0 20 40 60-300

-200

-100

0

100

200

300

Time (ms)

Phas

e A

cur

rent

(A)

0 20 40 60-30

-20

-10

0

10

20

30

Phas

e A

vol

tage

(kV)

Phase A currentPhase A voltage

Inception Extinction

0 20 40 60-300

-200

-100

0

100

200

300

Time (ms)

Phas

e A

cur

rent

(A)

0 20 40 60-30

-20

-10

0

10

20

30

Phas

e A

vol

tage

(kV)

Phase A currentPhase A voltage

Inception Extinction

Figure 1: Example of current and voltage waveform during a self-clearingtransient event at phase A (single phase to ground).

Single End Self-Clearing Transient Fault Location for Preventive Maintenance of Power Cable Systems

M. Nguyen Ngoc, N. Hadjsaid Grenoble Electrical Engineering Laboratory (G2Elab) and

Grenoble Institute of Technology (Grenoble INP) Grenoble, France

minh.nguyen-ngoc@g2elab.grenoble-inp.fr

F.Cochet Nexans

2 rue de la Fabrique CH-2016 Cortaillod, Switzerland

Abstract— Self-clearing transient faults can be considered as precursor of imminent failure of power cables. They exist during a very short duration (few ms) and cannot be detected by conventional protection relay. However, they weaken dielectric, causing other transient faults in the future with increasing frequency of occurrence until final insulation breakdown. Thus, imminent failures can be avoided by preventive maintenance if these transient faults are correctly detected and located.

This paper presents a method for locating single phase to ground transient faults based on current and voltage measurements at one end of a power cable. Both distance to fault and fault resistance can be estimated by a least square fitting algorithm. Cable capacitances are also considered in our model. The proposed fault locating algorithm has been validatedwith a small distribution feeder, with two values of grounding impedance.

Index Terms— Fault Location, Least Square Fitting, Preventive Maintenance, Self-clearing Transient Fault.

I. INTRODUCTION

It has been shown that power cables links with deteriorated insulation could resist several self-clearing faults without causing a power outage before the final failure [1][2][3][4]. This phenomenon is mainly detected when cable splices are corroded by water penetration. Self-clearing property can be explained by vapor evaporation due to discharge energy [1].When a discharge occurs inside a faulty splice, discharge energy causes rapid water evaporation. The latter develops high vapor pressure which can extinguish the arc within a very short time. Recorded events show typical duration of self-clearing transient fault of around ¼ cycles (5ms at 50Hz frequency). The first recorded event is very often a single phase to ground fault.

An example of current and voltage waveform during a self-clearing transient fault is shown in Fig.1. The curve has been obtained by simulation. Fault inception and fault extinction time were set to 20 ms and 26 ms respectively.

Due to its very short time of existence, a self-clearing transient fault is not detected by conventional protection relays. Therefore, the power is not interrupted during faults

activities and these faults are somehow “invisible”. The dielectric is weakened and new transient faults will take place with increasing frequency of occurrence. At a later stage, the defect can no longer be self-extinguished and can lead to a “serious” failure.

A self-clearing transient fault can be considered as one of the precursors of a power cable failure. As the first transient fault may occur well before the final breakdown (several months or weeks), the network operator could have enough time to repair or replace the faulty accessories (connectors, screen…). Therefore, failure during service can be avoided if these transient faults are correctly detected and localized. The detection and classification of self-clearing transient fault have been studied in different works [1][5][6][7][8]. However, for this type of fault, very little information can be found relating to fault location.

Due to its very short time of existence, a transient fault cannot be located by traditional impedance algorithms. One possible technique to localize short time transient fault is the travelling wave method [9][10]. However, this technique requires multiple measurement points and time synchronized means, thus additional investment.

