wavelet based noise cancellation technique for fault location on underground power cables

7/29/2019 Wavelet Based Noise Cancellation Technique for Fault Location on Underground Power Cables

1/14

Electric Power Systems Research 77 (2007) 13491362

Wavelet based noise cancellation technique forfault location on underground power cables

C.K. Jung a,, J.B. Lee a, X.H. Wang b, Y.H. Song c

a Department of Electrical Engineering, Wonkwang University, 344-2, Shinyong-dong, I ksan, Republic of Koreab School of Computing and Information System, Kingston University, Kingston upon Thames, Surrey KT1 2EE, London, UK

cDepartment of Computing and Information System, Brunel University, Middlesex UB8 3PH, London, UK

Received 29 December 2005; received in revised form 18 September 2006; accepted 16 October 2006

Available online 16 November 2006

Abstract

This paper describes a new algorithm to identify the reflective waves for fault location in noisy environment. The new algorithm is based on the

correlation of detail components at adjacent levels of stationary wavelet transform of current signal from one end of the cable. The algorithm is

simple and straightforward. Simulation results based on a real power transmission system proved it can detect and locate the fault in very difficult

situations.

2006 Elsevier B.V. All rights reserved.

Keywords: Fault location; Fault classification; Underground power cable system; Stationary wavelet transform

1. Introduction

Thepotential benefits of applying wavelet transform in powercable fault location have been recognized by many researchers

[19]. The wavelet transform has the ability to localize the

signals in both time and frequency domains. This makes it par-

ticularly useful in capturing the transients at one end or both

ends of the cable and locate the fault position. This refers to

single-ended or double-ended fault location. Between these two

approaches, single-ended approach is less expensive and more

reliable as it does not need communication link between the ends

of the cable and requires only one equipment to operate rather

than two at both ends. This reduces the errors caused by the

different equipment and synchronization of time at both ends.

Therefore, single-ended approach is more practical and accurate

in fault location.

The single-ended approach uses reflected transients from

either the fault or other end to locate the fault. This raises some

problems of detecting the reflected transients on underground

power cable system. If the reflections are from fault point, they

will be very weak because part of the signals will transmit to

Corresponding author. Tel.: +82 63 850 6735; fax: +82 63 850 6735.

E-mail address: [email protected] (C.K. Jung).

the other end from fault point. If the reflections are from the

other end, same problem still exists as part of the signals will

reflect back. At the same time, the signal will travel a long wayto reach the measurement end. Since the high frequency tran-

sients have a very high attenuation in the cables, the reflection

will become weak after the long way traveling. It is clear that

the magnitudes of the reflections are much smaller than the first

transient. In addition, the measurement will be noisy. Some-

times the noise level may be higher than the reflections. Then

how to discriminate the weak reflection from the noise is a big

issue.

Thetransients have many irregular signals, andall of them are

useable signal. However, only transients at specific frequency

are useful to locate the fault. The rest are useless. Therefore,

this paper considers unnecessary signals as noise. In this paper,

a new algorithm was proposed to discriminate the reflected sig-

nals from noise and thus locate the fault. The algorithm is based

on the correlation of the wavelet coefficients at multi-scales.

For wavelet transform, the stationary wavelet transform (SWT)

is introduced instead of conventional discrete wavelet trans-

form (DWT). Stationary wavelet transform uses upsampling at

each level of decomposition that causes redundancy. In wavelet

transform, thenumber of elements perscaleand location is fixed-

independent of scale. The redundancy increases the elements per

scale and location at coarse scales. In term of denoising, there

0378-7796/$ see front matter 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.epsr.2006.10.005
mailto:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_3/dx.doi.org/10.1016/j.epsr.2006.10.005http://localhost/var/www/apps/conversion/tmp/scratch_3/dx.doi.org/10.1016/j.epsr.2006.10.005mailto:[email protected]


2/14

1350 C.K. Jung et al. / Electric Power Systems Research 77 (2007) 13491362

is an advantage in having more orientations than necessary at

coarse scales. It is better in noisy signal processing [10,11].

