Unsynchronised two-terminal transmission-line fault-location without using line parameters

Unsynchronised two-terminal transmission-linefault-location without using line parameters

Y. Liao and S. Elangovan

Abstract: The paper presents a new two-terminal transmission-line fault-location algorithmwithout requiring line parameters. The voltage and current measurements at both ends of atransmission line during a fault are assumed to be available and no synchronisation of the data isrequired. The proposed algorithm is suitable for estimating the location of asymmetric faults on aline when line parameters are not available. Evaluation studies using both simulated and field dataare reported.

1 Introduction

Prompt and accurate location of faults in a large-scaletransmission system can accelerate system restoration,reduce the outage time and improve system reliability [1, 2].

Great efforts have been undertaken previously to developvarious algorithms for fault-location estimation based onrecorded data. Based on the available data, one-terminal,two-terminal, or multiterminal algorithms have beenproposed in the past. One-terminal algorithms estimatethe fault-location by using local data, and eliminate the needto transfer data from the other end of the line. However, theaccuracy of this type of algorithm is normally adverselyaffected by the fault resistance, although certain compensa-tion techniques may be adopted to alleviate this effect [1].To improve the accuracy of estimation, the authors of [2–4]have designed special one-end algorithms for estimating thelocation of faults on nondirect-to-earth neutral systemsand parallel lines. Two-terminal fault-location techniquesemploying measurements at both ends of the line have beenproposed in [5–10]. The authors of [5, 6] have presentedmethods using unsynchronised measurements for estimatingthe fault location and the synchronisation angle between themeasurements at the two terminals of the line. Sincesynchronised measurements have become more available,algorithms based on synchronised measurements have alsobeen invented [7–9].

Another type of algorithm utilises high-frequencytransients generated by faults to estimate the fault location[11–13]. These algorithms usually impose a higher demandon the accuracy of instrument transformers since high-frequency components of voltages or currents need to becaptured.

Advantage has also been taken of intelligent techniquesfor fault-location purposes. A genetic-algorithm-based

E-mail: [email protected]

Y. Liao is with Department of Electrical and Computer Engineering, Universityof Kentucky, 453 F. Paul Anderson Tower, Lexington, KY 40506-0046, USA

S. Elangovan is with Department of Electrical Engineering, Faculty ofEngineering, National University of Singapore, Kent Ridge Crescent,Singapore 119260

r The Institution of Engineering and Technology 2006

IEE Proceedings online no. 20060026

doi:10.1049/ip-gtd:20060026

Paper first received 14th December 2005 and in final revised form 11th April2006

IEE Proc.-Gener. Transm. Distrib., Vol. 153, No. 6, November 2006

method that formulates the fault-location problem as anoptimisation problem and searches the faults through thenetwork is described in [14]. A neural-network-basedapproach for locating faults on teed-networks is reportedin [15]. In [16] a method is proposed based on a radial basisneural network.

These algorithms are very instructive, but require the lineparameters to be available. In reality, values of lineparameters may not always be available. The authors of[17] designed a method for estimating the line parameters,but this method needs continuous monitoring of the lineduring normal operations, and also requires phasormeasurement units for data synchronisation.

This paper proposes an algorithm for estimating the faultlocation without the need for data synchronisation byutilising only the fault voltage and current data which doesnot require the prefault data. The approach is suitable forestimating fault location for asymmetric faults when lineparameters are not known.

2 Proposed approach

Consider the two-terminal line as shown in Fig. 1 [3]. EG

and EH represent the equivalent voltage sources at buses Pand Q. R indicates the fault point. The following notationsare used:

Vpa, Vpb, Vpc: phase a, b, c voltages during the fault atterminal P, respectively;

Ipa, Ipb, Ipc: phase a, b, c currents during the fault at terminalP, respectively;

Vqa, Vqb, Vqc: phase a, b, c voltages during the fault atterminal Q, respectively;

Iqa, Iqb, Iqc: phase a, b, c currents during the fault at terminalQ, respectively;

m: per-unit fault distance from terminal P.