In this paper, we focus on a simple and economic technique based on solving the current and voltage equations

Raa.x

Rcc.x

Rcc.x

Laa.x

Lbb.x

Lcc.x

1/2Caa.x

1/2Cbb.x

1/2Ccc.x

1/2Caa.x

1/2Cbb.x

1/2Ccc.x

1/2Cab.x

1/2Cac.x

1/2Cbc.x

1/2Cab.x

1/2Cac.x

1/2Cbc.x

Va

Vb

Vc

Var

Vbr

Vcr

Rf

icc

ibb

iaa

ia

ib

ic

ifRaa.x

Rcc.x

Rcc.x

Laa.x

Lbb.x

Lcc.x

1/2Caa.x

1/2Cbb.x

1/2Ccc.x

1/2Caa.x

1/2Cbb.x

1/2Ccc.x

1/2Cab.x

1/2Cac.x

1/2Cbc.x

1/2Cab.x

1/2Cac.x

1/2Cbc.x

Va

Vb

Vc

Var

Vbr

Vcr

Rf

icc

ibb

iaa

ia

ib

ic

if

Figure 2: Power cable lump model

Initialization x=0

Input : va, vb, vc,Ia, ib, ic and cable parameters

Solve system of equations (1) by NNLS to find (x, Rf)

(xnew-xold)<epsilon

Fault distance = x Fault resistance = Rf

Yes

No

Calculate iaa, ibb, icc by equation (2)Calculate if by equation (3)

Initialization x=0

Input : va, vb, vc,Ia, ib, ic and cable parameters

Solve system of equations (1) by NNLS to find (x, Rf)

(xnew-xold)<epsilon

Fault distance = x Fault resistance = Rf

Yes

No

Calculate iaa, ibb, icc by equation (2)Calculate if by equation (3)

Figure 3: Proposed algorithm to solve the system of differential equations (1). Nonnegative least square fitting (NNLS) technique is used to solve over determined system of equations.

directly in the time domain to find the fault distance. This location technique has been presented in [11][12][13]. However, in [11][12][13], the studied case is simple with only one cable - one load and cable capacitances have been neglected.

Our paper proposes an improvement of the least square fitting method by considering effect of cable capacitance and effect of loads on distance estimation. Validations have also been carried out on a small distribution feeder. The method uses only current and voltage measurement at one end of the cable without time synchronization. This case corresponds well to the real situation, where current and voltage sensors are often available at the beginning of each feeder, at the substation level.

II. FAULT LOCATION TECHNIQUES Consider an earth fault occurring on phase “a” via a fault

resistance Rf. As the fault duration is short, Rf can be considered constant. The distance between the fault point and the HV/MV substation (location of sensors) is x. The faulty cable section from substation to fault point can be modeled bya lump pi section as shown in Fig. 2. The fault is modeled by a resistance Rf connected between the fault point and the ground.

In time domain, the relationship between the sending voltage and the receiving voltage for phase “a” can be represented by equation (1):

)1(ffcc

acbb

abaa

aaaaaaa iRxdt

diLdt

diLdt

diLiRV RxxxRRR LLL

Where: Va: sending end phase voltages Raa, Laa: phase A resistance and self-inductance per length unit Lab, Lac : mutual inductances between phase A and two other phases per length unit Rf, if : fault resistance and fault current x: length of studied cable section

On the other hand, the currents iaa, ibb, icc depend on currents ia, ib, ic at the sending end as follows:

xdt

VVdCdt

VVdCdt

dVCii

xdt

VVdCdt

VVdCdt

dVCii

xdt

VVdCdt

VVdCdt

dVCii

bccbaccacccccc

cbbcabbabbbbbb

caacbaabaaaaaa

xxxCC VCVCic

xxxCC VCVCib

xxxCC VCVCia

)(2

)(22

)2()(2

)(22

)(2

)(22

Where: Caa, Cbb, Ccc : phase to ground capacitances per length unit Cab, Cac, Cbc : phase to phase capacitances per length unit Va, Vb, Vc : phase voltages measured at the sending end

In case of a single phase to ground fault, the fault current if is equal to the residual current:

ccbbaaf iiii cicbibaia (3)

In (1), cable parameters Raa, Laa, Lab, Lac (resistance and inductance per length unit) are given by cable manufacturers or can be measured. On the other hand, as given by (2), the currents iaa, ibb and icc are functions of (Va, Vb, Vc, ia, ib, ic, x). The values (Va, Vb, Vc, ia, ib, ic) are measured by voltage and current sensors installed in the substation. These values are not simple values but matrix of values recorded during fault event, from fault inception to fault extinction.

