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452 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 17, NO. 2, APRIL 2002

A New Fault Locator for Three-TerminalTransmission LinesUsing Two-TerminalSynchronized Voltage and Current Phasors

Ying-Hong Lin, Chih-Wen Liu, Member, IEEE, and Chi-Shan Yu

AbstractWith theadvent of thehigh synchronization accuracyof modern phasor measurement units (PMUs), a new approachfor accurately locating faults on three-terminal lines is proposed.Using the data measured from two terminals of three-terminallines, the proposed technique can provide an extremely accuratefault location. An EMTP/ATP simulator is used to demonstrate theperformance of the proposed fault locator. The simulation resultsshow that the accuracy of fault location is very high under variousfault resistance, fault locations, prefault loading conditions, sourceimpedance and fault types.

IndexTermsFault locator, phasor measurement units (PMUs),three-terminal lines.

I. INTRODUCTION

T HE DEVELOPMENT of fault location techniques is veryimportant, especially for the long lines in rough terrain, forreducing the crew repair expense and speeding up the restora-

tion of service for power utilities. In the past two decades, many

algorithms have been developed [1][9]. The majority of pub-

lished work is concerned with developing techniques for fault

location on two-terminal lines [1][7]. However, until recently,

relatively little work has been done in the development of fault

location technique for three-terminal lines [8], [9]. In the pastfew years, phasor measurement units (PMUs) have been rapidly

developed and the associated standards have been made in 1995

[10]. The PMUs are especially suitable for the implementation

of the fault locators due to their high synchronization. In our

previous papers [6], [7], a PMU-based approach for fault loca-

tion on two-terminal lines and the practical implementation of

PMU have been proposed. Such an approach forms the basis of

this work.

Owing to the dispute on the right of way, some two-terminal

transmission lines tapped with a source of generation via a new

tapping line have been existingat theTaiwan power system. This

fact cannot only drastically affect the degree of accuracy of the

fault locator for the original two-terminal lines, but also exposethe new tapping lines to be out of protection. So, the demand and

importance of developing a fault locator for such three-terminal

lines has increased.

Manuscript received August 29, 2000.Y.-H. Lin and C.-W. Liu are with the Department of Electrical Engineering,

National Taiwan University, Taipei, Taiwan, R.O.C.C.-S. Yu is with the Department of Electrical Engineering, National Taiwan

University, Taipei, Taiwan, R.O.C., and also with the Department of ElectricalEngineering, Private Kuang-Wu Institute of Technology, Taipei,Taiwan, R.O.C.

Publisher Item Identifier S 0885-8977(01)10326-2.

From the past literatures [8], [9], all of the proposed fault lo-

cation algorithms applied to three-terminal lines utilize the mea-

surements from all of three terminals. For example, Aggarwal

et al. [8] utilized the prefault measurements that are available

at three-terminals to estimate the synchronization errors among

themeasureddata. These error quantities were utilized to correct

the synchronization error of post-fault measurements and then

the corrected data can be used to calculate the fault location.

One drawback of such an approach is that their implementation

cost is high since the proposed approach needs to install threedata recorders. Besides, it is hard to perform a data synchro-

nization procedure among data recorders and thereby inevitably

increases the computation burden of the host computer signifi-

cantly. Using the iterative method, Girgis et al. [9] resolved theunknown synchronization errors and obtain the fault location.

However, the line model employed in [9] neglects the shunt ca-

pacitance. The paper cannot really reflect the nature of transmis-

sion lines and will further deteriorate the accuracy of the fault

location.

To cope with the mentioned problems, a new technique is pro-

posed. The proposed technique uses the same configuration as

fault locator for two-terminal lines [6], [7], i.e., just using two

PMUs equipped at two ends of transmission lines and is capable

of precisely locating faults independent of faults occurring on

any leg of three-terminal lines. The proposed technique not only

possesses the merit of less cost, but also utilizes distributed pa-

rameter model of lines to approach the reality of the transmis-

sion lines.

To explain the concepts, the paper is organized into five sec-

tions. The first of which is the introduction. In Section II, de-

scriptions of overall system configuration of PMU-based fault

locator for three-terminal lines are presented. In Section III, a

brief review of our previous proposed algorithms for two ter-

minal lines is introduced. Then, an extension to three-terminal

lines is presented. The algorithm for three-terminal lines willbe divided into two steps: the first step is to identify the faulted

leg. The second step is to locate a fault on the faulted leg. The

evaluation of the proposed algorithm is presented in Section IV.

