validation of facts models

7/24/2019 Validation of FACTS Models

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484 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 21, NO. 1, JANUARY 2006

A Platform for Validation of FACTS ModelsShan Jiang, Student Member, IEEE, U. D. Annakkage, Senior Member, IEEE, and A. M. Gole, Senior Member, IEEE

AbstractThe paper presents a platform system for the incor-

poration of flexible ac transmission systems (FACTS) devices. Theplatform permits detailed electromagnetic transients simulation as

it is of manageable size. It manifests some of the common problems

for which FACTS devices are used such as congestion management,stability improvement, and voltage support. The platform can be

valuable for the validation of reduced order models such as small

signal or transient stability models. The paper presents details on

the development and validation of a small signal based model with

the inclusion of a Unified Power Flow Controller. The validated

model is then used successfully for the design of a feedback con-

troller for improved damping.

Index TermsElectromagnetic transients simulation, FACTS,Prony analysis, small signal analysis, test platform, validation,UPFC.

I. INTRODUCTION

THE expansion of power transfer capability of transmis-

sion systems has been a major problem over the past two

decades. This, together with the advancement of solid-state

technology, has paved way to a series of new Power Electronic

devices which are capable of extending the power transfer ca-

pability limits of transmission systems through their flexibility

and response speed. Among them, Static Var Compensators

(SVCs), static synchronous compensators (STATCOMs), and

Thyristor Controlled Series Compensators (TCSCs) have been

widely accepted in the industry; whereas applications using theUnified Power Flow Controller (UPFC) are recently emerging

[1]. The most recent device in the family is the Interline Power

Flow Controller (IPFC), which has only been installed on an

experimental basis.

A large amount of research effort has gone into designing

these devices and studying the impact of these devices on the

performance of the power system. Modeling plays an important

role in such design and application studies. At the most detailed

level, electromagnetic transients simulation (emtp-type) based

models are used. In these models, the detailed three phase repre-

sentation of the system is simulated using a 1050 s time-step.

The operation of individual switching elements and control sys-

tems in the FACTS device as well as all magnetic saturation in

transformers is also fully represented. This level of modeling

is useful for confirming the operation of the FACTS device in a

local setting but is often considered too detailed for investigating

the impact of the device on the wider electrical network. Like-

wise, it does not yield information about the damping and sta-

bility margins in a straightforward manner. On the other hand, in

Manuscript received November 29, 2004; revised February 22, 2005. Paperno. TPWRD-00561-2004.

The authors are with the University of Manitoba, Winnipeg R3T 2N2,Canada.

Digital Object Identifier 10.1109/TPWRD.2005.852301

Fig. 1. One line diagram of the 12-bus power system.

transient stability modeling, only the electrical machines, con-

trols, and prime movers are represented using time domain dif-

ferential equations. A simplified fundamental frequency phasor

equivalent of the ac network is used, which permits larger time-

steps of up to 10 ms, thereby making possible the representation

of larger networks. Alternatively, Small Signal Analysis takes a

markedly different approach in which the network and electro-

mechanical device equations are converted at any given oper-

ating point into a set of linear differential equations. Eigenvalue

and Spectral Analysis applied to these equations yields useful

information on stability margins and damping and permits stan-dard controller design techniques to be effectively applied.One of the concerns that arises is whether the simplified

models such as the Small Signal or Transient Stability models

adequately represent the detailed system. Usually, simplifiedrepresentations are developed and benchmarked against a verysmall emtp-type model, which essentially includes the device

connected to a single machine or an infinite bus [2]. Similarlyother comparisons havebeen made that benchmarka small signalmodel with a transientstability model.Thistype of comparison isof limited use as it compares two simplifications with each otherrather than with the most accurate (emtp-type) representation.

This paper aims to address the above concern of validation by

proposing a platform system which is large enough to demon-strate electromechanical oscillation modes; and is yet smallenough to be completely realizable in an emtp-type form. This

system can be represented in different levels of detail which canthen be compared. The proposed platform has been designed sothat it manifests typical transmission bottlenecks and interarea

oscillations that can be alleviated by FACTS devices. Theprocedure for validation is elucidated by connecting a UPFCinto the platform (see Fig. 1) and comparing its small signalrepresentation against the detailed emtp-type representationusing the technique of Prony Analysis. The UPFC is installed

in line 78 of the platform system; its primary purpose is torelieve congestion in line 16.

