a modified wavelet-based fault classification technique

A modified wavelet-based fault classification technique

Omar A.S. Youssef �Faculty of Industrial Education, Suez Canal University, Suez, Cairo 11351, Egypt

Received 13 May 2002; received in revised form 22 August 2002; accepted 28 August 2002

Abstract

This paper presents a new Wavelet-based fault classification technique that utilises the HF components confined to scale-8 (level-

3) of Wavelet analysis of the three line currents in transmission line. Data window required for the algorithm is small (less than half

power frequency cycle based on 1.0 kHz sampling rate). In the paper firstly the theoretical background is reported and briefly

discussed in relation to reference ‘IEEE, T&D Conf. (2001)’. Then, an extended study is conducted, and the proposed method is

described in detail. Finally, some case studies are examined using the EMTP and MATLAB softwares in order to highlight the

performance of the method. It is proved that the proposed technique is reliable and appropriate for real-time measurement

algorithms and fault classification techniques.

# 2002 Elsevier Science B.V. All rights reserved.

Keywords: Wavelet transform; Multiresolution signal decomposition and reconstruction; Protective relaying; Transient analysis; Signal analysis

1. Introduction

Transmission lines relaying must be able to detect,

localise, estimate and classify disturbances on the supply

lines to safeguard the power systems. As a consequence,

it must be supported by suitable measurement and fast

acting methods. The main part of a protective relay is a

selector unit. This unit identifies the type of fault that

has occurred on the transmission line (LG�/LL�/LLG�/

LLL�/LLLG). In addition it has also to identify any

other abnormal state than a faulty one, i.e. load jumps,

transients, etc. An autoreclosing selection module is the

one responsible for the decision whether an arcing or a

non-arcing fault has occurred.

Fault classification techniques suggested before were

based on the variation of the current or voltage samples

of the three phases or the phasor quantities of the power

frequency information. In [2], the authors suggested to

classify the fault using Clark components of the current

samples. The technique was based on the assumption

that the line is ideally transposed and hence, it may have

difficulty in classifying a double line to ground fault. In

[3], a difficulty in discriminating a two-phase to ground

fault from a three-phase to ground fault was reported.

Phadke et al. [4,5], used a set of coefficients based on

the sequence current and voltage phasor components to

calculate the apparent impedance. The author in [6,7]

used the ratio of the change in the magnitude of the

superimposed currents to threshold value to classify the

fault. If this ratio is below another threshold value, then

the phase will be classified as unfaulted. A statistical

approach to classify faults was used in [8]. In [9], the

author relied upon an artificial neural network for fault

classification.Wavelet transform (WT) exhibits very attractive

features that make it ideal for studying transient signals

with more reliable discrimination than Fourier trans-

form. In contrast to Fourier analysis, which averages

frequency characteristics over time, wavelet decomposi-

tion localises features both in time and in frequency.

Applications of WT techniques in power systems have

been recognised in the recent years. In [10], the authors

present a comparative overview of Fourier, short time

Fourier (STF) and WTs, as applied to power system

transient’s analysis. In [11,12], the application of (WT)

to detect and classify power quality disturbances, is

given. The advantages of using WT for analysing

transients is demonstrated in [13]. In [1], the paper� Tel.: �/20-2-635-9384; fax: �/20-2-637-6596

E-mail address: [email protected] (O.A.S. Youssef).

Electric Power Systems Research 64 (2003) 165�/172

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0378-7796/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 3 7 8 - 7 7 9 6 ( 0 2 ) 0 0 1 7 1 - 2

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presents a wavelet-based technique for classification of

faults on transmission lines to provide a reliable and fast

estimation of fault type in real-time measurements. This

paper extends a detailed study on the Wavelet-basedfault classification technique presented in [1] and other

Wavelet-based techniques presented in [14,15]. A brief

introduction to WT is given before studying the

performance of the technique and discussing the effect

of different factors on its performance.

