MODERN ELECTRIC POWER SYSTEMS

Locating faults in parallel transmission lines underavailability of complete measurements at one end

J. Izykowski, E. Rosolowski and M. Mohan Saha

Abstract: Fault location in parallel transmission lines with availability of complete measurementsfrom one end of the lines is considered. Generalised models of fault loops and faults are used forformulation of the fault location algorithm. The derived algorithm has a very simple first-orderformula and does not require knowledge of impedances of the equivalent systems behind the lineterminals as well as use of pre-fault measurements. Application of the fault location algorithm toimpedance measurement of the adaptive distance protection is considered. An issue of improvingthe fault location accuracy by compensating for shunt capacitances of the lines is addressed.Results of the evaluation with use of ATP–EMTP simulations are reported and discussed.

1 Introduction

One-end fault location techniques [1–9], aimed at theinspection-repair purpose, are still a subject of great interestand are used in many applications, despite the muchsuperior performance of two-end techniques [10, 11].Communication links for sending the measurementsacquired at distant points of the transmission network arenot always provided and loss of communication also has tobe taken into account. The other reason for the interest isthat some one-end techniques can now be considered forapplication to protecting the transmission lines.Impedance-based fault location in power transmission

lines has been considered in many papers, as, for example,in the representative one-end approaches [1–3]. Location offaults in distribution networks can also be based on theimpedance principle [4]. This paper considers impedance-based fault location applied to parallel lines, which are veryoften used for transferring energy from the source to theutilisation centres.Generally, to derive one-end fault location algorithms,

the different availability of measurements acquired at oneend of the parallel lines can be considered. In the vastmajority of practical cases standard input signals (i.e. three-phase voltages/currents of the faulted line and a zerosequence current from the healthy line) are provided for thefault locator [1]. Limited availability of one-end measure-ments for the fault locator [5] is the other possibility, whichcan be met frequently in practice. It takes place especiallywhen one of the parallel lines is switched off and groundedat both ends. However, in some applications, even for bothlines in operation, measurement from the healthy linecannot be provided for the protective relay as well as for thefault locator. Fault location with such limited availability of

measurements appears as a very difficult task and has beenconsidered in [5].Remarkable improvement of one-end fault location can

be achieved by providing complete measurements from oneend of the parallel transmission lines [6–9]. In this case,instead of using only the zero sequence current from thehealthy line (as in the standard availability [1]), the completephase currents from the healthy line are provided.In this paper the fault location algorithm using complete

measurements from one end of the parallel lines presentedin [6–9] has been taken for further investigation. Considera-tions are first focused on providing the most compact formof the resultant fault location formula. This appears as avery important aim since the derived fault locationalgorithm is considered for direct application to adaptivedistance protection compensating for ‘the reactance effect’[1–3]. Secondly, for improving fault location accuracy in thecase of long lines, compensation for shunt capacitances isintroduced, taking into account the distributed long linemodel.

2 Basics of the fault location algorithm

Figure 1 shows the circuit diagram of the transmissionnetwork with parallel lines (ZLA, ZLB) taken for furtheranalysis. The vicinity of the lines is represented byequivalent systems behind the terminals of the lines (EMFs:EsA, EsB and source impedances: ZsA, ZsB) and the extra linkbetween the substations ZEQ. The terminals are denoted:

AA, BA, AB and BB (the substation is marked by the firstletter, while the line is marked by the second letter). It isconsidered that a fault occurs in the line LA at distanced(pu) and a fault location is performed by the fault locatorFLA or by the distance protection DPA (Fig. 1). In the caseof locating single phase-to-ground faults, one has to takeinto account a mutual coupling of the parallel lines(Z0m ¼mutual coupling impedance for a zero sequence).Figure 2 presents the equivalent circuit diagrams of the

parallel lines for particular sequence quantities. It isassumed in Fig. 2b, and in all further considerations, thatthe impedances for a negative sequence are equal to thecorresponding positive sequence impedances from Fig. 2a.Shunt capacitances of the lines for all sequence componentsare neglected at this stage of the derivation.