As a result, (1) represents a system of nonlinear differential equations of two unknowns (x, Rf). The number of equations is far larger than 2 and depends on the fault duration and sensors’ resolution. Therefore, we have an over determined system for two unknowns (x, Rf).

The proposed algorithm for solving the above described system of equations (1) is presented in Fig.3. The iteration method transforms nonlinear differential equations into linear equations of two unknowns (x, Rf). At each iteration, as the number of equations is larger than the number of unknowns,the two unknowns (x, Rf) can be found by nonnegative least square fitting (NNLS) [14]

III VALIDATION In order to validate the proposed fault location algorithm, a

simulation has been carried out in ATP/EMTP environment. Current and voltage sensors are represented by current and voltage measurement blocks in the program. The results are then exported to Matlab environment for processing.

Validations have been carried out for three cases. For the first case, a simple system with only one cable and one load wasconsidered. Effect of fault distance, fault impedance, fault duration and sensors resolution were studied. For the second case, effect of loads connected at the middle of cable wasconsidered. For the last case, fault location algorithm was applied on a small distribution feeder with 14 nodes.

The performance of the locating algorithm is evaluated by the following equation:

realcalculated xxerror d xx (4)

A. Case1: One end concentrated load In this section, a simple system with a cable of 10 km length,

feeding a load S=1.5+j0.5 MVA (Fig.4). The neutral of transformer 63/20 kV is grounded via an impedance of 40Ω.

Figure 4: Load concentrated at cable end

02

46

810

010

2030

4050

0200400600800

1000

Fault Distance (km)

Fault Resistance (Ohm)

Abs

olut

e er

ror (

m)

Figure 5: Error versus fault distance and fault resistance

The fault location algorithm’s error is shown in Figure 5.The error depends on fault distance and fault resistance. A

linear correlation is observed between the error and the fault resistance. There is no linear correlation between the fault distance and location error. This can be explained by the nonlinearity of variable x in (1). In the worst scenario, the location algorithm’s error is about 800m.

As explained in section II, the location algorithm uses system of equations (1) to compute the fault distance. Consequently, the number of equations in (1) can have an important effect on algorithm’s performance. The number of equations in (1) depends on the fault duration and the resolution of sensors.

In order to evaluate the influence of sensors’ resolution, simulations have been carried out with sampling rates of 104, 105

and 106 samples per second. Results shown in Fig. 6 has been obtained with a fault impedance of 0 Ω. As shown in Fig. 6, ahigher sampling rate results in a lower error in distance calculation. Errors can be reduced considerably by increasing sensors’ resolution from 104 to 105 samples per second. Further increase of sensors’ resolution, from 105 to 106 samples per second, does not lead to significant improvement. The same conclusion can also be obtained with other values of fault resistance.

It is to be noted that higher sensors’ resolution will also require longer calculation time. A sampling rate of 105 samples per second can be a compromise between location performance and calculation time. Therefore, calculations carried out in this paper have all been obtain with this resolution.

0 2 4 6 8 10 120

100

200

300

400

500

600

700

800

Fault distance (km)

Erro

r (m

)

1E4 samples per sec1E5 samples per sec1E6 samples per sec

Figure 6: Influence of sensor resolution, fault duration is fixed at 4 ms. Fault resistance is 0 Ohm

0 2 4 6 8 10 120

250

500

750

1000

1250

1500

Fault distance (km)

Erro

r (m

)

Fault duration 1msFault duration 4msFault duration 10ms

Figure 7: Influence of fault duration, sensor resolution is fixed at 105 samples per second. Fault resistance is 50 Ohm

Fig. 7 shows the influence of fault duration on fault location error. The location accuracy is improved with the increase of the fault duration. A fault lasting 10ms can be located with an error lower than 700m. With a very short fault duration, lasting about 1ms, error in distance estimation can be as high as 1500m.

