on the

following theory.

Both parallel banks work under identical voltages, therefore

their phase currents are driven by the individual admittances in

each phase of each bank:

( ) 11 AXAA YVVI ⋅−= ; ( ) 22 AXAA YVVI ⋅−= (14a)

( ) 11 BXBB YVVI ⋅−= ; ( ) 22 BXBB YVVI ⋅−= (14b)

( ) 11 CXCC YVVI ⋅−= ; ( ) 22 CXCC YVVI ⋅−= (14c)

The sum of the two neutral currents can be derived from the

above equations:

( ) ( ) ( ) 1111111 CXCBXBAXACBA1 YVVYVVYVVIIII ⋅−+⋅−+⋅−=++= (14d)

( ) ( ) ( ) 2222222 CXCBXBAXACBA1 YVVYVVYVVIIII ⋅−+⋅−+⋅−=++= (14e)

The differential current is a vectorial difference between the

two currents. By subtracting (14e) from (14d) one obtains:

( ) ( ) ( ) ( ) ( ) ( )21212121 CCXCBBXBAAXA11DIF YYVVYYVVYYVVIII −⋅−+−⋅−+−⋅−=−=

(14f)

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At the same time the total currents in each phase are driven

by the total admittance of the two banks in each phase:

( ) ( )2121 AAXAAAA YYVVIII +⋅−=+= (15a)

( ) ( )2121 BBXBBBB YYVVIII +⋅−=+= (15b)

( ) ( )2121 CCXCCCC YYVVIII +⋅−=+= (15c)

A

VBANK(0)

IA1

IA2

IA

IA

IA1

IA2

IDIF

window CT

grounded or

ungrounded

IN1

IN2

IN = I

A + I

B + I

C

IN = I

A1 + I

B1 + I

C1+...

+... IA2 + I

B2 + I

C2

Fig.8. Neutral current balance application.

Inserting equations (15) into equations (14) allows

eliminating the voltages and derive the all-current balance

equation for the two banks:

21

21

21

21

21

21

CC

CCC

BB

BBB

AA

AAADIF

YY

YYI

YY

YYI

YY

YYII

+−

⋅++−

⋅++−

⋅= (16)

Labeling:

21

21

AA

AAA

YY

YYk

+−

= ;

21

21

BB

BBB

YY

YYk

+−

= ;

21

21

CC

CCC

YY

YYk

+−

= (17)

One gets the following operating equation balancing the

protected bank:

( )CCBBAADIFOP IkIkIkII ⋅+⋅+⋅−= (18)

When the banks are identical, i.e. phases A are equal, phases

B are equal and phases C are equal, the operating equation

(18) simplifies to a straight overcurrent condition for the

measured neutral differential current.

It is justified to assume the balancing constants, k, are real

numbers. Still, this leaves the balance equation (18) with 3

unknowns. These unknowns can be calculated based on

several measurements taken under unbalanced conditions.

Alternatively, equation (18) may be re-written from phase

coordinates, into sequence components:

( )221100 IkIkIkII DIFOP ⋅+⋅+⋅−= (19)

It is justified to assume that the positive-sequence current

would leak into the operating quantity more considerably

compared with the zero- and negative-sequence components.

Therefore only the positive-sequence leakage can be

eliminated to improve sensitivity. This approach yields a

slightly simplified form of the mathematically accurate

equations (18) and (19):

11 IkII DIFOP ⋅−= (20)

With one unknown balancing factor (k1) the auto-setting or

self-tuning procedures can be implemented simply as:

1

1ˆ

I

Ik DIF= (under no-fault conditions) (21)

Unlike in previous methods, this compensating coefficient

may be a complex number.

Operating signal (18) or (19) implements proper

compensation for the inherent unbalance of the bank. Equation

(20) is a good practical approximation.

Equation (18) holds for primary currents, when applied to

secondary amperes, it takes the following form:

( )CCBBAA

DIFCT

CTDIFOP IkIkIk

n

nII ⋅+⋅+⋅⋅−= (22)

Typically the differential CT would be of lower ratio in

order to increase the level of the secondary current for internal

failures that call for increased sensitivity of protection. During

external faults, the differential current will be increased but not

dramatically.

The following characteristics apply to the neutral current

balance function [3]:

• The single element function does not indicate explicitly

the effected phase.


sensitive but secure operation (provision for a restraint

signal).

• Several independent thresholds shall be provided that can

be freely used for alarming and tripping.

• The positive-sequence compensating factor k1 shall be a

setting.

• Provision could be made to calculate the k-factor

automatically under manual supervision of the user, either

locally or remotely (auto-setting), or continuously in a

slow adjusting loop (self-tuning).

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(

3

d

)

V. SENSITIVITY TO INTERNAL BANK FAILURES

The key equations defining the outlined capacitor bank

protection methods ((1), (5), (11) and (18)) allow not only

proper compensation for the inherent bank unbalance, but also

facilitate analysis of sensitivity of protection.

Each of the four methods as described in this paper is

founded on a balance equation that assumes:

First, that the bank is intact in terms of experiencing a

ground or phase fault.

Second, that the inherent unbalance between the capacitor

phases does not change.

A ground or phase fault violating the first assumption results

in severe unbalance in the operating equations, and leads to

protection operation as expected. This aspect of operation is

backed-up by overcurrent protection, and therefore is of

secondary importance.

A short or open in a single or several cans violates the

second assumption, causes a minor unbalance in the operating

equations, and results in operation of protection set sensitive

enough given the size of the internal failure.

This latter way of responding to internal failures is critical

for analysis of protection sensitivity. For this purpose one

could assume nominal system voltages and resulting currents,

and use the operating equations to determine the amount of the

operating signals in response to any given unbalance in the

bank.

A. Sensitivity of the voltage differential function

For simplicity let us focus on the application to grounded

banks. Neglecting the phase index, the operating signal in this

method is (equation (1a)):

21 VkVV SETOP ⋅−=

The actual voltage-dividing ratio during internal failures of

the bank is:

TAPBUS

G1DTAP

G1DTAP

TAPBUS

G1DTAP

G1DTAPTAPBUSFAIL

C

C

Z

Z

Z

ZZk

−

−

−

−

−

−− +=+=+

= 11 (23a)

The tap voltage during the failure is:

FAILkVV

112 ⋅= (23b)

and the operating signal becomes:

FAIL

SETOP

k

kVV −⋅= 11 (23c)

As a percentage of the full bus voltage the operating signal

is:

%10011

⋅−=FAIL

SETOP

k

k

V

V (24d)

Equation (24d) yields a proportional relationship between

kFAIL and the operating voltage: a change by 1% in the k-value,

yields an extra 1% of nominal in the operating signal.

What is more interesting, however, is the relation between

changes in the bus-tap and tap-ground capacitances and the

increase in the operating voltage. Given equation (23a) one

can write:

%%%% G1DTAPTAPBUSFAILOP CCkV −− ∆=∆=∆=∆ (25)

The above signifies that a 1% change in either of the bus-to-

tap or tap-to-ground capacitances would yield 1% of bus

nominal in the operating voltage.

Depending on the serial/parallel arrangement of the cans, it

will take a certain amount of shorted/opened cans to cause a

single percentage change in the capacitance and an equivalent

increase in the operating voltage. The final assessment of

sensitivity has to take into account the actual arrangement of

the capacitor bank.

An interesting question is the optimum location of the tap.

Regardless of the number of parallel cans, the longer the

string, the higher the impedance. If so a single can failure

would cause a smaller percentage change in the overall

impedance/capacitance. For best sensitivity both the portions

(bus-tap and tap-ground) shall be kept as short as possible as

measured in the number of cans. In reality, the number of cans

is not a variable. Within this restriction, half of the total length

is the smallest possible length.

Therefore the exact middle position of the tap is optimum

from the point of view of sensitivity. Under the mid-tap both

the portions (bus-tap and tap-ground) are protected with the

same sensitivity measured in the number of cans.

Often, the tap is installed below the mid-point in order to

apply lower voltage VTs. This creates a classical trade-off

between optimum performance and low cost of installation.

B. Sensitivity of the compensated bank neutral voltage

unbalance function

The analysis shall start with the full operating equation (5):


10

in which the following assumptions can be made:

- The 1-k terms can be neglected for simplicity.

- The system zero-sequence voltage can be considered zero

(the system is practically always strong enough to

maintain the balance at the bus despite few cans affected

within the bank itself).

This leads to the following relationship:

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( ) xACABOP VkkV ⋅++= 13

1 (26a)

As both the k-values are close to unity, the above simplifies

to:

xOP VV ≈ (26b)

Equation (3e) helps calculating the amount of the neutral

point voltage. Assuming system zero-sequence voltage nil, the

equation can be re-arranged to calculate the value of Vx:

( ) ( )ACAB

ACCABBx

kk

kVkVV

++−+−

=1

11 (27a)

Assuming a balanced bus voltage:

02 1201,, ∠=⋅=⋅= aVaVVaV ACAB (27b)

One simplifies further:

( ) ( )ACAB

ACABAx

kk

kakaVV

++−⋅+−⋅

⋅=1

112

(27c)

Observing the k-values are real numbers close to unity and

using properties of the a-operand yields the following:

( ) ( )

ACAB

ABACACAB

A

x

kk

kkjkk

V

V

++

−++−=

1

2

3

2

11

(27d)

Because the actual operating equation (5) compensates for

the inherent bank unbalance, it is further justified to assume

the ratios of the impedances to be a perfect unity (say kAB), and

treat the other ratio as a variable (kAC correspondingly):

k

k

k

kjkj

V

V

A

x

+−

=+

+−−=

2

1

2

2

3

2

1

2

3

2

1

(27e)

The above equations means that only 1/3rd of the percentage

change in the ratio of impedances between any two phases will

be seen as a percentage of nominal bus voltage:

%%%3

1

3

1CkVOP ∆=∆=∆ (28)

For example it will take 3% in the drop of the phase A

impedance, to see 1% of bus nominal voltage as the Vx signal,

and thus the operating signal of the function.

The operating signal has an arbitrary factor 1/3rd to comply

with the common understanding of this method (equation (6)).

Using microprocessor-based relay technology this scaling is

not important as any scaling can be handled accurately. What

is important is the 1:3 ratio between the measured neutral point

voltage and changes in the capacitor impedance.

This reinforces using low-ratio VTs for measuring the

neutral-point voltage.

Relation (28) can also be used to calculate the required ratio.

For example, assuming target sensitivity for the function, one

calculates the effective operating signal as percentage of the

bus voltage. Using relay accuracy claim, one determines the

minimum secondary voltage that is required for the proper

operation of the relay. Combining the two requirements allows

calculating the ratio for the VT:

)(

%

33 MI1SEC

BUSVTX

V

VCn

⋅⋅

⋅∆= (29)

For example, with the target sensitivity of 1% of impedance

change on a 345kV bus, and the minimum relay voltage of

0.5V secondary, the maximum VT ratio is:

13285.033

34501.0=

⋅⋅

⋅=

V

kVnVTX

With this ratio, under SLG fault on the bus, the secondary

voltage would be 150V. This is well within the range of

modern relays. Assuming a relay conversion range of

260VRMS, the ratio can be lowered to 1328*150/260 = 766,

yielding the operating signal of 0.87V secondary at 1% change

in the capacitor impedance.

C. Sensitivity of the phase current balance function

Neglecting the phase index, the operating signal of this

method is (equation (11)):

IkII SETDIFOP ⋅−=

It is justified to assume the total capacitor current does not

change in response to the internal failure of limited size,

therefore the operating current as a percentage of the total

capacitor current equals the percentage change in the k-value:

%100

1k

I

IOP ∆=∆

(30a)

For example, 1% of change in the k-factor yields 1% of the

full current as measured by the split-phase CT.

Next step is to understand the impact of

impedance/capacitance changes on the changes in the k-factor.

From equation (10):

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21

21

XX

XXk

+−

=

Observing that the two reactances are very similar, one

obtains:

%%%2

1

2

1CXk ∆=∆=∆ (30b)

Equations (30) mean that for each % of change in the

impedance/capacitance of one of the parallel banks, there will

be increase in the differential current by 0.5% of the total bank

current.

Again, the above observation may be used to select the ratio

of the split-phase CT: the target accuracy allows calculating

the minimum primary operating signal; the minimum relay

sensitivity allows determining the minimum accurately

measured secondary signal; the ratio dictates the maximum CT

ratio that can be applied in this case:

`

)(

%

2 MI1SEC

1OMDIF

I

ICn

⋅⋅∆

= (31)

D Sensitivity of the neutral current balance

It is worth noticing that this method is a derivative of the

phase current balance approach (60P), and as such it has

identical sensitivity.

The balance equations for all three phases per the 60P

protection principle are:

021

21)( =

+−

−AA

AAAADIF

ZZ

ZZII (32a)

021

21)( =

+−

−BB

BBBBDIF

ZZ

ZZII (32b)

021

21)( =

+−

−CC

CCCCDIF

ZZ

ZZII (32c)

Observing that in the 60P method:

21)( AAADIF III −= ,

21)( BBBDIF III −= , (33a)

21)( CCCDIF III −=

While in the 60N method:

( ) ( ) K=++−++=−= 22211121 CBACBA11DIF IIIIIIIII

( ) ( ) ( )212121 CCBBAA IIIIII −+−+−=K (33b)

allows one to insert (33a) into (33b) and obtain:

)()()( CDIFBDIFADIFDIF IIII ++= (33c)

Now inserting (32a-c) into (33c) yields:

CC

CCC

BB

BBB

AA

AAADIF

ZZ

ZZI

ZZ

ZZI

ZZ

ZZII

21

21

21

21

21

21

+−

++−

++−

= (34a)

Observing the relation between the impedance and

admittance one can re-write the above into:

021

21

21

21

21

21 =+−

−+−

−+−

−CC

CCC

BB

BBB

AA

AAADIF

YY

YYI

YY

YYI

YY

YYII (34b)

Which is precisely the 60N balance equation as derived in

section 4.4 (equation (18)).

The above proves, that neglecting CT and relay accuracy the

60P and 60N functions have identical sensitivity. Specifically,

per each percent of change in the impedance/capacitance of

one of the banks, the differential CT would see an increase of

0.5% of the total bank current.

The phase variant of the method (60P) is easier to

compensate for the inherent bank unbalance. The neutral

variant of the method (60N) requires 1 CT and relay input,

compared with 3 sets for the phase version (60P). If applied

concurrently on one relay, the two functions may be treated as

partially redundant using different CTs and relay inputs.

VI. SENSITIVITY TO INSTRUMENTATION ERRORS

This section analyses impact of finite accuracy of Instrument

Transformers (ITs) and the relay on the four protection

methods.

It is important to notice that errors of instrument

transformers and the relay can be accounted for when tuning

the coefficients. If the tuning coefficients (k) are implemented

as real numbers, the magnitude errors can be eliminated, and

the impact of angular errors could be reduced. If the

coefficients are implemented as complex numbers, both

magnitude and angle errors can be accounted for.

However, the IT and relay errors will slightly change with

the magnitude of the signal and /or other factors such as

residual flux or temperature. Even if tuned at one particular

operating point, the method will show some errors at different

operating point due to the IT and relay inaccuracies. It is

important to realize, though, that these errors occur regardless

of the protection principle. By compensating for bank inherent

unbalance, and partially for IT and relay errors, the methods

presented in this paper are already less susceptible to

instrumentation errors. Detailed analysis follows.

Magnitude and angle errors of ITs and the relay can be

modeled as a complex multiplier applied for the analysis

purposes to the ideal transformation ratio of a given signal. For

example, a negative 0.5% magnitude error combined with a

0.3deg angle error can be modeled as:

( ) 03.0005.01, ∠−=⋅= bbnn IDEALACTUAL

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A. Impact of instrumentation errors on the voltage differential

function

For simplicity consider applications on grounded banks. The

operating signal in secondary volts is (equation (1c)):

A

VT

VTAAAOP V

n

nkVV 2

1

21)( ⋅⋅−=

Now assume that the equation was perfectly balanced

making the operating signal above a perfect zero, but one of

the VTs, say the tap VT (#2), works with an error of b. If so,

the operating signal becomes non-zero:

A

VT

VTAAAOP V

n

nbkVV 2

1

21)( ⋅⋅⋅−= (35a)

Assuming a perfect balance, equation (1c) can be solved for

the tap voltage:

AA

VT

VTAA

VT

VTAA VV

n

nkV

n

nkV 12

1

22

1

210 =⋅⋅→⋅⋅−= (35b)

Substituting (35b) into (35a) yields:

bVVbVV AAAAOP −⋅=⋅−= 1111)( (35c)

Or expressing the error as a proportion of the bus voltage:

%10011

)( ⋅−= bV

V

A

AOP (35d)

For example, with negative 0.5% magnitude error and

0.3deg angle error, the spurious operating voltage would read:

( ) %72.0%1003.0005.011 0

1

)( =⋅∠−−=A

AOP

V

V

The error is at the level that encroaches on the targeted

sensitivity settings. Note, however, that this method would

accommodate some of the error in the matching factor k,

leaving only a small variable fraction of this error unaccounted

for. Assuming 0.15% magnitude error for both the ITs and the

relay, and 0.2deg angle error gives 0.38% of bus voltage read

as a spurious operating signal.

It is important to understand that the method compares two

voltages. Both errors will play a role. They may cancel

mutually, or add up.

B. Impact of instrumentation errors on the compensated bank

neutral voltage unbalance function

The approach illustrated in the previous subsection applies

to this protection method as well. Examining the key operating

equation for secondary voltages (7) leads to a conclusion that

during normal system conditions four voltage components,

each of a very small or zero magnitude, are added as vectors:

neutral point bank voltage, system neutral voltage and two

phase voltages – the latter two with very small multipliers.

These four voltages are delivered by four VTs: (A,B,C,X) in

case of implementation (7a) with internally derived system

zero-sequence voltage; and (0,X,B,C) in case of

implementation (7b) with externally supplied system zero-

sequence voltage. For the purpose of error analysis, each of the

VTs shall be represented with its own ratio, potentially slightly

different than the nominal value.

When deriving the system zero-sequence voltage internally

the three phase voltages are added as vectors – small errors

could yield a relatively significant spurious system zero-

sequence voltage. The following derivative of equation (7a) is

useful:

( ) CVTACBVTABAVTxACABVTX

VT

OP VnkVnkVnVkknn

V ⋅⋅−⋅⋅−⋅−⋅++⋅⋅

= 13

1 (36a)

For the purpose of error analysis, the k-factors can be

assumed to be unity, and therefore:

CVTBVTAVTxVTX

VT

OP VnVnVnVnn

V ⋅−⋅−⋅−⋅⋅⋅

= 33

1 (36b)

Assume the above is perfectly balanced and an error in the

measurement of the bank neutral voltage is added, represented

by the complex number b:

CVTBVTAVTxVTX

VT

OP VnVnVnVbnn

V ⋅−⋅−⋅−⋅⋅⋅⋅

= 33

1 (36b)

From equation (36b):

CVTBVTAVTxVTX VnVnVnVn ⋅+⋅+⋅=⋅⋅3 (36c)

Substituting (36c) into (36b) gives:

( ) ( ) 0113

1VbVVVbV CBAOP ⋅−=++⋅−= (36d)

In other words, the error in the operating signal is

proportional to the system unbalance, with a small multiplier.

As a result, errors in the measurement of the bank neutral

voltage are of secondary importance. For example, assume a

system unbalance (V0) of 3% of bus nominal voltage, and a 5%

magnitude and 1deg angle error for the neutral point

transformer. Using equation (36d) one concludes that this error

introduces about 0.16% of bus nominal voltage as a spurious

operating signal.

Bus VTs must be much more accurate to facilitate sensitive

protection. Assume, a phase A VT is now exposed to

measurement errors:

CVTBVTAVTxVTX

VT

OP VnVnVbnVnn

V ⋅−⋅−⋅⋅−⋅⋅⋅

= 33

1 (37a)

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From equation (36b):

AVTCVTBVTxVTX VnVnVnVn ⋅=⋅−⋅−⋅⋅3 (37b)

Substituting (37b) into (37a) gives:

AOP VbV ⋅−= 13

1 (37c)

In other words, 1/3rd of the bus voltage “leaks” as a spurious

operating signal due to errors in the measurement. For

example, assume 0.3% magnitude error and 0.2deg angle

error. These errors in the A-phase voltage with all the other

measurements intact, i.e. with errors not adding and not

canceling, would yield according to equation (37c) 0.18% of

bus voltage as an error in the operating signal of this

protection method.

When using externally derived system zero-sequence

voltage (equation (7b)), requirements for the bank and system

neutral voltage measurements are relaxed, and the accuracy of

measurement of the two phase voltages becomes secondary

because of the low value of multipliers applied to the B and C

voltages.

Generally speaking the method is most impacted by the

accuracy of the measurement of the system neutral voltage.

This quantity is derived regardless of the method applied

(internally, externally to the relay) out of three vectors each

having significant magnitude compared with the target

sensitivity. Small magnitude and angle errors in sensing any of

the three vectors would become significant for this sensitive

protection function.

C. Impact of instrumentation errors of the phase current

balance function

When using a window-type CT to measure the differential

current, this method is quite immune to instrumentation errors.

From equation (12) the method balances the differential

current with a small fraction of the total bank current. Both

signals are low: the former because of the near-zero circulating

current; the latter because of the multiplier. As a result the

errors are decimated when they “leak” into the operating

signal.

Analysis of equation (12) yields the following expression the

error analysis:

IkbIbI DIFOP ⋅⋅−=⋅−= 11 (38)

For example, assume 2% of full bank current circulating in

the window CT (k = 0.02), and 5% magnitude and 3deg angle

error in the phase CT. According to equation (38) the spurious

operating signal will reach 0.14% of the total bank current.

D. Impact of instrumentation errors of the neutral current

balance function

As explained in the previous section, the neutral and phase

current balance methods are equivalent. The differential

neutral current is compensated for inherent unbalance by all

three currents (per equation (18)), but similarly to the phase

current balance method the multipliers for the phase currents

are small. Therefore, equation (38) applies to this method, and

yields the same results as to the impact of measurement errors.