2. The discrete wavelet transform

WT is a linear transformation that allows time

localisation of different frequency components of a

given signal. STF also achieves this same goal, but

with a limitation of using a fixed width windowingfunction. As a result, both frequency and time resolution

of the resulting transform will be apriori fixed. In the

case of WT, the analysing functions which are called

wavelets, having a finite duration in time, will adjust

their time-widths to their frequency in such a way that,

higher frequency wavelets will be very narrow and lower

frequency ones will be broader. This multi resolution

property is particularly useful for analysing faulttransients, which contain localised high frequency

components superposed on power frequency as ex-

plained in the following section.

WT of a sampled current waveform V (k ) can be

obtained by implementing the discrete WT, which is

given by:

DWT(V ; m; n)�1ffiffiffiffiffiffiam

0

p Xk

V (k)C��

n � kam0

am0

�

where, a0m and ka0

m are the scaling (dilation) and

translation (time shift) constants, respectively, while k

and m being integer variables. The scaling is given by 1,

1/a , 1/a2, . . . while the translation is given by 0, k , 2k , . . .

When the coefficients are sampled on a dyadic grid, in

which case, a0�/2 and a00�/1, a0

�1�/1/2, etc. . . . Fig. 1

illustrates a single-level Wavelet decomposition and

reconstruction process. Actual implementation of the

DWT, involves successive pairs of high-pass and low-

pass filters at each scaling stage of the WT, i.e.

successive approximations of the same function, eachapproximation providing the incremental information

related to a particular scale (frequency range), the first

scale covering the high frequency end of the spectrum

and the higher scales covering the lower end of the

frequency. Multilevel Wavelet decomposition and re-

construction procedure is shown in Fig. 2. In principle

any admissible wavelet can be used in the wavelet

analysis [16�/18]. The filter W , which is called thescaling filter (non-normalised), is finite impulse response

FIR of length 2N , of sum 1, of norm 1/sqrt(2),and is a

low-pass filter. From filter W , we define four FIR

filters, of length 2N and of norm 1, organised as follows:

LR�W

norm(W); LD�REV(LR)

HR�Q(LR); HD�REV(HR)

where LR, HR are the low-pass and high-pass recon-

struction filter coefficients, and LD, HD are the low-

pass and high-pass decomposition filter coefficients,

while, REV stands for reversing the coefficients, and Q

is the quadrature mirror filter.

Fig. 3 illustrates 4-level wavelet analysis of a typical

voltage signal during L�/G fault on a transmission line,

using Wavelet function db8 for sampling rate 1.0 kHz.The power spectral densities (one complete cycle analy-

sis just after fault inception) at different levels are

shown, and, from which it is clear that the HF contents

decrease with the level of analysis.

3. Model power system

The system configuration used in the simulation isshown in Fig. 4, using the EMTP/ATP [19] software. The

system is composed of a 300 km, 400 kV transposed

double-end fed transmission line and is provided with

70% series compensation. ZSA and ZSB represent the

Fig. 1. Single level Wavelet decomposition and reconstruction proce-

dure of a signal V. Fig. 2. Four-level Wavelet analysis of a signal V.

O.A.S. Youssef / Electric Power Systems Research 64 (2003) 165�/172166

equivalent source impedance’s. In the simulation, the

transmission line was represented using the distributed

parameters model, while local-, and remote-end sources

were simulated using lumped impedance’s model. The

parameters of the sample power system are:

1) Source parameters:

Z0�1:16� j13:3 V; Z1�0:655� j7:50 V

2) TL parameters: A 400 kV, 300 km with the

following:

Z0�0:2750� j1:03 V=km;

suspectance�0:008 mV=km

Z1�0:0275� j0:1350 V=km;

suspectance�0:130 mV=km

4. Algorithm

It has been shown before [14,15] that the Wavelet-

based LF component of a signal x0 at level-4 can be

calculated directly as:

Wx0�MAT4�x0

where MAT4 is denoted as the DWT matrix at level-4.Also, the online calculation of the LF components

(based on the moving data window approach) can be

calculated using the centrer row of the DWT matrix. In

general the method of calculations of both level-4 LF-,

and HF-components of the relaying signal based on

Wavelet analysis are summarised in the following

section.

4.1. Computation of level-4 LF components

4.1.1. Decomposition of LF components

. First level decomposition: x1L�/LD1�/x0.

. Second level decomposition: x2L�/LD2�/x1L.

. Third level decomposition: x3L�/LD3�/x2L.