Finally, the conclusion is given in Section V.

II. OVERALL SYSTEM CONFIGURATION

The proposed algorithm combined with PMUs and commu-

nication links forms the fault locator system. The overall system

configuration of the PMU-based fault locator for three-terminal

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LIN et al.: NEW FAULT LOCATOR FOR THREE-TERMINAL TRANSMISSION LINES 453

Fig. 1. Overall system configuration of the proposed fault locator.

transmission lines is shown in Fig. 1. For the clear explanation

of the proposed approach, the three-terminal line will be di-

vided into , , and . The lengths of these line segments

are , , and , respectively. The three-terminal transmis-

sion line is originally composed of and , and the orig-

inal line is labeled as . The outsides of are replaced by

Thevenins equivalence. Line is the tapping line. and

represent the voltage source and source impedance of the

source of generation, respectively. The PMUs are installed at

both ends of the original transmission line to synchronously

compute three-phase voltage and current phasors.

There are two important features in the installed PMUs. Oneis a synchronized clock generator named the global synchro-

nized clock generator (GSCG) [7] which has been built in

PMUs. The GSCG, whose frequency shift and synchronization

error can be respectively controlled well within 0.1 PPM

and 1 s, provides an extremely accurate synchronized clock

for data sampling. The other is the brand-new developed

filtering technique named the smart discrete Fourier transform

(SDFT) [11] that can extract the fundamental phasors from

sampling data under various system operation situations. The

performance of PMU-GSCG unit has been on-line demon-

strated very well in the 161 kV substations of the Taiwan

Power system [7]. These facts guarantee that the proposed

Fig. 2. Transmission lines.

fault locator performs the relaying task under synchronization

configuration.Theprinciple of theproposedalgorithm is outlined as follows.

After the fault occurs, the prefault and postfault synchronized

phasors will be transmitted to the central computer via commu-

nication channels. The proposed algorithm will be performed

at the central computer. These phasors are first transformed by

symmetrical transformation to decouple the coupling effect

among interphases. Then the superimposed positive-sequence

components can be extracted by the application of the principle

of superposition. The principle of superposition is presented at

Appendix A. The fault location for three-terminal lines will be

divided into two steps. The first step is to identify the faulted leg.

At this stage, the superimposed positive-sequence quantities are

used as input to the subroutine for identifying the faulted leg.The second step is to locate a fault on a specific faulted leg. In

the second step, it should be noted that two different quantities,

superimposed positive-sequence quantities and postfault posi-

tive-sequence quantities, will be adopted for locating a fault on

a different faulted leg. The superimposed quantities will be used

when a fault occurs on or . The postfault quantities areadopted when a fault occurs on . When a fault occurs on ,

it is essential to estimate the equivalent source impedance

outside the line first. After the source impedance is known,

the currents flowing from tapping line into the tap point can

be estimated by means of measured phasors at terminal . Then,

the previous proposed algorithm [6] will be applied by taking

the effect of infeed currents into account. When a fault occurs on

the , the similar process can be applied. When a fault occurs

on the tapping line , it is essential to estimate the voltage

source under the timing reference of PMUs by means of

prefault measured phasors. After these have been accomplished,

an exact fault location will be computed by means of the use of

postfault measured data.

III. BASIC PRINCIPLES

A. Review of the Previously Proposed Fault Location

Algorithm for Two-Terminal Lines

Initially, consider the transposed transmission lines shown inFig. 2 under sinusoidally steady state with angle frequency .

The following parameter matrices, including series impedance

matrix and shunt admittance matrix , characterize

the considered transmission line.

where and denote the self

and mutual series impedance per unit length, respectively, and

and denote the self and mutual

shunt admittance per unit length. The voltages and currents at a
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TABLE ISIMULATION RESULTS (FAULT OCCURS ON L )

superimposed circuit. Thus, the source impedances can be

given, respectively, by the following equations:

(19)

(20)

IV. PERFORMANCE EVALUATION

A. Simulation Example

A simulation system shown in Fig. 1 is selected to verify the

accuracy of the proposed algorithms. The parameters of the sim-

ulation system are

System voltage: 161 (kV) System frequency: 60 (Hz)

Transmission lines parameters:

In this work, an EMTP/ATP simulator is adopted and the total

time of simulation is (sec). The fault occurs at

the fourth cycle after the beginning of simulation. The data are

sampled at a sampling rate of 3.84 kHz. The error of locatingfault is measured as

Error

Actual Fault Location Estimated Fault Location

The Length of Line

(21)

B. Simulation Results and Discussion

Simulation results will be shown to evaluate the performance

of the proposed algorithm. First, the proposed algorithm is eval-

uated when a fault occurs on either line or tapping line .

