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AN ACCURATE FAULT LOCATOR FOR UNDERGROUND

DISTRIBUTION NETWORKS USING MODIFIED

APPARENT-IMPEDANCE CALCULATION

Tamer A. kawady, Abdel-Maksoud I. Taalab and Mahmoud El-Sad

Electrical Engineering Dept., Faculty of Engineering, Menoufiya University, Shebin El-Kom,Egypt.

Keywords: Apparent impedance, Cables, Distributionnetworks, Fault location, Power system protection.

Abstract

Underground distribution cables are usually characterized

with different technical difficulties regarding detecting andlocating their faults. Different factors participate into thesedifficulties including their remarkable charging currents,

cable construction and variations of their equivalency resultedfrom the variety of bonding and grounding methodologies. Inthis paper, a new fault location algorithm is proposed for

underground cables in particular. The algorithm is able toprecisely calculate the fault distance depending on modifyingthe basic apparent impedance approach to cope with theaforementioned characteristics of cable segments. In order toevaluate the performance of the proposed algorithm, differentinvestigation tests are performed depending on a typical 11kV underground distribution feeder in the Egyptian

distribution system. All applied test cases are prepared withMATLAB-Simulink using the SimPower toolbox withaccurate representation of power system elements utilizingdistributed parameter line models. Moreover, the performanceof the proposed algorithm is compared with the originalapparent impedance approach using the same simulationplatform. The applied test results cover a wide variety of faultconditions including fault resistance and loadingcircumstances. The results corroborate the efficacy of theproposed algorithm for locating such faults in undergrounddistribution systems.

1 Introduction

Fault location techniques raise nowadays an increasingly

importance for distribution networks owing to modern powersystem control requirements. The benefits of fault location

are: the fast repair to restore power system, improving systemavailability and performance, reduction of operating costs,and saving time. The fault location in complex urban cable

distribution system is presently difficult and time consuming.Consequently, a cable fault location technique with highaccuracy and high efficiency is increasingly demanded with

the increased use of underground cables nowadays in moderncities and large urban communities [1].

Underground cables are characterized with their own shortcircuit behaviour resulting from the unique profiles of their

electrical quantities, which are essentially based on the cabletype, size, conductor spacing and adopted groundingconfiguration. Unlike overhead lines, cables have quite lowimpedances resulting from the smaller spacing between thecable conductors. This results in different problems in severalareas including load sharing and short circuit levels. On the

other hand, smaller spacing between the cable conductors andthe sheath as well as the higher dielectric constants theirinsulations enlarges their capacitance significantly [2].

Fault location methods for underground cables networks canbe categorized in two categories; Tracer or Terminal ones.The tracer is exhaustive way to locate faulted section bywalking through the cable line. In contrast, terminalmethods are used to determine a fault location using phasormeasurement from single or double end of the cable line.Terminal methods of fault location are implemented usingfault impedance computation techniques or using travellingwave-based techniques. The latter was developed using either

pulse signal injection techniques or with analysing thegenerated fault transients [3], [4]. Recently, non conventionaltechniques such as Artificial Intelligence (AI) methods wereutilized for locating these faults as well [5]-[7].

On the other hand, utilizing impedance based fault locationcomputation methods with underground distribution networksfaces different problems. Underground cables arecharacterized with their own short circuit behaviour resultingfrom the unique profiles of their electrical quantities.Moreover, their electrical quantities are essentially based onthe cable type, size, conductor spacing and adopted groundingconfiguration. Cables have quite low impedances resulting

from the smaller spacing between the cable conductors. Onthe other hand, the smaller spacing between the cableconductors and the sheath as well as the higher dielectricconstants of the used insulations enlarges the cablecapacitance significantly. This perturbs the related protectivefunctions in particular with the absence of the propermathematical compensation of the resulting chargingcurrents. Thus, the effect of these factors on those impedance-based protection functions (including fault locationtechniques and distance relaying) is obvious. Since theperformance of fault location algorithms are mainlycharacterized with their mathematical cores and theirconsidered simplification assumptions, high charging currents

of cable segments play a basic role affecting most knownfault location algorithms.


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In this paper, a new fault location algorithm is introduced forunderground distribution systems using the apparentimpedance approach. To cope with the own characteristics ofunderground cables, the resulted estimation errors arecompensated. This consequently leads to realize an accurate

computation of occurring faults in such networks. Differentsimulation tests are applied using MATLAB to verify theperformance of the proposed algorithm.