0885-8977/$20.00 2006 IEEE


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JIANGet al.: PLATFORM FOR VALIDATION OF FACTS MODELS 485

II. SMALLPOWERSYSTEM FORMODELVALIDATION

The proposed test system, shown in Fig. 1, consists of 12

busses (six 230 kV busses, two 345-kV buses and four 22-kV

buses). The test system covers three geographical areas (Area

1, 2, and 3). Area 1 is predominantly a generation area with

most of its generation coming from hydro power. Area 2, situ-

ated between the main generation area (Area 1) and the mainload center (Area 3), has some hydro generation available but is

insufficient to meet local demand. Area 3, situated about 500 km

from Area 1, is a load center with some thermal generation

available. Furthermore, as Area 2 generation has limited energy

availability, the system demand must often be satisfied through

transmission. The transmission system consists of 230 kV trans-

mission lines with the exception of one 345-kV link between

areas 1 and 3 (between busses 7 and 8). Areas 2 and 3 have

switched shunt capacitors to support the voltage.

Powerflow studies reveal that in the event of a loss of genera-

tion in area 3, or a loss of the transmission line between busses 4

and 5, line 16 is overloaded while the transmission capacity ofthe parallel path through the 345 kV transmission line 78 is un-

derutilized. This congestion can be relieved by various FACTS

solutions such as TCSCs or SSSCs on line 12 or line 78;

IPFCs on lines 16 and 78; or, as in the example presented

here, a UPFC on line 78.

Further, the load center (Area 3) suffers from under-voltage

problems, which makes this test system suitable for studies on

application of SVC or STATCOM.

Small signal stability studies presented in Section IV show

that the platform system has poorly damped inter-area oscilla-

tion modes which can be improved by FACTS devices at various

locations. The study presented later in this paper shows one such

application.

It is also possible to use the platform to investigate the use of

FACTS devices to strengthen the network for the integration of

wind generation in Area 2. For example series FACTS devices

on lines 16 and/or line64 and/or line78 could make stronger

connections from Area 2 (with wind generation) to the other

areas.

Thus, it can be seen that the proposed platform can be useful

for studying FACTS device applications for congestion relief,

voltage support, transmission stability and integration of wind

generation. One such application, that of designing a UPFC-

based damping controller is discussed in this paper. It also be-

comes possible to validate reduced models such as Small SignalStability models against detailed emtp-type simulation for such

FACTS applications. These aspects will be covered in the re-

mainder of the paper.

III. DETAILEDELECTROMAGNETICTRANSIENTSIMULATION

MODEL OF UPFC

Because the electromagnetic transient simulation model

represents the system in extreme detail, it provides a means for

validating the small signal and other reduced models for the

network. For this purpose, the system in Fig. 1 is represented

in full, with detailed models for the synchronous machines

(including full representation of sub-transient effects), exciters.The lines can be represented with distributed parameters or as

Fig. 2. Emtp-type UPFC Model.

Fig. 3. Decoupled controller of shunt converter.

lumped pi-sections. The representation for the UPFC in the line

connecting busses 7 and 8 is shown schematically in Fig. 2.

Every switching device in each of the series and shunt con-

verters is modeled individually. Firing pulses for the converters

switches are generated by the sinusoidal pulse width modulator

(SPWM) that eliminates low-frequency harmonics and makes

the output waveform conform to the desired fundamental

frequency voltage waveform. The reference waveform for the

SPWM modulator is generated from direct and quadrature

components Vd, Vq. As shown in Fig. 3, in the shunt converter,

they are selected to provide the appropriate real and reactive

powers from the shunt element using a decoupled controller

[3]. The real power order is generated from a dc bus voltage

controller and the reactive power is directly ordered (often set

to zero for unity power factor operation). The decoupled control

system ensures that a change in the real power order can be

implemented without any transient in the reactive power and

vice versa. The series converters controller can be modeled insimilar detail if necessary; however in this particular study, the

d and q components of the series injected voltage are directly

ordered to ensure the required load flow.