J. Izykowski and E. Rosolowski are with the Wroclaw University ofTechnology, Wyspianskiego 27, Wroclaw 50-370, Poland

M. Mohan Saha is with the ABB Automation Technologies, V.astera( s SE-72159, Sweden

r IEE, 2004

IEE Proceedings online no. 20040163

doi:10.1049/ip-gtd:20040163

Paper first received 30th January 2003 and in revised form 8th October 2003

268 IEE Proc.-Gener. Transm. Distrib., Vol. 151, No. 2, March 2004

To derive the location algorithm, the fault loopcomposed according to the classified fault type is con-sidered. This loop contains the faulted line segment(between points AA and F) and the fault path itself. Ageneralised model for the fault loop is stated as follows:

V AA P dZ1LAIAA P RF

X2i¼0

aFiIFi ¼ 0 ð1Þ

where:

d¼ unknown and sought distance to fault (pu),

Z1LA ¼ positive sequence impedance of the faulted line LA,

V AA P ; IAA P ¼ fault loop voltage and current composedaccording to the fault type (Table 1),

RF¼ fault resistance,

IFi ¼ sequence components of the total fault current (i¼ 0 –zero sequence, i¼ 1 positive sequence, i¼ 2 – negativesequence),

aFi ¼weighting coefficients (Table 2),

Fault loop voltage and current can be expressed in terms oflocal measurements and by using the share coefficients a0;a1; a2 gathered in Table 1 [5, 9]:

V AA P ¼ a1V AA1 þ a2V AA2 þ a0V AA0 ð2Þ

IAA P ¼ a1IAA1 þ a2IAA2 þ a0Z0LAZ1LA

IAA0 þ a0Z0mZ1LA

IAB0 ð3Þ

ZsA

BBAB

IAB line LB (healthy)

line LA(faulted)

FLA(DPA)

ZEQ

ZLB

dZLA (1–d )ZLA

dZ0m

RF

~ ~

ZsB

EsBEsA

IAA

VAA

(1–d )Z0m

VF

IF

AABA

F

Fig. 1 One-end fault location for mutually coupled parallel lines under providing complete measurements at one end

AA BAIAA1

Z1sA

dZ1LA

Z1sB

(1–d )Z1LA

Z1LB

AB BB

F

VAA1

~ ~

E1sA E1sB

IAB1

IF1

IF1

a

AA BAIAA2

Z1sA

dZ1LA

Z1sB

(1–d )Z1LA

Z1LB

AB BB

F

VAA2

IAB2

IF2

IF2

b

Z0sBZ0sA

F

BA

= B

B

dZ0m

Z0LB − Z0m

d(Z0LA – Z0m)

IAB0

IAA0IAA0+IAB0

AA

= A

B

(1–d )(Z0LA – Z0m)

(1–d)Z0m

VAA0

IF0

IF0

c

Fig. 2 Equivalent circuit diagrams of parallel lines fora Positive sequenceb Negative sequencec Zero sequence

Table 1: Share coefficients used for determining fault loopsignals (2), (3)

Fault type a1 a2 a0

a–g 1 1 1

b–g a2 a 1

c–g a a2 1

a–b, a–b–g

a–b–c, a–b–c–g 1 a2 1 a 0

b–c, b–c–g a2 a a a2 0

c–a, c–a–g a 1 a2 1 0

a ¼ exp j2p=3ð Þ; j ¼ffiffiffiffiffiffiffi1

p

Table 2: Weighting coefficients used for estimation of thevoltage drop across a fault resistance

Fault type aF1 aF2 aF0

a–g 3 0 0

b–g 3a2 0 0

c–g 3a 0 0

a–b 1 a2 0 0

b–c a2 a 0 0

c–a a 1 0 0

a–b–g 1 a2 1 a 0

b–c–g a2 a a a2 0

c–a–g a 1 a2 1 0

a–b–c

(a–b–c–g) 1 a2 0 0

a ¼ exp j2p=3ð Þ; j ¼ffiffiffiffiffiffiffi1

p

IEE Proc.-Gener. Transm. Distrib., Vol. 151, No. 2, March 2004 269

where:

Z0LA ¼ zero sequence impedance of the faulted line LA,

Z0m ¼ zero sequence impedance for a mutual couplingbetween the lines LA and LB.