Overall the relative insensitivity of the current balance

methods to instrumentation errors can be understood by

realizing only small portions of the phase currents are used for

compensation, while the differential currents – if measured via

window CTs – are not exposed to any significant errors.

VII. COMPARISON WITH TRADITIONAL METHODS

Traditionally, either a given function is desensitized to

account for inherent bank unbalances and instrumentation

errors. Or, a historical value of the non-zero operating quantity

is subtracted (S-changes) before comparing with a pickup

threshold (P) resulting in the rate-of-change mode of

operation:

PVVx >−∆ 0 (neutral unbalance) (39a)

PIDIF >∆ (phase or neutral current balance) (39b)

The rate-of-change approach improves sensitivity to some

extent but has limitations.

First, it is an approximation. As derived in section 4, the

“leaking” values are proportional to present values of some

other signals related to the bank (example: differential current

in the phase balance method proportional to the total bank

current). When the currents do not change, the delta method

works satisfactory. But when the currents change, such as

during close-in external faults, subtracting an old value will

not compensate correctly. Time delay or other inhibit method

may be needed to ride through such conditions.

Second, the rate-of-change approach will not provide for a

sustained operating signal. When the delta-t window slides

entirely into the fault, the operating signal will reset. This

creates a problem when time-delayed operation is assumed.

Methods for inherent bank compensation presented in

section 4 identify the true cause of the unbalance, and as such

are accurate under system balanced conditions, minor

unbalances, and major system events such as close-in faults.

Their operating signals are sustainable allowing time delayed

alarming and tripping with no restrictions.

Major system unbalance is an important condition to

consider. For example, assume a close in ground fault

elevating both the system zero-sequence voltage and the bank

neutral point voltage. The compensated neutral unbalance

method is based on equation (5):


10

During the outlined ground fault event, Vx and V0 assume

significant values and will balance perfectly as long as the

relay uses proper settings for the inherent bank unbalance

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compensation (k-values) and the instrumentation errors are low

enough compared with the applied setting. The other two

voltage components are of secondary importance as they use

small multipliers.

Simplifying one can write the following balance equation for

this function:

0VVV xOP −= (40a)

In other words, the operating signal is a vectorial difference

of two voltages. In order to better cope with errors and avoid

penalizing sensitivity an optimized restraining signal can be

created as follows:

0VVV xREST += (40b)

Note that the above signal is not a classical restraint in the

form of a sum or average of the magnitudes. This would affect

sensitivity of the function. Instead the restraint is a vectorial

sum of the two voltages.

To understand better how this approach works, consider

external fault and internal bank failure.

Assume an external fault producing 20% of system zero-

sequence voltage. Assume further, the bank neutral point

voltage is measured as 002.0 ∠pu while the system zero-

sequence voltage is measured as 0517.0 ∠pu due to finite

accuracy of instrument transformers and the relay, transients,

etc. If so, the function even if perfectly compensated for the

bank inherent unbalance would see an operating signal of:

pupupuVOP 034.0517.002.0 00 =∠−∠=

If used to trip instantaneously without a restraint the

function will have to be set above this level.

Calculate the proposed restraining signal:

pupupuVREST 37.0517.002.0 00 =∠+∠=

Note that the applied definition of the restraint practically

doubles the two involved signals. Assuming a slope is used for

tripping, it will take 0.034/0.37 = 9.2% of slope to restrain the

operation.

Consider an internal bank failure under 5% of system

unbalance (system zero-sequence voltage). Assume further, the

bank failure changes the neutral point voltage by 2% of bus

voltage at the angle of 180deg (worst case):

0

0 005.0 ∠= puV ,

000 007.018002.0005.0 ∠=∠−∠= pupupuVx .

The operating signal is:

pupupuVOP 02.0005.0007.0 00 =∠−∠=

The restraining signal is:

pupupuVREST 12.0005.0007.0 00 =∠+∠=

Assume a 10% slope setting is applied. The ratio between

the operate and restraining signals is 0.02/0.12 = 17% allowing

for sensitive operation given the slope of 10%.

Change in the voltage at 180degrees is the worst case. Under

the best case scenario one obtains 0.08pu of restraint, or

0.02/0.08 = 25% of the operate-to-restraint ratio.

Careful application of restraint allows further improvement of

security while maintaining good sensitivity of the capacitor

bank protection functions.

VIII. SUMMARY

This paper derives correct balance equations for short circuit

protection of shunt capacitor banks taking into account

inherent unbalances in the protected bank. Four methods are

derived: voltage differential, compensated neutral voltage

unbalance, phase current balance, and neutral current balance.

As can be seen from key equations (1), (5), (11), and (18)

the proper way of balancing the bank (or banks) involves

instantaneous values of currents or voltages. Subtracting the

residual unbalance as a time-delayed signal (a historical, or a

constant value), and responding to the delta changes does not

constitute a proper, sensitive and secure operating equation for

protective relaying purposes.

The methods presented in this paper compensate for both

bank and system unbalances. Therefore they are insensitive to

major system events such as close-in faults. Presently used

relaying techniques might misoperate on such system

conditions, as they typically disregard system unbalances and

compensate for the bank unbalance assuming no, or minor

system unbalances.

The exact balance equations developed in this paper open a

chance to perform manual, or automated adjusting of the

operating logic in order to accommodate the inherent

unbalance of the bank either due to un-repaired failures,

temperature or seasonal changes, or changes due to removing,

shorting, or repairing the cans. This can be done as auto-

setting, i.e. one time adjustment after the repair and under user

supervision, or as self-tuning, i.e. a continuous tracing of the

slightly changing capacitor reactances in order to maintain

optimum sensitivity to internal failures, and security during

system unbalances.

The voltage differential, phase and current balance methods

are subject to self-tuning under any conditions; the neutral

voltage unbalance is subject to self-tuning as long as the

neutral point voltage is above the measuring error level. When

applied in the self-tuning mode the methods continuously

compensate for temperature and seasonal changes, in a slow

loop of modifying their balancing coefficients based on actual

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values. Note that the majority of the balancing coefficients

developed in this paper are ratios of impedances. As such they

are already greatly insensitive to temperature and seasonal

changes.

If implemented in the self-tuning mode a given method shall

still monitor the total drift in the operating signal even if very

slow, and alarm if the amount of the drift signifies a danger of

possible future failure, or a series of minor failures that went

undetected or unattended to.

The involved balancing factors although in theory are

complex numbers, could be very well represented by real

numbers (uneven loss tangents of the capacitors in the bank,

and errors of instrument transformers cause small imaginary

parts of the matching factors). With the matching factors being

real numbers, inherent unbalance of a capacitor bank can be

easily zeroed out in the protection equations using only 1, 2 or

a maximum of 3 coefficients. These coefficients can be tuned

by measurements, and simple engineering calculations.

The paper analyses sensitivity of the developed methods and

derives practical equations for the amount of the operating

signals given the size of the bank failure. Also, impact of

instrumentation errors (instrument transformers and relays) is

analyzed quantitatively allowing one to optimize the secondary

system design, and select settings based on data.

REFERENCES

[1] IEEE Std. C37.99-2000: “Guide for the Protection of Shunt Capacitor

Banks”, June 2000.

[2] Kasztenny B., Brunello G., Wester C.: “Capacitor Bank Fundamentals

and Protection”, Proceedings of the 56th Annual Conference for

Protective Relay Engineers, College Station, TX, April 8-11, 2003.

[3] Capacitor Bank Protection and Control Relay, Instruction Manual,

General Electric Publication, 2006.

Bogdan Kasztenny holds the position of Protection and System Engineering

Manager for the protective relaying business of General Electric. Prior to

joining GE in 1999, Dr.Kasztenny conducted research and taught protection

and control at Wroclaw University of Technology, Texas A&M University,

and Southern Illinois University.

Between 2000 and 2004 Bogdan was heavily involved in the development

of the Universal RelayTM series of protective IEDs, including a capacitor bank

relay.

Bogdan authored more than 140 papers, is the inventor of several patents,

Senior Member of the IEEE, and the Main Committee of the PSRC.

In 1997, he was awarded a prestigious Senior Fulbright Fellowship. In

2004 Bogdan received GE’s Thomas Edison Award for innovation.

Ed Clark received his B.S. in Electrical Engineering from the University of

Florida and joined Florida Power & Light Company in 1979. Ed has worked

as a protection & control field engineer for 18 years and as a relay staff

engineer for the past 9 years. Currently his role consists of the design and

standardization for transmission and generation protection systems. His

experience has included protection applications for large capacitor banks at

transmission voltage up to 500kV. Ed is a member of IEEE and a registered

P.E. in the state of Florida.

Joe Schaefer is responsible for developing and testing protective relay

standards related to generation, transmission, and distribution applications.

His most recent designs include relay protection for grounded and

ungrounded transmission capacitor banks up to 500kV. Previously, Joe was

employed as a protection field engineer responsible for relay equipment from

480v to 500kV applications including nuclear plant relaying. Joe received his

BSEE from the University of Florida and joined Florida Power and Light

Company in 1987.

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Dynamic Simulations Help

Improve Generator Protection

Ramón Sandoval, Comisión Federal de Electricidad

Armando Guzmán and Héctor J. Altuve, Schweitzer Engineering Laboratories, Inc.

Abstract—This paper describes a digital simulation study of a

set of two 160 MW generating units operating in the Juan de Dios

Bátiz Paredes thermal power station, in Topolobampo, Sinaloa,

Mexico. This plant belongs to Comisión Federal de Electricidad,

the national Mexican utility. We first discuss the factors that

limit the active and reactive power delivered by a generating

unit, such as thermal and voltage limits, power-system imposed

limits, and the minimum excitation limiter. We then describe

generator protection functions related to the capability curve.

Later, we propose a P-Q plane-based scheme that provides gene-

rator loss-of-field protection and capability-curve violation

alarming. Finally, we present the simulation results of loss-of-

field and loss-of-synchronism conditions of one of the two gene-

rating units for several cases, including different initial load con-

ditions, different loss-of-field modes, and different numbers of

units on line.

I. INTRODUCTION

Power-generating plants represent approximately 50 per-

cent of the capital investment in an electric power system.

Generator outages caused by faults, abnormal operating condi-

tions, or even generator protection misoperation are very cost-

ly when they occur. Synchronous generators are exposed to

more harmful operating conditions than any other power sys-

tem element. A complete generator protection system must

include a variety of protection functions to respond to the dif-

ferent possible abnormal operating conditions.

Modern generator-protection relays include virtually all the

required protection functions. Multifunction relays can pro-

vide even small-capacity generators with complete protection

at low cost. However, selecting the protection functions that a

particular generator needs and determining appropriate setting

values require a thorough knowledge of the protected ma-

chine. Therefore, dynamic digital simulation using available

computer programs is a highly recommended tool for protec-

tion engineers.

This paper describes a digital simulation study of a set of

two 160 MW generating units operating in the Juan de Dios

Bátiz Paredes thermal power station, in Topolobampo, Sina-

loa, Mexico. The plant belongs to Comisión Federal de Elec-

tricidad, the national Mexican utility. These generators are

interconnected with two substations of the national Mexican

power system through two 230 kV transmission lines. The

simulation includes the generators and their control systems,

the step-up transformers, the transmission lines, and an equiv-

alent of the power system beyond the area of interest. Genera-

tor models include speed and voltage regulators and power

system stabilizers. These models were validated using the re-

sults of factory and commissioning tests of both units.

After discussing the factors limiting the output of generat-

ing units, the paper describes traditional protection functions

related to the capability curve, such as stator thermal, rotor

thermal, motoring, overvoltage, undervoltage, and loss-of-

field protection. The paper proposes P-Q plane-based loss-of-

field protection and capability-curve violation alarming func-

tions. The simulation results for several cases of generator

loss-of-excitation and loss-of-synchronism conditions illu-

strate the impact of initial load, loss-of-field mode, and num-

ber of generator units on line. Simulation results for each case

include graphics showing the behavior of power, voltage, and

current as functions of time and also the resulting trajectory in

the impedance plane. Introducing the time variable, we present

the simulation results in the three-dimension resistance-

reactance-time space. Finally, a P-Q plane representation

completes the set of graphic tools for analyzing the generator,

power system, and protection behavior.

II. FACTORS LIMITING THE ACTIVE AND REACTIVE POWER

DELIVERED BY A GENERATING UNIT

A power system must continuously meet the variable de-

mand for active and reactive electric power. To meet this re-

quirement, the system should have enough reserve of active

and reactive power and the capability to control active and

reactive power at all times.

Active- and reactive-power flows in a power system are

relatively independent. For a transmission line connecting two

sources, active-power flow depends mainly on the angle be-

tween the voltages at the line terminals. Active power flows

from the leading-voltage line end to the lagging-voltage line

end. On the other hand, reactive-power transfer depends main-

ly on the voltage magnitudes. Reactive power flows from the

line terminal having higher voltage magnitude to the line ter-

minal with lower voltage magnitude.

Power-system operating frequency strongly depends on the

active-power balance. Therefore, active-power control is

closely related to frequency control. Power-system operating

voltage magnitudes depend mainly on reactive-power balance.

As a consequence, there is a close relationship between reac-

tive-power control and voltage control in the power system.

Synchronous generators have the capability of generating

active power and of generating (overexcited generator) or ab-

sorbing (underexcited generator) reactive power.

Speed turbine governors of generating units provide prima-

ry local control of active-power generation at generating

plants. Additionally, automatic generation control (AGC),

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performed by control center computers, processes real-time,

system-level information and sends remote control commands

to a number of generating units located in the control area.

Automatic voltage regulators (AVRs) provide generator-

voltage control. An AVR is a closed-loop control system that

compares the generator terminal voltage to a reference set

point and adjusts the excitation to keep the voltage within an

operation band.

Several factors limit the active and reactive power that a

generating unit can deliver to the power system under given

operating conditions. These factors include the generator ca-

pability curve (determined by the machine design), voltage

limits, power-system stability limits, the minimum excitation

limiter (MEL), and the overexcitation limiter (OEL).

A. Generator Capability Curve

Synchronous generators are rated in terms of the maximum

MVA output that they can carry continuously without over-

heating, at a specified voltage and power factor. Generator

capability curves provided by the manufacturer represent the

machine thermal limits in a P-Q plane at nominal voltage (see

Fig. 1).

1) Active- and Reactive-Power Limits

The active-power output is limited by the prime mover ca-

pability to a value within the MVA rating. The driving torque

available for the turbine imposes this limit. The turbine is

usually sized to deliver rated MW at rated power factor. The

vertical line through point B of Fig. 1 represents the typical

generator active-power limit. However, there are cases in

which the turbine is rated below this value.

The continuous reactive-power output capability is limited

by three factors: armature-current limit, field-current limit,

and stator-end region heating limit.

Fig. 1 Generator capability curve

a) Armature-Current Limit

The armature-current limit results from the stator copper

power losses. There is a maximum current that the generator

armature can carry continuously without exceeding the allow-

able operating temperature. In the P-Q plane the armature-

current limit defines a circle with center at the origin. At rated

voltage, the circle radius equals the generator MVA rating

(curve BC in Fig. 1):

( ) 0,0Q,PCenter = (1)

Radius = Rated MVA (2)

b) Rotor-Current Limit

Copper power losses in the rotor winding impose a limit to

the generator field current. The relationship between the active

and reactive powers for a given field current is a circle (curve

AB in Fig. 1) centered at the negative part of the Q-axis [1]

[2].

Fig. 2 depicts a generator connected to a power system.

The generator internal voltage and synchronous reactance are

Eq and Xd, respectively. The generator terminal voltage is Vt.

The generator model assumes constant field current and neg-

lects saliency effects and stator resistance. Neglecting saliency

effects means assuming the direct-axis reactance Xd to be

equal to the quadrature-axis reactance Xq. The power system

voltage and reactance are Es and Xs, respectively. Xs includes

the reactances of the step-up transformer and the equivalent

power system. For this configuration the center position and

radius of the rotor-current limit circle are:

( )d

2t

X

V,0Q,PCenter −= (3)

d

tq

X

V•ERadius = (4)

jXd Xs

EsEqVt

Fig. 2 Simple power-system diagram

The circles representing the rotor-current limit and the ar-

mature-current limit intersect at a point (point B in Fig. 1),

which represents the machine nameplate MVA and power

factor rating.

c) Stator-end region heating limit

The armature end region heating imposes a third operation-

al limit to the generator in the underexcited region (curve CD

in Fig. 1). The main generator magnetic flux is a radial flux,

parallel to the stator laminations. However, the armature end-

turn leakage flux is an axial flux, perpendicular to the stator

laminations. The resulting eddy currents in the laminations

produce localized heating in the end region.

When the generator operates in an overexcited condition,

the field current is high and the retaining ring is saturated by

the resulting high magnetic flux. The high reluctance of the

retaining ring keeps end leakage flux in a low value. On the

other hand, for underexcited generator operation, the field

current is low, the retaining ring is not saturated, and the lea-

kage flux is high. Furthermore, in the underexcited generator

condition, the flux produced by the armature currents adds to

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the flux produced by the field current; as a result, the end turn

flux enhances the axial flux in the end region. The resulting

heating effect in the armature end region limits the generator

output, particularly in a round-rotor machine [3] [4].

Reference [4] shows that the stator end heating limit of the

capability curve (curve CD in Fig. 1) is a circle centered at the

positive part of the Q-axis, under the assumption that the end

core leakage flux is proportional to the main air gap flux and

that the thermal energy produced by eddy currents is propor-

tional to the square of the end region magnetic flux.

According to [4], the center position and radius of the sta-

tor-end heating limit circle are:

( )d

2t

1X

VK,0Q,PCenter = (5)

d

t2

X

V•KRadius = (6)

Where:

fa2f

2f

2ffa

1NN2NN

NNNK

−+

−−= (7)

( )fa2

a2

ft

2N N 2 N N K

∆ K

−+θ

= (8)

Nf and Na are the number of turns of the field and armature

windings, respectively; ∆θ is the maximum permissible conti-

nuous temperature rise above the no-load temperature in the

end core region; Kt is a proportionality constant relating the

thermal energy with the square of the end region magnetic

flux.

Actual generator capability curves may not comply with

(7) and (8). For example, the stator-end heating limit of the

Juan de Dios Bátiz Paredes power station generators (Fig. 3) is

a circle centered at the point (54.8 MW, 139.9 MVAR), with a

radius of 244 MVA. On the other hand, the actual capability

curve depicted in Fig. 5 does comply with (7) and (8). The

circle is centered at the point (0 MW, 750.2 MVAR), and its

radius equals 918.2 MVA.

2) Effect of Voltage and Coolant Pressure

From the previous analysis it is clear that the circles

representing the three generator thermal limits in the capabili-

ty curve depend on the armature voltage. Manufacturers typi-

cally provide generator capability curves at nominal voltage.

Using (1) through (6) we may derive the capability curve for

other voltage values.

Generator power output capability also depends on the ef-

fectiveness of the cooling system. In hydrogen-cooled genera-

tors, for example, the capability is a function of hydrogen

pressure. Fig. 3 shows the capability curve at nominal voltage

of a 160 MW hydrogen-cooled steam turbine-driven generator

at rated armature voltage (the Juan de Dios Bátiz Paredes

thermal power station generator). The capability curve is real-

ly a family of curves with the coolant pressure as a parameter.

The dotted straight lines in the figure are the loci of constant

power factor.

150

100

50

0

50

100

150

200

0.95

0.90

0.85

0.80

0.60

0.95

0.90

0.850.80

0.60

50 100 150 200

Q (MVAR)

P(MW)

MEL

35 kPa

103 kPa

206 kPa

H Pressure2Lagging

Power

Factor

Leading

Power

Factor

OEL

Fig. 3 Capability curve at nominal voltage of a 160 MW, 202 MVA, 15 kV,

0.9 PF, 3600 RPM, 60 Hz, hydrogen-cooled steam-turbine generator

B. Voltage Limits

The generator terminal voltage is restricted to an operating

band determined either by the generator or the step-up trans-

former operating voltage limits. The permissible operating

range of cylindrical-rotor [5] or salient pole generators [6] is

±5 percent rated voltage, at rated kVA, frequency and power

factor. Transformers should meet two voltage requirements for

any primary or secondary tap position. The transformer should

be capable of operating at 110 percent rated voltage with no

load. The primary winding should also be capable of operating

continuously at the voltage required to produce 105 percent

rated voltage at the secondary terminals with rated transformer

load at 0.8 power factor.

C. Steady-State Stability Limit (SSSL)

Another limit to the power delivered by the generating unit

is system stability. Power systems normally operate close to

the nominal frequency. All synchronous machines connected

to the power system operate at the same average speed. The

generator speed governors maintain the machine speed close

to its nominal value. There is a balance between generated and

consumed active power under normal power system operating

conditions.

Random changes in load and system configuration con-

stantly take place and impose small disturbances to the power

system. The property of a power system to keep the normal

operating condition under these small slow changes of system

loading is what we call steady-state stability or system stabili-

ty for small perturbations.

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For the two-machine power system depicted in Fig. 2, the

active-power transfer Pe is given by:

δ+

= sinXX

EEP

sd

sq

e (9)

Where the system power angle δ is the angle between Eq

and Es. Fig. 4 depicts three power-angle curves, which are

plots of (9) for different values of the internal generator vol-

tage Eq (Eq0 > Eq1 > Eq2). The dashed horizontal line represents

the mechanical power Pm provided by the prime mover to the

generator. This ideal lossless system operates at the point

where the mechanical power input to the generator equals the

electrical power delivered to the system (Pm = Pe). Hence, the

value of angle δ corresponds to the intersection of the Pm

straight line with the power angle curve.

We may increase the load in small steps (Pm increases) un-

til we reach the tip of the power curve. The system remains

stable until the power angle δ = 90°. Beyond the curve maxi-

mum (δ > 90°) a load increase causes a decrease in the trans-

fer power and the system loses synchronism. The value of Pe

for δ = 90° represents the SSSL for this ideal lossless system.

This is the maximum power that the electrical system can

transfer.