. Fourth level decomposition: x4L�/LD4�/x3L.

I.e. x4L�/DECL�/x0 where; DECL�/LD4�/LD3�/

LD2�/LD1.

4.1.2. Reconstruction of level-4 LF components

. First level reconstruction: y1L�/LR11�/x4L.

. Second level reconstruction: y2L�/LR12�/y1L.

. Third level reconstruction: y3L�/LR13�/y2L.

. Fourth level reconstruction: y4L�/LR14�/y3L.

I.e. y4L�/LR14LR13�/LR12�/LR11�/y1L�/REC�/x4L

where; RECL�/LR14�/LR13�/LR12�/LR11, and LDn

(LRn ) is level-n LF decomposition (reconstruction)

matrix as illustrated in [14,15]. Hence; y4L�/MAT4L�/

x0 where; MAT4L�/RECL�/DECL�/LR14�/LR13�/

LR12�/LR11�/LD4�/LD3�/LD2�/LD1.

4.2. Computation of level-4 HF components

4.2.1. Decomposition of level-4 HF components

The same analysis is followed as in the case of LF

decomposition procedure except that the fourth level

decomposition becomes: x4H�/HD4�/x3H, i.e. x4H�/

DECH�/x0 where; DECH�/HD4�/LD3�/LD2�/LD1.

4.2.2. Reconstruction of level-4 HF components

The same analysis is followed as in the case of LF

reconstruction procedure except that the first level re-

construction becomes; y1H�/HR11�/x4H instead of

y1L�/LR11�/x4L i.e. y4H�/LR14�/LR13�/LR12�/

HR11�/y1H�/RECH�/x4H where; RECH�/LR14�/

LR13�/LR12�/HR11. Hence y4H�/MAT4H�/x0 where;

MAT4H�/RECH�/DECH�/LR14�/LR13�/LR12�/

HR11�/HD4�/LD3�/LD2�/LD1. MAT4L,4H are 20�/

20 (8�/8) in case of 20(8) samples data window. The

values of the elements of the centre rows of these

matrices are:

1) For db8 function and 20 samples data window:

. MAT4L (10,:)�/[0.0302 0.0329 0.0354 0.03790.0402 0.0424 0.0444 0.0463 0.0479 0.0493

0.0503 0.0509 0.0512 0.0509 0.0501 0.0487

0.0468 0.0444 0.0414 0.0380].

Fig. 3. Low-frequency components of a typical voltage signal and

their power spectral densities (PSD) during LG fault on a TL

(sampling rate 1.0 kHz).

Fig. 4. Power system under consideration.

O.A.S. Youssef / Electric Power Systems Research 64 (2003) 165�/172 167

. MAT4H (10,:)�/[�/0.0287 �/0.0126 0.0050

0.0232 0.0405 0.0542 0.0627 0.0650 0.0614

0.0539 0.0442 0.0323 0.0192 0.0065 �/0.0047 �/

0.0133 �/0.0191 �/0.0241 �/0.0293 �/0.0338].2) For db4 function and eight samples data window:

. MAT3L (4,:)�/[0.0921 0.0894 0.0878 0.0875

0.0826 0.0746 0.0680 0.0622].

. MAT3H (4,:)�/[0.0057 �/0.0398 �/0.0681 �/

0.0768 �/0.0856 �/0.0864 �/0.0666 �/0.0258].

3) For sym4 function and eight samples data window:

. MAT3L (4,:)�/[0.1042 0.1432 0.1776 0.1756

0.1571 0.1362 0.1096 0.0789].. MAT3H (4,:)�/[�/0.0387 0.0465 0.1312 0.1078

0.0510 �/0.0283 �/0.1096 �/0.1025].

5. Feature extraction

Based on 1.0 kHz sampling rate, and eight samples

data window, fault classification is performed using the

features extracted from level-3 HF wavelet analysis (the

frequency band confined to this level is 62.5�/125 Hz)

according to the following rules:

1) AG Fault: is characterised by the numerical values

of the sum of HF-components of Ia,b,c�/o , i.e.

jHF3(Ia�/Ib�/Ic)j�/o . Also, jHF3(Ib�/Ic)j�/o , and

jHF3(Ib�/Ic)jB/o .