Fault loop signals (2), (3) are expressed in terms of therespective symmetrical components of the measuredvoltages and currents (the last subscript denotes thesymmetrical component type). This notation is convenientfor further considerations; however, it is fully equivalent tothe description traditionally used for distance protection.For example, considering a single phase-to-ground fault (a–g fault), the fault loop signals for a distance protection arecommonly defined as:

V AA P ¼ V AAa ð4Þ

IAA P ¼ IAAa þZ0LA Z1LA

Z1LAIAA0 þ

Z0mZ1LA

IAB0 ð5Þ

where:

V AAa; IAAa ¼ voltage and current from the faulted line (AA)and for the faulted phase (a),

IAA0; IAB0¼ zero sequence currents from the faulted (AA)and the healthy (AB) lines.

It can be proved that signals (4), (5) are identical to signals(2), (3) after substituting the share coefficients for a–g faultfrom Table 1 and analogously for the remaining fault types.A voltage drop across the fault path (the third term in

(1)) is expressed by using of sequence components of thetotal fault current ðIF 0; IF 1; IF 2Þ and the weightingcoefficients ðaF 0; aF 1; aF 2Þ. These coefficients can be deter-mined by considering the boundary conditions for aparticular fault type. However, there is some leeway in thisdetermination. Firstly, it is proposed to use this leeway toavoid zero sequence quantities, and for not using the zerosequence line impedance, which is considered to be theunreliable parameter [9]. This aim can be accomplished bysetting aF 0 ¼ 0 as shown in Table 2. Secondly, the freedomin establishing the weighting coefficients can be used todetermine the preference for using particular sequencequantities. In Table 2 preference for using the positivesequence currents has been assumed. The other alternativesets of weighting coefficients are provided in [9].In consequence of setting aF 0 ¼ 0 (as in Table 2) further

application of (1) requires determination of only the positiveðIF 1Þ and the negative ðIF 2Þ sequence components of thetotal fault current. Considering the two different paths inthe circuits of Fig. 2a and 2b:

(i) the faulted line segment (AA–F) adjacent to the localsubstation,

(ii) the whole healthy line (AB–BB) together with the remotesegment of the faulted line (BA–F), one obtains:

IF 1 ¼IAA1

Z1LBZ1LA

IAB11 d

ð6Þ

IF 2 ¼IAA2

Z1LBZ1LA

IAB21 d

ð7Þ

Substituting (6), (7) into (1) and introducing the weightingcoefficients from Table 2 yields:

V AA P dZ1LAIAA P RF

1 dN12 ¼ 0 ð8Þ

where:

N 12 ¼ aF 1 IAA1 Z1LBZ1LA

IAB1

þ aF 2 IAA2

Z1LBZ1LA

IAB2

Resolving (8) into real and imaginary parts gives:

realðV AA P Þd realðZ1LAIAA P Þ RF

1 drealðN 12Þ ¼ 0 ð9Þ

imagðV AA P Þ d imagðZ1LAIAA P ÞRF

1 dimagðN12Þ

¼ 0 ð10ÞElimination of the agent (RF/(1d)) yields the followingformula for a sought distance to fault:

d ¼ imagðV AA P ÞrealðN 12Þ realðV AA P ÞimagðN12ÞimagðDV AA P ÞrealðN 12Þ realðDV AA P ÞimagðN 12Þ

ð11Þwhere:

DV AA P ¼ Z1LAIAA P

The formula (11) can be written down in an more evencompact alternative form:

d ¼ imagðV AA PN12Þ

imagðZ1LAIAA PN12Þ

ð12Þ

where:

N 12¼ conjugate of N 12 from (8).