δ0 δ1

P

δ δ2 = 90°

Pm

Pe Eq0

Eq1

Eq2

Fig. 4 Power-angle curves for different generator excitation levels

The power system may also lose synchronism for a fixed

value of mechanical power if the generator internal voltage Eq

is reduced. This loss-of-synchronism could occur if the opera-

tor reduces generator excitation to absorb reactive power from

the system. Fig. 4 shows the effect of reducing the internal

voltage from an initial value Eq0 to a lower value Eq2: the

power angle increases from δ0 to 90°, and the system reaches

the SSSL. Any further decrease of the internal voltage makes

the system unstable.

It has been shown [1] [7] that, for the ideal lossless system

depicted in Fig. 2, the system SSSL plots in the P-Q plane as a

circle centered at the positive part of the Q-axis. The center

position and radius of the SSSL circle are:

−=

ds

2t

X

1

X

1

2

V,0)Q,P(Center (10)

+=

sd

2t

X

1

X

1

2

VRadius (11)

The previous analysis is valid for the case of manual vol-

tage regulator operation. In this case, the generator excitation

remains fixed for each power angle curve in Fig. 4. Hence,

(10) and (11) describe the manual regulator SSSL locus in the

P-Q plane. Typically, when the power system is strong (Xs is

low) the SSSL locus is outside the generator capability curve.

However, on weak systems, the manual SSSL can be more

restrictive than the generator capability in the underexcited

region.

Under automatic operation (AVR), the voltage regulator

rapidly varies the field current in response to system operating

conditions. This changes the maximum value of the power

angle curve upwards or downwards as required by the system.

This dynamic response improves the SSSL as compared to

that resulting from manual regulator operation. The effect of

AVR on SSSL depends on the voltage regulator gain, the reg-

ulator time constant, and the field time constant [1] [8].

D. Minimum-Excitation Limiter (MEL)

Power system operation conditions or equipment failure

may require generators to operate in an underexcited condition

to absorb reactive power from the power system. During light

system loads, transmission lines behave as reactive-power

sources. Generators are required to draw excess reactive pow-

er to prevent high-voltage system conditions. An AVR failure

in a generator could drive this unit to an overexcited condition

and create an excess of reactive power that needs to be ab-

sorbed by nearby generators. These nearby generators may

reach underexcited operating conditions.

As stated previously, three factors may limit the capability

of a synchronous generator to operate in the underexcited re-

gion. In this region, core-end heating, power-system stability,

or allowable operating voltage limit the generator capability to

absorb reactive power.

MEL is a control function included in the automatic vol-

tage regulator (AVR) that acts to limit reactive-power flow

into the generator. During normal operation, the AVR keeps

generator voltage at a preset value. When system conditions

require the generator to absorb reactive power in excess of the

MEL set point, the MEL interacts with the AVR to increase

terminal voltage until reactive-power inflow is reduced below

the setting. The MEL operating characteristic plots as a line in

the P-Q plane. Fig. 3 shows the MEL characteristic as a

straight line for this particular generator. For other MEL de-

signs, the characteristic may be a curve or its approximation

by linear segments, as shown in Fig. 5.

The MEL is typically set based on the most limiting of two

conditions: the manual regulator SSSL or the generator unde-

rexcited capability limit [1] [4]. Fig. 6 depicts the MEL cha-

racteristic set according to this criterion. This figure corres-

ponds to the actual generator and power system data of the

Juan de Dios Bátiz Paredes power station (see Appendix A).

The SSSL characteristic is represented at nominal voltage. In

this case, the capability curve is more restrictive than the

SSSL. For weaker power systems the SSSL may be the most

restricting factor.

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P (MW)

0

50

100

150

200

250

300

50

100

150

200

Q (MVAR)

50 100 150 200 250 300 350

3.0 kg/cm

H Pressure2

2

2.0 kg/cm2

0.90

Lagging

Power

Factor

0.95

Leading

Power

Factor

Fig. 5 Capability curve at nominal voltage of a 312 MW, 347 MVA, 20 kV, 0.9 PF, 3600 RPM, 60 Hz, hydrogen-cooled steam-turbine generator

Fig. 6 Typical setting of the generator MEL

.

When the power system is in the recovery stage after a dis-

turbance, there may be a need for some generators to violate

the underexcited operation limit on a short-term basis. If the

generator manufacturer permits this operating condition, and

the MEL function could be disabled, we should detect the

MEL violation and issue an alarm. The operator has the re-

sponsibility of limiting this mode of operation to prevent ge-

nerator damage [1].

E. Overexcitation Limiter (OEL)

OEL is a control function included in the AVR that pro-

tects the generator from overheating resulting from prolonged

field overcurrent. OEL detects the field-overcurrent condition

and acts with time delay to ramp down the excitation to a pre-

set value (typically 100–110 percent of rated field current [2]).

The OEL operating characteristic plots as a line in the P-Q

plane. Fig. 3 shows the OEL characteristic as a straight line

for this particular generator.

III. GENERATOR PROTECTION FUNCTIONS

RELATED TO THE CAPABILITY CURVE

Several generator protection functions are intended to pre-

vent the machine from violating capability-curve limits to

some extent. These protection functions are stator thermal,

rotor thermal, motoring, overvoltage, undervoltage, and loss

of field.

A. Stator-Thermal Protection

Thermal protection for the generator stator core and wind-

ings is intended to protect the generator from the overheating

resulting from overload, failure of cooling systems and loca-

lized hot spots caused by core lamination insulation failures or

by localized or rapidly developing winding failures [9] [10].

As mentioned before, the continuous output capability of a

generator is expressed in kilovolt-amperes (kVA) available at

the terminals at a specified frequency, voltage, and power fac-

tor. In general, generators may operate successfully at rated

kVA, frequency, and power factor for a voltage variation of

5 percent above or below rated voltage. Under emergency

conditions, the generator may exceed the continuous capabili-

ty for a short time. Reference [5] expresses the armature-

winding short-time thermal capability for cylindrical-rotor

machines as a set of time and current pairs of values (see Ta-

ble I) that define an inverse time-current curve.

TABLE I

SHORT-TIME STATOR THERMAL CAPABILITY FOR CYLINDRICAL-ROTOR SYNCHRONOUS GENERATORS [5]

Time (seconds) 10 30 60 120

Armature current

(percent of rated current) 218 150 127 115

Generators typically have temperature sensors (resistance

temperature detectors or thermocouples) supplied by the man-

ufacturer that measure the temperature at different points of

the winding. Generator overload protection receives informa-

tion from these sensors to continuously monitor winding tem-

perature. In attended generating stations, overload protection

typically issues an alarm. In unattended stations, the protec-

tion may initiate corrective action or trip the unit when preset

temperature limits are exceeded.

In generators lacking temperature sensors, overload protec-

tion may be provided by a relay function responding to the

measured armature current. In the past, an inverse-time over-

current relay provided this function. The relay was coordi-

nated with the generator short-time capability curve derived

from the time-current pairs given in Table I [9]. A better solu-

tion is for the relay function to emulate the thermal behavior

of the generator. This thermal-overload protection function is

available in some digital generator multifunction relays.

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A failure of the generator cooling system may result in rap-

id deterioration of the stator-core lamination insulation and/or

stator-winding conductors and insulation. Generator overload

protection based on temperature sensors also responds to the

winding overheating that results from cooling-system failures.

There may be additional sensors to monitor the coolant tem-

perature, flow, or pressure, which may be connected to an

alarm, to automatically reduce load to safe levels, or to trip.

Overload protection based on the measured armature current

does not provide protection against cooling system failures.

Localized hot spots in the stator core result from high eddy

currents that find conducting paths across the damaged insula-

tion between laminations. Lamination insulation may fail by

generator misoperation (prolonged over- or underexcitation

operation, for example), by lamination vibration, by foreign

objects, or by damage to the core during installation or main-

tenance. Temperature sensors located at strategic positions can

detect hot spots. However, detection is only partial, since it is

not possible or practical to cover the entire core and windings

with the detectors. At present, only large steam-turbine gene-

rators have this type of protection, which normally issues an

alarm.

B. Rotor-Thermal Protection

Thermal protection for the generator field includes protec-

tion for the main field winding circuit and protection for the

main rotor body, wedges, retaining ring, and amortisseur

winding [9] [10].

The field winding may operate continuously at a current no

greater than that required for producing rated kVA at rated

power factor and voltage. For power factors less than rated,

the generator output must be reduced following the overex-

cited branch of the capability curve to keep the field current

within these limits. Under abnormal conditions, such as short

circuits and other system disturbances, the generator may ex-

ceed these limits for a short time. Reference [5] expresses the

short-time thermal capability for cylindrical-rotor machines as

a set of time-current pairs defining an inverse time-current

curve (see Table II).

TABLE II SHORT-TIME ROTOR THERMAL CAPABILITY

FOR CYLINDRICAL-ROTOR SYNCHRONOUS GENERATORS [5]

Time (seconds) 10 30 60 120

Field current (percent of rated current)

209 146 125 113

A typical rotor thermal protection element measures direct-

ly or indirectly the dc field current or voltage and operates on

an inverse-time curve that coordinates with the curve resulting

from the time-current pairs given in Table II.

Thermal protection of the generator rotor body is difficult

to provide. Other generator protection functions prevent rotor-

thermal damage, such as negative-sequence, loss-of-

excitation, or loss-of-synchronism protection.

C. Motoring Protection

Motoring of a generator takes place when the energy

supply to the prime mover is cut off while the generator is on

line and excited. The generator operates as a synchronous mo-

tor driving the prime mover. There is no danger for the gene-

rator in this operating condition, but the prime mover may

suffer damage during motoring. In addition, the mechanical

load that the prime mover presents to the generator (operating

as a synchronous motor) may be high. This load represents an

active-power loss for the power system.

For steam turbines, motoring causes overheating and po-

tential damage to the turbine blades and other turbine parts.

The main purpose of steam flow through a turbine is delive-

rery of energy to rotate the rotor. This steam flow also takes

out of the turbine the heat caused by winding losses resulting

from the rotation of the turbine rotor and blades in a steam

environment. During motoring, the blades and other turbine

parts overheat, because there is no steam flow through the

turbine to dissipate the heat. Steam turbines may even over-

heat when the generator is operating at no load or in a light

load condition. Turbine manufacturers provide information on

the permissible time that steam turbines may operate in a mo-

toring condition.

Other types of prime movers may experience different

problems during motoring. Hydraulic turbines may suffer ca-

vitation of the blades on low water flow during motoring. Gas

turbines may have gear problems when rotating as a mechani-

cal load. Diesel-engine generating units are in danger of ex-

plosion and fire from unburned fuel.

Motoring protection is therefore necessary for all generat-

ing units except hydro units designed to operate as synchron-

ous condensers [9] [10]. This external protection complements

the detection means embedded in the generator control sys-

tem. The most widely applied motoring protection uses a

time-delayed power directional element to detect the active

power reversal caused by the motoring condition. A motoring

protection relay generally trips the main generator breaker(s)

and the field breaker(s), transfers the auxiliaries, and provides

a trip signal to the prime mover [9] [10].

The power-element setting depends on the type of prime

mover. The power required to motor the unit equals the load

imposed by the prime mover plus mechanical losses. Typical

values in percentage of rated power are [10]: steam turbines:

0.5–3 percent; hydro turbines: 0.2–2 percent; gas turbines: up

to 50 percent; diesel engines: up to 25 percent. The power-

element setting range should include both negative and posi-

tive active-power values.

The power element should have a time delay to prevent mi-

soperation for power swings caused by system disturbances or

when synchronizing the machine to the system. This time de-

lay should be below allowable turbine motoring times. Typical

values are in tens of seconds.

In some hydraulic, steam, and gas turbine generating units,

intentional motoring is permitted as a normal operating condi-

tion. Some examples are: motoring the unit to accelerate the

rotor during starting conditions, operating a hydraulic unit as a

synchronous condenser or in a pump/storage mode, and se-

quential tripping of steam-turbine units. Motoring protection

should not interfere with this permissible operating condition.

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D. Overvoltage and Undervoltage Protection

Overvoltage is an abnormal condition most likely to occur

in hydrogenerators, where load rejection may cause overspeed

levels of more than 200 percent of normal and significant

overvoltage. Typical generator overvoltage protection includes

an instantaneous voltage element set at 130–150 percent of

nominal voltage and an inverse-time voltage element set at

approximately 110 percent of nominal voltage. This protection

typically trips the generator main breaker, trips the field

breaker, and transfers unit auxiliaries [9] [10].

It is possible to detect undervoltage generator operation us-

ing an inverse-time or definite-time undervoltage element. We

may set this element at approximately 95 percent of nominal

voltage and use it to issue an alarm so the operator can remedy

the undervoltage condition whenever possible.

E. Loss-of-Field Protection

A generator may totally or partially lose excitation as a re-

sult of accidental field breaker tripping, field open circuit,

field short circuit (slip-ring flashover, for example), voltage

regulator failure, or loss-of-excitation system supply.

1) Effect of the Loss-of-Field Condition on the Generator

and the Power System

When a generator loses excitation, the rotor field gradually

extinguishes, and the magnetic coupling between rotor and

stator magnetic fields eventually diminishes to a point where

the machine loses synchronism. The rotor speed increases to a

value for which the machine, operating as an induction gene-

rator, produces the active power demanded by the power sys-

tem in this new condition. This value is lower than the active

power delivered by the generator before losing excitation.

Operating as an induction machine, the generator draws large

amounts of reactive power from the system, which produces

high armature-current values (in the order of two to four times

rated current) and depresses the voltage. In addition, slip-

frequency eddy currents induce in the rotor, having a magni-

tude proportional to the generated power.

When initially operating at light load, the generator may

not lose synchronism as a result of the loss of field. In this

case, the machine operates as a synchronous generator based

on the principle of reluctance. In any case, the machine needs

to receive large reactive-power amounts from the system to

establish the magnetic field.

Both the machine and the power system are at risk when a

generator loses excitation. The generator may suffer rotor or

stator overheating, and experience large pulsating torques as a

result of operating as an asynchronous machine [11]. The

power system may have voltage problems.

The severity of the disturbance depends primarily on the

initial generator load [1]. The impedance of an induction gene-

rator is a function of slip: the higher the slip, the lower the

machine impedance. The induction-generator slip strongly

depends on the generator initial load: a higher initial load pro-

duces a higher induction-generator slip value. Lower generator

impedance means higher reactive-power consumption, higher

stator and rotor currents, and lower terminal voltage. The

worst case is when the generator loses excitation at full load,

where slip may reach values of 2–5 percent [1]. Other factors

conditioning the severity of the loss-of-excitation disturbance

are the system impedance and the mode-of-excitation failure.

Generator stator overheating depends on the armature-

current value. As mentioned before, the worst case occurs

when the generator is operating at full load when it loses exci-

tation.

Rotor overheating depends on initial loading and the other

factors just mentioned and also on the rotor design. In a cylin-

drical rotor, induced eddy currents circulate through the rotor

body and the rotor-coil wedges. They also flow through the

field circuit if the field is shorted or closed through a field

discharge resistor. These currents may overheat and damage

the rotor in a few seconds. Salient-pole rotors (hydro genera-

tors) typically have amortisseur windings through which in-

duced slip frequency currents can circulate. If the ammortis-

seur winding can withstand eddy currents, the rotor is not a

limiting factor for operation as an induction generator.

There are no general guidelines on the permissible time a

generator may operate without field [10]. Generator manufac-

turers should provide this information.

The power system is the other possible limitation to gene-

rator operation without field. The reactive-power deficit may

cause a voltage collapse, especially if a large generator con-

nected to a weak system loses excitation. Another possibility

is the loss of steady-state stability, as mentioned before. When

these problems arise, the system may lose voltage or syn-

chronous stability in a few seconds. Voltage sag at the genera-

tor terminals during the loss-of-field condition is a good indi-

cator of the power system not being able to withstand the dis-

turbance.

2) Protection Schemes

The previous analysis shows that synchronous generators

must have some kind of loss-of-field protection in addition to

the protection functions included in the excitation system.

This protection should provide an early alarm to permit the

operator to restore the field in the case of an accidentally

tripped field breaker. After a time delay, the protection must

trip the main generator breaker and the field breaker (to mi-

nimize damage in cases of field short circuits or slip-ring fla-

shovers), and transfer unit auxiliaries. In some cases it may be

necessary to trip the turbine stop valves also.

Generator loss-of-field protection has received special at-

tention [9] [10] [12]–[14]. Mason [12] introduced the concept

of using a “distance element of the so called mho family” to

detect loss of field; the relay receives the generator terminal

voltage and current as input signals. This offset mho element

characteristic is depicted in Fig. 7, showing the originally rec-

ommended settings: a circle diameter equal to the synchronous

reactance Xd, and a negative offset equal to half the direct-axis

transient reactance (–Xd’ /2).

The apparent impedance measured by the relay when the

generator loses the field describes a trajectory in the imped-

ance plane (see Fig. 7) that starts at the impedance value cor-

responding to the generator initial load. This point is in the

first quadrant of the impedance plane when the generator in-

itially operates in a lagging condition (delivering reactive

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power), or it is located in the fourth quadrant when the genera-

tor initially operates in a leading condition (consuming reac-

tive power).

The apparent impedance does not reach a final constant

value when the machine gets to the new steady state after los-

ing excitation. The apparent-impedance value corresponds to

the active power delivered and reactive power consumed by

the generator operating as an induction generator in the new

steady-state condition. This impedance value depends on slip

and hence on the initial load value. In the steady state the in-

duction-generator slip oscillates. As a result, active and reac-

tive power and the apparent impedance value also vary with

time. The apparent impedance describes a first loop in the

fourth quadrant (corresponding to the first pole slip), as shown

in the real impedance trajectory depicted in Fig. 7, and contin-

ues to oscillate in this region.

When the generator is initially operating at full load, the

first apparent-impedance loop occurs around a point with a

resistance value determined by the average active power deli-

vered by the induction generator and with a reactance value

that is close to the average of the generator d-axis and q-axis

transient reactances (Xd’ and Xq’). On the other hand, for the

generator operating initially at no load, generally there is no

loss of synchronism, and the first loop apparent-reactance val-

ue will vary in between the d-axis and q-axis synchronous

reactances (Xd and Xq). For other initial-load conditions, the

first pole slip produces an impedance loop in a region with

reactance values between those of the full-load and no-load

initial conditions. This is the case shown in Fig. 7. However,

as subsequent oscillation cycles take place, the impedance

locus moves in a larger area of the impedance plane, as we

will see in the simulation results presented in Section V.

During stable and unstable power swings, the impedance

measured by the loss-of-field relay also describes a trajectory

in the impedance plane. The relay may misoperate if the tra-

jectory penetrates the operating characteristic. A small relay

characteristic may prevent excursions of the power swing im-

pedance trajectory in the relay operating region. However, the

practice is to enhance security for power swings by delaying

operation of the loss-of-field relay. A time delay of approx-

imately 0.5–0.6 s is generally adequate [10] [13], but transient

stability simulation studies to determine relay time-delay set-

tings are highly recommended.

Fig. 7 Loss-of-field protection using a negative-offset mho element

For the generator reactance values that existed when Ma-

son introduced the offset mho characteristic for loss-of-field

protection (Xd was in the range of 1.1 to 1.2 p.u.), the settings

shown in Fig. 7 normally provided detection of loss of excita-

tion conditions for any initial generator loading. These settings

also ensured relay security for power swings without requiring

a time delay.

Modern generators have larger reactance (Xd is typically

about 1.5–2 p.u.). The larger relay characteristic may infringe

on the underexcited branch of the capability curve and prevent

fully using the machine capability in this region. The initial

recommendation, of reducing the characteristic diameter to

1 p.u., limited loss-of-field detection only to cases of high

initial generator loading. Later, the distance element concept

was enhanced using two negative-offset mho element charac-

teristics [13]. Fig. 8 illustrates the enhanced characteristic

suitable for generators with large direct axis reactance. Zone 1

serves to detect loss of field for high load conditions (the most

severe condition for both the generator and the system). A

time delay of about 0.1 s [10] provides security against tran-

sients. Zone 2 detects loss of excitation for light loads and

operates with time delay to override power swings. A time

delay of 0.5–0.6 s should provide security for power swings.

However, it is recommended to set this element based on tran-

sient stability studies.

The settings shown in Fig. 7 and Fig. 8 for the negative-

offset loss-of-field element [10] [13] do not take into account

the generator capability curve, the steady-state stability cha-

racteristic, and the MEL characteristic.

Fig. 8 Two-zone loss-of-field protection using negative-offset mho elements

Tremaine and Blackburn [14] introduced a characteristic

that uses a combination of a positive-offset mho element and a

directional element. With the setting shown in Fig. 9 [10], this

characteristic is just outside the SSSL characteristic, to pre-

vent the system from going unstable. However, this setting

does not consider the capability curve and the MEL characte-

ristic. System impedance Xs in Fig. 9 includes the step-up

transformer impedance plus the system equivalent impedance.

The directional element provides security for close-in external

faults. This scheme should issue an alarm, allowing the opera-

tor to correct the low- or lost-excitation condition [10]. The

scheme should also initiate time-delayed tripping. A typical

time-delay setting range is 10 s to 1 minute [7].

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Fig. 9 Loss-of-field protection using a positive-offset mho element super-

vised by a directional element

This concept was enhanced using an additional negative-

offset mho element [9] [10] to protect generators with large

direct axis reactance values. Fig. 10 illustrates the enhanced

two-zone characteristic. Zone 1 should have a time delay of

0.2 to 0.3 s to override power swings and other transients.

Zone 2 should issue an alarm and initiate time-delayed trip-

ping, with 1 minute as a typical delay.

The one-zone and two-zone positive-offset schemes

(Fig. 9 and Fig. 10) also include an undervoltage element (typ-

ically set to 0.8–0.9 of generator nominal voltage) to monitor

the effect of the loss of excitation on the power system. A

low-voltage condition means that the system may collapse.