2) BC Fault: is characterised by:jHF3(Ia�/Ib�/Ic)jB/o ,jHF3(Ib�/Ic)jB/o , and jHF3(Ib�/Ic)j�/o .

3) BCG Fault: is characterised by jHF3(Ia�/Ib�/Ic)j�/

o , jHF3(Ib�/Ic)j �/o , and jHF3(Ib�/Ic)j�/o .

The classification technique flow chart is shown in

Fig. 5, with o�/0.001.It should be pointed out that

theoretically o should be zero but practically due to

mismatch of generators and transformers windings,

imperfection of TLs transposition, and after trying

different system configurations, a reasonable value foro 0.001 is selected.

6. Results of digital simulation

An extensive series of simulation studies have beenconducted using the EMTP/ATP software on the model

system described earlier. The proposed technique is

tested using simulated data obtained from the software.

The simulations provide samples of line currents

sampled at a rate of 1.0 kHz (20 samples per power

frequency cycle based on 50 Hz). Data from the

simulations are used as input to the algorithm to identify

its response. MATLAB has been used as the programmingsoftware. A total of 648 fault cases were simulated to

test the various features of the algorithm. The L�/G fault

for the three phases a, b, c (3 cases). The selected fault

inception angles were 90,180, 270 and 3608 from phase

(a) voltage zero-crossing (4 cases). The fault resistance

considered to simulate fault currents with the same

energisation angles were 0.001, 0.1 and 10.0 V (3 cases).

Fault locations were varied in steps of 20% of line length

(6 cases). Source capacities considered were 5.0, 15.0 and

30.0 GVA (3 cases). Three-level signal decomposition

and reconstruction process is followed to calculate level-

3 HF components of the three line currents based on

Fig. 5. Fault classification flow chart.


eight, and 20 samples data windows. The sum and

difference of level-3 HF components of every two-line

currents are calculated. Also, jHF3(Ia�/Ib�/Ic)j is calcu-

lated to determine whether there is a L�/L fault or a

ground fault. For L�/L faults (jHF3(Ia�/Ib�/Ic)jB/o ), the

faulty phases are identified by the six quantities

(jHF3(Ia9/Ib)j, jHF3(Ia9/Ic)j, and jHF3(Ib9/Ic)j as fol-

lows:

1) Phase�/ground faults are identified by jHF3(Ia�/

Ib)jB/o and HF3(Ia�/Ib)j�/o for CG fault, jHF3

(Ia�/Ic) jB/o and HF3(Ia�/Ic)j�/o for BG fault, and

jHF3(Ib�/Ic)jB/o and jHF3(Ib�/Ic)j�/o for AG

fault.

2) Phase�/phase�/ground faults are identified by

jHF3(Ia9/Ib)j�/o for ABG fault, jHF3 (Ia9/Ic) j�/

o for ACG fault, and jHF3(Ib9/Ic)j�/o for BCG

fault.

3) A phase�/phase fault is classified as BC fault if

jHF3(Ib�/Ic)jB/o and jHF3(Ib�/Ic)j�/o , and so on.

Tests carried out on the algorithm have been divided

into two main categories regarding data window width

and Wavelet functions:

1) Eight samples data window with db4 and sym4.

2) Twenty samples data window with db8 and sym8.

Sample results are described in the following section

1) AG fault: Figs. 6�/9 illustrate the signal features

extracted from AG fault at a distance 30 km. Fig. 7

illustrates the frequency spectrum of the three line

currents at different levels of Wavelet analysis. Fig.

8 shows the waveforms of LF and HF components

of line currents at different levels, while Fig. 9

displays the classification quantities, from which it

can be shown that: jHF3(Ia�/Ib�/Ic)j�/o , jHF3(Ib�/

Ic)j�/jHF3(Ia�/Ib)j and �/jHF3(Ia�/Ic)j, jHF3(Ib�/

Ic)jB/jHF3(Ia�/Ib)j and B/jHF3(Ia�/Ic)j2) BC fault: A similar set of figures to that shown in

case of AG fault is presented in Figs. 10�/13for a

typical BC fault at a distance 100 km from the local

end. In Fig. 13, the following relations: jHF3(Ia�/

Ib�/Ic)jB/o , jHF3(Ib�/Ic)jB/jHF3(Ia�/Ib)j and B/

jHF3(Ia�/Ic)j, and jHF3(Ib�/Ic)j�/jHF3(Ia�/Ib)jand �/jHF3(Ia�/Ic)j can be observed.