IV. SMALLSIGNALSTABILITY MODEL

A. Generator Model

In the small signal model, the generators with their exciters

are represented by the typical fourth-order dynamic model

(third-order generator plus afirst-order exciter)

(1)

(2)


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(3)

(4)

These equations can be linearized and expressed in the com-

pact form for number of generators, as shown in (5) and (6).

The derivation of this model is found in [4] and [5]

(5)

(6)

where

is the change in current injected by generator to the

network, and is the voltage of the network node to which

the generator is connected.

B. UPFC Model

Charging of the capacitor on the dc link of UPFC is modeled

as

(7)

where is the capacitance of the dc bus capacitor, is

the voltage of the dc bus, is the real power drawn into the

dc link from the shunt (exciter) branch of UPFC, and is the

real powerflowing out of the dc link into the transmission linethrough the booster side of UPFC. The PI Controller that main-

tains at the reference setting of is modeled as

(8)

where is the d component of the shunt current that is in

phase with the voltage Vs (see Fig. 4), and are PI con-

troller gains. Any time delays in PWM and associated controls

are modeled as

(9)

where we have the following.

1) , and are the reference control settings of the

UPFC, namely, the in-phase injected voltage, quadrature

injected voltage, and shunt current, respectively.

2) , and are the in-phase injected voltage,

quadrature injected voltage, and quadrature shunt cur-

rent, respectively.

3) , and are the time constants used to modelthe PWM time delay associated with , and .

Fig. 4. UPFC small signal model.

The voltage and current relationship for the UPFC are given by

(10)

(10)

where and are, respectively,

the sending end and receiving end line currents expressed as

two-dimensional (2-D) vectors consisting of the real and imag-

inary parts of the current phasor. Similarly, and are 2-D

vectors representing the sending and receiving end voltages, and

is a 2-D vector representing the boost voltage or the voltage

injected in series with the transmission line. The matrix in

(10) is the dq to xy transformation matrix. Equations (7)(10)

can be linearized to obtain the set of differential and algebraic

equations (11)(13). A detailed derivation of the elements of all

coefficient matrices is given in [5]

(11)

(12)

(13)

where

is a state variable associated with the PI controller.

The voltage-current relation of the network is modeled as

(14)

The state-space representation of the complete power system

can be obtained in the standard format of (15) and (16) by elim-

inating and from the differential-algebraic equations

of the dynamic devices (5), (6) and (11)(13) and the network

equations (14).

(15)(16)


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TABLE IMODES OFOSCILLATION

TABLE IIPARTICIPATIONFACTORS

V. ANALYSIS ANDVALIDATION OFSMALLSIGNALMODEL

The small signal model yields important information about

the oscillation modes and damping. This information is vali-

dated for accuracy using the full emtp-type representation.

A. Small Signal Eigenvalues

The system has three generators with each equipped with an

exciter. Each generator introduces three state variables, and each

exciter introduces one state variable. The UPFC introducesfivestate variables. Therefore, the order of the system matrix is

17. The complex conjugate pairs of eigenvalues of system ma-

trix correspond to oscillation modes. Table I shows the eigen-

values corresponding to electromechanical oscillation modes

for the selected operating point of the power system. Note that

the oscillation frequencies of the three modes are 0.75, 0.85, and

1.12 Hz.

Further information about the oscillation modes can be ob-

tained from the participation factors and mode shapes. The par-

ticipation factors represent the activity of state variables in a

given mode [4]. Table II shows the participation factors of the

state variables in the three modes of oscillation. Each columnof Table II gives the participation factors for a given mode. It

can be noticed that the activity of generator G2 dominates in

0.85 Hz, as indicated by the relatively large participation factor

(0.4632) of state . Similarly, G3 dominates in the 1.12-Hz

mode, and G4 dominates in the 0.75-Hz mode.