B. Case2: Presence of load between sensors and the fault point

As current sensors are installed at the substation level, they measure not only the fault current but also currents supplied to loads. Consequently, it is important to consider the loads’ effect,especially loads connected between current sensors and the fault point. In this section, the influence of a load connected in the middle of the cable as shown in Figure 8 was studied.

Figure 8: Load between sensors and fault point

Figure .9 presents the influence of load connected to node A from Fig. 8, on calculated fault distances. Two fault points, F1 and F2 have been studied. As shown in the figure, the load S1 has the tendency to reduce the calculated fault distance. It can also be stated that the influence of load S1 increases with distance L2.

0 1 2 3 4 53000

4000

5000

6000

7000

8000

9000

10000

Load power at node A (MVA) - power factor 0.8

Cal

cula

ted

faul

t dis

tanc

e (m

)

Fault point F2, Rf = 50 Ohm

Fault point F2, Rf = 0 Ohm

Fault point F1, Rf = 0 Ohm

Fault point F1, Rf = 50 Ohm

Figure 9: Influence of load connected between sensors and fault point

At fault point F2, a fault resistance of 50Ω, the calculated fault distance is reduced by 811 m when load S1 increases from 0 to 5MVA (from 8549m to 7738m). However, as the true fault distance is 8000m, the error is reduced from 549m to 262m. In the same condition, if fault resistance is close to 0Ω, the calculated fault distance is reduced from 7990m to 7325m. Consequently, the error in this case increases from 10m to 675m.

In general, a load of several MVA connected between sensors and the fault point can modify the calculated fault distance by several hundred meters. At the same time, the error can be deteriorated or improved, depending on the fault resistance and the fault position. In order to limit the effect of loads, one possible solution is to take load currents into consideration. Load currents can be measured by additional current sensors or can be

estimated from smart meters measurement. However, in this work, for the sake of simplicity of calculations, the errors due to load are accepted.

C. Case 3: Validation on a small distribution feeder In this section, the performance of the proposed fault location

algorithm has been studied with a small distribution feeder (15 nodes) as shown in Fig. 10. The nominal system voltage and frequency is 20kV and 50Hz respectively. The neutral of 63/20kV transformer is grounded via an impedance Z. Two values of grounding impedance were considered: Z = 40Ω and Z = 12+j12 Ω. Cables lengths and loads are shown in Table I. Five fault points, from F1 to F5 have been studied. The fault duration is fixed to 4ms. Voltages and currents are measured at node 1 with a resolution of 105 samples per second.

Figure 10: Studied distribution feeder (not in scale)

TABLE I. CONFIGURATION OF STUDIED FEEDER

Cables Loads

Connected nodes Length (m) Connected node Load (MVA)

1 – 2 1000 8 0.2+j0.09

2 – 3 1000 9 0.2+j0.12

3 – 4 1000 3 0.3+j0.1

4 – 5 2000 13 0.3+j0.1

5 – 6 2000 11 0.2+j0.05

6 – 7 2000 12 0.3+j0.2

2 – 8 1000 14 0.4+j0.2

8 – 9 1000 15 0.2+j0.15

4 – 10 1000 7 0.2+j0.07

10 – 13 1000

10 – 11 1000

11 – 12 1000

5 – 14 1000

6 – 15 1000

With earthing impedance Z = 40 Ω, calculated fault distance and fault resistance obtained with different fault positions are shown in Table II. The results showed a relatively good approximation of the fault distance, except two cases for which the localisation error is higher than 1000 m. These cases are obtained when the fault occurs at point F2 (with resistance of 50Ω) and point F5 (with fault resistance of 1 Ω).