Thus, a distance to fault (12) can be determined with useof the digital algorithms developed for the reactive powercalculation. Obtaining such compact first-order formulas(11) or (12) appears very attractive for application toadaptive distance protection for the parallel lines. Theobtained location procedures (11), (12) do not requireknowledge of the impedances of the equivalent sourcesbehind the terminals of the parallel or use of the pre-faultmeasurements.It is worth realising that the classic distance relay

determines the fault loop impedance from the fault loopsignals (2), (3):

ZAA P ¼ RAA P þ jXAA P ¼ V AA P

IAA Pð13Þ

Impedance measurement (13) is affected by ‘the reactanceeffect’, relevant for resistive faults and the presence of pre-fault power flow [1–3]. In consequence of that, a quality ofprotection can be adversely influenced. However, fault loopimpedance measurement can be accomplished with thederived fault location algorithm according to:

ZAA FL ¼ RAA FL þ jXAA FL

¼ imagðV AA PN12Þ

imagðZ1LAIAA PN12Þ

Z1LA ð14Þ

The sample heavy fault case considered in Section 4illustrates an effectiveness of the compensation for ‘thereactance effect’ when performing the measurementsaccording to (14).

3 Improvement of fault location accuracy

The fault location algorithm (11) or (12) has been derived,neglecting shunt capacitances of the parallel lines. However,

270 IEE Proc.-Gener. Transm. Distrib., Vol. 151, No. 2, March 2004

high accuracy for locating faults in long parallel linesrequires compensation for these capacitances. The compen-sation has to be performed separately for each of thesequences. However, due to limited space, only thecompensation for the positive sequence is presented.Compensation for the remaining sequence components isperformed analogously.Figure 3 shows the circuit diagram of the parallel lines for

a positive sequence with shunt capacitances included. Inthis case the voltage drop across the faulted line segment

(AA–F) can be calculated with the current ðICAA1Þ obtainedfrom the measured current ðIAA1Þ after deducing the shuntcurrent. Such compensation requires iterative calculations.In Fig. 3, for simplicity, the lumped model is shown.However, considering the long line model [10] the ithiteration is performed as:

ICAA1ðiÞ ¼ IAA1 0:5dði1ÞB1LAAtanh 1V AA1 ð15Þ

where:

d(i1)¼ distance to fault from the previous iteration (i–1),

l¼ total line length (km),

Atanh 1 ¼

tanhð0:5ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiZ

01LAB

01LA

qdði1ÞlÞ

0:5

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiZ 01LAB

01LA

qdði1Þl

B01LA ¼ B1LA=l ¼ jo1C1LA=l¼ positive sequence admit-

tance of the faulted line per km length (S/km),

Z 01LA ¼ Z1LA=l¼ positive sequence impedance of a faulted

line per km length (O/km).

The result obtained without taking into account the

shunt capacitance effect (11) or (12) is considered as ‘dði1Þ’for the first iteration. The iterative calculations arecontinued until the difference between the two consecutiveestimates of distance to fault are less than the pre-definedthreshold value.Positive sequence impedance of the faulted line segment

(between points AA and F) with consideration of thedistributed long line model equals:

Z longAA F ¼ dði1ÞZ1LAAsinh 1 ð16Þ

where:

Asinh 1¼ sinhðffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiZ

01LAB

01LA

qdði1ÞlÞ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiZ

01LAB

01LA

qdði1Þl

Similarly, a fault path current, which is used to calculate thevoltage drop across a fault resistance, can be determinedtaking into account the shunt capacitances effect [9].However, introducing the compensation when calculatingonly the voltage drop across a faulted line segment is ofprime importance to ensure adequate fault locationaccuracy improvement.