The post-fault data used to compute the fault location is three

TABLE IISIMULATION RESULTS (FAULT OCCURS ON L )

cycles after fault occurring. Table I shows the results of fault

location under various fault types, fault resistance and fault lo-

cations when fault occurs on line . Table II shows those when

fault occurs on line . The sign # beside each fault locationerror in Tables I and II denotes that the faulted leg is identified

correctly. Simulation results on Table I reveal that 1) For var-

ious fault types, the maximum variation of fault location errors

caused by change of actual fault locations is 0.27%. This de-

notes that the proposed algorithm is almost not affected by the

locations of faults. 2) For various fault locations, the maximum

variation of fault location errors caused by different fault types

is 0.239%. This shows that the degree of accuracy of proposed

approach is nearly independent to fault types. 3) The final ob-

servation is that the fault resistance has little effect on the accu-

racy of the proposed approach. From the simulation results on

Table I, the average error of fault location is 0.077% and max-

imum error is 0.28%. Since the distance between two towers is0.3 km in the Taiwan power system, such a degree of accuracy

meets the need.

The average error of fault location estimation on is 0.17%

and maximum error is 0.471% under all tested cases. There are

two primary reasons that the fault location error on is greater

than that on . The first is that we take shunt capacitance in

transmission lines into account and such a complex model of

lines reduces the strength of constraints for iterative calcula-

tion. The second is that the procedure of estimating the internal

voltage source will also incur the error on fault location.

The proposed algorithm is also evaluated with the variation of

variable parameters like the equivalent source impedance, pre-

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Fig. 6. The principle of superposition.

Fig. 7. The superimposed network under the condition that fault occurs ontransmission lines without tapping lines.

Fig. 8. Superimposed network under the condition that fault occurs on theleft-hand side of tap point.

Fig. 9. The superimposed network under the condition that fault occurs on thetapping line L .

The proof of criteria for faulted leg identification is given in

the following.

Criterion 1: If , then the fault is on the

right-hand side of tap point.

Proof: We prove this criterion by a contradiction, that is, if

the fault is not on the right-hand side of tap point, then

.

Case 1: Consider a fault occurring on a transmission line

tapped with a source of generation shown in Fig. 8. It is assumed

that the fault occurs on the left-hand side of tap point. Initially,

the transmission line is intentionally regarded as lines without

being tapped with a source of generation. Equation (A.6) will

yield a pseudo fault location . Then, the and

will be represented as follows:

(A.7)

(A.8)

where the is the voltage at pseudo fault location and is

the length of line .

Moreover, according to the Fig. 8, the and are

also expressed as follows:

(A.9)

(A.10)

where is the length of the line , is the actual fault loca-tion and is the voltage at the actual fault location.

Arranging (A.7)(A.10), one can obtain the following

equation:

(A.11)

Arranging (A.11), we have

(A.12)

Taking the real parts of both sides of (A.12) and manipulating

them, one can obtain

(A.13)

where denotes the real part of a complex number.

Defining the following relationship:

(A.14)

Based on the assumption that the source impedance ( ,

and ) and the transmission line are highly inductive,

the phase differences between each other of , and

are less then 90 . Then

(A.15)

where denotes magnitude of a complex number, and super-

script denotes the conjugate of that.

Substituting the result of (A.15) into (A.13), one can obtain

(A.16)

Since , then

(A.17)

Case 2: Consider a fault occurring on the tapping line

shown in Fig. 9. According to the principle of deriving (A.6),

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LIN et al.: NEW FAULT LOCATOR FOR THREE-TERMINAL TRANSMISSION LINES 459

the must be a real number and equal to . So, one can

obtain

(A.18)

The combination of the results in cases 1 and 2 give the proof.

Criterion 2: If , then the fault is on the

left-hand side of tap point.Proof: The criterion is proved by a similar method de-

scribed above. So, the proof is omitted.

Criterion 3: If , then the fault is on the tap-

ping line

Proof: From the results of criterion 1 and 2, it is obvious

that the criterion 3 is true.

ACKNOWLEDGMENT

The authors would like to thank Dr. J.-A. Jiang for reading

the manuscript and making a number of helpful suggestions.