The undervoltage element operates to accelerate Zone 2 trip-

ping in this case. A typical time delay is 0.25–1 s. The shorter

time delay is recommended for the one-zone scheme and the

longer time delay for the two-zone scheme [10]. On the other

hand, a normal voltage condition means that the system with-

stands the generator loss-of-excitation condition. There is no

need for accelerating Zone 2 operation in this case.

Fig. 10 Two-zone loss-of-field protection using positive- and negative-offset mho elements supervised by a directional element

We have to plot the capability curves, MEL, and SSSL

characteristics in the impedance plane in order to analyze the

operation of the loss-of-field protection relays that have the

characteristics shown in Fig. 7 through Fig. 10. Every point of

these curves in the P-Q plane plots as a point in the impedance

plane at a given voltage magnitude.

A given apparent complex power Sejφ

value corresponding

to an angle φ in the complex P-Q plane plots as an impedance

Zejφ

with the same angle in the impedance plane; the imped-

ance magnitude Z depends on S and the generator terminal

voltage Vt [7] [15]:

( ) ϕ=ϕ+ϕ= j2t

2t e

S

Vsinjcos

S

VZr

(12)

With Vt expressed in kV and S in MVA, (12) gives the im-

pedance value in primary ohms. We obtain the impedance

value in secondary ohms by multiplying the impedance value

in primary ohms by the current transformer ratio CTR and

dividing the result by the voltage transformer ratio VTR.

Fig. 11 depicts the impedance plane representation of the

capability curve and MEL characteristic of a 202 MW genera-

tor. Impedance values are expressed in secondary ohms at the

generator voltage. The generator capability curve corresponds

to that of Fig. 3 with a generator hydrogen pressure of

206 kPa; it is plotted at nominal voltage in the impedance

plane. Fig. 11 also shows the SSSL characteristic at nominal

voltage. Notice that in the impedance plane, the forbidden

operation region is inside the curves.

The generator has a positive-offset, two-zone loss-of-field

protection scheme, including an undervoltage element that

accelerates Zone 2 operation for low-voltage conditions dur-

ing the loss-of-field event. Fig. 11 also shows the relay charac-

teristic with the actual settings, which coincide with those

shown in Fig. 10. For simplicity, the directional element is not

shown. From Fig. 11, it is clear that Zone 2 of the relay cha-

racteristic is set just outside the SSSL characteristic to prevent

the system from losing steady-state stability. However, the

relay characteristic is inside the capability curve in this case.

This leaves a region between the relay characteristic and the

capability curve where the generator is not protected [16]. If a

partial loss-of-field condition results in an impedance value

that stays in this region long enough, the generator may suffer

damage.

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–20 –10 0 10 20 30 40–50

–40

–30

–20

–10

0

10

20

30

Positive-Sequence Apparent Impedance

Real [Sec. Ohms]

Imag [Sec. Ohms]

Z1 Relay

SSSL

MEL

Z2 Relay

Capability

Curve

Fig. 11 Impedance-plane representation of generator capability curve, MEL,

SSSL, and loss-of-field relay characteristic. The relay is set according to Fig. 10 to prevent the system from losing steady-state stability.

For better generator protection, the loss-of-field element

should be set to allow MEL to operate, to prevent the system

from losing steady-state stability, and to protect the generator

from stator-end region damage, as shown in Fig. 12. This fig-

ure shows the capability curve and MEL characteristic of a

312 MW generator. The capability curve, represented in the

impedance plane at nominal voltage, is that of Fig. 5 with a

generator hydrogen pressure of 3 kg/cm2. Impedance values

are expressed in primary ohms at the generator voltage.

Fig. 12 Impedance-plane representation of generator capability curve, MEL,

SSSL, and the loss-of-field relay characteristic. The relay is set to protect the generator from stator-end heating damage and to prevent the system from

losing steady-state stability.

Fig. 13 depicts a P-Q plane representation of the characte-

ristics shown in Fig. 11. The generator capability curve and

the MEL characteristics are taken directly from Fig. 3. This is

an advantage of the P-Q plane representation. The SSSL and

relay characteristics are plotted at nominal voltage. The SSSL

characteristic plots as a circle in the P-Q plane, according to

(10) and (11).

–50 0 50 100 150 200 250–150

–100

–50

0

50

100

150Positive-Sequence Power

MW

MVAR

Relay

Directional

Element

MEL

Z2 Relay

Z1 Relay

SSSL

Fig. 13 P-Q plane representation of generator capability curve, MEL, SSSL, and loss-of-field relay characteristic. The relay is set according to Fig. 10 to

prevent the system from losing steady-state stability.

Fig. 13 also shows the two-zone relay characteristic. We

can see that Zone 2 of the relay characteristic is a circle both

concentric with and inside the SSSL circle as a result of the

setting shown in Fig. 10. As mentioned before, this prevents

the system from losing steady-state stability but leaves the

generator unprotected according to the capability curve.

Application of offset mho elements is the most common

solution to loss-of-field protection today. However, using an

element having a linear characteristic in the P-Q plane (see

Fig. 14) has also been proposed [7] [17]. This characteristic

translates into an offset circular characteristic in the imped-

ance plane.

Fig. 14 Loss-of-field relay having a linear characteristic in the P-Q plane

In a practical implementation of this solution [17], it is rec-

ommended to set the characteristic following the generator

capability curve, the SSSL characteristic, or the MEL charac-

teristic as defined by the user. The loss-of-field element is

supervised by an undervoltage element and an overcurrent

element. If only the loss-of-field element operates, the relay

issues an alarm. If, additionally, the undervoltage element

and/or the overcurrent element operate, the relay initiates

time-delayed tripping. The operating time follows an inverse

law as a function of the generator armature current, ending

with a minimum definite-time delay.

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IV. P-Q PLANE-BASED GENERATOR

PROTECTION AND SUPERVISION

A digital design provides the flexibility to create relay cha-

racteristics in the P-Q plane that are tailored by the capability

curve and SSSL as required. We may define a tripping charac-

teristic for loss-of-field protection and an alarm characteristic

to detect violations of the capability curve. An advantage of

this scope is that we can directly use information on the gene-

rator capability curve and SSSL to set the relay. There is no

need to transfer all the characteristics to the impedance plane.

A. Loss-of-Field Protection Characteristic

The P-Q plane-based loss-of-field protection scheme (see

Fig. 15) includes a loss-of-field element, two active-power

elements, and an undervoltage element (not shown Fig. 15).

The active-power elements act as blinders that restrict cov-

erage along the P axis. This supervision increases the scheme

security for power swings. The left-side active-power element

characteristic coincides with the Q axis. The right-side active-

power element characteristic adapts to the generator load con-

dition: its setting is equal to the measured predisturbance ac-

tive power, plus 20 percent of generator-rated active power.

The upper limit of the right-side active-power element setting

is the generator MVA rating; alternatively, the user may select

an upper limit value, the turbine MW rating, for example.

The relay operating characteristic in the P-Q plane (see

Fig. 15) is the shadowed region below the loss-of-field ele-

ment characteristic and between the characteristics of the ac-

tive-power elements.

When the generator operating point in the P-Q plane falls

inside the relay operating region, the scheme issues an alarm

signal and initiates delayed generator tripping.

0 50 100 150 200 250 300 350 400 450-200

-150

-100

-50

0

50

100

150

200

250

MW

MVAR

Capability Curve

MELSSSL

Loss of Field

Element

Loss of Field

Protection Characteristic

Operating Region

Active Power

Elements

Fig. 15 Loss-of-field element characteristic in the P-Q plane set to coordi-nate with the generator capability curve when the SSSL characteristic is out-

side the capability curve

The loss-of-field element setting shown in Fig. 15 is a good

choice for the case when the SSSL characteristic is outside the

capability curve. In this case, we set the loss-of-field element

characteristic to coincide with the capability curve to protect

the generator from stator-end core heating. This setting per-

mits full use of the generator capability to absorb reactive

power, beyond the MEL setting.

When the SSSL characteristic is inside the generator capa-

bility curve (as may occur in a weak power system), the SSSL

characteristic becomes the factor that limits the amount of

reactive power that the generator can absorb. In this case, we

set the loss-of-field element characteristic just inside the SSSL

characteristic, as shown in Fig. 16.

0 50 100 150 200 250 300 350 400 450-200

-150

-100

-50

0

50

100

150

200

250

MW

MVAR

Capability Curve

MELSSSLCapability

Curve

Loss of Field

Element

Loss of Field

Protection Characteristic

Operating Region

Active Power

Elements

Fig. 16 Loss-of-field element characteristic in the P-Q plane set to coordi-

nate with the SSSL when the SSSL characteristic is inside the capability curve

The P-Q plane-based protection scheme also includes an

undervoltage element, typically set to 0.8–0.9 of generator

nominal voltage. The undervoltage element operates to accele-

rate scheme operation when a low-voltage condition indicates

that the system may collapse. For normal voltage conditions

during the loss-of-field event, there is no need for accelerating

operation, because the system is strong.

B. Alarm Characteristic

The alarm characteristic in the P-Q plane (see Fig. 17) is

formed by the upper and right-side branches of the capability

curve, by the loss-of-field element characteristic, and by an

active-power characteristic that coincides with the Q axis. The

alarming region is outside the characteristic. When the SSSL

characteristic is outside the capability curve (as in Fig. 15), the

alarm characteristic fully coincides with the generator capabil-

ity curve. This is the case depicted in Fig. 17. When the SSSL

characteristic is inside the capability curve (as in Fig. 16), the

lower side of the alarm characteristic lies inside the capability

curve, coinciding with the loss-of-field element characteristic.

Depending on the limit violated by the generator operating

point (P,Q), the alarm element issues one of the following

alarms:

• Armature-Current Limit Violation

• Rotor-Current Limit Violation

• Loss-of-field/Underexcitation Condition

• Motoring Condition

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|

-200

-150

-100

-50

0

50

100

150

200

250

MVAR

0 50 100 150 200 250 300 350 400 450

MW

SSSL

Relay Alarm

Characteristic

MEL

Alarming Zone

Fig. 17 The alarm characteristic is formed by the capability curve, the loss-

of-field protection characteristic, and an active-power characteristic coincid-

ing with the Q axis.

C. Combined Characteristic

Once the generator capability curve and the SSSL characte-

ristic have been defined, the relay characteristic can be de-

fined. We also need to obtain measurements of the generator

active- and reactive-power output values. Since this relay re-

sponds to balanced generator operating conditions, positive-

sequence P and Q values are a good choice for relay quanti-

ties.

Fig. 18 depicts the relay combined characteristic for loss-

of-field protection and capability-curve violation alarming. In

this case, the loss-of-field element is set according to the ca-

pability curve. Measured positive-sequence P and Q values

define the machine operating point in the P-Q plane. The op-

erating point is tested against the relay characteristic to deter-

mine whether the generator is operating in normal or abnormal

conditions. For an abnormal operating condition, the relay

generates an alarm and, in the case of a loss-of-field condition,

initiates delayed tripping.

For example, when the generator operates in a normal con-

dition at the point PA,QA, there is no relay operation or alarm-

ing. When the generator operates at the point PB,QB, the relay

issues an alarm indicating violation of the armature-current

limit. Finally, when the generator operating condition is at the

point PC,QC, the loss-of-field element alarms and initiates de-

layed tripping.

0 50 100 150 200 250 300 350 400 450-200

-150

-100

-50

0

50

100

150

200

250

MW

MVAR

MELSSSL

PB, QB

Generator Normal Operation

Zone (Alarming Outside of the

Zone)

PA, QA

PC, QC

Relay

Protection

Zone

Fig. 18 Relay combined characteristic provides loss-of-field protection and

capability-curve violation alarming.

D. Setting Relay Characteristic

Fig. 19 shows the information required to define the relay

characteristic, including both loss-of-field protection and ca-

pability-curve violation alarming.

Fig. 19 P and Q points required for defining the relay characteristic

Points (P0,Q0), (P1,Q1), (P2,Q2), and (P3,Q3) define the ca-

pability curve and also serve to define the alarm characteristic

totally or partially. We may also derive point (P1,Q1) from the

generator rated MVA and power factor data.

Points (P4,Q4) and (P5,Q5) define the loss-of-field element

characteristic. For linear or circular characteristics, these two

points allow making an exact representation. For other types

of characteristics, we can make a fair approximation for the

sake of relay setting using these two points. If required, it is

possible to get a more accurate representation of the loss-of-

field element characteristic by providing more pairs of P,Q

points. This could be the case of a user-defined loss-of-field

element characteristic.

A digital relay may automatically select the settings of the

loss-of field and alarm characteristics by using the information

given in Fig. 19, and also generator-impedance data and sys-

tem-impedance data. To set the loss-of-field element as in

Fig. 15, the relay makes point (P4,Q4) coincide with (P3,Q3)

and point (P5,Q5) coincide with (P2,Q2). To set the loss-of-

field element as in Fig. 16, the relay selects the characteristic

to be a circle, with points (P4,Q4) and (P5,Q5) placed just in-

side the SSSL circle (not shown in Fig. 19). Equations (10)

and (11) define the SSSL circle.

We can select the operating relay characteristic for alarm-

ing and/or generator tripping from several (two or more) relay

characteristic options based on the generator cooling-system

status and generator operating conditions. Fig. 3 and Fig. 5

show capability curves for different cooling-system pressures;

these curves can be used to define the relay characteristic for

the different cooling conditions.

Appendix B describes methods to program into a digital re-

lay the generator capability curve, MEL, and SSSL characte-

ristics, using information provided by the user.

V. GENERATOR DYNAMIC SIMULATION STUDY

A. EMPT Model Description

The EMTP model simulates two 160 MW steam-powered

units connected to the Mexican Power System (see Fig. 20)

The generating units operate in the Juan de Dios Bátiz Paredes

thermal power station that belongs to Comisión Federal de

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Electricidad, the national Mexican utility. This power station

is interconnected with two substations of the national Mexican

power system through two 230-kV transmission lines.

Fig. 20 One-line diagram of the power-system section of interest for digital

simulation

The simulation model includes the generators and their

control systems, the step-up transformers, the transmission

lines, and an equivalent of the power system beyond the area

of interest. Generator models include the turbine speed gover-

nor, automatic voltage regulator, and power system stabilizer

(PSS) with actual transfer functions and setting values. Gene-

rator models were validated using the results of factory and

commissioning tests of both units. Some protective relay func-

tions under evaluation are also included in the simulation.

Appendix A provides data on the generating units and asso-

ciated power system.

For these simulations, we assume that MEL and OEL are

disabled. MEL really has no effect for the loss-of-field modes

considered in this study (field short circuit and field breaker

opening); OEL would operate in only one case (for the other

generator on line), but its operation would occur outside of the

simulation time that we report.

The block diagram of Fig. 21 shows how the power-

frequency and the excitation-system control loops of the gene-

rating units have been modeled in EMTP. This figure shows

the relationship between the different control systems and

their interaction with the turbine and the generator. The speed-

droop characteristic (percentage change in frequency that

would cause the output power of the units to change by

100 percent) has been set to 5 percent. Fig. 43 (Appendix A)

provides additional information on the excitation-system con-

trol.

Fig. 21 Block diagram of the generating-unit power-frequency and excita-

tion-system control loops

B. Simulation Cases

The study includes EMTP simulation of loss-of-field and

loss-of-synchronism conditions of one of the two 160 MW

units for five different cases. The study covered the following

groups of cases:

1. Two different initial load conditions in the generator that

loses excitation: 40 MW (25 percent of rated active pow-

er) and 150 MW (94 percent of rated active power).

2. Two different modes of loss of field:

a. Field short circuit (slip-ring flashover, for example).

b. Field breaker opening during normal operation (hu-

man error or interlock override, for example). Break-

er opening leaves a 0.2 Ω discharge resistor con-

nected in the field circuit. This resistance value is

very close to that of the field circuit.

3. Two different initial operating conditions in the power

station: one generator and two generators on line.

The next section presents and discusses the simulation re-

sults for five of the cases analyzed in this study:

• Case 1: Loss of excitation of one generator (with the

other generator on line) because of a field short circuit

while the generator is carrying 150 MW.


other generator on line) because of a field short circuit

while the generator is carrying 40 MW.


other generator on line) because of a field breaker

opening with discharge resistor insertion while the ge-

nerator is carrying 150 MW.

• Case 4: Loss of excitation of one generator (only this

generator on line) because of a field short circuit while

the generator is carrying 150 MW.

• Case 5: Loss of synchronism of one generator (only

this generator on line) because of a temporary external

fault, without generator-control systems.

C. Simulation Results

1) Case 1: Loss of excitation of one generator (with the

other generator on line) because of a field short circuit while


In this case, the loss of excitation is the result of a field

short circuit when the generator is carrying 150 MW,

0 MVAR, which represents 94 percent of rated active power.

Fig. 22 shows the effect of the loss of excitation on the gene-

rator positive-sequence active- and reactive-power output,

terminal voltage, and armature current. The loss of field oc-

curs at 2.1 s of simulation time.

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Fig. 22 Behavior of active and reactive power, armature current, and ter-

minal voltage when the generator loses excitation because of a field short circuit while the generator is carrying 150 MW (Case 1)

Fig. 22 shows that the generator loses synchronism (signif-

icant active-power oscillations start) approximately 8 s after

the loss of field. Significant oscillations take place as a result

of pole slipping and the effect of saliency (different d-axis and

q-axis reactance values) [1]. All these factors combine to pro-

duce slip variations during the slip cycle. In the first 7 s of

machine operation without excitation (see Fig. 22), the active

power diminishes slowly from 150 MW to about 135 MW

until the machine loses synchronism, and then falls abruptly to

approximately 70 MW in the first pole slip. Subsequent oscil-

lations (not shown) take place around an average value of ap-

proximately 100 MW. The reactive power drawn by the gene-

rator varies almost linearly from zero to an average of

-200 MVAR. As a result, the armature current grows approx-

imately 106 percent, from 5.8 kA (0.75 p.u.) to 12 kA (1.55

p.u.). The terminal voltage drops approximately 25 percent,

from 8.8 kV (1.016 p.u.) to an average value of about 6.6 kV

(0.76 p.u.).

Fig. 23 depicts the impedance plane representation of

Case 1, with all the values expressed in secondary ohms. This

is a version of Fig. 11, but with the impedance trajectory add-

ed and the MEL characteristic eliminated for simplicity.

Fig. 23 Representation of Case 1 in the impedance plane. Relay characteris-

tics are inside the capability curve. Both loss-of-field element zones operate in this case.

As mentioned with reference to Fig. 11, this generator has

a positive-offset, two-zone loss-of-field protection scheme,

including an undervoltage element. Fig. 23 shows the relay

characteristic with the actual settings, corresponding to those

shown in Fig. 10. For simplicity, the directional element is not

shown. The undervoltage element is set to 87 percent of the

nominal voltage, equivalent to a phase-to-ground voltage of

7.5 kV.

The impedance trajectory starts at (24, 0) Ω. This point in

the impedance plane corresponds to the initial operating con-

dition (150 MW, 0 MVAR) in the P-Q plane. Within the simu-

lation time frame, the impedance trajectory penetrates both

zones of the relay characteristic and describes a loop around

the point (4, –8) Ω. The machine is operating as an induction

generator in this region. With a setting of 7.5 kV, the under-

voltage element also operates in this case. Its operation takes

place 5.5 s after the loss-of-field condition (see Fig. 22).

To keep this figure simple, we only show the first 11 s of

simulation time. Oscillations resulting from the out-of-step

machine operation generate an oscillatory impedance trajecto-

ry after this initial stage. In Case 3, we will present 30 s of

simulation and discuss this effect.

We use a three-dimension resistance-reactance-time (R-X-

t) space to introduce the time variable in the impedance-plane

analysis [16]. Fig. 24 shows the R-X-t representation of

Case 1. The relay characteristic is a collection of circles that

forms a cylinder. We only show the Zone 2 characteristic.

Relay operation results from the impedance trajectory pene-

trating this cylinder.

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Fig. 24 Representation of Case 1 in the resistance-reactance-time space

gives a three-dimension view of the loss-of-field process.

We can define the instant in which the impedance trajecto-

ry penetrates the relay characteristic by developing projections

of the R-X-t space on the R-t or the X-t planes. Fig. 25 shows

the projection of Fig. 24 on the R-t plane. The gray rectangle

represents the loss-of-field element characteristic (Zone 2) as

seen in this projection. We can see that Zone 2 initiates opera-

tion 2.9 s after the loss of field.

Fig. 25 Representation of Case 1 in the resistance-time plane (projection of

Fig. 24 on the R-t plane) shows the instant in which the impedance trajectory

penetrates the Zone 2 characteristic.

Fig. 26 depicts a P-Q plane representation of Case 1. This

figure is a version of Fig. 13, but without the traditional loss-

of-field relay characteristics and including the P-Q plane-

based loss-of field element characteristic. Fig. 26 also shows

the loss-of-excitation P-Q trajectory. The small variation of

active power and the significant variation of reactive power in

this time span translate into an almost vertical loss-of-field

trajectory in the P-Q plane.

The right-side active-power element of the P-Q plane-

based loss-of-field element adaptively sets to 182 MW, result-

ing from the initial load of 150 MW plus 20 percent of the

rated power of 160 MW (see Fig. 26). The loss-of-field ele-

ment, set to coincide with the capability curve in this case (the

SSSL characteristic is outside the capability curve), detects the

loss-of-excitation condition, issues an alarm, and initiates de-

layed tripping. The active-power elements restrict the operat-

ing zone just to the area needed to reliably detect the loss-of-

field condition. Hence, the loss-of-field element operating

zone fits very well to the almost vertical loss-of-field P-Q tra-

jectory.

Fig. 26 Representation of Case 1 in the P-Q plane. The P-Q plane-based

loss-of-field element characteristic is set to coincide with the generator capa-bility curve. The loss-of-field P-Q locus describes an almost vertical trajecto-

ry.


other generator on line) because of a field short circuit while


This case serves to analyze the effect of the intial load

when compared to Case 1. The generator loses excitation at a

load of 40 MW, 0 MVAR, which is 25 percent of rated active

power. Fig. 27 shows that, after some small initial oscillations,

the generator gets to a new steady state without losing syn-

chronism, and remains operating as a synchronous generator

based on the reluctance principle. The reluctance torque re-

sulting from machine saliency (Xd ≠ Xq) allows this cylindric-

al-rotor generator to deliver 25 percent of rated load without

losing synchronism. However, because the generator lost exci-

tation, it needs to draw reactive power from the system to es-

tablish an armature-reaction magnetic flux.