TABLE II. RESULTS OBTAINDED WITH NEUTRAL IMPEDANCEZ = 40 Ω

Fault position

Fault distance -m /Fault resistance Ω(Real values)

Fault distance -m /Fault resistance Ω

(Calculated)Error

F1

1500m, 1 Ω 1521m / 1.44 Ω 21 m

1500m, 30 Ω 1605 m / 36.65 Ω 105 m

1500m, 50 Ω 1683 m / 62.11 Ω 183 m

F2

2500 m, 1 Ω 2745 m / 0 Ω 245 m

2500 m, 30 Ω 3347 m / 26.06 Ω 847 m

2500 m, 50 Ω 3682 m / 46.14 Ω 1182 m

F3

4500 m, 1 Ω 4080 m / 2.2 Ω 420 m

4500 m, 30 Ω 4627 m / 30.5 Ω 127 m

4500 m, 50 Ω 5001 m / 50.97 Ω 501 m

F4

5500 m, 1 Ω 4930 m / 3.45 Ω 570 m

5500 m, 30 Ω 5442 m / 33.6 Ω 58 m

5500 m, 50 Ω 5770 m / 54.98 Ω 270 m

F5

8000 m, 1 Ω 6886 m / 4.67 Ω 1114 m

8000 m, 30 Ω 7578 m / 27.89 Ω 422 m

8000 m, 50 Ω 8170 m / 43.45 Ω 170 m

TABLE III. RESULTS OBTAINDED WITH NEUTRAL IMPEDANCEZ = 12+J12 Ω

Fault position

Fault distance -m /Fault resistance Ω(Real values)

Fault distance -m /Fault resistance Ω

(Calculated)Error

F1

1500m, 1 Ω 1535 m, 1.2264 Ω 35 m

1500m, 30 Ω 1971 m, 24.59 Ω 471 m

1500m, 50 Ω 2282 m, 27.76 Ω 782 m

F2

2500 m, 1 Ω 2224 m, 2.01 Ω 276 m

2500 m, 30 Ω 2851 m, 27.41 Ω 351 m

2500 m, 50 Ω 3384 m, 41.37 Ω 884 m

F3

4500 m, 1 Ω 3652 m, 6.17 Ω 848 m

4500 m, 30 Ω 4270 m, 32.07 Ω 230 m

4500 m, 50 Ω 4707 m, 50.35 Ω 207 m

F4

5500 m, 1 Ω 4888 m, 2.696 Ω 612 m

5500 m, 30 Ω 5478 m, 31.15 Ω 22 m

5500 m, 50 Ω 5874 m, 51.42 Ω 374 m

F5

8000 m, 1 Ω 5250 m, 8.51 Ω 2750 m

8000 m, 30 Ω 7021 m, 27.39 Ω 979 m

8000 m, 50 Ω 7936 m, 40.50 Ω 64 m

Results obtained with an earthing impedance Z = 12+j12 Ω are showed in Table III. In this case, the error is generally lower than 1000m. However, when the fault occurs at point F5 with afault resistance of 1 Ω, the algorithm gives a significant error of 2750m.

Results obtained with a distribution feeder are less accurate compared to case 1 with one cable – one load (section A). This situation can be explained by the fact that load’s effect is neglected, and the lump model is probably not appropriate for this application. Further investigation is needed in order to find a better cable model.

IV CONCLUSION AND PERSPECTIVE

In this paper, a simple and economic way to locate transient self-clearing fault has been studied. The fault location technique is based on solving a system of differential equations during the fault event, by using nonnegative least square fitting method.

With a simple case with only one cable feeding one load, the fault can be located with quite good accuracy. The error in distance estimation is less than 800m. The location accuracy is improved with the increase of the fault duration and sensors’ resolutions. In order to avoid time consuming simulations, asampling rate of 105 samples per second has been chosen as a compromise between location performance and calculation time.

The presence of load between sensors and fault point reduces the calculated fault distance. With a load of several MVA connected between sensors and the fault point, the calculated fault distance can be reduced by several hundred meters. Consequently, the error in distance estimation can be improved or deteriorated, depending on the fault point and the fault resistance.

Validations were also carried out with a small distribution feeder. With grounding impedance of 40Ω, a quite good approximation of fault distance can be obtained. The largest error in this case is about 1100m. The same conclusion can be obtained with grounding impedance of 12+j12 Ω, except for one case where the error is of 2750m. The error in distance approximation can be explained by effect of loads and cable capacitances model, which are quite difficult to consider in a complex distribution network.