2 Proposed locator description

The mathematical basis of the proposed algorithm can besummarized as follows. First, the available voltage and

current signals at the sending end are extracted, sampled andtheir related phasors are then estimated using the knownDiscrete Fourier Transform (DFT) computation. Upon the

fault type, the related apparent impedance parametersincluding the selected voltage and current quantities are

determined. A preliminarily fault distance can be estimatedusing the conventional apparent impedance computation.Finally, a dedicated compensation mechanism is iterativelyexecuted optimizing the resulting fault distance of the

occurring fault.

The core of the apparent impedance approach depends on

calculating the apparent seen impedance at the locatorposition using the available measuring quantities at the

sending end. Fig. 1 shows the single line diagram of a typical11 k V distribution feeder stepped down from a MV network.Upon the extracted voltages and currents at the locator

position, the apparent voltage Vapp, seen by the locator, can be

expressed as,

FFIRIx FsLapp ZV (1)

Then, the unknown equation part of "IFRF" can be replacedby "IFsRFs", in which RFs is the apparent part of faultimpedance seen form the relay location. IFs is the seen faultcurrent from sending end. The relation between the total andthe apparent fault resistances can be expressed as,

)C(RR FFs x (2)where the correction factor C(x) depends on the fault currentcontribution from both ends and can be therefore an

imaginary value. Equation (1) can be rewritten by dividing by

IFsyielding,

Fs

Fs

RxI

Lappapp

ZZV

(3)

Equation (3) can be considered as the main equation to findout the seen apparent impedance (Zapp) from the locator

location. In order to get the unknown fault distance x, theequation should be simplified by considering only a realcorrection factor. The above equation can be solved by

equating the real and imaginary parts in both equation sides.Further details are available in [8], [9].

According to the equivalent sequence network shown in Fig.2 for a ground fault on phase "a", the corresponding sequencecurrent passing through the first cable section can be written

Fig.1 One line diagram of a typical distribution feeder.

Fig. 2 equivalent sequence networks for phase-ground fault.

as a function of the sequence currents (I1, I2 and I0) andcapacitive sequence currents (ICAP 1, ICAP 2and ICAP 0) as,

0

2

1

0

2

1

0

2

1

capI

capI

capI

I

I

I

SFI

SFI

SFI

(4)

Then, the current flowing in phase "a" in the first cablesection can be calculated as,

IT.La= IF1s+ IF2s+ IFos (5)

Similarly, sequence voltages at the fault point F can bedescribes as follows.

SFI

SFI

SFI

Z

Z

Z

U

U

U

FV

FV

FV

0

2

1

*

000

02

0

001

0

2

1

0

2

1

(6)

The related voltage at the fault point F is,

VaF= V1F + V2F+ V0f (7)

The preceding equation was rewritten as a function of themeasured voltage at the locator position Ua yielding,


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CA

B

Refrence

+BC

A B[IaT.L+k.IFos]Z1]Z1

A

C

Ua

3IF1. Rf

F

Fig 3 Phasor diagram of the faulty phase voltage at the locator

position

VaF

= Ua- ( I

aT.L+ K . I

Fos).Z

1= 3RF.IF

1 (8)

Equation (8) was rewritten as,

Ua= ( IaT.L+ K . IFos).Z1+3RF .IF1 (9)

where K = (Z0- Z1)/ Z1 and Z1, Z2 and Z0 are the sequenceimpedances of the cable section.

Equation (9) can be represented by the shown phasor diagramin Fig. 3. Using geometrical triangular relations, the followingequation can be written as,

BASinM

ACSin

y

CB

sin (10)

where X, Y and M were designated for magnitudes of "Ua","(IaT.L+ KIFos)Z1" and "3RFIF1" and A, B, C were designatedfor their angles respectively. Rewriting equation (10) yielded,

CBSin

ACSiny

(11)

CBSin

BASinM x

(12)

Then the fault distance can be rewritten as,

Fault Distance = kmoa ZKII

y

/1 (13)

As seen by the latter equation, the calculated "Fault Distance"is estimated using the zero-sequence current at the locatorposition and the zero-sequence capacitive current located atthe sending end, which is calculated as,

IF1= IF0= Io Icap_o (14)

Calculating the fault distance is repeated until an acceptableconvergence of two consecutive iterations is reached asdescribed in Fig. 4. For each iteration (), the correspondingfault distance is computed using the sequence currents at thelocator position, the lumped capacitive current at the sendingend and the related angles derived in the preceding equations.

Similarly, fault distances for other fault types can becomputed.