Note that the new method is based on fundamentalfrequency phasors, and all the above listed voltages andcurrents are fundamental frequency phasors.

It is assumed that the three phase voltages and currents atterminals P and Q are available, and the line is a transposedline. No synchronisation of the data at P and Q is required.

639

EG

P Q

R

m 1-m EH

paV

pbV

pcV

qaV

qbV

qcV

paIpbI pcI

qaIqbI qcI

Fig. 1 System diagram used in the development of the new algorithm

2.1 Proposed approach for earthed faultsThis Section presents the approach that is applicable toearthed faults, assuming that the network has a configura-tion allowing zero-sequence currents to flow in the network.The outline of the approach is presented here with moredetailed derivation referred to the Appendix (Section 6).

Based on Fig. 1, we have [5, 6].

Vpa

Vpb

Vpc

26664

37775� m

Rs þ jXs Rm þ jXm Rm þ jXm

Rm þ jXm Rs þ jXs Rm þ jXm

Rm þ jXm Rm þ jXm Rs þ jXs

26664

37775

Ipa

Ipb

Ipc

26664

37775

¼

Vqa

Vqb

Vqc

26664

37775� ð1� mÞ

8>>><>>>:

Rs þ jXs Rm þ jXm

Rm þ jXm Rs þ jXs

Rm þ jXm Rm þ jXm

26664

Rm þ jXm

Rm þ jXm

Rs þ jXs

37775

Iqa

Iqb

Iqc

26664

37775

9>>>=>>>;

ejd ð1Þ

where Rs, Xs, Rm, Xm are the total self resistance, selfreactance, mutual resistance and mutual reactance of theline, respectively; and d is the synchronisation angle betweenmeasurements at terminals P and Q.

Define:

x ¼ ½m; d;Rs;Xs;Rm;Xm�T ð2Þwhere x is a vector of unknown variables and T is a vectoror matrix transpose operator.

Equation (1) can be written as three complex equations,each of which can be separated into the real part andimaginary part. As a result, six real equations with sixunknown variables can be obtained as

fiðxÞ ¼ 0; i ¼ 1; . . . ; 6 ð3ÞThe Newton–Raphson approach can be used to solve theunknowns as follows.

Define the following function vector:

f ðxÞ ¼ ½f1ðxÞ; f2ðxÞ; f3ðxÞ; f4ðxÞ; f5ðxÞ; f6ðxÞ�T ð4ÞThe Jacobian matrix J(x) is calculated as

J ijðxÞ ¼@fiðxÞ@xj

; i ¼ 1; . . . ; 6; j ¼ 1; . . . ; 6 ð5Þ

where Jij(x) is the element in the ith row and jth columnof J(x).

The unknowns can be obtained following an iterativeprocedure. In the kth iteration, the unknowns are updated

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using the equation

xkþ1 ¼ xk � Dx ð6Þ

Dx ¼ ½JðxkÞ��1f ðxkÞ ð7Þwhere xk, xkþ1 are the values of x before and after the kthiteration, respectively; Dx is the update for x at the kthiteration; and k is the iteration number starting from 1.

The iteration can be terminated when the update Dx issmaller than the specified tolerance. Derivation of equationsfi(x)¼ 0 and Jij(x) is illustrated in the Appendix (Section 6).

When implementing the proposed algorithm, the follow-ing techniques can help to speed up convergence. Duringeach iteration, the value of d is constrained to be between� p and p by adding or subtracting 2p. The fault locationis kept between zero and one by setting it to zero whenit becomes negative and setting it to one when it exceedsone. Other variables are constrained as positive values bysetting them to initial values when they become negative.Simulation studies, as presented below, will show thatthis accelerating method works well and will not causeuncontrollable oscillations in the convergence process.