After brief review of the stationary wavelet transform in sec-

ond section, fault classification algorithm and noise cancellation

technique for fault location will be discussed in Sections 4 and

5, based on a real cable system described in Section 3. The algo-

rithms will be tested by simulations in Section 6. Thelast section

concludes the paper.

2. Stationary wavelet transform

In this section, the basic principles of the SWT method will

be presented. In summery, the SWT method can be described

as at each level, when the high and low pass filters are applied

to the data, the two new sequences have the same length as the

original sequences. To do this, the original data is not decimated.

However, the filters at each level are modified by padding them

out with zeros.

Supposing a function f(x) is projected at each step j on the

subset Vj (. . . V3 V2 V1 V0). This projection is definedby the scalar product cj,k of f(x) with the scaling function (x)

which is dilated and translated:

cj,k = f(x), j,k(x) (1)

j,k(x) = 2j(2jx k) (2)

where(x) is the scaling function, which is a low-pass filter. cj,k,

is also called a discrete approximation at the resolution 2j.

If(x) is the wavelet function, the wavelet coefficients are

obtained by:

j,k = f(x), 2j(2jx k) (3)

where j,k is called the discrete detail signal at the resolution 2j.

As the scaling function (x) has the property:

1

2x

2

=n

h(n)(x n),

where h(n) is the low-pass filter. cj+1,k can be obtained by direct

computation from cj,k

cj+1,k =n

h(n 2k)cj,n and1

2x

2

=n

g(n)(xn)

(4)

where g(n) is the high-pass filter.The scalar products f(x),2(j+1)(2(j+1)x k) are com-

puted with:

j+1,k =n

g(n 2k)cj,n (5)

Eqs. (4) and (5) are the multi-resolution algorithm of the

traditional discrete wavelet transform. In this transform, a down-

sampling algorithm is used to perform the transformation. That

is one point out of two is kept during transformation. Therefore,

the whole length of the function f(x) will reduce by half after the

transformation. This process continues until the length of the

function becomes one.

However, for stationary or redundant transform, instead of

downsampling, an upsampling procedure is carried out before

performingfilterconvolution at eachscale. The distance between

samples increases by a factor of 2 from scale j to the next. cj+1,kis obtained by:

cj+1,k = l

h(l)cj,k+2jl (6)

and the discrete wavelet coefficients:

j+1,k =l

g(l)cj,k+2jl (7)

where l indicates the finite length.

3. Model system

The diagram of a real power cable system to be discussed in

this paper is shown in Fig. 1. It is a single core cable transmission

system with the voltage of 154 kV. The total length of the cableis 6.284 km. It consists of five crossbonded major sections with

three minor sections foreach major section. As usual,the sheaths

are jointed and crossbonded between two sections.

In this paper, the single line to ground fault is considered

in real power cable system to test the proposed algorithm and

Alternative Transient Programs (ATP) program is used for sys-

temmodelingand simulation. Thesampling frequency is 1 MHz,

the propagation velocities of traveling wave on power cable sys-

tem is 1.67487 105 km/s. The applied fault inception angle is

0, 45, 60 and 90, respectively. In order to calculate the dis-

tance to fault point, single line to ground fault is supposed to

occur at 13 km from A S/S. Fault resistance is assumed to be

0, 0.5 and 1, respectively.

4. Algorithm for fault classification

Wavelet transform decomposes the signal into approxima-

tion and detail coefficients, forming approximations and details.

The approximations are the high-scale, low-frequency com-

ponents of the signal, while the details are the low-scale,

high-frequency components. The decomposition process can be

iterated.

Normally the first level detail in wavelet transform contains

the information to detect the fault. In order to detect the fault,

threshold is set. If the signal exceeds the threshold, then it issupposed that a fault has occurred. However, the spike can be

detected on all phases. It is difficult to discriminate on which

phase the fault is. For many signals, the low frequency contents

are the most important parts. They give the signal their identities

to some extents. For SWT decomposition, the approximation

contains the low frequency components. The more levels the

signals are decomposed, the lower frequency the components

will be.