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Fig. 27 Behavior of active and reactive power, armature current, and ter-minal voltage when the generator loses excitation because of a field short

circuit while the generator is carrying 40 MW (Case 2)

In this case (see Fig. 27), the active power falls from

40 MW to approximately 36.5 MW in 30 s, and the reactive

power drawn by the generator varies from zero to

-110 MVAR. As a result, the armature current grows from

1.52 kA (0.195 p.u.) to 5.2 kA (0.67 p.u.) and remains below

nominal current. The terminal voltage drops approximately

13 percent, from 8.82 kV (1.018 p.u.) to 7.652 kV (0.88 p.u.).

It is clear from these results that a loss of field with light load

is much less stressful for both the generator and the power

system than a loss of field with high load.


Case 2. The impedance trajectory starts at the point (90, 0) Ω

(not shown in the figure), corresponding to the initial operat-

ing condition (40 MW, 0 MVAR) in the P-Q plane. The im-

pedance trajectory penetrates both zones of the relay characte-

ristic and ends at the point (7, –23) Ω. The machine operates

as a reluctance synchronous generator in this region. The un-

dervoltage element, set to 7.5 kV, does not operate in this case

(see Fig. 27).

Fig. 28 Representation of Case 2 in the impedance plane; both loss-of-field

element zones operate

Fig. 29 shows the R-X-t representation of Case 2. We fur-

ther projected the simulation in Fig. 29 on the R-t plane (not

shown) and determined that Zone 2 initiated operation 14 s

after the loss-of-field.


showing the impedance trajectory for 30 s

Fig. 30 depicts a P-Q plane representation of Case 2, in-

cluding the P-Q plane-based loss-of-field element characteris-

tic. As in the previous case, the loss-of-excitation trajectory is

almost vertical in the P-Q plane. The right-side active-power

element of the P-Q plane-based loss-of-field element assumes

in this case a setting of 72 MW, resulting from the initial load

of 40 MW plus 20 percent of the rated power. Again, the relay

operating zone fits very well to the loss-of-field P-Q trajecto-

ry. The loss-of-field element detects the P-Q trajectory leaving

the generator capability curve, issues an alarm, and initiates

delayed tripping.

Fig. 30 Representation of Case 2 in the P-Q plane. The right-side active -

power element adaptively sets to the generator initial load. The P-Q trajectory

is almost vertical.


other generator on line) because of a field breaker opening

with discharge resistor insertion while the generator is carry-

ing 150 MW.

This case serves to analyze the effect of the breaker dis-

charge resistor inserted in the field as compared to a field

short circuit (Case 1). The generator loses excitation at a load

of 150 MW, 0 MVAR (94 percent of rated active power) be-

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cause of a field breaker opening with insertion of a 0.2 dis-

charge resistor in the field circuit. Fig. 31 shows that the gene-

rator loses synchronism around 4 s after the loss of field. The

reactive power falls abruptly to negative values even before

the loss of synchronism, indicating that the magnetic field

disappears rapidly, and then starts oscillating. The effect of the

discharge resistor is to reduce the time constant of the expo-

nentially decaying magnetic flux, thus accelerating the loss of

synchronism.

Fig. 31 shows 30 s of simulation time. It is therefore possi-

ble to observe several cycles of the machine oscillatory tran-

sient process while operating as an induction generator. The

oscillation amplitude and frequency decrease with time as a

result of the machine governor taking action to control speed.

In this case (see Fig. 31), the active power falls from 150 MW

to approximately 50 MW in 30 s, and the reactive power

drawn by the generator varies from zero to approximately

-125 MVAR. The armature current, after relatively large oscil-

lations, reaches an average value of 6 kA (0.77 p.u.), very

close to the initial value of 6.8 kA (0.75 p.u.). However, in

30 s the terminal voltage drops approximately 14 percent,

from 8.8 kV (1.016 p.u.) to an average value of about 7.5 kV

(0.87 p.u.).

Fig. 31 Behavior of active and reactive power, armature current, and ter-

minal voltage when the generator loses excitation by field breaker opening with discharge resistor insertion while the generator is carrying 150 MW

(Case 3)

Fig. 32 depicts the impedance-plane representation of

Case 3. As in Case 1, the impedance trajectory starts at (24, 0)

Ω, corresponding to the initial operating condition (150 MW,

0 MVAR) in the P-Q plane. During the 30 s of simulation time

that we show, the impedance trajectory reflects the result of

several cycles of machine oscillations after losing synchron-

ism. After penetrating both zones of the relay characteristic for

the first time and making a loop around the point (6, –9) Ω,

the impedance trajectory oscillates, and moves into and out of

the relay characteristic several times. In real life, loss-of-field

protection operates before 30 s and trips the machine. Hence,

the impedance trajectory ends before 30 s. The undervoltage

element, set to 7.5 kV, operates 2.9 s after the loss of field (see

Fig. 31).

Fig. 32 Representation of Case 3 in the impedance plane. The impedance

trajectory moves into and out of the relay characteristic as the generator oscil-

lates.



shown) and determined that Zone 2 initiated operation 1.36 s

after the loss-of-field. In this case, Zone 2 starts operating

before the generator loses synchronism as a result of the rapid

magnetic-flux decaying process, which then resulted in a rapid

increase of the reactive power drawn by the generator.


showing impedance oscillations

Fig. 34 depicts a P-Q plane representation of Case 3. The

loss-of-excitation P-Q trajectory descends rapidly and almost

vertically to penetrate the P-Q plane-based loss-of-field ele-

ment characteristics before starting to oscillate.

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Fig. 34 Representation of Case 3 in the P-Q plane; P-Q trajectory reflects

machine oscillations

4) Case 4: Loss of excitation of one generator (only this

generator on line) because of a field short circuit while the

generator is carrying 150 MW.

This case serves to analyze the effect of having only one

generator on line at the moment of the loss of field, as com-

pared to Case 1, in which there are two generators on line. The

generator loses excitation at a load of 150 MW, 0 MVAR

(94 percent of rated active power). Fig. 35 shows that the ge-

nerator loses synchronism approximately 7 s after the loss of

field, 1 s faster than with two generators on line.

In this case (see Fig. 35), the active power falls from

150 MW to approximately 60 MW in the first pole slip, and

then oscillates around an average value of 100 MW (not

shown in the figure). The reactive power drawn by the genera-

tor varies from zero to an average of –150 MVAR. Recall that

in Case 1 the other generator injects reactive power to support

voltage and the generator that lost the field needs to draw up

to –200 MVAR. The armature current grows approximately

80 percent from 5.8 kA (0.75 p.u.) to an average value of

about 10.5 kA (1.35 p.u.). The terminal voltage drops approx-

imately 35 percent, from 8.8 kV (1.016 p.u.) to an average

value of about 5.7 kV (0.66 p.u.). This voltage drop, higher

than that in Case 1, results from not having a neighboring ge-

nerator to support voltage.

Fig. 35 Behavior of active and reactive power, armature current, and ter-minal voltage when the generator loses excitation because of a field short

circuit while the generator is carrying 150 MW with only one generator on

line (Case 4)


Case 4. As in Cases 1 and 3, the impedance trajectory starts at

(24, 0) Ω, corresponding to the initial operating condition (150

MW, 0 MVAR) in the P-Q plane. Within the simulation time

frame, the impedance trajectory penetrates both zones of the

relay characteristic and initiates a loop around the point (3, –7)

Ω when the machine loses synchronism.

Fig. 36 Representation of Case 4 in the impedance plane; both loss-of-field

element zones operate



shown) and determined that Zone 2 initiated operation 2.9 s

after the loss-of-field.

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Fig. 38 depicts a P-Q plane representation of Case 4. The

loss-of-excitation P-Q trajectory descends almost vertically

and penetrates the P-Q plane-based loss-of-field element cha-

racteristic.

Fig. 38 Representation of Case 4 in the P-Q plane

5) Case 5: Loss of synchronism of one generator (only this

generator on line) because of a temporary external fault,

without generator control systems.

In this case, the generator loses synchronism as a result of

an external temporary three-phase fault. In the prefault condi-

tion there is only one generator on line, carrying 155 MW,

0 MVAR. Generator AVR, speed control, and power-system

stabilizer are out of operation in this simulation. We represent

the power system in this simulation as an ideal voltage source

in series with a reactance Xs of 0.374 primary ohms at 15 kV.

Xs includes the generator step-up transformer and the power-

system equivalent. The critical clearing time for this system

configuration is 190 ms. In this case, we applied the fault dur-

ing 191 ms for the system to become unstable. Fig. 39 shows

the effect of the loss of synchronism on the generator positive-

sequence active and reactive-power output, terminal voltage,

and armature current.

Fig. 39 Behavior of active and reactive power, armature current, and ter-minal voltage when the generator loses synchronism as a result of a temporary

external fault (Case 5)

Fig. 39 shows the oscillations of all variables resulting

from the out-of-step condition. The active power varies be-

tween 200 and –150 MW, and the reactive power oscillates

between 0 and –150 MVAR. As a result, the armature current

varies between 8 and 23 kA (1.03 to 2.96 p.u.) and the termin-

al voltage oscillates between 0 and 6.2 kV (0 to 0.72 p.u.). The

fact that the terminal voltage drops to zero once per oscillation

cycle indicates that the relay is located at the system electrical

center. Fig. 39 also shows that the slip frequency grows with

time as a result of the rotor acceleration increasing with every

new pole slip.

Fig. 40 depicts the impedance-plane representation of

Case 5. The impedance locus describes the typical circular

loops of an unstable two-machine power system. There are

multiple penetrations of the impedance trajectory in the relay

Zone 1, one per oscillation cycle. The impedance locus is al-

ways inside Zone 2, but the directional element (not shown in

Fig. 40) resets this zone almost once per oscillation cycle.

Given the prevailing low-voltage condition, the undervoltage

element, set to 7.5 kV, operates at the beginning of the out-of-

step condition (see Fig. 39). Time delay of both zones should

prevent relay misoperation for this unstable power swing.

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Fig. 40 Representation of Case 5 in the impedance plane. The impedance

locus describes the typical circular loops of an unstable two-machine power system.

Fig. 41 shows the R-X-t representation of Case 5. Again, it

is clear that the trajectory stays inside Zone 2, which is the

only zone represented in this figure.


showing the result of system unstable oscillations

Fig. 42 depicts a P-Q plane representation of Case 5, in-

cluding the traditional and the P-Q plane-based loss-of-field

element characteristics. Traditional relay characteristics are

represented at nominal voltage. Oscillations of active and

reactive power describe almost elliptical trajectories in this

plane. Fig. 42 clearly shows the advantage of the active-power

elements acting as blinders to restrict relay coverage along the

active-power axis. The loss-of-field P-Q trajectories spend less

time inside the P-Q plane-based loss-of-field element operat-

ing zone than they would spend inside the traditional relay

operating zone. Hence, the active-power blinders provide an

inherent security for power swings to the P-Q plane-based

loss-of-field element.

Fig. 42 Representation of Case 5 in the P-Q plane. The P-Q locus describes

almost elliptical trajectories. Active-power blinders provide security for pow-er swings to the loss-of-field P-Q plane-based element.

VI. CONCLUSIONS

1. The following factors limit the active and reactive power

that a generating unit can deliver to the power system un-

der given operating conditions:

a. The generator capability curve (determined by the

machine design)

b. Voltage limits

c. Power system stability limits

d. Minimum excitation limiter (MEL)

e. Overexcitation limiter (OEL)

2. Traditional rules for determining generator loss-of-field

settings may result in settings that do not provide proper

generator protection for certain operating conditions.

3. Providing proper settings for the loss-of-field relay re-

quires knowledge of the generator capability curve and

SSSL characteristic.

4. A digital relay design provides the flexibility for creating

relay characteristics in the P-Q plane for loss-of-field pro-

tection and for capability-curve violation alarming. These

characteristics are tailored by the capability curve and the

SSSL, as required.

5. The P-Q plane-based loss-of-field protection scheme in-

cludes the following elements:

a. One loss-of-field element with a characteristic that fits

to the most limiting of two curves: the capability

curve or the SSSL characteristic.

b. Two active-power elements that act as blinders to en-

hance scheme security for power swings.

c. One undervoltage element that accelerates scheme op-

eration when a low-voltage condition during the loss-

of-field condition indicates that the system may col-

lapse.

6. Dynamic simulation of loss-of-field and power-swing

conditions is highly recommended for selecting and set-

ting loss-of-field protection schemes. The simulation

models should include the generator and its control sys-

tems, the step-up transformer, and the external power sys-

tem. Generator models should include at least the turbine

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speed governor, automatic voltage regulator, and power

system stabilizer (PSS). These generator models should

be validated using field test results.

7. Simulation results may be presented in an impedance

plane together with the time dimension. This three-

dimension resistance-reactance-time (R-X-t) space allows

you to visualize the apparent impedance trajectory as time

progresses. Make projections of the R-X-t representation

on the R-t or the X-t planes to determine the instant at

which relay elements start operation.

8. The impact of the loss-of-field condition on the generator

and the power system depends mainly on the generator in-

itial loading condition. In our simulations, we found that

with an initial load of 150 MW, the generator loses syn-

chronism as a result of the loss-of-field condition in all

the cases. With an initial load of 40 MW, the generator,

operating without excitation, remained in synchronism,

working as a reluctance synchronous generator.

9. Insertion of a discharge resistor in the field circuit when

the field breaker opens reduces the time constant of the

exponentially decaying magnetic flux, thus accelerating

the loss of synchronism.

10. When two generators are on line, the loss-of-field condi-

tion of one of them causes a lower voltage depression

than when only one generator is on line. However, with

two generators on line, the generator that loses excitation

consumes more reactive power and has higher armature

current because of the higher voltage.

11. Loss-of-synchronism simulation results show that using

active-power blinders to restrict the width of the loss-of-

field element characteristic along the real axis of the P-Q

plane enhances scheme security for power swings.

VII. APPENDIX A. POWER SYSTEM DATA

External Power System Data (Cases 1 Through 4)

Positive-sequence equivalent

impedance

9.4669 + j41.1368 ohms at 230 kV

Equivalent source (phase voltage)

134.5 kV

Generator Data

Rated voltage 15 kV

Rated MVA 202 MVA

Rated active power (turbine) 160 MW

Poles 2

Xd 1.540 p.u.

Xq 1.520 p.u.

Xd´ 0.170 p.u.

Xq´ 0.246 p.u.

Xd´´ 0.123 p.u.

Xq´´ 0.123 p.u.

Tdo´ 9.1 s

Tdo´´ 0.035 s

Tqo´´ 0.054 s

Total inertia constant (H) 3.18 kW-s/kVA

Step-Up Transformer Data

Rated MVA 120/200 MVA

Rated voltage 15/230 kV

Z% 8.1% at 120 MVA

Connection DY11

Governor

Droop 5%

Field Circuit and Excitation System

Nominal field voltage 280 Vdc

Nominal field current 1290 Adc

Field resistance 0.1947 Ω

Field discharge resistance 0.2 Ω

Control systems See Fig. 43

Protection Scheme

CTR 10000/5

VTR 15000/120

Loss-of-field relay settings See Fig. 10

s02.01

1

+3.273

s75.01

s47.01∗

++

s21

s2

+ s5.01

s21

++

1.0s15.01

s2.01∗

++

Vt

P

–+

+

–Efd

Vref

AVR

PSS

+5 p.u.

+0.05 p.u.

–0.05 p.u.

–3.76 p.u.

Fig. 43 Generator control-system block diagram

VIII. APPENDIX B: METHODS TO DEFINE THE GENERATOR

CAPABILITY CURVE, MEL, AND SSSL CHARACTERISTICS

Three methods to define these characteristics are:

1. Create a reference table with P and Q points, obtained

from the characteristic, and perform a linear interpolation

between adjacent points to approximate the actual curve.

This gives a piecewise linear approximation.

2. Create a reference table with P and Q points, obtained

from the characteristic, and use a curve-fitting algorithm

to obtain the expressions (for example, quadratic equa-

tions) that approximate the different curves composing

the capability curve.

3. Use circle equations to approximate the different curves

composing the capability curve.

We can use each one of these methods to approximate the

capability curve, MEL, and SSSL characteristics. Circle equa-

tions (Method 3) typically provide fairly accurate approxima-

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tions of capability curves and SSSL characteristics; MEL cha-

racteristics may require a linear interpolation or a quadratic

curve fitting. As an example, we discuss the application of

Method 3 to define the capability curve.

Fig. 19 shows the capability curve and four points: (P0,Q0),

(P1,Q1), (P2,Q2) and (P3,Q3). With these points, we can deter-

mine the three circle equations to approximate the capability

curve.

A. Armature-Current Heating Limit

The armature-current heating limit curve shown in Fig. 44

can be approximated with the following circle equation:

( ) φ≤β≤α−+=β β forC•ie•RS •i (13)

Where R is the radius of the circle, C defines the position

of the circle center (C = 0 in this case), φ is the circle upper

limit that corresponds to the minimum lagging power factor

(PFLag), and –α is the circle lower limit that corresponds to the

minimum leading power factor (PFLead).

Fig. 44 Armature-current heating limit circle

We can determine R, φ, and α from (14), (15), and (16):

nomSR = (14)

( ) ( )nom11–

Lag1– S/PcosPFcos ==φ (15)

( ) ( )nom21–

Lead1– S/PcosPFcos ==α (16)

Where PFLag is the minimum lagging power factor, PFLead

is the minimum leading power factor, and Snom is the generator

nominal capacity.

B. Field-Current Heating Limit

The field-current heating limit curve shown in Fig. 45 can

be approximated with the following circle equation:

( )2

forCieRSi π

≤β≤ρ•+•=β β• (17)


of the circle center, and ρ is the circle lower limit.

Fig. 45 Field-current heating limit circle

We need to solve (18), (19), and (20) to obtain R, C, and ρ:

1PcosR =ρ• (18)

1QCsinR =+ρ• (19)

0QCR =+ (20)

C. Stator-End Core Heating Limit

The stator-end core heating limit curve shown in Fig. 46

can be approximated with the following circle equation:

( ) γ≤β≤π+=β β–•

2

3forC•ie•RS

•i (21)


of the circle center, and –γ is the circle upper limit.

Fig. 46 Stator-end core heating limit circle

We need to solve (22), (23), and (24) to obtain R, C, and γ.

2PcosR =γ• (22)

2QsinR–C =γ• (23)

3QR–C = (24)

IX. REFERENCES

[1] D. Reimert, Protective Relaying for Power Generation Systems. Boca

Raton: CRC Press, 2006.

[2] P. Kundur, Power System Stability and Control. New York: McGraw-

Hill, 1994.

[3] S. B. Farnham and R. W. Swarthout, “Field excitation in relation to

machine and system operation,” AIEE Trans., vol. 72, pt. III, no. 9, pp.

1215−1223, Dec. 1953.

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[4] S. S. Choy and X. M. Xia, “Under excitation limiter and its role in pre-

venting excessive synchronous generator stator end-core heating,” IEEE

Trans. Power Syst., vol. 15, no. 1, pp. 95−101, February 2000.

[5] Requirements for Cylindrical Rotor Synchronous Generators, 1989.

ANSI Std. C50.13−1989.

[6] Standard for Requirements for Salient-Pole Synchronous Generators

and Generator/Motors for Hydraulic Turbine Applications, 1982. ANSI

Std. C50.12−1982.

[7] J. L. Blackburn, Protective Relaying, Principles and Applications, 2nd

Edition. New York-Basel: Marcel Dekker, Inc., 1998.

[8] F. P. DeMello and C. Concordia, “Concepts of synchronous machine

stability as affected by excitation control,” IEEE Trans. Power App.

Syst., vol. PAS−88, No. 4, pp. 316−329, April 1969.

[9] IEEE Guide for AC Generator Protection, 1995, IEEE Standard

C37.102−1995.

[10] Draft Guide for AC Generator Protection, IEEE Standard

C37.102/D7−200X, April 2006.

[11] C. K. Seetharaman, S. P. Verma, and A. M. El-Serafi, “Operation of

synchronous generators in the asynchronous mode,” IEEE Trans. Power

App. Syst., vol. PAS−93, pp. 928−939, 1974.

[12] C. R. Mason, “A new loss of excitation relay for synchronous genera-

tors,” AIEE Trans., vol. 68, pt. II, pp. 1240−1245, 1949.

[13] J. Berdy, “Loss-of excitation protection for modern synchronous genera-

tors,” General Electric Co. Document GER-3183.

[14] R. L. Tremaine and J. L. Blackburn, “Loss-of-field protection for syn-

chronous machines,” AIEE Trans., vol. 73, pt. III, pp. 765−772, August

1954.

[15] P. M. Anderson, Power System Protection. New York: IEEE

Press/McGraw-Hill, 1999.

[16] R. Sandoval, “The three dimensions of impedance: loss of field protec-

tion of a synchronous machine,” VIII Iberoamerican Symposium on

Power System Protection, Monterrey, N.L., Mexico, May 21–26, 2006

(in Spanish).

[17] M. Stein, Application Guide A03–0211, ASEA Relays, December 1983.

X. BIOGRAPHIES

Ramón Sandoval is a protection engineer for Comisión Federal de Electrici-

dad at Topolobampo Thermal Power Station. He has worked for CFE since 1992 in electrical maintenance of power and industrial equipment such as

induction motors, synchronous generators, breakers, AVRs, and step-up trans-

formers. For the last five years he has been a power station protection engi-neer, installing, testing, and applying different types of protective equipment

commonly used in industrial plants and power systems. This includes a varie-

ty of electromechanical, static and digital multifunction relays. He received training in power system modeling and simulation from LAPEM using ATP

and has worked developing field procedures for protective relay testing using

power system simulators and transient simulation software.