The elements of the right eigenvector indicate the response of

state variables when the corresponding mode is excited. There-

fore, by observing the magnitude and phase of the elements of

the eigenvector corresponding to the state variables ,

and , one can predict the relative magnitudes and phase an-

gles of the rotor oscillations when the particular mode is excited.

This information can be plotted on the complex plane to obtain

what is known as the mode shape [4]. The modes shapes of thethree oscillatory modes are shown in Figs. 57.

Fig. 5. Mode shape of 0.75-Hz mode.



In Section VI, a damping controller for the UPFC is designed

in order to improve the damping of oscillations. Considering

the topology of the network in Fig. 1, the UPFC is directly in

the path between the infinite bus and generator G3, and thus a

damping controller for the UPFC can be expected to be most ef-fective in improving the damping of modes related to G3. Partic-


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Fig. 8. Dominant mode of G2 from Prony analysis.


ipation factors suggest that this mode is the 1.12-Hz mode. The

mode shape diagrams also suggest similar conclusions. It is evi-

dent from these diagrams that the rotor angle of Generator 3 os-

cillates when the 0.75-Hz mode is excited (Fig. 5) and when the

1.12-Hz mode is excited (Fig. 7). On the other hand, Fig. 6 indi-

cates that there is negligible influence on Generator 3 when the

0.85-Hz mode is excited. As the UPFC in line 78 primarily af-

fects the power in Generator 3, this suggests that the damping of

the 1.12-Hz mode and/or the 0.75-Hz mode could be improved

with its installation. A more quantitative evaluation of the effec-

tiveness of controllers is presented in Section VI. The frequency

information obtained from the eigen-analysys is verified againstthe simulation results from a detailed electromagnetic transient

simulation model in Section V-B.

B. Validation Using Electromagnetic Transients Simulation

An electromagnetic transient simulation of the power system

with a switching level detailed model of the UPFC was per-

formed using PSCAD/EMTDC. The disturbance applied was a

1% increase of the reference setting of the quadrature injected

voltage of the UPFC for a period of 100 ms. Figs. 811 show

the simulated waveforms for the speeds of gener-

ators 24 and the sending end power, respectively. Superposed

on the emtp-type simulations are the waveforms obtained fromtime-domain simulation of the linearized Small Signal Analysis


Fig. 11. Comparison of sending end real power of small signal model versus

emtp-type model.

TABLE IIIPRONYANALYSIS OFPSCAD WAVEFORMS

equations. The close agreement validates the Small Signal Anal-

ysis model.

The electromagnetic simulation can also be used to verify

the modal frequencies, damping and participation factor infor-

mation. Prony Analysis was performed in order to validate the

small signal model. Results of Prony analysis on the waveforms

from emtp-type simulation of the speed of three machines

, and the sending end power of the transmission

line on which the UPFC is located (line 78) are tabulated in

Table III. The following observations can be made by com-

paring this information with the eigenvalues given in Tables I

and II, which were obtained from the small signal model.

1) Although the 1.12-Hz mode is presented in all four wave-forms (Prony analysis estimates in the range 1.11 Hz to


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TABLE IVCONTROLLABILITYINDEX

1.13 Hz), as expected from the participation factor anal-ysis in Table II, it is most prominent in . The damping

for this mode (in ) is 3.74%, which compares well

with the 3.30% damping calculated from the small signal

model in Table I.

2) As expected from the theoretical participation factors, the

0.85-Hz mode (estimated by Prony Analysis as 0.79 Hz)

is prominent in . Although both Prony analysis based

observation and models attribute the poorest damping to

this mode, the observed value of 3.56% is significantly

different from the 1.07% predicted by theory. However,

this error may be due to the small magnitude of the ob-

served signal and due to interference with the relativelyclose 0.75-Hz mode.

3) Again, as predicted by Small Signal theory, Prony anal-

ysis confirms that the 0.75-Hz mode is prominent in ,

with an observed damping of 8.245%, in comparison

to the 7.17% from Small Signal Analysis. Both theory

and simulation observations show that this mode has the

highest damping.