3) BCG fault: Figs. 14�/17 illustrate the features

extracted from a typical BCG fault at a distanceFig. 6. Voltage and current waveforms during an AG fault at 30 km

from local end, Rf�/0.1 V.

Fig. 7. Power spectral density (PSD) of Ia,b,c at different decomposi-

tion levels during the AG fault of Fig. 6.

Fig. 8. LF and HF components of Ia,b,c at different decomposition

levels during the AG fault of Fig. 6.

Fig. 9. The sum of HF components of Ia,b,c, and Ib,c, and the difference

of Ib,c at different decomposition levels during the AG fault of Fig. 6.


40. In Fig. 17, the relations: jHF3(Ia�/Ib�/Ic)j�/o ,

jHF3(Ib�/Ic)j�/jHF3(Ia�/Ib)j and �/jHF3(Ia�/Ic)j,and jHF3(Ib�/Ic)j�/jHF3(Ia�/Ib)j and �/jHF3(Ia�/

Ic)j are satisfied.

7. Effect of sampling rate and data window width

The effect of sampling rate and data window width on

the computation of level-3 HF components of line

current using limited data window as compared with

the case when using large data window and for different

wavelet functions is illustrated in Fig. 18. Noting that

the following abbreviation stands for: sampling rate

kHz/data window in samples/Wavelet function.

Fig. 10. Voltage and current waveforms during an BC fault at 60 km

from local end, Rf�/1 V.

Fig. 11. PSD of Ia,b,c at different decomposition levels during the BC

fault of Fig. 10.


levels during the BC fault of Fig. 10.

Fig. 13. The sum of HF components of Ia,b,c, and Ib,c, and the

difference of Ib,c at different decomposition levels during the BC fault

of Fig. 10.

Fig. 14. Voltage and current waveforms during an BCG fault at 40 km

from local end, Rf�/0.1 V.

Fig. 15. PSD of Ia,b,c at different decomposition levels during BCG

fault.


S2W20db4 2 kHz/20 samples/db4

S4W8db4 4 kHz/8 samples/db4

S8W8db4 8 kHz//8 samples/db4

S8W20db8 8 kHz//20 samples/db8

It can be observed that using high sampling rate

together with comparatively large data window

(S8W20db8) leads to better results than using low

sampling rate together with comparatively large data

window (S2W20db4).

8. Effect of wavelet function

In Fig. 19, Symlet wavelet functions (sym4,8) have

been selected and the results were compared with those

obtained in Fig. 18. It has been found that selecting

sym8(sym4) function instead of db8(db4) has no effect

of the computation of the computation.

9. Conclusion

This paper presents a proposed modified Wavelet-

based fault classification technique. The main features

of the new technique is its utilisation of the higher

frequency components (62.5�/125 Hz based on 1.0 kHz

sampling rated) present in the three line currents for

fault classification process using small data window. Thetechnique was successfully tested with data obtained

through computer simulations with eight and 20 samples

data. This proposed technique can actually be imple-

mented in real time.

References

[1] O.A.S. Youssef, ‘Fault classification based on wavelet trans-

forms’, paper#01TD069, IEEE, T&D Conference, 28 October�/2

November, 2001, Atlanta, GA.

[2] W.D. Breingan, M.M. Chen, T.F. Gallen, Laboratory investiga-

tion for a digital system for the protection of transmission lines,

IEEE Transactions on Power Apparatus and Systems PAS 98 (2)

(1979) 350�/368.

[3] M.M. Elkateb, W.J. Cheetham, ‘A new approach to high speed

selection’, Second International Conference on Developments in

Power-System Protection, June 1980, London, pp. 350�/368.

[4] A.G. Phadke, M. Ibrahim, T. Hlibka, Fundamental basis for

distance relaying with symmetrical components, IEEE Transac-


levels during the BCG fault of Fig. 14.