2.2 Proposed approach for phase-to-phaseunearth faultsFor a phase-to-phase unearth fault, there will be bothpositive- and negative-sequence voltages and currents in thenetwork. Applying symmetrical component transformationto (1) will result in the following two complex equations [5]:

Vp1 � mðR1 þ jX1ÞIp1 ¼ ½Vq1 � ð1� mÞ� ðR1 þ jX1ÞIq1�ejd ð8Þ

Vp2 � mðR1 þ jX1ÞIp2 ¼ ½Vq2 � ð1� mÞ� ðR1 þ jX1ÞIq2�ejd ð9Þ

where Vp1, Vp2 are positive- and negative-sequence faultvoltages at terminal P, respectively; Ip1, Ip2 are positive- andnegative-sequence fault currents at terminal P, respectively;Vq1, Vq2 are positive- and negative-sequence fault voltages atterminal Q, respectively; Iq1, Iq2 are positive- and negative-sequence fault currents at terminal Q, respectively; R1 is thetotal positive sequence resistance of the line; and X1 is thetotal positive sequence reactance of the line.

Equations (8) and (9) can be separated into four realequations with four unknown variables m, d, R1 and X1.Similar procedures to those outlined in Section 2.1 can beutilised to estimate these unknowns.

Note that, if the fault is a three-phase symmetrical fault,there will not be enough information to estimate theunknown variables. The derivation indicates that the


algorithm does not require the fault resistance and sourceimpedances to be known.

Although the algorithm derivation is based on thesimplified model as shown in Fig. 1, the algorithm isapplicable for more complex systems as long as the voltageand current measurements at the two ends of the line areavailable. The derivation in Section 2.1 does not considermutual coupling between double-circuit lines, which maycause certain errors in fault location for double-circuit lines.Using the approach in Section 2.2 can reduce such errorssince no zero sequence components are utilised.

3 Evaluation studies

3.1 Studies based on EMTP simulationSimulation studies using the electromagnetic-transientsprogram (EMTP) have been carried out to evaluate themethod [18]. A 500kV transmission-line system is used inthe simulation studies, with detailed parameters referred top. 1622 of [9]. The values of line parameters per unit lengthare taken from [9], with the line length being varied in oursimulation studies. The per-unit system is utilised with avoltage base of 500kV and an apparent-power base of 1000MVA. EMTP has been employed to simulate all types ofunsymmetrical faults at different locations. When applyingthe algorithm for fault location, the line parameters are notused at all. Representative results are given below.

Table 1 shows the estimates for phase-A-to earth (AE)and phase-B-to-phase-C-to earth (BCE) faults with a faultresistance of 4O for a line of 100km with synchronisationangle d equal to 0.1745 rad (101). The actual values for Rs,Xs, Rm and Xm are 0.0910, 0.2490, 0.0290 and 0.1020,respectively. The actual fault location is 0.3 or 0.5. Astarting value of 0.5, 0, 0.5, 0.5, 0.35 and 0.35 for m, d, Rs,Xs, Rm and Xm, respectively, is utilised for all cases. InTable 1, the unit for angle d is radians. The resultsdemonstrate clearly that the algorithm is able to estimatethe fault-location fairly accurately.

To show the effects of shunt capacitance, Fig. 2 depictsthe fault-location estimates for phase-A-to-earth faults witha fault resistance of 4O for lines with different lengths, withactual fault locations being 0.3, 0.5 and 0.8, respectively.It can be seen that, while shunt capacitance has adverseimpacts, the errors are still within 3% for lines shorter than160km.

The convergence behaviour of the algorithm has beenstudied by varying the starting values. The method is quiterobust and insensitive to starting values, and convergesquickly to the correct solution within about ten or feweriterations. Table 2 shows the fault location estimate andrequired iteration number by utilising various startingvalues for a phase-A-to earth fault with a fault resistanceof 4O and fault location of 0.3p.u. on a line of 50km. A 101

Table 1: Fault-location and line-parameter estimates for AEand BCE faults for a line of 100km (d¼ 0.1745 rad, Rf ¼ 4X )

Scenarios Estimated values

m d Rs Xs Rm Xm

AE fault (m¼ 0.3) 0.3097 0.1703 0.0966 0.3029 0.0361 0.1452

AE fault (m¼ 0.5) 0.4999 0.1745 0.0914 0.2514 0.0289 0.1039

BCE fault (m¼ 0.3) 0.3103 0.1699 0.0970 0.3075 0.0365 0.1494

BCE fault (m¼ 0.5) 0.5001 0.1744 0.0867 0.2519 0.0243 0.1043


synchronisation error has been added to the measurementsat terminal Q.