Armando Guzmán (M 1995, SM 2001) received his BSEE with honors from

Guadalajara Autonomous University (UAG), Mexico, in 1979. He received a diploma in fiber-optics engineering from Monterrey Institute of Technology

and Advanced Studies (ITESM), Mexico, in 1990, and his MSEE from Uni-

versity of Idaho, USA, in 2002. He served as regional supervisor of the Pro-tection Department in the Western Transmission Region of the Federal Elec-

tricity Commission (the electrical utility company of Mexico) in Guadalajara,

Mexico for 13 years. He lectured at UAG in power system protection. Since 1993 he has been with Schweitzer Engineering Laboratories in Pullman,

Washington, where he is presently Research Engineering Manager. He holds

several patents in power system protection and metering. He is a senior mem-ber of IEEE and has authored and coauthored several technical papers.

Héctor J. Altuve received his BSEE degree in 1969 from the Central Univer-

sity of Las Villas, Santa Clara, Cuba, and his Ph.D. in 1981 from Kiev Poly-technic Institute, Kiev, Ukraine. From 1969 until 1993, Dr. Altuve served on

the faculty of the Electrical Engineering School, at the Central University of

Las Villas. He served as professor, Graduate Doctoral Program, Mechanical and Electrical Engineering School, at the Autonomous University of Nuevo

León, Monterrey, Mexico, from 1993 to 2000. In 1999–2000, he was the

Schweitzer Visiting Professor at Washington State University’s Department of Electrical Engineering. In January 2001, Dr. Altuve joined Schweitzer

Engineering Laboratories, Inc., where he is currently a Distinguished Engi-

neer and Director of Technology for Latin America. He has authored and coauthored more than 100 technical papers and holds three patents. His main

research interests are in power system protection, control, and monitoring. Dr.

Altuve is an IEEE Senior Member and a PES Distinguished Lecturer.

Copyright © CFE / SEL 2006


TP6260-01

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Resumen:

El generador síncrono es el núcleo del sistema eléctrico de

potencia, y es el elemento que está más expuesto a condiciones

anormales debidas a perturbaciones en el sistema; por esto los

esquemas de protección deben cubrir cualquier condición de falla

que pueda afectar su operación nominal.

!ormalmente los esquemas cubren cualquier condición

anormal de operación; pero solo algunos dispositivos son

diseñados para proteger la influencia eléctrica en los elementos

mecánicos del turbogenerador al evaluar la variación angular a

frecuencias por debajo de la frecuencia síncrona. En este trabajo

se propone utilizar la variación de los ángulos de fase del voltaje y

corriente en terminales del generador para crear una lógica de

operación en función del contenido subsíncrono en el par eléctrico

y de la coincidencia con las frecuencias criticas de oscilación

torsional.

Palabras claves: Resonancia Subsincrona, Interacción

Torsional Subsincrona, Relevador de Corriente Subsincrona,

Fourier, Prony

I. INTRODUCCIÓN

a RSS es una condición del sistema eléctrico de potencia, donde la red de transmisión intercambia energía con el turbogenerador en una o más frecuencias por debajo de la

frecuencia síncrona del sistema; este intercambio de energía, que es de tipo oscilatoria, puede estar o no amortiguada. Bajo esta condición se generan pequeños voltajes inducidos en la armadura por la oscilación que se presenta en el rotor, resultando en grandes magnitudes de corriente a frecuencias subsíncronas; además, si se considera que el elemento resistivo de la red es positivo, entonces estas corrientes producen una componente oscilatoria que afecta el par torsional y reproduce una oscilación, en el rotor. Normalmente los esquemas de protección implementados detectan y protegen contra la mayoría de las fallas a las que está sometido un generador. Si consideramos que bajo la condición de presencia de RSS es importante proteger al generador de los transitorios originados en la red de transmisión.

La lógica de operación de estos esquemas deben tomar en cuenta los resultados reportados por las pruebas a los equipos de protección contra la presencia de RSS realizados en la planta generadora de Navajo, Mohave durante el invierno de 1975-1976 [1,2,5]. Básicamente los resultados describen que las componentes de frecuencia subsíncrona de la corriente de armadura están directamente relacionadas con las magnitudes y frecuencias del par eléctricos y con la fatiga mecánica resultante en la flecha [2,5]. La combinación de los filtros estáticos, para el control de excitación de los amortiguamientos y relevadores especializados en identificar corrientes subsíncronas o fatiga torsional representan un esquema de coordinación de protecciones para prever y proteger al turbogenerador en presencia de RSS e ITSS [6].

II. PROTECCIÓN CONTRA RESONANCIA

SUBSÍNCRONA E INTERACCIONES TORSIONALES

SUBSÍNCRONAS

La protección para los turbogeneradores utilizando relevadores contra la posibilidad de daño debido a la presencia de RSS, es conocida como contramedidas de RSS. Normalmente, se consideran dos tipos de contramedidas, las cuales se clasifican en a) Contramedidas o Acción de Control del Sistema y b) Relevadores de Protección contra RSS y sus Fenómenos. A. Acciones de Control del Sistema de Potencia Una Acción de Control se define como toda acción o modificación que sufra el sistema eléctrico de potencia con el propósito de reducir el impacto de la Resonancia Subsíncrona en sus elementos; para esta condición se pueden colocar filtros en los controles, que interactúen entre el sistema turbina-generador y el sistema de potencia; además se consideran estrategias que se aplican en la operación del sistema, para efectuar la localización de unidades de generación que particularmente puedan presentar este problema [2,3].

Propuesta de una Lógica de Protección considerando el contenido Subsíncrono del Par Eléctrico en

Terminales del Turbogenerador 1José A. Castillo J 1David Sebastian Baltazar 1Daniel Olguin Salinas 2C. A. Rivera Salamanca [email protected] [email protected] [email protected] [email protected] 1 Instituto Politécnico Nacional, SEPI ESIME ZAC., Programa. de Postgrado en Ing. Eléctrica, 07300, México, D.F. 2 Departamento de Energía, Unidad Azcapotzalco, Universidad Autónoma Metropolitana. 02200, México, D.F

L

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B. Relevadores de Protección contra RSS e ITSS

Los relevadores contra RSS y sus fenómenos asociados, normalmente son instalados directamente en los turbogeneradores [2]. B.1 Monitoreo Torsional Este equipo proporciona datos para evaluar la severidad de las vibraciones torsionales de la flecha, debidas a las oscilaciones o disturbios eléctricos en la red de la transmisión. Además permite que el turbogenerador sea vigilado continuamente, pero no ofrece protección continua contra los efectos de oscilaciones debidas a corrientes subsíncronas [2,3]. El dispositivo detecta variaciones de la velocidad del rotor y convierte los datos de la oscilación, por medio de circuitos análogos, en valores de pares torsionales. El monitor torsional tiene capacidad de registrar estos datos, para cualquier disturbio eléctrico transitorio donde el par torsional de la flecha se acerca o excede al nivel de la resistencia material con que está construida la flecha. Entonces estos datos pueden ser analizados por fabricantes para estimar la pérdida de vida, debido a esta fatiga de la flecha. La segunda generación de estos dispositivos, proporciona directamente la estimación de los daños que sufre la flecha debido a la fatiga que producen pares torsionales a la que se ve expuesta. Esta característica adicional permitirá a unidades generadoras, que han disparado y están fuera de línea, a regresar más rápidamente al servicio debido a la operación del relevador de RSS. Las entradas de información a estos monitores incluyen generalmente suficiente información sobre cantidades eléctricas de las terminales del generador, para una descripción del historial de los pares torsionales del turbo-generador, y una recopilación de muestras de datos de la variación de velocidad del rotor [2,3,6].

B.2 Relevadores de Corriente Subsíncrona

El relevador de corriente subsíncrona utiliza una técnica especial para detectar los bajos valores de las corrientes subsíncronas y emplea una lógica especial para determinar si estas corrientes representan un peligro potencial para el turbogenerador. Ante la presencia de cualquier disturbio, se pueden causar cambios en las corrientes eléctricas del sistema, produciéndose corrientes transitorias a frecuencias naturales (fer), que se incluyen en las corrientes del sistema a frecuencia fundamental (fo).

Las corrientes a la frecuencia del estator fe interactúan con los flujos de la máquina, a frecuencia fundamental del sistema fo, produciendo pares en el entrehierro de la máquina, causando que el rotor del generador oscile a la frecuencia fo -fer. Los pares en el entrehierro tienden a decaer en el mismo rango de tiempo que la corriente del transitorio. Si alguno de estos pares eléctricos a frecuencia subsíncrona corresponde a

un par a frecuencia natural fn, de la flecha, puede provocar incremento de la oscilación resultante [2,3,7,8]. Si la magnitud inicial de la corriente transitoria, es considerablemente alta con respecto al tiempo de decaimiento transitorio, la oscilación a frecuencia subsíncrona que se presenta en la flecha, aumenta a un nivel peligroso en el turbogenerador. Para detectar la presencia del fenómeno, el relevador debe identificar la magnitud inicial y el tiempo en que decae el transitorio de las corrientes subsíncrona, antes que la oscilación aumente su magnitud de manera peligrosa. Cuando el eje del turbogenerador oscila a frecuencia subsíncrona, se producen corrientes y voltajes en las terminales de la máquina a frecuencias de fo + fn y fo – fn.

El sistema mostrado en la figura 1 presenta las entradas del relevador que son las tres corrientes de armadura y el voltaje en terminales. La componente de 60 Hz de la corriente de armadura es obtenida por un multiplicador agregado al filtro pasa-banda, esto da una aproximación de las componentes subsíncronas presentes en los pares eléctricos.

Figura 1. Diagrama esquemático del Relevador de Corriente Subsíncrona [2,3,7,8].

Las salidas del multiplicador puede incluir componentes adicionales a las frecuencias de oscilación como (fo+fer) y (fo-

fer), presentes en la secuencia positiva de la corriente de fase y en la frecuencia fundamental del sistema.

III. MODELADO DE SISTEMAS ELÉCTRICOS DE POTENCIA PARA EL ESTUDIO DE FENÓMENOS

TORSIONALES. La evaluación de ITSS requiere una caracterización completa de la dinámica electromecánica del generador, la dinámica de la red de transmisión eléctrica, así como la representación de los controles involucrados con el sistema de potencia. Conceptualmente, el comportamiento dinámico del sistema eléctrico se representa como la interacción de subsistemas físicos que interactúan a través del modelo dinámico de la red de transmisión. Cada subsistema dinámico se representa por un modelo parcial de estado de la forma:

[ ] [ ]

[ ] [ ]

n1,...,k

)()()(

)()()(

=

+=

+=

tDtCt

tBtAtdt

d

kkkkk

kkkkk

aXb

aXX

(1)

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Donde Xk es el vector de variables de estado, para el k-ésimo subsistema o componente, los cuales pueden representarse por un modelo de conexión algebraica como:

[ ] [ ]

[ ] [ ] )()()(

)()()(

2221

1211

tLtLt

tLtLt

kkk

kkk

ubb

uba

+=

+= (2)

En donde uk es el vector de variables de control y las

submatrices [Ak], [Bk],[Ck] y [Dk] establecen las características de cada subsistema y representan en general, sensitividades asociadas al del modelo parcial de estado con respecto al propio modelo o a la interconexión del mismo con otros subsistemas.

Las submatrices [Lij], por otra parte, representan las

relaciones físicas que describen la interconexión entre los distintos elementos o subsistemas.

IV. SISTEMA DE PRUEBA.

La lógica operación propuesta en la sección anterior, es implementada en el sistema de prueba de la IEEE para el estudio de Resonancia Subsíncrona [1].

El sistema describe el modelo de un turbogenerador de

892.4 MVA a 23 k[V], conectado a un bus infinito a través de una línea de transmisión de 500 k[V], compensada por un banco de capacitores a diferentes niveles de compensación a la base de 100 MVA. Todos los datos no especificados están en p.u. a la base del sistema. La figura 2 muestra el sistema de prueba.

Fig. 2. Sistema de Prueba IEEE para el estudio de RSS [1].

En la figura 3 se muestra el modelo de seis masas de la

flecha del sistema mecánico del turbogenerador, utilizado para analizar el efecto del fenómeno oscilatorio subsíncrono.

Figura 3. Sistema de seis masas de la flecha del turbogenerador [1].

A. Respuesta a la Frecuencia

Para lograr tener un enfoque más claro del problema de RSS y fenómenos asociados; se realizan simulaciones en el dominio de la frecuencia para determinar el comportamiento y frecuencias de oscilación de los modos torsionales de la flecha, para esto se utiliza el programa de fenómenos oscilatorios subsíncronas (PAFOS) [4]. Se consideraron tres condiciones de prueba diferentes niveles de compensación serie fija (Xc = 20 %, 50 % y 70 de XL ).

Las tablas 1 - 3 muestran los modos torsionales resultantes del caso de prueba, las características de compensación modifican los niveles de amortiguamiento de cada modo, provocando que la frecuencia de oscilación varié muy poco al modificar el nivel de compensación de línea. En las siguientes figuras se muestra el desplazamiento rotacional sufrido por la turbina debido a las diferentes condiciones del caso de prueba.

Tabla 2. Modos torsionales con Xc=50%

Modo de oscilación

Eigenvalor

Frecuencia (Hz)

Origen

8 9

10 11 12 13

-0.1817± 298.1766i 0.2009± 202.5930i -0.0203± 160.0025i -0.5609± 126.3152i

-0.2515±100.169i -0.7978±10.0430i

47.456 32.243 25.465 20.103 15.942 1.598

Modos torsionales de la

máquina síncrona

15 -5.3855±138.6218i 22.062 Modo subsíncrono de la red

*Parte real en (1/s). Parte Imaginaria en (rad/s)


Modo de oscilación

Eigenvalor

Frecuencia (Hz)

Origen

8 9

10 11 12 13

-0.1817± 298.1766i -0.0416± 202.8000i -0.1480± 160.4125i -0.3607± 126.7335i

0.1760±100.6805i -0.7978±11.1777i

47.456 32.276 25.530 20.107 16.023 1.779


máquina síncrona


*Parte real en (1/s). Parte Imaginaria en (rad/s)


Modo de oscilación

Eigenvalor

Frecuencia (Hz)

Origen

8 9

10 11 12 13

-0.1817±298.1766i -0.2209±203.0060i -0.2203±160.6178i -0.6659±127.0210i -0.2415±99.1459i -0.7834±10.0269i

47.456 32.309 25.563 20.216 15.780 1.598


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Fig. 4. Comportamiento de los Modos torsionales con un nivel de compensación del 20 %.

Fig. 5. Comportamiento de los Modos torsionales con un nivel de compensación del 50 %.

Fig. 6. Comportamiento de los Modos torsionales con un nivel de compensación del 70 %

En figuras 4-6 se muestran el comportamiento de los modos torsionales a diferentes niveles, es de esperarse que el efecto de la compensación sea más evidente en el desplazamiento rotacional sufrido por la turbina a un 70 % de compensación serie fija. Esto significa que si las corrientes de oscilación del estator ocurren a frecuencias resonantes del sistema eléctrico, la oscilación subsíncrona puede auto-excitarse debido a la interacción Torsional, esto se puede presentar cuando la componente en fase, del par oscilante, dividido entre la velocidad es mayor que el amortiguamiento mecánico de la máquina; solamente que esta auto-excitación de oscilaciones subsíncronas corresponda a una frecuencia natural de la flecha (pares muy pequeños) o a corrientes del estator, pueden dar como resultado un alto nivel de fatiga.

B. Respuesta en el dominio del Tiempo.

El normalmente la dinámica de los sistemas de potencia está representado por un comportamiento no-lineal y no-estacionario. En consecuencia el análisis de las características dinámicas del sistema será descrito más exactamente por los modelos matemáticos no lineales. En este trabajo se utilizó la transformada discreta de Fourier como técnica de procesamiento de señales y el análisis de Prony para muestrear el contenido de frecuencias subsíncronas que tiene el par eléctrico, el cual está directamente asociado con el comportamiento torsional a través del flujo de corriente subsíncrona de secuencia positiva en la armadura del generador, este flujo induce corrientes en el rotor a frecuencia fo – fer ; la resistencia del sistema eléctrico a la frecuencia resonante fer , produce que la resistencia negativa del generador sea menor, provocando que la corriente subsíncrona tienda a incrementarse.

Tabla 4. Comparación entre los modelos de Fourier y de Prony *

*n y Q son constantes enteras Si aplica el análisis de prony al par eléctrico, es posible identificar su contenido subsíncrono; de esta forma se encuentra que existen frecuencias coincidentes con las frecuencias de oscilación torsional encontradas con el Eigenanalisis, considerando los diferentes niveles de compensación en el sistema de prueba. Con esta identificación es factible probar una lógica de operación de un relevador que procese este contenido junto con las frecuencias de oscilación natural de la flecha. El método de Prony es una técnica para ajustar datos de muestras uniformes (espaciados igualmente) por una combinación lineal de funciones lineales amortiguadas. A diferencia del enfoque convencional de análisis de Fourier donde solo se obtienen amplitudes y frecuencias, el método de Prony permite obtener información adicional sobre la fase y amortiguamiento modal. En las figuras 7 - 9 se muestra la respuesta del par eléctrico, al análisis espectral de Fourier y de Prony. La respuesta en el tiempo se simuló haciendo un muestreo de 208 (µs) y 16 muestras por ciclo, con un tiempo de estudio total de 3 s.

Dato Modelo de Fourier Modelo de Prony

Registro en el tiempo

y(tk )=y(k),

k=0,1,...,N-1

con espaciamiento ∆t y longitud del registro

T=N∆t

1

( ) i

nt

i

i

y t B eλ

=

= ∑

( )1

cosQ

i i i

i

A tω φ=

= +∑

2 ( 1) /i ij iλ ω π= = − Γ

1

( ) i

nt

i

i

y t B eλ

=

= ∑

( )1

cosi

Qt

i i i

i

Ae tσ ω φ

=

= +∑

i i ijλ σ ω= +

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Fig. 7. Comportamiento del Par Eléctrico.

Fig. 8. Espectro de Fourier del Par eléctrico a Frecuencias Subsíncronas.

Fig. 9. Respuesta del Par Eléctrico al análisis de Prony

En las tablas 5 - 7 se muestran los modos asociados del Par eléctrico resultante del análisis de Prony, los niveles de compensación hacen variar el amortiguamiento de cada modo de oscilación.

Tabla 5. Modos asociados al Par Eléctrico (Prony)



Si se comparan los modos asociados al par eléctrico con los modos torsionales de las tablas 1-3, se identifica que por lo menos existe un modo oscilando casi a la misma frecuencia torsional, al tener un 50% y 70% de compensación serie fija, es evidente que el problema de RSS que se da en el sistema, por el disparo del banco de capacitores, se refleja directamente en la turbina del generador, ya que el modo frecuencia oscilación eléctrica subsíncrona, influye en la reducción del nivel de amortiguamiento de los modos torsionales llevando a una inestabilidad que puede provocar daños severos al sistema mecánico del turbogenerador, debido a la aparición de la interacción torsional subsíncrona.

V. PROPUESTA DE LA LÓGICA DE OPERACIÓN.

Bajo estas condiciones se puede estudiar la variación del ángulo de fase para obtener una imagen del desplazamiento angular del generador. Los modos de oscilación del generador pueden ser determinados por la medición del ángulo de fase del voltaje en las terminales del generador, que están directamente asociadas al par eléctrico. Como se muestra en la ecuación (4).

( ) cos(2 )

( ) cos(2 )

( )

abc

abc

a a b b c c

v t V f t

i t I f t

Pe t v i v i v i

π φ

π φ

= +

= +

= + +

(4)

Xc= 50%

Modo de oscilación

Frecuencia (Hz)

Amortiguamiento Energía Relativa

1 12.156834 0.356123 0.000117 2 28.022722 0.033443 0.065333 3 32.840858 -0.010508 0.412635

Xc= 70%

Modo de oscilación

Frecuencia (Hz)


1 2 3 4

0.0000 16.030787 22.010841 31.938821

0..0000 -0.060097 0.143654 0.071398

0.049557 0.540206 0.030218 0.001899

Xc=20%

Modo de oscilación

Frecuencia (Hz)


1 2 3 4

0.0000 21.075843 40.664052 41.079728

0..0000 0.284267 0.069763 0.030968

0.051935 0.001106 0.010710 0.057263

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Donde vabc, iabc son los valores instantáneos de los parámetros de voltaje y corriente en terminales del generador [11].

Si se considera que:

( ) cos(2 )

2

abc nom

nom

v t V f t

f t

π φ

π φ

= +

Θ = +

(5)

Las frecuencias que no son nominales puede representarse con

el argumento Θ en función del coseno.

2 2nomf t f tπ π φΘ = + ∆ +

Donde (6)

∆f = fnom - f

En la figura 10 se muestra el diagrama de flujo de la lógica propuesta, considerando que en el sistema de transmisión se conectan los bancos de capacitores, por lo que se realizó un estudio previo de respuesta a la frecuencia obteniendo las frecuencias de torsionales de oscilación del sistema mecánico del turbogenerador. Debido a esto se determinó que en el contenido subsíncrono del par eléctrico existen frecuencias coincidentes que pueden ser asociadas a la aparición de pares torsionales que se contraponen a los pares naturales, influenciando la disminución de los niveles de amortiguamiento entre turbinas, provocando la fatiga torsional en cada una de las secciones de flecha.

Fig. 10. Lógica propuesta de Operación.

La lógica propuesta considera, una combinación de filtrado y análisis espectral del par eléctrico para determinar las componentes subsíncronas de las corrientes en terminales.

El monitoreo torsional se utiliza para llevar un control de la acumulación de fatigas torsionales en la flecha, la cual puede llevar un daño importante y en los casos más extremos a fracturarse.

Existen casos donde la excesiva corriente inducida en el rotor simula ser un transitorio que provoca la oscilación debido al alto flujo de corriente circulante en la superficie de la flecha, bajo estas condiciones es indispensable considerar la lógica de operación de la protección.