Fig. 17. The sum of HF components of Ia,b,c, and Ib,c, and the

difference of Ib,c at different decomposition levels during the BCG

fault of Fig. 15.

Fig. 18. Voltage signal and its level-3 LF components (cases:

S2W20db8, S8W8db4, S4W8db4, S8W20db8).

Fig. 19. Voltage signal and its level-3 LF components (cases:

S2W20sym8, S8W8sym4, S4W8sym4, S8W20sym8).


tions on Power Apparatus and Systems PAS 96 (2) (1977) 635�/

646.

[5] A.A. Girgis, R.G. Brown, Application of kalman filtering in

computer relaying, IEEE Transactions on Power Apparatus and

Systems PAS 100 (7) (1981) 3387�/3397.

[6] A.A. Girgis, R.G. Brown, Application of kalman filtering in

computer relaying, IEEE Transactions on Power Apparatus and

Systems PAS 100 (7) (1981) 3387�/3397.

[7] A.A. Girgis, R.G. Brown, Adaptive kalman filtering in computer

relaying: fault classification using voltage models, IEEE Transac-

tions on Power Apparatus and Systems PAS 104 (5) (1985) 1168�/

1177.

[8] T. Sakaguchi, A statistical decision theoretical approach to digital

relaying, IEEE Transactions on Power Apparatus and Systems

PAS 99 (5) (1980) 1918�/1926.

[9] T. Dalstein, B. Kulicke, Neural network approach to fault

classification for high speed protective relaying, IEEE Transac-

tions on Power Delivery 10 (2) (1995) 1002�/1011.

[10] D.C. Robertson, I.C. Octavia, J.S. Mayer, W.B. Gish, Wavelets

and electromagnetic power system transients, IEEE Transactions

on Power Delivery 11 (2) (1996) 1050�/1058.

[11] S. Santoso, E.J. Powers, W.M. Grady, P. Hofmann, Power

quality assessment via wavelet transform analysis, IEEE Transac-

tions on Power Delivery 11 (2) (1996) 924�/930.

[12] S. Santoso, E.J. Powers, W.M. Grady, Power quality disturbance

data compression using wavelet transform methods, IEEE

Transactions on Power Delivery 12 (3) (1997) 1250�/1257.

[13] W.A. Wilkinson, M.D. Cox, Discrete wavelet analysis of power

systems transients, IEEE Transactions on Power Systems 11 (4)

(1996) 2038�/2044.

[14] O.A.S. Youssef, ‘New Algorithm to Phase Selection Based on

Wavelet Transforms’, paper#2001TR446, IEEE Transactions on

Power Delivery, February (2002) in press.

[15] O.A.S. Youssef, ‘A wavelet-based technique for discrimination

between faults and magnetising inrush currents in transformers’,

paper#TPWRD-00027-2002, IEEE Transactions on Power De-

livery (2002) in press.

[16] S. Mallat, A theory for multi-resolution signal decomposition: the

wavelet representation’, IEEE Pattern Analysis and Machine

Intelligence 11 (7) (1989) 674�/693.

[17] I. Daubechies, S. Mallat, A.S. Willsky (Eds.), IEEE Transactions

of Information Theory, Special Issue on Wavelet Transforms on

Multi-resolution Signal Analysis, vol. 38, No. 2, March 1992.

[18] D.M. Dummy, in: Y. Meyer (Ed.), Wavelets and Applications,

Springer, New York, 1992.

[19] Electromagnetic Transient Program (EMTP) Rule Book, EPRI EL

6421-1, vol. 1 and 2, June 1989.

Biographies

Omar Youssef (M’92) was born in Cairo, Egypt in

1945. He received the B.Sc., M.Sc., and Ph.D. in

Electrical Engineering from University of Cairo, Faculty

of Engineering in 1966, 1976, and 1979, respectively.

From 1966 he has undertaken lecturing or consulting

assignments in Libya, Nigeria, Saudi Arabia, Iraq,

Qatar. On 1999 he has been invited as a Visiting

Research Fellow at University of Bath, UK. He iscurrently the Deputy Dean to Graduate Studies and

Research, Faculty of Industrial Education, University of

Suez Canal, Suez, Egypt.


a modified wavelet-based fault classification technique

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