3.2 Studies based on field dataThis Section presents estimation results by using two fieldcases, both of which are phase-to-earth faults. In both cases,waveforms at both ends of the line are available and theFourier transform is utilised to extract the fundamental-frequency phasors.

3.2.1 Field case 1: In the first case, the system is a500kV, 138.69km transmission line with a similar config-uration to that shown in Fig. 1. The actual fault distance is57.82km from terminal P. The voltage and currentwaveforms at terminal P are shown in Fig. 3. The per-unitsystem is utilised with a voltage base of 500kV and anapparent-power base of 100 MVA. The voltage and currentphasors obtained from the recorded data are shown inTable 3.

Without any knowledge of the values of line parameters,the proposed algorithm is applied to estimate the faultlocation. Starting values of 0.5, 0, 0.5, 0.5, 0.35 and 0.35 form, d, Rs, Xs, Rm and Xm, respectively are utilised, and thealgorithm converges after eight iterations and the faultlocation is estimated as 55.84km, with an error of 1.98km

40 60 80 100 120 140 1600.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

m=0.3

m=0.5m=0.8

Fa

ult

loca

tion

est

ima

tion

(p

.u.)

Line length (km)

Fig. 2 Effects of shunt capacitance on fault-location estimation

Table 2: Effects of starting values on algorithm convergencecharacteristics

Initial values Estimatedfaultlocation

Iterationnumber

m d Rs Xs Rm Xm

0.5 0 0.02 0.2 0.01 0.1 0.3054 5

0.5 0 0.02 0.5 0.01 0.3 0.3054 7

0.5 0 0.05 0.5 0.01 0.1 0.3054 7

0.5 0 0.05 0.5 0.04 0.4 0.3054 6

0.5 0 0.1 0.1 0.05 0.05 0.3054 5

0.5 0 0.2 0.2 0.1 0.1 0.3054 5

0.5 0 0.3 0.3 0.15 0.15 0.3054 5

0.5 0 0.5 0.5 0.25 0.25 0.3054 5

0.5 0 0.5 0.5 0.35 0.35 0.3054 5

0.5 0 1 1 0.5 0.5 0.3054 6

641

or 1.43% of the total line length. It can be seen that a fairlyaccurate estimate has been achieved.

3.2.2 Field case 2: In the second case, the line is a161kV, 93.12km tapped line, with a configuration asshown in Fig. 4. The actual fault location is 85.11km frombus Q. Fault records at bus P and bus Q are available forfault location. The voltage and current phasors obtainedfrom the recorded data are shown in Table 4. The per-unitsystem is utilised with a voltage base of 161kV and anapparent-power base of 100 MVA.

Without any knowledge of the values of line parameters,the algorithm is applied to estimate the fault location. Thesame starting value as used in the first field case is utilised,and the algorithm converges after nine iterations and thefault location is estimated as 87.71km fromQ, which has anerror of 2.60km or 2.79% of the total line length. Twopossible reasons contribute to this error. First, the shuntcapacitance of the line is not modelled by the algorithm.

Table 3: Calculated voltage and current phasors for fieldcase 1

Quantities Values (p.u.)

Vpa 0.71253+ j 0.71835

Vpb 0.027296� j 0.46566

Vpc � 0.96676+ j 0.35402

Ipa � 4.9741� j 3.0075

Ipb � 39.1991� j 13.7695

Ipc 1.7197� j 1.7414

Vqa 0.054162 + j 0.99844

Vqb 0.54877� j 0.38948

Vqc � 0.90144� j 0.42359

Iqa 0.32874+ j 5.6612

Iqb � 15.2273� j 48.4533

Iqc � 1.7765� j 1.0783

Load

Bus P Bus Q

Fig. 4 Line configuration for the second field case

0 50 100 150 200 250 300 350 400 450-2

-1

0

1

2

Samples

A

BC

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

-50

0

50

100

Samples

A

BC

Vol

tage

(p.u

.)C

urre

nt(p

.u.)