For fault detection and classification, the 4th level approxi-

mations of current on phasesAC will be used. If thefault occurs

on phase A, the magnitude of approximation on phases B and C

are very low comparing to that on phase A after some delayed


3/14

C.K. Jung et al. / Electric Power Systems Research 77 (2007) 13491362 1351

Fig. 1. Underground power cable system.

Fig. 2. Flow chart for fault detection and classification.

sampling time from the fault inception. Then an algorithm is

established to classify the fault.

For every sampling point exceeding the threshold on the first

detail, approximations of the three-phase currents on 4th level

are calculated as A4j, where j = 1, 2 and 3 for three phases.

The maximum approximation among three phases is denoted

as Amax. Then the absolute ratio of the approximations on each

single phase to the maximum approximation is calculated. The

ratio on the faulty phase should be unity since its approximation

is equal to the maximum value, while the ratios on the other two

phases are near zero because of the weak signals. Therefore, if

two ratios are near zero, it can deduce that a fault has occurred,

and the faulty phase can be classified as the one whose ratio is

equal to unity. A simple flow chart of the procedure is shown is

Fig. 2.

Faults on phase A were applied for testing the fault detection

and classification algorithm. However, an extensive investiga-

tion has been carried out to study the fault with various condi-

tions which include the different positions, inception angles andfault resistance. The calculated ratios are shown in Table 1. The

ratios on all faulty phases show unity because its approximation

is equal to the maximum value regardless of fault conditions,

while the ratios on other two phases are near zero. From these

results, the fault on which phase will be easily identified.

5. Noise cancellation technique

After applying the wavelet transform the details of the first

level are shown in Figs. 3 and 4 in case of fault at 1 and 2 km.

As shown in these figures, many spikes appeared because of the

reflected transients from both fault point and other end of thecable including many noises.

Therefore, it is very difficult to discriminatewhichtransient is

the fault generated. This makes the fault location by the wavelet

transformation impossible.

How to remove the noise interference is a big issue and up to

date no solutions have been provided. A new solution based on

correlation of multiple scales of the transients will be presented.

As shown in Figs. 3 and 4, it is very difficult to discriminate

the fault transients by the first level details. However, only one

Table 1

Ratio under different fault conditions

Fault conditions = 0 = 45 = 60 = 90

Fault

resistance ()

Fault distance

(km)

ra rb rc ra rb rc ra rb rc ra rb rc

0 1 1.000 0.0537 0.0513 1.000 0.0513 0.0512 1.000 0.0519 0.04 1.000 0.0436 0.0407

2 1.000 0.0459 0.0447 1.000 0.0460 0.0446 1.000 0.0447 0.0435 1.000 0.0355 0.0337

3 1.000 0.0436 0.0362 1.000 0.04 0.04360 1.000 0.0426 0.0355 1.000 0.0341 0.0242

0.5 1 1.000 0.0505 0.0485 1.000 0.0483 0.0482 1.000 0.0466 0.0449 1.000 0.0487 0.0456

2 1.000 0.0433 0.0421 1.000 0.03 0.0409 1.000 0.04091 0.0385 1.000 0.0402 0.0386

3 1.000 0.0409 0.0337 1.000 0.0398 0.0324 1.000 0.0374 0.0279 1.000 0.0378 0.0279

1 1 1.000 0.0449 0.0431 1.000 0.0429 0.0431 1.000 0.0397 0.0385 1.000 0.0456 0.0419

2 1.000 0.0376 0.0367 1.000 0.0367 0.0358 1.000 0.0326 0.0321 1.000 0.0369 0.0355

3 1.000 0.0352 0.0280 1.000 0.0343 0.03 1.000 0.0308 0.0343 1.000 0.0343 0.0254


4/14


Fig. 3. First level details of the wavelet transform at 1 km fault according to fault resistance (fault inception angle: 0): (a) fault resistance: 0 ; (b) fault resistance:

0.5; (c) fault resistance: 1 .

transient is significant with the high value while the magnitudes

of the other transients are relatively low. It is discovered that the

wavelet maxima at a scale 2j will propagate to another maxima

at the coarser scale 2j+1 if both maxima belong to the same

maxima line [12]. For the white noises, on average, the number

of maxima decreases by a factor of 2 when the scale increases by

2. Half of the maxima do not propagate from the scale 2j to the

scale 2j+1. We adopted a simple algorithm to remove the noise

relied on the variations in the scale of the wavelet transform data

of the signal by using direct multiplication of the wavelet data at

adjacent scales [13]. Our approach to detect the fault transients

and locate the fault also bases on the variation of the wavelet

data at adjacent scales by using the direct multiplication. It is

simple, quick and straightforward.