VI. CONCLUSIONES

En este trabajo de investigación se describen y proponen condiciones que pueden ser utilizadas para diseñar la lógica de operación de un relevador digital de corriente subsíncrona, bajo los conceptos de la resonancia subsíncrona y sus fenómenos asociados (Efecto del generador de inducción, interacción torsional subsíncrona y pares transitorios). En particular, se enfoca la investigación a utilizar la información que arroja el estudio del contenido subsíncrono del par eléctrico para analizar la variación del ángulo de fase con el cual se puede tener una imagen del desplazamiento rotacional que describe el comportamiento y excitación de los modos torsionales de la flecha del sistema turbina-generador. La coincidencia de frecuencias encontradas en el par eléctrico permite justificar la evaluación de la variación del ángulo de fase. Los resultados mostrados plantean que utilizando esta evaluación es posible generar una lógica de operación en un relevador que considere las características subsíncronas del voltaje y corriente en las terminales del generador.

VII. REFERENCIAS

[1] IEEE committee. First Benchmark Model for Computer Simulation of Subsynchronous Resonance. IEEE, Trans, Power Appar. Syst. . p.p. 1565-1572, Sep/Oct 1977.

[2] P.M. Anderson. “Power system protection”. Mc Graw Hill, 1999

[3] IEEE Subsynchronous Resonance Working Group of the System IEEE subsynchronous Resonante Working Group, Series Capacitor Controls And settings As Countermeasures to Subsynchronous Resonante, IEEE “Transaction Power Apparatus and System”, Vol. PAS-101, No.6, June, 1982, pag. 1281-1287

[4] Castillo Jiménez José A., “ Análisis de Dispositivos FACTS (CEV,

CSCT y UPFC) para interacciones torsionales subsíncronas de

Turbogeneradores en Sistemas Eléctricos de Potencia”, Tesis de Maestría, SEPI - ESIME - IPN, Ciudad de México, México, Agosto, 2003

[5] C.E.J. Bowler, D.H.Baker, N.A Mincer, P.R.Vandiveer, Operation an test of the Navajo SSR protective equipment, IEEE “Transaction Power Apparatus and System”, Vol. PAS-97, No. 4, July/Aug, 1978, pag. 1030-1035

[6] Jan Stein, Horst Fick, The torsional stress analyzer for continuously monitoring turbina-generators, IEEE “Transaction Power Apparatus and System”, Vol. PAS-99, No. 2, March/April 1980, pag. 703-710

[7] B.L Agrawal, R.G. Farmer, Application of subsynchronous oscillation relay-type SSO, IEEE “Transaction Power Apparatus and System”, Vol. PAS-100, No. 5, May, 1981, pag. 2442-2451

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[8] S.C. Sun, S.Salowe, E.R Taylor, Jr, C.R. Mummert, A subsynchronous oscillation relay- type SSO. , IEEE “Transaction Power Apparatus and System”, Vol. PAS-100, No. 7, July, 1981, pag. 3580-3589

[9] GE Energy, Turbina- Generador Torsional Stress Relay (TSR) & Torsional Stress Analyzer (TSA), Product Information, 2004

[10] Altuve Ferrer Héctor Jorge “Protección de sistemas eléctricos de potencia”. Facultad de ingeniería eléctrica, Universidad Central de Las Villas Santa Clara, Cuba, 1991

[11] Benmouyal, Gabriel. Schweitzer, E. O, Guzman A., Synchroned Phasor Measurement in Protective Relays for Protection, Control and Analysis of Electric Power Systems, “ 29th Annual Wester Protective Relay Conference”, Spokane, Washington, October 22-24, 2002

VIII. APENDICE

Datos del Sistema de Prueba IEEE para el estudio de RSS [1]: A.1. Generador Sincrono (pu). Xd = 1.79 Xq = 1.71 X ffd = 1.7 X kk1d = 1.666 X kk1q = 1.695 X kk2q = 1.825 X md = 1.66 X mq = 1.58 Ra = 0.0015 R ffd = 0.001 R kk1d = 0.0037 R kk2q =0.0182 R kk1q = 0.0053 X' d = 0.169 X' q = 0.228 X'' d = 0.135 X'' q = 0.2 Xl = 0.13 T' d0 = 4.3 s T' q0 = 0.85 s T'' d0 = 0.32 s T'' q0 = 0.05 s A.2. Transformador y Línea de Transmisión (pu). RT = 0.01 XT = 0.14 RL = 0.02 XL = 0.56 A.3 Pares de las Turbinas y Gobernador FH = 0.3 TCH = 0.3 s KG = 25 FI = 0.26 TRH = 7.0 s TSR = 0.2 s FA = 0.22 TC0 = 0.2 s TSM = 0.3 s FB = 0.22 A.4. Regulador de Voltaje y Sistema de Excitación KE = 50 s TA = 0.01 s TE = 0.002 s A.5. Condiciones iniciales de operación (pu). PG = 0.9 Vt = 1.05 PF = 0.9 (-)

A.6.Constantes de Inercia y de resorte

TABLA A

Masa

Sección de la Flecha

Constante de Inercia

H en s

Constante de Resorte

K(pu)

Constante de Resorte (pu)

T/rad

HP 0.092897 HP-IP 7,277 19.303

IP 0.155589 IP-LPA 13,168 34.929

LPA 0.858670 LPA-LPB 19,618 52.038

LPB 0.884215 LPB-GEN 26,713 70.858

GEN 0.868495 GEN-EXC 1,064 2.822

EXC 0.0342165

VIII. AUTORES

José A. Castillo J. Nació en la cd. de México.. Es egresado como Ingeniero Electricista por la Universidad Autónoma Metropolitana en 1999. Maestro en Ciencias en Ingeniería Eléctrica por la Sección de Estudios de Posgrado e Investigación de la E.S.I.M.E - I.P.N en 2003. Actualmente esta inscrito al programa de Doctorado en la sección de graduados de la escuela superior de ingeniería mecánica y eléctrica, SEPI-ESIME-IPN, Unidad Zacatenco, México.

.DAVID SEBASTIA' BALTAZAR. Nació en San Jerónimo Michoacán. Obtuvo el título de Ingeniero Industrial en Eléctrica en 1991 del Instituto Tecnológico de Morelia. El grado de Maestro en Ciencias (1993) y Doctor en Ciencias (1999) en Ingeniería Eléctrica en la Sección de Estudios de Posgrado e Investigación de la E.S.I.M.E - I.P.N. Realizó una estancia Posdoctoral en la Universidad de Saskatchewan, Canadá durante el periodo de Agosto del 2000 a Julio del 2002. Actualmente es profesor de tiempo completo de la SEPI-ESIME-IPN. Sus áreas de interés son la protección y medición de sistemas eléctricos de potencia.

Daniel Olguín Salinas. Ingeniero Electricista de la Escuela Superior Ingeniería Mecánica y Eléctrica del Instituto Politécnico Nacional (1971). Maestro en Ciencias en Ingeniería Eléctrica de la Sección de Graduados e Investigación de la Escuela Superior de Ingeniería Mecánica y Eléctrica del Instituto Politécnico Nacional (1976). Doctor en Ciencias en Ingeniería Eléctrica, en la Universidad de Londres (1979). Actualmente es profesor investigador de la SEPI-ESIME-IPN.

Carlos Alberto Rivera Salamanca Es Licenciado en Electricidad egresado de la Universidad Pedagógica y Tecnológica de Colombia (1983). Maestro en Ciencias en Ingeniería Eléctrica y Doctor en Ciencias en la SEPI-ESIME-IPN (1989 y 2000 respectivamente). Desde 1990 es Profesor Investigador en la UAM-Azcapotzalco. Ha dirigido y participado en Proyectos de Investigación en la UAM. Actualmente es profesor invitado en la Facultad de Ingeniería Electromecánica de Duitama, de la Universidad Pedagógica y Tecnológica de Colombia. Su área de interés incluyen el análisis y control de fenómeno transitorios.

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Enhanced Motor Protection With the

Slip-Dependent Thermal Model:

A Case Study

Patrick Whatley, Plant Power and Control Systems, LLC

Mark Lanier, Lee Underwood, and Stan Zocholl, Schweitzer Engineering Laboratories, Inc.

Abstract—Protection of induction motors can be enhanced with

today’s microprocessor-based protective relays and a slip-

dependent thermal model. This paper briefly introduces the

concept of the thermal model and explains how to apply a slip-

dependent thermal model to better protect motors in retrofit

applications, where very little data are available. In such cases,

assumptions must be made to estimate safe locked-rotor times

based on historical motor starting times and electromechanical

relay settings. These assumptions are then checked by reviewing

motor start report data collected on the initial starts of the

motor. Thermal capacity measured during start is used to

validate the improved protection and settings may then be

revised without the risk of a trip on normal starts. The motor

start reports from multiple motors will be presented, along with

the protection settings produced in this manner. The paper

describes how microprocessor-based protection is successfully

provided for all conditions in this application, replacing the

thermal overload protection, which had been blocked for two

minutes during starting because of the difficulties in starting

high-inertia loads.

I. INTRODUCTION

Many motors in industrial facilities have been in service

for thirty or more years with electromechanical protective

relays. These relays are nearing the end of their service life

and need to be replaced. Modern microprocessor-based relays

are the natural choice for these retrofit applications and offer

many improvements over electromechanical overcurrent

relays, electromechanical or static thermal-replica relays, or

thermal overload relays. These enhancements include

improved thermal modeling of the motor heating, event

reporting, sequential event reporting, motor start reports,

motor start trending, motor operating statistics, additional

protection features, and additional control functions.

However, information about the thermal capabilities of

these motors is practically non-existent, since the original

manufacturer’s information (thermal limit curves) is often

lost. In addition, older motors may have been rewound,

rendering the original motor manufacturer’s data suspect.

Typically, the only information available to set a new

microprocessor-based relay for an existing motor is the motor

nameplate information, existing electromechanical protective

relay settings, and operator experience of typical starting

times.

NEMA MG 1 [1] lists the required information the motor

manufacturer must provide on the motor nameplate.

The pertinent nameplate information needed to set a

microprocessor relay includes:

• Rated-Load Amperes (FLA)

• Locked-Rotor kVA Code Letter or Locked-Rotor

Current in Amperes

• Service Factor (SF)

• Time Rating—typically continuous for a medium

voltage motor

• RPM at Rated Load (Rated Speed)

The existing thermal overload or electromechanical (EM)

relay may or may not provide adequate thermal protection for

the motor. However, one can be fairly certain the curve

selected on an existing EM relay allows the motor to start

without tripping.

The protection engineer calculates the approximate

locked-rotor current using the locked-rotor code letter, and

uses this current to determine the trip time on the existing

curve. For example, if the code letter is “G”, then the locked-

rotor current is in the range of 5.6–6.29 kVA/hp.[1] Once the

motor horsepower and rated voltage are known, the locked-

rotor current can be calculated. The trip time for this current

is then determined from the existing EM relay time current

curve. This time is used as the initial assumption for the

motor safe hot locked-rotor time setting (LRTHOT1).

Operators in an industrial facility typically know how long

high inertia loads take to accelerate under varying loading

conditions. For instance, a large induced draft fan in a power

plant may take anywhere from 10 to 60 seconds to start. The

damper positioning in the fan ductwork, or pitch of the fan

blades, affects loading during the motor start and thus affects

acceleration time to rated speed. An operator may know,

based on either experience or control system trend

information, that a particular fan takes a maximum of 40

seconds to start. In comparison, the EM relay in this same

application may have a trip time of 50 seconds at locked-rotor

current. In this case, the operator’s experience may override

the existing EM relay setting, allowing the protection

engineer to use 40 seconds as the motor safe hot locked-rotor

time as a starting point for the motor protection.

These data collection methods estimate the motor safe hot

locked-rotor time. Although the motor nameplate has most of

the information needed to set modern microprocessor relays,

an estimate is required because the nameplate does not state

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how long the motor can withstand locked-rotor current

before the rotor bars melt or warp. Safe hot locked-rotor time

is required to set the thermal model of the relay. The

estimated safe hot locked-rotor time can be used as a starting

point for the relay setting.

Given the estimated safe hot locked-rotor time, the motor

can be started with reasonable assurance that rotor bar heating

during the start will be limited to a safe level. The thermal

capacity used during starting can then be examined from one

or more motor start reports. Based upon how close the relay

measures to 100% thermal capacity (trip level) during

starting, the LRTHOT1 setting can be reduced to better

protect the motor.

Solutia Inc. manufactures Acrilan® acrylic fiber at their

manufacturing facility in Decatur, AL. This facility has had

thermal overloads protecting motors in the plant since

installation in the 1960s. Plant Power and Control, LLC (in

Alabaster, AL) replaced the motor protection on a 600 hp

induced draft fan, a 500 hp induced draft fan, and a 350 hp

blower motor at this facility within the last year. These

motors are the basis for the case study presented in this paper.

Years ago, the initial starts of the large fan motors caused

undesired trips during motor inrush. The plant personnel

installed a time-delay auxiliary relay that shorted the thermal

overload relay contact for two minutes during starting. After

the time-delay relay timer expired, the short was removed and

the thermal overload was placed back into service. Since the

most likely time for a motor to fail is during a start, when

currents are highest, new protection with improved reporting

of motor operations was requested for these aging motors.

II. SLIP-DEPENDENT THERMAL MODEL

Most microprocessor-based relays available today attempt

to calculate the heating in the motor by measuring the current

only. The various manufacturers’ models calculate the

heating in terms of what is commonly called thermal capacity

or thermal register, where 0% is completely cooled and 100%

is the trip threshold. This thermal capacity is accumulated

based upon the measured current, such that during motor

starting, the protection is essentially an I2t element, with

maximum starting time dictated by the hot motor safe-stall

time. Problems arise when starting motors with high-inertia

loads, as the time required to start the motor may approach or

even exceed the hot safe-stall time. The protection provided

by induction disk overcurrent relays is similar.

The relay chosen for the replacement upgrades described

in this paper uses a thermal model that calculates motor slip

during the start. The relay calculates the slip based upon

measured current and voltage and two settings entered by the

user. The required settings are:

• Full-load Slip (in pu of synchronous speed)

• Locked-rotor Torque (in pu of full-load torque, also

called rated torque)

The relay uses the calculated slip to compute the positive-

and negative-sequence rotor resistance throughout the motor

start. Calculation of rotor resistance accurately reflects the

heating that takes place in the motor during a start and results

in longer allowable acceleration times before tripping than

would be allowed by an I2t element. The details of this

thermal model are documented in [2].

III. EXAMPLE 1: 600 HP INDUCED DRAFT FAN

The first motor examined was a 600 hp induced draft (ID)

fan in the Unit 6 power plant boiler. The only data available

for this motor was taken from the motor nameplate, as no

thermal limit curves were available. The data used from the

nameplate to set the protection was:

• Rated-Load Amperes (FLA) = 149 A

• Locked-rotor kVA Code Letter was not available on

the motor nameplate. Based on typical data,

6.5 • FLA was used as a starting point.

• Service Factor (SF) = 1.0

• Time Rating – continuous

• RPM at Rated Load (Rated Speed) = 1189 rpm

• Voltage = 2300 V

We selected most of the required settings from this data.

Full-load amps was set directly to the FLA of the motor

(149 A). The service factor was set to 1.05 to provide a small

margin above rated conditions, since discussions with the

operators revealed that the motor might be operated slightly

overloaded under some conditions. The SF setting affects the

stator overload (motor running) model, but does not affect the

rotor model, which is of primary concern during starting. The

decision to allow this slight overload does, of course,

compromise the running protection of the motor.

Full-load slip is easily calculated as:

0092.0FLS

1200/11891FLS

ns/nr1FLS

=

−=

−=

The locked-rotor torque was unavailable for this motor, so

we estimated that the locked-rotor torque was likely in the

range of 1.10–1.30, based on large fan motor data available

from similar facilities. An LRQ setting of 1.25 was selected.

The LRQ setting affects the rotor resistance the relay uses for

the locked-rotor condition with a higher LRQ setting

increasing the calculated rotor resistance. Thus, a higher LRQ

setting is conservative and will result in slightly higher

thermal capacity used over the course of the motor start.

The final setting to be made in the starting portion of the

thermal model of the relay was the safe hot locked-rotor time.

Since the existing protection was thermal overloads, a

reasonable locked-rotor time from existing settings was

indeterminate, and no motor thermal capability curves were

available. The remaining piece of viable information came

from operator experience. The expected acceleration time,

according to the operators, was in the 30-second range. Based

on this, the hot locked-rotor time (LRTHOT1) was set to

25 seconds for the initial start attempt. The initial thermal

model settings for the relay are summarized in Table 1.

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TABLE 1

600 HP BOILER ID FAN INITIAL RELAY SETTINGS

Setting "ame Initial Value

FLA 149 A

FLS 0.0092

LRQ 1.25

LRA 6.5 • FLA

SF 1.05

LRTHOT1 25 seconds

Fig. 1 contains plots of motor current, voltage measured at

the relay, measured slip, and calculated thermal capacity for

the initial start. This plot was produced with available

software using motor start report data recorded by the relay.

As shown in Fig. 1, the initial start attempt showed the actual

motor acceleration time to be about 1000 cycles, or just under

17 seconds. Furthermore, the thermal capacity used was

extremely low, only reaching 38.5% of thermal capacity. The

slip calculated by the relay during the motor start is shown,

and as expected it trends down from 100% at locked-rotor to

rated slip when the current drops to full-load amps.

It should be noted that this start attempt was done with the

inlet dampers to the fan closed, which resulted in the load

starting much faster than if the start were attempted with the

dampers open. When the dampers are open on starting, the

fan must move air through all of the ductwork and boiler. The

plant operators stated that the fan is typically started with the

dampers closed.

A simulation of the motor start was performed in

MATLAB software to see how closely the actual quantities

measured by the relay tracked with the simulated data based

on the known motor parameters. This simulation is discussed

in detail in the Appendix. The simulated motor currents,

voltages, and thermal capacity matched the measured data

very well, as shown in Fig. 2.

Fig. 1. Motor Start Report for Unit 6 ID Fan (600 hp)

0 2 4 6 8 10 12 14 16 18

0

0.2

0.4

0.6

0.8

1

Seconds

Volts(p

u)

Fig. 2. Comparison of MATLAB Simulation for Unit 6 ID Fan (600 hp): Current, Voltage, Thermal Capacity (U), and Slip

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IV. EXAMPLE 2: 500 HP INDUCED DRAFT FAN

The second motor examined was a 500 hp induced draft

(ID) fan in the Unit 5 power plant boiler. Again, the only

data available for this motor was taken from the motor

nameplate, as no thermal limit curves were available. The

data from the nameplate used to set the protection was:


• Locked-rotor kVA Code Letter was not available on

the motor nameplate. Based on typical data,

6.5 • FLA was used as a starting point.


• Time Rating—continuous



Since the majority of the data was similar to the 600 hp ID

fan, the settings were nearly identical. Full-load amps was set

directly to the FLA of the motor (107 A). The service factor

was set to 1.05 to provide a small margin above rated

conditions. Full-load slip was set to 0.0092 as in the 600 hp

motor and locked-rotor torque was set to 1.25 as well. Safe

hot locked-rotor time was set to 25 seconds since the thermal

overloads had been blocked during starts of this motor also.

The initial thermal model settings for the relay are

summarized in Table 2.

TABLE 2

500 HP BOILER ID FAN INITIAL RELAY SETTINGS


FLA 107 A

FLS 0.0092

LRQ 1.25

LRA 6.5 • FLA

SF 1.05

LRTHOT1 25 seconds

The motor start report in Fig. 3 was collected on 6/6/07,

approximately three months after the initial installation. The

actual motor acceleration time was approximately

10 seconds, significantly lower than the 17-second accelera-

tion time of the 600 hp motor. As expected, with a

programmed 25-second safe hot locked-rotor time and an

acceleration time of 10 seconds, the thermal capacity used

was low, only reaching 40%. The slip calculated by the relay

during the motor start is shown and, as expected, it trends

down from 100% at locked-rotor to rated slip when the

current drops to full-load amps.

Since this motor had been in service approximately three

months when this start report was collected, additional report

data was collected from the relay to verify the consistency of

recorded starting data across multiple starts. Fig. 4 shows the

Motor Operating Statistics Report for this motor. This report

accumulates the data shown until an operator manually clears

the report.

From this report we can see that 12 motor starts have

occurred since 2/1/2007 and that the average Thermal

Capacity Used (TCU) is 40.7%, with a peak of 46.0%. The

relay was also able to learn the required starting capacity by

recording the thermal capacity used for the last 5 successful

motor starts and multiplying the largest of these 5 thermal

capacities by 115%. This data is shown as Learn Parameters:

Start TC (%). The learned starting thermal capacity is used

by the relay to prohibit a subsequent motor start until the

rotor has adequately cooled. Since the motor accelerates to

full speed in less than the programmed safe locked-rotor

time, the time required for the motor to remain stopped

before another start attempt is very short, allowing a fast

restart time.

An additional report was captured to get refined start data

across one-month intervals. The Motor Start Trend Report

shown in Fig. 5 captures up to eighteen 30-day averages of

the motor start information. From this report we can see that

the motor starts were consistent in terms of average starting

time and thermal capacity used. From this data we also

surmised that the starting conditions (i.e., fan damper

position) were the same; else we would have seen an

excursion in the Start %TCU. Note that there were only 10

starts recorded in this trend report versus 12 starts in the

operating statistics report. The Motor Start Trend Report was

cleared on 3/7/2007, whereas the operating statistics report

was reset on 2/1/2007. The two additional starts evidently

occurred between these dates.

Fig. 3. Motor Start Report for Unit 5 ID Fan (500 hp)

Fig. 4. Motor Operating Statistics Report for Unit 5 ID Fan (500 hp)

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Fig. 5. Motor Start Trend Report for Unit 5 ID Fan (500 hp)

V. EXAMPLE 3: 350 HP BLOWER MOTOR

The third motor examined was a 350 hp blower in the

power plant boiler. Although this was a new motor

installation, the motor manufacturer did not provide motor

thermal limit curves so the only data available for this motor

was taken from the motor nameplate. The data from the

nameplate needed to set the protection was:


• Locked-rotor kVA Code Letter = G


• Time Rating—continuous



Since the majority of the data was similar to the 600 hp ID

fan, the settings were nearly identical. Full-load amps was set

directly to the FLA of the motor (82 A). The service factor

was set to 1.05 to provide a small margin above rated

conditions. Full-load slip was set to 0.0092 as in the 600 hp

motor and locked-rotor torque was set to 1.25 as well. Safe

hot locked-rotor time was set to 25 seconds.