Input system Configuration and

Cable line parameters

Acquire sending-end Voltage andCurrent after fault

Calculate: U(I)& I (I)

Icap(I) =U(I)/ XC (I)Ifs(I) = I(I) - Icap(I)

2,1,0 )(I IFSTLa II

PUT: IF1= IF0S

Yes

Yes

No

No

= +1

Fig. 4 Schematic of the overall iterative fault distancecomputation.

3 Simulated evaluation tests

In order to evaluate the performance of the proposedalgorithm, different investigation tests are performeddepending on a typical 11 kV underground distribution feeder

in the Egyptian distribution system. All applied test cases areprepared with MATLAB-Simulink using the SimPowertoolbox with accurate representation of power system

elements utilizing distributed parameter line models.Moreover, the performance of the proposed algorithm is

compared with the original apparent impedance approachusing the same simulation platform. The applied test resultscovered a wide variety of fault conditions including fault

resistance and loading circumstances. This enables tovisualize a broad evaluation of the performance of the

proposed algorithm for locating faults in undergrounddistribution systems.

3.1 Selected simulation scheme

A part of El-Khiry distribution feeder was selected as asimulation example for this study. It is considered as a typicalexample for our targets comprising of 11 load busses asdescribed in Fig. 5. The feeder supplies the loads throughXLPE cable (3*240Alu) supplied from El-Khiry Substation.The main transformer in the substation is a 25MVA, 66/11kV. Each concentrated load at each bus was fed via a 0.5MVA, 11 / 0,38 kV. Details for cable segment lengths and

loads in each bus are illustrated in Tables 1 and 2respectively.


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Fig. 5 Schematic of the selected distribution feeder

Element Length, km

1-2 5.22

2-3 0.6

3-4 0.4

4-5 0.255-6 0.03

6-7 0.25

7-8 0.15

8-9 0.2

9-10 1.3

10-11 0.22

Table 1 Lengths of the cable segments.

Bus no. Load no. Load impedance

2 Load 1 0.25 + J 0.115

3 Load 2 0.25 + J 0.12

4 Load 3 0.25 + J 0.12

5 Load 4 0.18+ J 0.11

6 Load 5 0.17 + J 0.009

7 Load 6 0.13 + J 0.08

8 Load 7 0.17 + J 0.009

9 Load 8 0.1 + J 0.06

10 Load 9 0.4 + J 0.2

11 Load 10 0.04 + J 0.02

Table 2 Load impedances at each bus in p.u.

3.2 Testing examples

For each fault case, the voltage and current signals at thelocator location were extracted at the locator position. These

extracted signals were then sampled at a frequency of 1600Hz. The corresponding phasor quantities were computed

using the "Discrete Fourier Transform", DFT, which has beennominated amongst different digital filter routines as the mostdependable filter for relay implementation. It is characterizedwith a maximum gain at the frequency of the fundamental and

zero gain for the dc and integer higher order harmonics. Faultdistance was then computed with the proposed schemedescribed in the last section. The computed fault distance was

compared with its corresponding actual fault distance tocompute the resulting estimation error as,

100% xlengthlinetotal

faultcalculatedlocationfaultactualError

(15)

Examples of applied test results were demonstrated asfollows.

D(km) Rf=0.0001

Rf=10

Rf=20

Rf=60

Rf=120

1.0 1.0035 1.0133 1.0302 1.092 1.1737

2.0 2.0115 1.9905 2.0119 2.1081 2.25

2.5 2.5172 2.468 2.4998 2.614 2.7834

3.0 3.0234 2.9595 2.9877 3.1189 3.31353.5 3.531 3.4425 3.4746 3.62 3.84

4.0 4.0392 3.9253 3.937 4.1267 4.3653

4.5 4.548 4.4085 4.4491 4.63 4.887

5.0 5.058 4.8892 4.9369 5.1338 5.4

5.23 5.325365 5.1155 5.1625 5.3657 5.6472

Table 3 Estimated fault distance with variation of faultresistance

Different test cases were applied with different fault distancesand fault resistances Table 3 summarized some selected casescovering the entire range of the first cable section with faultresistance of .000001 , 10 , 20 , 60 , and 120

respectively.

Fig.6 (a), (b) and (c) demonstrated the performance of theproposed locator as compared with the conventional apparent

impedance approach for 0, 10 and 120 fault resistancealong the entire range of cable length of the first segments. Asrevealed, both algorithms show the same performances forsolid faults as shown in Fig. 6 (a). The superiority of the

proposed algorithm was obvious for other non-solid faultconditions as seen in Fig. 6 (b) and (c).