Supposingthe signalis decomposed by thewavelet at n levels,

the detail coefficients will be D1, D2, . . ., Dn. Then the details

at first two scales will be multiplied directly, give a correlation

Corr1 as in Eq. (8). Next the correlation is rescaled to the first

detail by Eq. (9).

Corr1 = D1D2 (8)

Corr new1 = Corr1

PD1

PCorr12n (9)


5/14


Fig. 4. First level details of the wavelet transform at 2 km fault according to fault resistance (fault inception angle: 45): (a) fault resistance: 0 ; (b) fault resistance:

0.5; (c) fault resistance: 1.

where PD1 =

D21 and PCorr1 =

Corr12 are the powers of

detail D1 and Corr1. n is iteration number.

Next is to compare the absolute value of Corr new1 and D1.

Values where D1 is more than Corr new1 are identified and

stored in a new variable. This one is regarded as the new detail

at level one, D1 new1.

Then the Corr new1 and D3 will be multiplied directly, give

a correlation2 Corr2 such as Eq. (10). Next the correlation is

rescaled to the first detail by Eq. (11):

Corr2 = Corr new1D3 (10)

Corr new2 = Corr2

PCorr new1

PCorr22n (11)

where PCorr new1 =

Corr new12 and PCorr2 =

Corr22 are

the powers of Corr new1 and Corr2 and n is iteration number.

As the first procedure, to compare the absolute value of

Corr new1 and Corr new2, the values where Corr new1 more

than Corr new2 are identified and stored in a new variable. This

one is D1 new2.

Finally, Corr new2 and D4 will be multiplied directly, giving

a correlation Corr3 and rescaled Corr new3 as in Eqs. (12)


6/14


and (13) as the same as above, and D1 new3 will be stored as

usual:

Corr3 = Corr new2D4 (12)

Corr new3 = Corr3PCorr new2PCorr3

2n (13)

If at this stage, more than two fault transients can be detected

at D1 new3, then locate the fault using the absolute value of D1new3 and stop the algorithm. If only one fault transient can be

detected at D1 new3, then the algorithm will be repeated at the

next iteration and finished when the signal detection is satis-

fied. The whole procedure can be described by the flowchart in

Fig. 5.

Fig. 6. Lattice diagram in case of near half fault.

Fig. 5. Flow chart of noise cancellation procedure for fault location.


7/14


Fig. 7. Noise cancellation procedure at the 1 km fault (fault resistance: 0, fault inception angle: 90, n = 1): (a) D1; (b) D1 new1; (c) D1 new2; (d) abs(D1 new3).


8/14


Fig. 8. Noise cancellation procedure at the 1 km fault (fault resistance: 0.5, fault inception angle: 45, n = 1): (a) D1; (b) D1 new1; (c) D1 new2; (d) abs(D1 new3).


9/14


Fig. 9. Noise cancellation procedure at the 2km fault (fault resistance: 0.5, fault inception angle: 90, n = 1): (a) D1; (b) D1 new1; (c) D1 new2; (d) abs(D1 new3).


10/14




11/14


Fig. 11. Noise cancellation procedure at the 2 km fault (fault resistance: 1, fault inception angle: 45, n = 3): (a) D1; (b) D1 new1; (c) D1 new2; (d) abs(D1 new3).


12/14




13/14


6. Simulation results

In this section, the noise cancellation technique is applied for

fault location on underground power cable system. In order to

test this algorithm, the faults on the first half, at 13 km from A

S/S, are only to be considered.