Fig. 3 Voltage and current waveforms at one terminal for the firstfield case

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Secondly, the load currents at the load taps along the linemay also cause errors.

4 Conclusions

When unsynchronised voltages and currents during a faultfrom two ends of a transmission line are available, if the lineparameters are not available, no existing fault-locationalgorithms can be applied to estimate the fault location.This paper presents a feasible solution. Evaluation studiesusing both simulated data and field data have demonstratedthat the method is fairly accurate. Convergence-behaviourstudies have also manifested that the method is not sensitiveto starting values and quickly converges to the correctsolution within around ten iterations.

5 References

1 Eriksson, L., Saha, M.M., and Rockefeller, G.D.: ‘An accurate faultlocator with compensation for apparent reactance in the faultresistance resulting from remote-end infeed’, IEEE Trans. PowerAppar. Syst., 1985, 104, (2), pp. 424–436

2 Zhang, Q., Zhang, Y., Song, W., and Yu, Y.: ‘Transmission line faultlocation for phase-to-earth fault using one-terminal data’, IEE Proc.C, Gener. Transm. Distrib., 1999, 146, (2), pp. 121–124

3 Liao, Y., and Elangovan, S.: ‘Digital distance relaying algorithm forfirst-zone protection for parallel transmission lines’, IEE Proc. C,Gener. Transm. Distrib., 1998, 145, (5), pp. 531–536

4 Izykowski, J., Rosolowski, E., and Saha, M.M.: ‘Locating faults inparallel transmission lines under availability of complete measure-ments at one end’, IEE Proc. C, Gener., Transm. Distrib., 2004, 151,(2), pp. 268–273

5 Novosel, D., Hart, D.G., Udren, E., and Garitty, J.: ‘Unsynchronizedtwo-terminal fault location estimation’, IEEE Trans. Power Deliv.,1996, 11, (1), pp. 130–138

6 Girgis, A.A., Hart, D.G., and Peterson, W.L.: ‘A new fault locationtechnique for two-and three-terminal lines’, IEEE Trans. Power Deliv.,1992, 7, (1), pp. 98–107

7 Kezunovic, M., and Perunicic, B.: ‘Automated transmission line faultanalysis using synchronized sampling at two ends’, IEEE Trans. PowerSyst., 1996, 11, (1), pp. 441–447

8 Lin, Y.H., Liu, C.W., and Chen, C.S.: ‘A new PMU-based faultdetection/location technique for transmission lines with considerationof arcing fault discrimination – part I: theory and algorithms’, IEEETrans. Power Deliv., 2004, 19, (4), pp. 1587–1593

9 Brahma, S.M.: ‘Fault location on a transmission line usingsynchronized voltage measurements’, IEEE Trans. Power Deliv.,2004, 19, (4), pp. 1619–1622

10 Zamora, I., Minambres, J.F., Mazon, A.J., Alvarez-Isasi, R., andLazaro, J.: ‘Fault location on two-terminal transmission lines based onvoltages’, IEE Proc. C. Gener. Transm. Distrib., 1996, 143, (1), pp. 1–6

11 Bo, Z.Q., Johns, A.T., and Aggarwal, R.K.: ‘A novel fault locatorbased on the detection of fault generated high frequency transients’.Proc. 6th Int. Conf. Developments in Power System Protection,Nottingham, England, March 1997

12 Evrenosoglu, C.Y., and Abur, A.: ‘Travelling wave based faultlocation for teed circuits’, IEEE Trans. Power Deliv., 2005, 20, (2),pp. 1115–1121

Table 4: Calculated voltage and current phasors for fieldcase 2

Quantities Values (p.u.)