REFERENCES[1] A. T. Johns and S. Jamali, Accurate fault location technique for power

transmission lines, Proc. Inst. Elect. Eng. C, vol. 137, no. 6, pp.395402, Nov. 1990.

[2] M. Sachdev and R. Agarwal, A technique for estimating transmissionline fault location from digital impedance relay measurement, IEEETrans. Power Delivery, vol. 3, pp. 121129, Jan. 1988.

[3] T. T. Takagi, et al., Development of a new fault locator using the one-terminal voltage and current data, IEEE Trans. Power App. Syst., vol.PAS-101, pp. 28922898, Aug. 1982.

[4] L. Erikson, M. Saha, and G. D. Rockfeller, An accurate fault locatorwithcompensation forapparent reactance in the faultresistanceresultingfrom remote-end infeed, IEEE Trans. Power App. Syst., vol. PAS-104,pp. 424436, Feb. 1985.

[5] D. J. Lawrence, L. Z. Cabeza, and L. T. Hochberg, Development ofan advanced transmission line fault location systemPart II: Algorithm

development and simulation, IEEE Trans. Power Delivery, vol. 7, pp.19721981, Oct. 1992.[6] J.-A. Jiang, J.-Z. Yang, Y.-H. Lin, C.-W. Liu, and J.-C. Ma, An

adaptive PMU based fault detection/location technique for transmissionlinesPart I: Theory and algorithms, IEEE Trans. Power Delivery,vol. 15, pp. 486493, Apr. 2000.

[7] J.-A. Jiang, Y.-H. Lin, J.-Z. Yang, T.-M. Too, and C.-W. Liu, Anadaptive PMU based fault detection/location technique for transmissionlinesPart II: PMU implementation and performance evaluations,

IEEE Trans. Power Delivery, vol. 15, pp. 11361146, Oct. 2000.

[8] R. K. Aggarwal, D. V. Coury, A. T. Johns, and A. Kalam, A practicalapproach to accurate fault location on extra high voltage teed feeders,

IEEE Trans. Power Delivery, vol. 8, pp. 874883, July 1993.[9] A. A. Girgis, D. G. Hart, and W. Peterson, A new fault location tech-

nique for two and three terminal lines, IEEE Trans. Power Delivery,vol. 7, pp. 98107, Jan. 1992.

[10] IEEE Standard for Synchrophasors for Power System, IEEE Std 1344-1995, May 1996.

[11] J.-Z. Yangand C.-W. Liu, A precise calculationof powerfrequency and

phasor, IEEE Trans. Power Delivery, vol. 15, pp. 494499, Apr. 2000.[12] H. W. Dommel, EMTP Theory Book. Vancouver, BC: MicrotranPower Syst. Anal. Corp., May 1992, pp. 4-504-56.

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Ying-Hong Lin was born in Taipei, Taiwan, R.O.C., in 1970. He received theB.S. degree in electrical engineering from Taiwan University of Technology,Taipei, Taiwan, R.O.C., and the M.S. degree from National Taiwan University(NTU), Taipei, in 1995 and 1999, respectively. Currently, he is pursuing thePh.D. degree in electrical engineering at NTU.

His current research interests include the application of GPS and PMU inpower systems.

Chih-Wen Liu (M94) was born in Taiwan, R.O.C., in 1964. He received theB.S. degree in electrical engineering from National Taiwan University (NTU),Taipei, Taiwan, and the M.S. and Ph.D. degrees in electrical engineering fromCornell University, Ithaca, NY, in 1987, 1992, and 1994, respectively.

Since 1994, he has been with NTU, where he is Associate Professor of elec-trical engineering. His main research area is in application of computer tech-nology to power system monitoring, operation,protection and control. His otherresearch interests include GPS time transfer and chaotic dynamics and their ap-plication to system problems.

Dr. Liu serves as a Reviewer for IEEE T RANSACTIONS ON CIRCUITS ANDSYSTEMS,IEEETRANSACTIONS ON POWER SYSTEMS,andIEEETRANSACTIONSON POWER DELIVERY.

Chi-Shan Yu was born in Taipei, Taiwan, R.O.C., in 1966. He received the B.S.and M.S. degrees in electrical engineering from National Tsing Hua University,Beijing, China, in 1988 and 1990, respectively. He is currently pursuing thePh.D. degree in electrical engineering at National Taiwan University, Taipei,Taiwan.

Since 1991, he has been with Private Kuang-Wu Institute of Technology andCommerce, Taipei, where he is an Instructor of electrical engineering. His cur-rent research interests are computer relaying and transient stability control.

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