Fig. 6 shows the lattice diagram of the characteristic of travel-

ing wave as the ground fault occurs on the first half. In this case,

after the arrival time of the first and second reflections at A S/S

are successfully detected using noise cancellation technique, the

distance(X) to fault point can be calculated by Eq. (14):

X =c(TP2 Tp2)

2(14)

where c is the propagation velocity on underground power

cable system, and Tp1 and Tp2 are the arrival times of first and

the second transients, respectively.

Fig. 7 shows the noise cancellation procedure when the

ground fault occurred at 1 km. In this case, fault resistance is

0 and fault inception angle is 90. As shown in the figure,at the first level detail (Fig. 7(a)), it is hard to discriminate the

reflected points because of the noises. However, after rescal-

ing using multiple scales correlation, the noise is significantly

removed. As shown in D1 new2 (Fig. 7(c)) the reflected point

at A S/S can be easily detected. Finally, the distance to fault

point can be calculated using the absolute value of D1 new3

(Fig. 7(d)). In this case, the first and the second arrival times

are 0.016667 and 0.016678 s, and the propagation velocity is

1.67487 105 km/s as discussed in Section 3. The calculated

distance is 0.921 km which is very close to the exact fault dis-

tance of 1 km.

In terms of fault at 1 km with fault resistance of 0.5 andfault inception angel of 45, the noise cancellation procedure is

shown in Fig. 8. Many noises in D1 are gradually removed from

D1 new1 to D1 new3. From these results, the distance to fault

point can be calculated using the absolute value of D1 new3. In

Fig. 8(d), the first and the second reflection time are 0.014587

and 0.014599 s. The calculated distance is 1.005 km which is

also very close to the exact fault distance of 1 km.

In case of fault at 2 km with fault resistance of 0.5 and

fault inception angel of 90, as shown in Fig. 9, the distance

cannot be calculated because D1 new2 and D1 new3 have just

one reflection signal at the first iteration (n = 1). In this case,

algorithm will automatically go to the next step, n = 2. Fig. 10

shows thenoise cancellationresult at the second iteration (n =2).

In Fig. 10(d), the time of first and second reflections are easily

detected at 0.016673 and 0.016697 s. Therefore, the calculated

distance to fault point is 2.009 km. It is quite accurate.

Figs. 11 and 12 show the noise cancellation results when

the ground fault occurred at 2 and 3 km, respectively. In these

two figures, the appropriate signals for fault location can be

detected at the third iteration (n = 3) and the second iteration

(n = 2), respectively.

In Fig. 11(d), the arrival times of the two reflections are

0.014593 and 0.014618 s. Therefore, the calculated distance to

fault point is 2.093 km. The arrival times of reflected signals

in Fig. 12(d) are 0.016679 and 0.016715 s, and its distance is3.014 km.

The criterion used for evaluating the algorithm is the location

error which is defined as:

Error (%) =|actual location-calculated location|

total line length 100 (15)

This algorithm has been tested for a variety of simulated fault

conditions which include changing fault resistance from 0 to 1,

fault inception angle from 0 to 90 and fault location between

1 to 3 km. The maximum location error is less than 3% and the

average error is 1.132%. The errors for fault location in all faultconditions are shown in Table 2.

As shown in Figs. 712 and Table 2, it is possible to discrim-

inate the reflected signal from noises by the application of the

algorithm proposed in this paper. This method is very useful in

detecting the fault in noisy environment.

Table 2

Errors for fault location in different fault conditions

Fault distance

[km]

Fault inception

angle

Fault resistance []

0 0.5 1

Calculated

distance [km]

n Error [%] Calculated

distance [km]

n Error [%] Calculated

distance [km]

n Error [%]

1 0 0.921 1 1.257 1.005 1 0.079 1.005 2 0.079

45 1.005 1 0.079 1.005 1 0.079 1.005 1 0.079

60 1.005 1 0.079 1.005 1 0.079 1.005 1 0.079

90 0.921 1 1.257 0.921 1 1.257 0.921 1 1.257

2 0 2.093 3 1.479 2.093 3 1.479 2.093 3 1.479

45 2.093 2 1.479 2.093 2 1.479 2.093 3 1.479

60 2.009 1 0.143 2.093 2 1.479 2.093 2 1.479

90 2.009 1 0.143 2.009 2 0.143 2.093 2 1.479

3 0 3.182 3 2.896 3.182 3 2.896 3.182 4 2.896

45 3.098 3 1.559 3.098 3 1.559 3.098 4 1.559

60 3.098 3 1.559 3.098 3 1.559 3.098 4 1.559

90 3.098 3 1.559 3.014 2 0.222 3.098 4 1.559

Average error [%]: 1.132.