4 Conclusion

Underground distribution systems are characterized with theirunique features that usually raise their own complexitiesregarding protection functions. For fault location

computation, in particular, the considerable charging currentsplay a basic role affecting most of the known single-endcomputational fault location schemes. The proposed

algorithm in this paper shows a high performance for locatingfaults in underground distribution feeders. Its basic coredepends on calculating the corresponding fault location with

the apparent impedance approach. An iterative compensationmechanism was utilized in order to eliminate the resultingestimation errors owing to the charging currents in cablesegments. All simulation test results show a remarkable

performance for locating faults in cable segments even withhigh values of fault resistances.


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0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

0.2

0.4

0.6

0.8

1

1.2

1.4

Fault Distance (km)

E

rror

"L to G" fault with fault resistance:0.00001

(a)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

1

2

3

4

5

Fault Distance (km)

Error

"L to G" fault with fault resistance:10

(b)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

5

10

15

20

25

Fault Distance (km)

Error

"L to G" fault with fault resistance:120

(c)Fig. 6 Performance of the proposed algorithm as compared

with the conventional apparent impedance approach(a) Solid fault

(b) 10fault resistance(c) 120fault resistance

Acknowledgements

The authors are expressing their gratitude to the Egyptian"Scientific and Technological Development Fund" (STDF),

Egypt, for funding this work.

References

[1] H. Lother , Power cables and their applications

,Published by Siemens Aktiengesellschaft, Berlin andMucher 1979.

[2] J.-H. Sun, Fault location of underground cables using

trav4elling wave, KIEE Trans., pp. 19721974, Jul.2000.

[3] S. Potivejkul, P. Kerdonfag, S. Jamnian, and V.

Kinnares, Design of lowvoltage cable fault detector,in Proc. IEEE Power Eng. Soc.Winter Meeting, Jan.

2000, vol. 1, pp. 724729.

[4] Ebrons .,Lubkeman D.L , White M . A neural networkapproach to the detection of incipient faults on Powerdistribution feeders IEEE tans. On Power Delivery,Vol.5,n.2,PP. 905-914,April 1990 .

[5] Chen Z.,Maun j.-c.Artificial neural network approach

to single-ended fault locator for transmission lines.IEEE trans.on Power systems,Vol.15,n. 1,PP.370-375,February 2000.

[6] Andr Filomena, Mariana Resener, Rodrigo H. Salimand Arturo Bretas, "Extended Impedance-Based FaultLocation Formulation for Unbalanced UndergroundDistribution Systems", IEEE PES General Meeting2008, 20-24 July, 2008.

[7] El Sayed Tag El Din, Mahmoud Gilany, MohamedAbdel Aziz and Doaa Ibrahim, "An PMU DoubleEnded Fault Location Scheme for Aged PowerCables", IEEE PES General Meeting 2005, 12-16June, 2005.

[8] Girgis and E.Makram, "Application of adaptivekalman filtering in fault classification, distanceprotection and fault location using microprocessor" ,IEEE Trans. On power systems , Vol. 3, No. 1,Feb.1988,pp. 301-309.

[9] Girgis, d. Hart, W. Peterson, A new fault locationtechnique for two and three terminal lines, IEEETrans. on Power Delivery, Vol. 7, No. 1, Jan. 1992,pp. 98-107.

Biographies

Tamer A. Kawady (M02) was born in Shebin El-kom,

Egypt on Sept. 30, 1972. He received his B.Sc. (honors) andM.Sc. degrees in Electrical Engineering, Menoufiya

University, Egypt, Ph.D. degree (excellent) from TechnicalUniversity Darmstadt, Germany in 1995, 1999 and 2005respectively. Dr. Kawady is currently an assistant professor at

Menoufiya University, Egypt since April 2005. His interestsare in digital protection, Power system simulation using the

Electromagnetic Transient Program (EMTP) and ArtificialIntelligence applications to power system protection.

Abdel-Maksoud I. Taalab (M99SM03) received his B.Scdegrees in 1969, in ElectricalEngineering from MenoufiyaUniversity, Egypt, M.Sc. and Ph.D degrees from Manchester

University (UMIST), U.K., in 1978, and 1982, respectively.In the same year of his graduation, he was appointed as anassistant professor at the Menoufiya University. He joined

GEC Company in 1982. He is now a full Professor at thedepartment of Electrical Engineering, Faculty of Engineeringand vice dean of the Desert Environment Institute, MenoufiyaUniversity. His interests are in hvdc transmission systems,power system protection, and power electronics applications.

Mahmoud El-Sad was born in Edko, Egypt, 1985. Hereceived his B.Sc. degrees in Electrical Engineering,

Menoufiya University, Egypt in 2007. He is currently ademonstrator in Minoufiya University and working in his

master in the area of power system protection.

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