4 Evaluation by using ATP-EMTP simulations

The detailed ATP-EMTP [12] model of parallel transmis-sion system (Fig. 1) including the fault locator measurementchains has been developed. The 400kV, 300km paralleltransmission lines were represented by the Clarke model.The model included both the capacitive voltage transfor-mers (CVTs) and the current transformers (CTs). Theanalogue filters were also implemented using the second-order Butterworth model with cut-off frequency equal to350Hz. Fault location was performed by estimating thephasors with the use of the DFT algorithm working with 20samples per cycle. On the other hand, for distanceprotection application, the half cycle data window of thefilters was applied.A variety of fault cases have been generated and used to

test the fault location algorithm. In the analysis differentspecifications of faults, different shortcircuit powers of theequivalent systems behind the line terminals have beentaken into account.Figures 4–6 present results for the sample heavy fault

case, with the following main specifications:

fault type: a–g,

fault resistance: 15O, actual fault location: 0.8pu,

pre-fault power flow: from the station B to A (EsB leadsEsA by 351).

Figure 4 shows the waveforms of the input signals. Forthis far end fault (d¼ 0.8pu) and high fault resistance(RF¼ 15O), the changes in the voltages (Fig. 4a) andcurrents (Figs. 4a and b) are very small.Fault loop impedance measurement according to the

classic distance relay (11) and by applying the developedlocation algorithm (12), respectively, is shown in Figs. 5a, b.The components of the impedance (12) are much closer tothe actual values for the faulted line segment (resistance:dR1LA, reactance: dX1LA) than the values obtained in theclassic distance relays (11). ‘The reactance effect’, relevantfor measurement (11), can lead to the lack of tripping forthis fault, which is inside the first zone, usually set to 85% ofthe line impedance. On the other hand, when using thederived fault location algorithm (12), the tripping will bereliably issued.Testing showed accuracy of fault location to be

satisfactory. Maximum fault location error only slightlyexceeds 2% if shunt capacitances are not taken into accountand is around 0.3% when compensation is introduced forthe long line model.Figure 6 shows the estimated fault distance for the

sample fault case and its averaged value for the last 20 ms ofthe post-fault interval. Without the compensation (Fig. 6a)

AA BA

dZ1LA (1– d )Z1LA

Z1LB

AB BB

F

V AA1

I AB1

0.5B1LB 0.5B1LB

0.5dB1LA 0.5(1– d )B1LA

CF1I

CAA1I

AA1I

Fig. 3 Positive sequence equivalent circuit diagram of parallel lineswith included shunt capacitances

IEE Proc.-Gener. Transm. Distrib., Vol. 151, No. 2, March 2004 271

one obtains dð0Þaver: ¼ 0:7806 pu, and thus the error is around2%. After performing two iterations of the compensat-ion (Fig. 6b), the error decreases up to 0.26%

ðdð2Þaver: ¼ 0:7974 puÞ.

5 Conclusions

A new accurate fault location algorithm for the parallel lineshas been presented. Complete phase currents from both the

faulted and the healthy lines as well as the phase voltagesare the inputs of the fault locator. The flow of currentsthrough the healthy line path has been used to derive thealgorithm. Thus, the algorithm is capable of locating faultswhen both parallel lines are in operation. In the case wherethis is not so, the standard fault location algorithms have tobe applied.The algorithm presented is of compact form and

does not require source impedances. Usage of pre-faultsignals is also avoided. This is important as the remotesource impedance cannot be measured locally, and pre-faultmeasurements can in some cases be unreliable or evenunavailable. The adverse influence of uncertaintywith respect to a zero sequence impedance of thetransmission line is partly limited since the voltage dropacross a fault path is determined by excluding zero sequencecomponents.The fault location algorithm delivered is very simple and

compact. An application of the algorithm to the adaptivedistance protection of parallel lines has been proposed. Theheavy fault case shows the effectiveness in compensating for‘the reactance effect’.To ensure high accuracy for locating faults in long

parallel lines compensation for shunt capacitances of thelines is introduced by using the long line model. Evaluationby using a large number of ATP-EMTP simulations provedeffectiveness and high accuracy of the presented faultlocation algorithm.