14/14


7. Conclusions

Fault location on underground power cable system is very

difficult because the measurements include many noises. In this

paper, in order to detect, classify the fault and discriminate the

transients and the reflected signal from noise, a new algorithm

based on multiple scale correlation of wavelet transform was

presented using current signal from one end. By this algorithm,

faulty phase can be detected and classified by the approximation

components of three phases on 4th level. Then the details at

first level are rescaled until the clear transients are identified.

It proved that the noises can be significantly removed by the

proposed algorithm.

The algorithm was validated by simulation on real power

cable system. From these results, the faults can be detected and

located even in very difficult situations, such as at inception

angles of 0 and 90.

Acknowledgements

This work has been supported by KESRI (R-2003-B-274),

which is funded by Ministry of Commerce, Industry and Energy

(MOCIE).

References

[1] X.H. Wang, Y.H. Song, C. Ferguson, Wave propagation characteristics

on crossbonded underground power transmission cables and sheath fault

location, Eur. Trans. Electric Power (ETEP) 13 (2) (2003) 127131.

[2] X.H. Wang, Y.H. Song, Sheath fault detection and classification based on

wavelet analysis, Eur. Trans. Electric Power (ETEP) 16 (4) (2006) 327

344.

[3] F.H. Magnago, A. Abur, Fault location using wavelets, IEEE Trans. Power

Deliv. 13 (October (4)) (1998) 14751480.

[4] E. Styvaktakis, M.H.J. Bollen, I.Y.H. Gu, A fault location technique using

high frequency fault clearing transients, IEEE Power Eng. Rev. 19 (May

(5)) (1999) 5060.

[5] M.M. Tawfik, M.M. Morcos, A novel approach for fault location ontransmission lines, IEEE Power Eng. Rev. 18 (November (11)) (1998)

5860.

[6] A.M. Gaouda, S.H. Kanoun, M.M.A. Salama, A.Y. Chikhani, Generation,

wavelet-based signal processing for disturbance classification and mea-

surement, IEE Proc. Transm. Distrib. 149 (May (3)) (2002) 310318.

[7] I.K. Yu, Y.H. Song, Wavelet transform and neural network approach to

developing adaptive single-pole auto-reclosingschemesfor EHV transmis-

sion systems, IEEE Power Eng. Rev. 18 (November (11)) (1998) 6264.

[8] F.N.Chowdhury, J.L.Aravena, A modularmethodologyfor fastfault detec-

tionand classificationin power systems,IEEE Trans.ControlSyst.Technol.

6 (September (5)) (1998) 623634.

[9] Z.Q. Bo, M.A. Redfern, G.C. Weller, Positional protection of transmission

line using fault generated high frequency transient signal, IEEE Trans.

Power Deliv. 15 (3) (2000) 888894.

[10] X.H. Wang, R.S.H. Istepanian, Y.H. Song, Microarray image de-noisingusing stationary wavelet transform, in: Proceedings of the 4th IEEE Con-

ference on Information Technology Applications, 2003, pp. 1518.

[11] H. Ye, G. Wang, S.X. Ding, A new fault detection approach based on

parity relation and stationary wavelet transform, in: IEEE Proceeding of

the American Control Conference, June 2003, pp. 29912996.

[12] Stephane Mallat, Wen Liang Hwang, Singularity detection and processing

with wavelet, IEEE Trans. Inform. Theory 38 (2) (1992) 617643.

[13] Y. Xu, J.B. Weaver, D.M. Healy, J. Lu, Wavelet transform domain filters:

a spatially selective noise filtration technique, IEEE Trans. Image Process.

3 (6) (1994) 747758.

wavelet based noise cancellation technique for fault location on underground power cables

Documents