Vpa 0.67226+ j 0.68317

Vpb 0.11376� j 0.96417

Vpc �0.53707+ j 0.26145

Ipa �0.067062+ j 0.0061619

Ipb �0.15252� j 0.11224

Ipc 1.05173+ j 17.9774

Vqa 0.89801+ j 0.46016

Vqb �0.10941� j 0.99178

Vqc �0.69545+ j 0.49139

Iqa 0.36547� j 0.38002

Iqb �0.59806� j 1.3732

Iqc 0.52749+ j 2.9982


13 Ancell, G.B., and Pahalawaththa, N.C.: ‘Maximum likelihoodestimation of fault location on transmission lines using travelingwaves’, IEEE Trans. Power Deliv., 1994, 9, (2), pp. 680–689

14 Luo, S., Kezunovic, M., and Sevcik, D.R.: ‘Locating faults in thetransmission network using sparse field measurements, simulationdata and genetic algorithms’, Electric Power Syst. Res., 2004, 71, (2),pp. 169–177

15 Lai, L.L., Vaseekar, E., Subasinghe, H., Rajkumar, N., Carter, A.,and Gwyn, B.J.: ‘Fault location of a teed-network with wavelettransform and neural networks’. Proc. Electric Utility Deregulationand Restructuring and Power Technologies, April 2000, pp. 505–509

16 Mahanty, R.N., and Gupta, P.B.D.: ‘Application of RBF neuralnetwork to fault classification and location in transmission lines’, IEEProc. C, Gener. Transm. Distrib., 2004, 151, (2), pp. 201–212

17 Chen, C.S., Liu, C.W., and Jiang, J.A.: ‘A new adaptive PMU basedprotection scheme for transposed/untransposed parallel transmissionlines’, IEEE Trans. Power Deliv., 2002, 17, (2), pp. 395–404

18 Leuven EMTP Centre: ‘Alternative Transient Program, User manualand rule book’, Leuven, Belgium, 1987

6 Appendix: Derivation of equations fi (x)¼ 0 andJij (x)

Let Vpa, Vpb, Vpc, Ipa, Ipb, Ipc, Vqa, Vqb, Vqc, Iqa, Iqb and Iqc beai+jbi, i¼ 1,y,12, respectively. Then the first complexequation in (1) can be written as

ða1 þ jb1Þ � mðRs þ jXsÞða4 þ jb4Þ� mðRm þ jXmÞfa5 þ a6 þ jðb5 þ b6Þg� ða7 þ jb7Þðcos dþ j sin dÞþ ð1� mÞðRs þ jXsÞða10 þ jb10Þðcos dþ j sin dÞþ ð1� mÞðRm þ jXmÞfða11 þ a12Þþ jðb11 þ b12Þgðcos dþ j sin dÞ ¼ 0 ð10Þ


The real part of (10) is

f1ðxÞ ¼ a1 � mðRsa4 � Xsb4Þ� mRmða5 þ a6Þ þ mXmðb5 þ b6Þ� a7 cos dþ b7 sin d

þ ð1� mÞðRsa10 � Xsb10Þ cos d� ð1� mÞðRsb10 þ Xsa10Þ sin dþ ð1� mÞfRmða11 þ a12Þ� Xmðb11 þ b12Þg cos d� ð1� mÞfRmðb11 þ b12Þþ Xmða11 þ a12Þg sin d ¼ 0 ð11Þ

Then, the derivatives of f1(x) with respect to x can be easilyderived. For example, we have

@f1ðxÞ@m

¼� ðRsa4 � Xsb4Þ � Rmða5 þ a6Þ þ Xmðb5 þ b6Þ

� ðRsa10 � Xsb10Þ cos dþ ðRsb10 þ Xsa10Þ sin d� fRmða11 þ a12Þ � Xmðb11 þ b12Þg cos dþ fRmðb11 þ b12Þ þ Xmða11 þ a12Þg sin d

ð12Þ

Derivation of the derivatives of f1(x) with respect to other

variables, equations fi(x)¼ 0 and J ijðxÞ ¼ @fiðxÞ@xj

for i¼2,y, 6 can be obtained similarly and is not shown here.

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Unsynchronised two-terminal transmission-line fault-location without using line parameters