0 20 40 60 80 100 120−4

−3

−2

−1

0

1

2

3

4

time, ms

phas

e vo

ltage

s (×

105 ),

V

a

0 20 40 60 80 100 120

−1500

−1000

−500

0

500

1000

1500

time, ms

faul

ted

line

phas

e cu

rren

ts, A

b

0 20 40 60 80 100 120−1500

−1000

−500

0

500

1000

1500

time, ms

heal

thy

line

phas

e cu

rren

ts, A

c

Fig. 4 Waveforms of fault locator input signals for the samplefault casea Phase voltagesb Phase currents of the faulted linec Phase currents of the healthy line

0 10 20 30 40 50 600

10

20

30

40

50

post-fault time, ms

faul

t loo

p re

sist

ance

, Ω

RAA_FL

RAA_P

dR1LA

a

0 10 20 30 40 50 6040

60

80

100

120

post-fault time, ms

faul

t loo

p re

acta

nce,

Ω

XAA_FL

XAA_P

dX1LA

b

Fig. 5 Impedance measurement for the sample fault casea Fault loop resistanceb Fault loop reactance

272 IEE Proc.-Gener. Transm. Distrib., Vol. 151, No. 2, March 2004

6 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 Wiszniewski, A.: ‘Accurate fault impedance locating algorithm’, IEEProc. C, Gener. Transm. Distrib., 1983, 130, (6), pp. 311–314

3 Moore, P.J., Whittard, R., and Johns, A.T.: ‘A novel earth faultlocation technique utilising single ended measurements’. Proc. IEEE/KTH Stockholm Power Tech Conf., Stockholm, Sweden June 1995,paper SPT IC 12–03–0515, pp. 406–410

4 Aggarwal, R.K., Aslan, Y., and Johns A.T.: ‘An interactive approachto fault location on overhead distribution lines with load taps’. Proc.Int. Conf. on Developments in Power System Protection, Nottingham25–27 March 1997, Conference Publication No. 434, pp. 184–187

5 Izykowski, J., Kawecki, R., Rosolowski, E., and Saha, M.M.:‘Accurate location of faults in parallel transmission lines underavailability of measurements from one circuit only’. Proc. 14th PowerSystems Computation Conf. (PSCC), Seville, Spain June 2002,Session 08, paper 6, pp. 1–7

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

7 Zhang, Q., Zhang, Y., Song, W., Yu, Y., and Wang, Z.: ‘Faultlocation of two-parallel transmission line for non-earth fault usingone-terminal data’. Proc. IEEE Winter Meeting, New York, USA31 January – 4 February 1999, Paper PE433-PWRD-0-10-1998,pp. 1–6

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

9 Saha, M.M., Wikstrom, K., Izykowski, J., and Rosolowski, E.: ‘Newfault location algorithm for parallel lines’. 7th Int. Conf. onDevelopments in Power System Protection, Amsterdam, April2001, pp. 407–410

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

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

12 Dommel, H.: ‘Electromagnetic transients program’ (BPA, Portland,Oregon, USA, 1986)

0 10 20 30 40 50 600.5

0.6

0.7

0.8

0.9

1.0

post-fault time, ms

dist

ance

to fa

ult,

pu

(0)daver. = 0.7806 pu

a

0 10 20 30 40 50 600.5

0.6

0.7

0.8

0.9

1.0

post-fault time, ms

dist

ance

to fa

ult,

pu

(2)daver. = 0.7974 pu

b

Fig. 6 Fault location for the sample fault casea Estimated distance to fault under neglecting the shunt capacitancesb Estimated distance to fault with included compensation

IEE Proc.-Gener. Transm. Distrib., Vol. 151, No. 2, March 2004 273