With the confidence in accuracy gained from the above anal-

ysis, the small signal model can now be used effectively for Con-

troller Design, as described in the next section.

VI. DESIGN OFDAMPINGCONTROLLER

The question arises as to whether the UPFC placed in line

78 for transmission congestion relief can also be modulated to

damp system oscillations. Ideally one would like to increase the

damping of the poorly damped 0.85- and 1.12-Hz modes. Con-

trollability analysis performed on the small signal model can de-

termine if such modes can be damped at all, after which linear

control design theory can be used to select the optimal feedback

controller. There are three reference control settings available

in the UPFC for damping control. These are , and .

The effectiveness of using these inputs can be evaluated by cal-

culating the controllability indices of the modes [4]. These in-

dices are easily obtained once the eigenvalues and eigenvectorsof the small signal system are evaluated. The controllability in-

dices are given in Table IV. The relatively large magnitude of

the indices for the 1.12-Hz mode using inputs and indi-

cate the suitability of using these inputs to improve the damping

of that mode. Very small indices for the 0.85-Hz mode indicate

that this mode is not controllable using any of the control inputs

of the UPFC. Thesefindings are consistent with the mode shape

based arguments made in Section V-A.

Based on the above analysis, an output feedback damping

controller is designed to improve the damping of the 1.12-Hz

mode by modulating either the or input. The feedback

signal is generated by multiplying the selected output marked

for feedback with a simple proportional gain. The outputs(real power of generator G1, G2, G3), and

TABLE VEIGENVALUE SENSITIVITY TOFEEDBACK GAIN

TABLE VIMODES OFOSCILLATION: WITHFEEDBACK CONTROL

Fig. 12. Damping effect on the sending end real power. Small signal model.

(real power of UPFC sending end) are considered as feedbackcandidates. The effectiveness of each of these signals is evalu-

ated by calculating the eigenvalue sensitivity to feedback gain

[6]. These sensitivities are given in Table V. As the objective

is to move the real partof eigenvalue in order to improve the

damping, the sensitivity index with the largest real part identi-

fies the most effective feedback signal, which is . However,

in a practical controller, it is usually desirable to choose a

local signal, hence the second best signal is selected. The

larger sensitivity of thereal partof the eigenvalue with than

with implies that is the better choice for the controller

input. Once the feedback structure (i.e., feedback and input) is

identified, the gain of the feedback controller can be selected.Using a feedback gain of 0.3 produces a new set of eigenvalues

for the system, with the three poorly damped ones shown in

Table VI. Note the slight change in the frequency from 1.12

to 1.10 Hz and the improved damping of this mode from 3.30

(as in Table I) to 4.35. Time domain simulation of the small

signal model with and without feedback as in Fig. 12 shows

this additional damping.

Once again, as shown in Fig. 13, detailed emtp-type simu-

lation produces nearly identical responses to those obtained in

Fig. 12 for the small signal model. Using Prony Analysis on the

detailed simulation waveforms the frequencies and damping are

determined, as in Table VII. The damping as observed from the

most prominent signal for this mode is improved from 3.74to 4.92, which compares well with the theoretical value of 4.35.


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Fig. 13. Damping effect on the sending end real power. emtp-type model.

TABLE VIIPRONYANALYSIS OFPSCAD WAVEFORMS: WITHFEEDBACK CONTROL

TABLE VIIIBUSDATA

VII. CONCLUSION

The paper presents a platform that can be used for FACTScontroller studies. The platform has been selected to demon-

strate a number of problems for which FACTS devices offer po-

tential solutions. These include congestion relief, voltage sup-

port, and stability improvement. The system was selected so that

it is large enough to show interarea oscillations and yet man-

ageable so that detailed electromagnetic transients solutions are

possible.

The platform provides a valuable tool for benchmarking re-

duced-order models. The example in the paper shows how the

small signal model developed for a UPFC is incorporated into

the small signal framework. Detailed comparisons with emtp-

type simulations show close agreements with the Small Signal

Analysis in the time domain and in the observed frequencies anddamping as determined by Prony Analysis.