The error obtained by our method is quite significant in some cases. However, the calculated fault distance can be used to identify the faulty cable section. In the next step, the faulty section can be isolated and the fault point can be located with better accuracy by traditional offline methods.

As perspectives of this work, it is necessary to improve the accuracy of fault location method. A better model of cables should be studied, with consideration of cable screen. It is also interesting to study a more realistic network, such as mixed network with different types of cables. On the other hand, in order to limit effects of loads, load currents should be taken into account. Load currents can be measured by additional current sensors or through an estimate from smart meters measurement. Finally, some experiments with physical components (cables, transformers…) are also necessary to fully validate the proposed method.

REFERENCES

[1] L. A. Kojovic et J. Williams, C.W., « Sub-cycle detection of incipient cable splice faults to prevent cable damage », in IEEE Power Engineering Society Summer Meeting, 2000, 2000, vol. 2, p. 1175

1180 vol. 2. [2] R. Moghe, M. J. Mousavi, J. Stoupis, et J. McGowan, « Field

investigation and analysis of incipient faults leading to a catastrophic failure in an underground distribution feeder », in Power Systems Conference and Exposition, 2009. PSCE ’09. IEEE/PES, 2009, p. 1 6.

[3] F. Koehler, S. Cobben, et F. Provoost, « Self-Extinguishing Faults in MV Cable Networks - Feasibility Study of Fault Prediction », in International Conference on Renewable Energies and Power Quality (ICREPQ’12), Santiago de Compostela (Spain), 2012.

[4] C. L. Benner et B. D. Russell, « Distribution incipient faults and abnormal events: case studies from recorded field data », in Protective Relay Engineers, 2004 57th Annual Conference for, 2004, p. 86 90.

[5] B. Kasztenny, I. Voloh, C. G. Jones, et G. Baroudi, « Detection of Incipient Faults in Underground Medium Voltage Cables », in Protective Relay Engineers, 2008 61st Annual Conference for, 2008, p. 349 366.

[6] A. Edwards, H. Kang, et S. Subramanian, « Improved Algorithm for Detection of Self-clearing Transient Cable Faults », in IET 9th International Conference on Developments in Power System Protection, 2008. DPSP 2008, 2008, p. 204 207.

[7] J. Stoupis, A. Madwesh, et D. Lubkeman, « Cable Fault Detection », U.S. Patent WO/2008/05722116-mai-2008.

[8] T. S. Sidhu et Z. Xu, « Detection of Incipient Faults in Distribution Underground Cables », IEEE Transactions on Power Delivery, vol. 25, no 3, p. 1363 1371, juill. 2010.

[9] IEEE Standard C37.118, IEEE Guide for Determining Fault Location on AC Transmission and Distribution Lines. IEEE, 2005.

[10] A. Borghetti, M. Bosetti, M. Di Silvestro, C. A. Nucci, et M. Paolone, « Continuous-Wavelet Transform for Fault Location in Distribution Power Networks: Definition of Mother Wavelets Inferred From Fault Originated Transients », IEEE Transactions on Power Systems, vol. 23, no 2, p. 380 388, mai 2008.

[11] M. B. Djuric, Z. M. Radojevic, et V. V. Terzija, « Time domain solution of fault distance estimation and arcing faults detection on overhead lines », IEEE Transactions on Power Delivery, vol. 14, no 1, p. 60 67, janv. 1999.

[12] N. Luijk, « Online Fault Localisation in Oil Impregnated paper low voltage cable », in 17th International Conference on Electricity Distribution (CIRED), Barcelona, 2003.

[13] M. M. Alamuti, H. Nouri, R. M. Ciric, et V. Terzija, « Intermittent Fault Location in Distribution Feeders », IEEE Transactions on Power Delivery, vol. 27, no 1, p. 96 103, janv. 2012.

[14] C. . Lawson et R. . Hanson, Solving Least Squares Problems. Prentice-Hall, Chapter 23, p.161, 1974.