The initial thermal model settings for the relay are

summarized in Table 3.

TABLE 3 350 HP BLOWER INITIAL RELAY SETTINGS


FLA 82 A

FLS 0.0092

LRQ 1.25

LRA 6.5 • FLA

SF 1.05

LRTHOT1 25 seconds

The motor start report in Fig. 6 was also collected on

6/6/07, approximately three months after the initial

installation. The actual motor acceleration time was

approximately 10.5 seconds, and, as expected with a

programmed 25-second safe hot locked-rotor time, the

thermal capacity used was low, only reaching 33%. The slip

calculated by the relay during the motor start is shown and,

as expected, it trended down from 100% at locked-rotor to

rated slip when the current dropped to full-load amps

Additional reports were collected from this motor as well,

since the relay had been in service for approximately three

months. From the Motor Operating Statistics Report in Fig. 7

we can see that there were 16 motor starts since 1/30/2007

and that the average Thermal Capacity Used (TCU) was

34.0% with a peak of 35.9%. The learned starting thermal

capacity of 38% was very much in line with the average

starting thermal capacity and should allow restarts of the

motor in a short amount of time.

The Motor Start Trend Report shown in Fig. 8 shows that

the motor starts were very consistent in terms of average

starting time and thermal capacity used. Note that there were

only 15 starts recorded in this trend report versus 16 starts in

the operating statistics report. The Motor Start Trend Report

was cleared on 4/4/2007, whereas the Motor Operating

Statistics Report was reset on 1/30/2007; therefore, the

additional start occurred between these dates.

A simulation of the Motor Start Report in Fig. 6 was also

performed in MATLAB software to see how closely the

actual quantities measured by the relay tracked with the

simulated data based on the known motor parameters. The

simulated motor currents and thermal capacity matched the

measured data very well as shown in the appendix.

Fig. 6. Motor Start Report for Blower Motor (350 hp)

Fig. 7. Motor Operating Statistics Report for Blower Motor (350 hp)

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Fig. 8. Motor Start Trend Report for Blower Motor (350 hp)

VI. ANALYSIS AND SETTING RECOMMENDATIONS

Since the new microprocessor-based relays are able to

provide protection during all phases of motor operation, all

three of the motors in this facility have better protection than

originally provided by the thermal overloads; and, as can be

seen from the various reports, the operators obtain much

better information on the motor starting characteristics.

However, the question remains: how much can we improve

the protection and still allow the motor to safely start?

The easiest relay setting to change to provide faster

tripping for a true locked-rotor condition is the safe hot

locked-rotor time setting. We might reduce the applied time

of 25 seconds to a time slightly longer than the measured

acceleration time of the motors and still be reasonably certain

that the motor will not trip on normal starts. The simulation

can be used to evaluate how much of a reduction might be

appropriate.

Observation of the start data for the three motors shows

that the thermal capacity used is fairly low for all starts.

There are several possible reasons for this:

1. Actual starting time is less than the relay setting

LRTHOT1.

2. Actual starting current is less than the LRA1 setting,

because of reduced voltage during the start as well as the

lack of certainty in the actual locked-rotor current value

when the setting was selected.

3. Function of the slip-dependent thermal model, which, by

calculating rotor resistance, tracks actual motor heating

during a start more accurately than a relay with an I2t

characteristic.

In order to assess the impact of Item 3, the effect of Items

1 and 2 can be effectively removed by using the simulation to

start the motors with 1 pu voltage at the motor terminals, and

by reducing the safe locked-rotor time setting in the thermal

model simulation.

Based upon the motor start data collected and previously

presented, adjustments for hot locked-rotor time (LRTHOT1)

might be:

• 600 hp ID Fan LRTHOT1 = 18 seconds



Simulations were performed for the 350 hp motor with the

proposed setting revisions for two cases:

1. Motor terminal voltage applied at 1.0 pu motor voltage.

2. Motor terminal voltage applied at 0.80 pu motor voltage.

The results of these cases are shown in Fig. 9 and Fig. 10.

0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time, seconds

Roto

r Therm

al C

apacity, P

U

Fig. 9. 350 hp Motor, LRTHOT1 = 12 sec, V = 1.0 pu

0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time, seconds

Roto

r Therm

al C

apacity, P

U


Note that although the starting time was longer, the

thermal capacity used with 0.80 pu voltage was not

significantly higher than the thermal capacity used with

1.0 pu voltage, and there was no concern for the relay

reaching the thermal trip threshold (Rotor Thermal

Capacity = 1) for either case. This result was somewhat

expected, since reduced voltage results in reduced starting

current (resulting in less rotor heating) and reduced motor

torque results in proportionally longer starting time (resulting

in greater rotor heating).

A final simulation was performed at 0.80 pu voltage and

LRTHOT1 = 8 seconds, which was LESS than the total

acceleration time for these conditions. Fig. 11 shows that the

thermal element would not operate during a normal start.

Fig. 12 illustrates how long the thermal element would

require to trip the motor should the rotor remain locked under

these same conditions. While an EM relay or microprocessor

I2t thermal element would have to be set longer than 12

seconds at 80% of locked-rotor current to ensure that the

motor would start, the slip-dependent model tripped faster

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than the acceleration time of 12 seconds for true locked-rotor

conditions yet still allowed normal starts.

0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time, seconds

Roto

r Therm

al C

apacity, P

U


0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time, seconds

Roto

r Therm

al C

apacity, P

U

Fig. 12. 350 hp Motor, LRTHOT1 = 8 sec, V = 0.8 pu, Rotor Locked

These simulations show that, with the slip-dependent

model, setting the relay hot locked-rotor time based on

observed acceleration time (or perhaps even less than the

observed acceleration time) does not compromise the ability

of the motor to start with voltage conditions ranging from

80%–100% of the motor rated voltage.

However, calculating the lowest setting possible that will

still ensure the ability to start the motor requires analysis

tools that are typically unavailable to protection engineers.

An acceptable compromise was to set the thermal model hot

safe stall time equal to or slightly greater than the observed

acceleration time. With the slip-dependent thermal element,

we were assured that the motor would not trip under normal

starting conditions. Yet, assuming that the motor was

properly sized during the original facility design effort to

accelerate the load without damage, we were also assured

that the motor was adequately protected.

Consequently, the hot locked-rotor time settings for the

three example motors could have been reduced significantly,

as proposed. However, the operators at this facility elected to

forego the adjustments to ensure that the motors would

successfully start should they ever have to be started under

other operating scenarios (such as dampers open). The

recommended protection is still superior to the original

protection, which had to be blocked during starting to

prevent nuisance trips.

VII. CONCLUSIONS

Motor protection can be greatly enhanced today with

microprocessor-based relays, even with very little motor data

available. The slip-dependent thermal model protects the

motor and allows for long acceleration times, as compared to

traditional microprocessor I2t elements and electro-

mechanical relays. Settings can be applied and if desired,

refined over the course of operation of the load and varying

operating characteristics. The motor start reports and trend

information in modern relays are valuable tools for

improving protection over time. Simulations of motor starts

under reduced voltage conditions indicate that the calculated

thermal capacity used does not increase significantly;

therefore, inappropriate tripping is unlikely to occur when the

motor is started under minimum expected voltage conditions.

VIII. APPENDIX: MOTOR STARTING COMPUTER SIMULATION

Analyzing induction motor starting requires the use of

electrical, mechanical, and thermal models that interact as

shown in Fig. 13. In the electrical model, the voltage, V, and

the slip, S, determine the rotor current. The summation of all

torques acting on the motor shaft defines the mechanical

model. Here, the slip-dependent load torque and the moment

of inertia resist the driving torque developed by the motor.

The thermal model is the differential equation for heat rise

due to current in a conductor and is defined by the thermal

capacity, the thermal resistance, and the slip-dependent I2R

watts. As the ultimate protection criteria, the thermal model

is used to estimate the rotor temperature, U, resulting from

the starting condition with initial temperature U0. A

recursive solution is used since the rotor impedance changes

continuously with slip.[3]

)S(RI 2

Fig. 13. Motor System Block Diagram

As complex as this process may appear, we can add a few

standard values and do the complete analysis with the

minimum information given. The electrical and mechanical

models for the motor and load combination are determined

using an iterative process, which involves adjusting the

model parameters until the simulation results match the

measured currents and voltages. The source voltage and

impedance are used to adjust the motor current at locked-

rotor to the measured value, and a portion of the source

impedance so determined is applied between the relay and

the motor to ensure that the simulated relay voltage matches

the measured relay voltage.

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A. Estimating Input Data for the 350 HP 1200 RPM Blower

Fan Motor

The voltage and horsepower are used to calculate the full-

load current.

82230038.0

350746

V38.0

hp746FLA =

⋅⋅

⋅=

⋅⋅= (1)

This information may also be available from the motor

nameplate.

The locked-rotor current of 6.7 • FLA was determined

from the relay motor start report and the rated speed was

determined from the nameplate. The locked-rotor torque was

taken to be 1.25. The motor data items that define the

electrical and the thermal model are:

Rated Horsepower HP 350 hp

Rated Speed FLW 1188 rpm

Synchronous Speed SynW 1200 rpm

Locked-rotor Torque LRQ 1.25 pu

Full-load Current FLA 82 A

Locked-rotor Current LRA 550 A

Hot Stall time Limit TO 25 sec

Cold Stall Time Limit TA 30 sec

B. Defining the Electrical Model

The motor modeling program uses the motor menu data to

generate the pu impedances of the Steinmetz equivalent

circuit of the motor including the slip-dependent positive-

and negative-sequence rotor resistance and reactance (see

Fig. 14).

Locked-rotor current:

7.6FLA

LRAI

L== (2)

Rotor resistance at rated speed:

001.0SynW

FLWSynWR

N=

−= (3)

Locked-rotor resistance:

0278.0I

LRQR

2

L

L== (4)

Stator resistance:

0.003R3R NS =⋅= (5)

Total series resistance:

0.0308RRR SL =+= (6)

Total series impedance:

0.149I

1Z

L

== (7)

Total series reactance:

0.1458RZX 22 =−= (8)

Locked-rotor reactance:

0.07292

XXL == (9)

Stator reactance

0.0729XXX LS =−= (10)

Rotor reactance at rated speed

0.0896X)R))(1(tan(9.2X SS0 =−+°= (11)

Positive-sequence rotor resistance:

NNL1 RS)R(RR +⋅−= (12)

Positive-sequence rotor reactance:

NNL1 XS)X(XX +⋅−= (13)

Negative-sequence rotor resistance:

NNL2 RS)(2)R(RR +−⋅−= (14)

Negative-sequence rotor reactance:

NNL2 XS)(2)X(XX +−⋅−= (15)

The above calculations result in the equivalent circuit

shown in Fig. 14.

Fig. 14. Steinmetz Model

We can now use the program to calculate the

characteristic of rotor torque and current versus slip at rated

volts by varying the slip from 1 to 0. This characteristic,

shown in Fig. 15, will be useful in defining the input watts of

the thermal and mechanical models. The load torque shown

is defined in the following section.

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6

7

Speed

Current, Torq

ue

Motor Torque

Motor Current

LoadTorque

Fig. 15. Current and Torque with Motor Model Parameters

C. Defining the Mechanical Model

The mechanical model is the equation expressing the

summation of torques acting on the shaft:

dt

dωM)Q(Q LM =−

(16)

where QM is the motor torque, QL is the load torque, M is the

combined moment of inertia of the motor and the drive, and

ω is the velocity. The equation, expressed in time discrete

form and when solved for slip, becomes:

DT

ωωM)Q(Q 0

LM

−=−

(17)

ω)(1S

ωDTM

)Q(Qω 0

LM

−=

+−

=

(18)

The electromechanical power developed by the rotor is

represented by the losses in the slip-dependent load resistor

in Fig. 14. Consequently, the positive-sequence mechanical

power is:

1

21M R

S

S1IP

−⋅=

(19)

where 2

1I is the positive-sequence rotor current.

Dividing the power PM by the velocity, (1 - S), gives the

motor torque:

S

RIQ 1

21

M

⋅=

(20)

Fig. 16 shows the typical contour of the load torque versus

speed curve of a pump or fan. The load torque is

characterized by an initial breakaway torque value, L, and

momentary decrease followed by the increase to its final

value, F. The program uses the empirical equation:

25

L ωFω)(1LQ ⋅+−⋅= (21)

Fig. 15 shows the load torque relative to the motor torque.

The torque difference (QM - QL) is the accelerating torque as

expressed by (17). The accelerating power and the moment

of inertia determine the time it takes the motor to reach the

peak torque and attain rated speed.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Speed

Torq

ue (pu)

Fig. 16. Contour of Load Torque

Typical values for the load are shown with the moment of

the inertia specified in units of lb-ft2. Since all the model

parameters are specified in pu of motor base values, the WR2

is converted to the inertia constant, M, using the following

relation:

R

2

Q

SynW

60

2π

g

WRM ⋅⋅=

(22)

where g is the acceleration due to gravity, SynW is the

synchronous speed, and QR is the torque calculated from

rated speed and horsepower:

FLW

RHP5252QR ⋅=

(23)

With this motor and load, the moment of inertia of

4450 lb-ft2 produces an approximate 10-second starting time

to match the measured starting time.

D. Defining the Thermal Model

Fig. 17 shows the first order thermal model that

incorporates the I2t properties of the rotor thermal limit

curves as well as the effect of the slip-dependent positive-

and negative-sequence rotor resistance on the input watts.

The I2t value of the operating temperature is used as the

thermal resistance to ensure that one pu input produces the

operating temperature.

Fig. 17. Rotor Thermal Model

The following discrete form of the differential equation of

the rotor thermal model is processed each sample period to

calculate the temperature U:

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For I > 2.5

1nTh

22

N

221

N

1n U

C

∆tI

R

RI

R

RU −+

+=

(24)

For I ≤ 2.5

1n

ThThTh

22

N

22

N

1n U

CR

∆t1

C

∆tI

R

RI

R

RU 1 −⋅

−+

+=

(25)

where the thermal capacitance CTh = RL/RN and the thermal

resistance RTh = (IL)2(TA – TO). I1 and I2 are the positive- and

negative-sequence currents, respectively. Note that the

thermal resistance is only considered when the current drops

below 2.5 pu, so that the calculation of temperature is

adiabatic for starting current. At each sample, Un is compared

to the trip threshold and asserts the trip signal if the limiting

temperature is exceeded.

Slip (S) must be determined in order to calculate the slip-

dependent rotor resistance. The speed algorithm applied to

the 350 hp motor is as follows:

=

1

1

I

VrealR

(26)

where V1 and I1 are the positive-sequence motor voltage and

current measured at each sample.

1.2A = (27)

RL and R(1), which is the initial value of R measured

during start, are used to determine the stator resistance Rs

which includes the source resistance:

A

RR(1)Rs L−=

(28)

then

( ) ))R(RRA(R

RS

NLS

N

−−−=

(29)

and

NNLr R)SR(RR +−= (30)

The comparison plots shown in Fig. 18 through Fig. 21

validate the accuracy of the simulation and its use as a tool

for determining optimum motor protection setting.

0 5 10 150

1

2

3

4

5

6

7

8

Time, Seconds

Current, P

U

Measured

Simulation

Fig. 18. Simulated and Measured Current for 350 hp Blower Motor

0 2 4 6 8 10 120

0.2

0.4

0.6

0.8

1

Time seconds

V R

ela

y, P

U m

oto

r base

MeasuredSimulation

Fig. 19. Simulated and Measured Voltage at the Relay in PU Motor Base Voltage for 350 hp Blower Motor

0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time, seconds

Roto

r Therm

al C

apacity, P

U

Simulated

Measured

Simulated

Measured

Simulated

Measured

Fig. 20. Simulated and Measured Rotor Thermal Capacity, TCURTR, for 350 hp Blower Motor

0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time, seconds

Slip

, P

U

SimulatedMeasured SimulatedMeasured

Fig. 21. Simulated and Measured Slip for 350 hp Blower Motor

© 2007 Plant Power and Control Systems, LLC / Schweitzer Engineering Laboratories, Inc.

All rights reserved. 20070912 • TP6293-01


SIPSEP-08-21

www.uanl-die.net

IX. REFERENCES

[1] NEMA MG-1-1998, “Motors and Generators,” National Electrical

Manufacturers Association, New York, 1998.

[2] S. E. Zocholl, “Tutorial: From the Steinmetz Model to the Protection

of Inertia Drive Motors,” presented at the 34th Western Protective

Relay Conference, Spokane, WA, October 2001.

[3] S. E. Zocholl, AC Motor Protection, Schweitzer Engineering

Laboratories, Inc., pp.6–21, 2004.

X. ADDITIONAL READINGS

S. E. Zocholl, E. O. Schweitzer, and A. Aliaga-Zegarra, “Thermal Protection

of Induction Motors Enhanced by Interactive Electrical and Thermal

Models,” IEEE Transactions on Power Apparatus and Systems, vol. PAS-

103, No. 7, July 1983.

S. E. Zocholl and G. Benmouyal, “On the Protection of Thermal Processes,”

IEEE Transactions on Power Delivery, vol. 20, issue 2, pp. 1240–1246,

April 2005.

IEEE Guide for the Presentation of Thermal Limit Curves for Squirrel Cage

Induction Motors, IEEE Standard. 620-1996.

XI. BIOGRAPHIES

Patrick Whatley, P.E., holds a B.S. in Electrical Engineering from Auburn

University and an M.S. in Power Engineering from the University of South

Florida. After several years in the industrial division of General Electric, he joined Florida Power & Light (FPL), working in the Protection and Control,

Substation, and Transmission departments. Since 1997, he has been

employed with Plant Power & Control Systems (PP&CS), an engineering, consulting, and OEM equipment manufacturing company where he oversees

all technical issues and reviews equipment design. Mr. Whatley is a

registered professional engineer in Alabama, Florida, Georgia, and Mississippi.

Mark E. Lanier, P.E., received his B.S. in Electrical Engineering from the

University of South Carolina in 1989. He joined Duke/Fluor Daniel, a subsidiary of Duke Energy, upon graduation as an electrical power systems

engineer where he worked for fourteen years designing coal- and gas-fired

power plant electrical systems. In 2003 he left Duke Energy and joined Schweitzer Engineering Laboratories, Inc. as a field application engineer. He

is a registered professional engineer in the State of South Carolina.

Mr. Lanier also received his M.B.A. from the University of South Carolina in 2007.

Lee Underwood, P.E., received a B.S. in Electrical Engineering from the

University of Virginia in Charlottesville in 1990. From 1990 to 1996, Lee worked as a Design and Systems Engineer for Duke Power Oconee Nuclear

Station, with emphasis on dc power systems, medium and low voltage

switchgear, and protective relaying. In 1996, he joined Duke/Fluor Daniel, and participated in the design and construction of electrical systems for coal-

fired power plants. Mr. Underwood joined Schweitzer Engineering

Laboratories, Inc. as a field application engineer in 2004. He is a member of the IEEE Power Engineering Society and a registered professional engineer.

Stanley (Stan) Zocholl has a B.S. and an M.S. in Electrical Engineering

from Drexel University. He is an IEEE Life Fellow and a member of the Power Engineering Society and the Industrial Application Society. He is also

a member of the Power System Relaying Committee. He joined Schweitzer

Engineering Laboratories in 1991 in the position of Distinguished Engineer. He was with ABB Power T&D Company Allentown (formerly ITE, Gould

BBC) since 1947 where he held various engineering positions, including

Director of Protection Technology.

His biography appears in Who’s Who in America. He holds over a dozen

patents associated with power system protection using solid state and

microprocessor technology and is the author of numerous IEEE and Protective Relay Conference papers. He received the Power System

Relaying Committee Distinguished Service Award in 1991. He was the

Chairman of PSRCW G J2 that completed the AC Motor Protection Tutorial. Mr. Zocholl is the author of two books, AC Motor Protection,

second edition, ISBN 0-9725026-1-0 and Analyzing and Applying Current

Transformers, ISBN 0-9725026-2-9.

233

I N D I C E DE AUTORES

Adamiak Mark 67, 107

Altuve Héctor J. 27, 189

Alzate Julian 51

Andrade Luis de 21

Ariza James 79

Baltasar David Sebastián 213

Castillo J. José A. 213

Cimadevilla R. 127

Clark Ed 173

De la O Serna Jose A. 139

Dionisio Alfredo 67

Dolezilek Dave 27

Erwin Davis 51

Estrada José L. 45

Espinosa Daniel 51

Finney Dale 45

Flores Victor Manuel 79

Garrity John T. 45

Gers Juan M. 79

Gómez J. 127

Gonzáles Guillermo 27

Guel Manuel 27

Guerrero C. 37

Guzmán Armando 89, 189

Hernández Jesús 15

Hernández Acosta Bladimir 167

Hou Daqing 155

Kasztenny Bogdan 1, 107, 173

Lanier Mark 221

López S. 127

Loza Pedro 27

Madani Vahid 67

Mamani Jose Luis 147

Martínez Martínez Enrique 101

Meklin Anatoliy 67

Méndez R. 37

Monjarás Martín 27

Mora Alcaraz Eduardo O. 167

Muñoz Ignacio 27

Mynam Venkat 89

Plata Garza Miguel Ángel 139

Rivera S. Carlos A. 213

Reichard Michael L. 45

Rojas Eliana. 15

Sandoval Ramón 189

Sánchez Pantoja Luis 147

Schaefer Joe 173

Sebastian D. 37

Servando Sánchez 27

Sorrentino Elmer 15, 21

Taylor Edward 67

Tenorio J.J. 37

Underwood Lee 221

Voloh Ilia 1

Yáñez Iván 27

Whatley Patrick 221

Zocholl Stan 221

Zweigle Greg 89

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