TABLE IXCONFIGURATION OFTRANSMISSIONLINE

Fig. 14. Transmission line structure.

TABLE XBRANCHDATA(SYSTEMBASE: 100 MVA)

The Platform can be extended to the study of other FACTS

devices in a similar manner.

APPENDIX

The data pertaining to the power system shown in Fig. 1 aregiven in the following tables.

Table VIII(a) shows the loads and shunt compensation at load

buses 18, and Table VIII(b) shows the specified voltage and

real power generation at generator buses 912. In the transient

model, the loads are represented as fixed impedances.

The geometrical and physical parameters for the transmission

lines are as shown in Table IX and Fig. 14. All 230-kV lines are

assumed to have the same geometrical and physical parameters

(except for different lengths). The 230-kV line is based on Man-

itoba Hydros Glenboro-South to Rugby line, and the 345-kV

line has a typical structure selected from Table 2.7.1 of the EPRI

transmission line reference book [7]. Table X shows the line

lengths for each of the 230- and 345-kV lines, as well as the se-ries impedances and shunt reactances resulting from the above


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TABLE XITRANSFORMERDATA(SYSTEMBASE: 100 MVA)

TABLE XIIGENERATOR ANDEXCITERDATA

TABLE XIII

UPFC DATA

line geometries for an equivalent- representation, corrected for

long-line effects (see also Tables XIXIII).

REFERENCES

[1] L. Gyugyi, Unified power-flow control conceptfor flexibleac transmis-sion systems,in Proc. Inst. Elect. Eng., vol. 139, 1992, pp. 323331.

[2] L. Y. Dong, L. Zhang, and M. L. Crow,A new control strategy for theunified controller,in Proc. IEEE PES Winter Meet., vol. 1, Jan. 2002,pp. 562566.

[3] I. Papic, P. Zunko, D. Povh, and M. Weinhold, Basic control of uni-fied powerflow controller,IEEE Trans. Power Syst., vol. 12, no. 4, pp.17341739, Nov. 1997.

[4] P. Kundur,Power System Stability and Control. New York: McGraw-Hill, 1994.

[5] S. Limyingcharoen,Application of Unified Power Flow Controllers inPower System Stability Enhancement,Ph.D. dissertation, Dept. Elect.Electron. Eng., Univ. Auckland, Auckland, New Zealand, Mar. 1999.

[6] F. L. Pagola, I. J. Perez-Arriaga, and G. C. Verghese,On sensitivities,residues, and participations: Applications to oscillatory stability analsisand control,IEEE Trans. Power Systems, vol. 4, pp. 278285, 1989.

[7] Transmission Line Reference Book (345 kV and Above), Second ed.Palo Alto, CA: Elect. Power Res. Inst., 1987, p. 39.

Shan Jiang (S04) received the B.Sc. and M.Sc. (Eng.) degrees in electricalengineering from Chongqing University, Chongqing, China, in 1989 and 1993,

respectively. He is currently pursuing the Ph.D. degree with the University ofManitoba, Winnipeg, MB, Canada.

His research interests are FACTs and power system control.

U. D. Annakkage (M95SM04) received the B.Sc. (Eng.) degree in electricalengineering from the University of Moratuwa, Moratuwa, Sri Lanka in 1982

and the M.Sc. and Ph.D. degrees from the University of Manchester Instituteof Science and Technology (UMIST), Manchester, U.K., in 1984 and 1987, re-

spectively.He is presently a Professor with the University of Manitoba, Winipeg, MB,

Canada. His research interests include power system stability and control, secu-rity assessmentand control, operation of restructured power systems, and powersystem simulation.

A. M.Gole (M82SM04) received the B.Tech. degree in electricalengineeringfrom the Indian Institute of Technology, Bombay, India, in 1978 and the Ph.D.degree from the University of Manitoba, Winnipeg,MB, Canada, in 1982.

He currently holds the NSERC Industrial Research Chair in Power SystemSimulation at the University of Manitoba. His research interests include tran-

sients simulation and power electronics applications in transmission.

Prof. Gole is a Professional Engineer in the Province of Manitoba.

validation of facts models

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