Wavelet Transform Approach to DistanceProtection of Transmission Lines

A. H. Osman, Student Member, IEEE O. P. Malik, Fellow, IEEE

Dept. of Electrical and Computer EngmeermgUniversity of Calgary, T2N 1N4, Canada

Abstract: An apphcatlon of wavelet transform to digital distanceprotection for transmission hnes is presented in this paper. Faultsimulation is earned out using the Power System Computer AidedDesign program (PSCAD). The simulation results are used as aninput to the proposed wavelet transform protection-relayingtechnique. The technique N based on decomposing the voltage andcurrent signats at the relay location using Wavelet Filter Banks(WFB). From the decomposed signals, faults can be detected andclassified. Also the fundamental voltage and current phasors,which are needed to calculate the impedance to the fault point canbe estimated. Results demonstrate that wavelets have highpotentiat m distance relaying.

Keywords: Distance Protection Relaying,Wavelets.

1.INTRODUCTION

Power Systems,

Great attention has been paid to distance relayingtechniques for the protection of transmission lines. Themain target of these techniques is to calculate theimpedance at the fundamental frequency between the relayand the fault point. According to the calculated impedance,the fault is identified as internal or external to the protectionzone. This impedance is calculated from the measuredvoltage and current signals at the relay location. In additionto the fundamental frequency, the signals are usuallycontain some harmonics and DC component, which affectthe accuracy of the phasors estimation [1].

Recently, distance relays have experienced muchimprovement due to the adoption of digital relaying, Signalprocessing is one of the most important parts of theoperation of the digital distance protection. Until recently,Fourier analysis and Kalman filtering methods were themam tools in signal processing for distance relaying [2].The trip/no trip decision has been improved compared tothe electromechanical or solid-state relays. However, thereach accuracy of these methods 1s affected by the differentfault conditions particularly in the presence of highfrequency and DC offset in the signals.

Wavelet transform as an alternative solution to themetmoned approaches for distance relaying of transmissionlines is introduced in this paper. Wavelets are a recentlydeveloped mathematical tool for signal processing.

Compared to Fourier analysis, which relies on a single basisfunction, wavelet analysis uses basis functions of a ratherwide functional form. The basic concept in wavelettransform is to select an appropriate wavelet function“mother wavelet” and then perform analysis using shiftedand dilated versions of this wavelet. Wavelet can be chosenwith very desirable frequency and time characteristics ascompared to Fourier techniques. The basic difference isthat, in contrast to the short time Fourier transform whichuses a single analysis window, the wavelet transform usesshort windows at high frequencies and long windows at lowfrequencies. The basic functions in wavelet transformemploy time compression or dilation rather than a variationin time frequency of the modulated signal [3],

This work describes tbe application of wavelettransform in detecting and classifying faults as well asextracting the voltage and current fundamental phasorsneeded to calculate the impedance to the fault point.

Il. WAVELET TRANSFORM

Wavelet transform was introduced at the beginning ofthe 1980s and has attracted much interest in the fields ofspeech and image processing since then, Its potential

applications tO POWer industry have been discussed recently[4 – 7]. A brief introduction to the wavelet transform isgiven here, more details can be found in [8, 9].

There are two fundamental equations upon which

wavelet calculations are based; the scaling function, tit)

and the wavelet function Y(t):

q(t) =N5 ;hk 47(2t -k) (1)

!4) =fi pkd2t - k) (2)

The functions are two-scale difference equations based on achosen scaling function tp, with properties that satisfycertain admission criteria and discrete sequence:h, and gk = (-I)* h,.Lrepresenting discrete filters that solve

each equation. The scaling and wavelet functions are theprototype of a class of orthonormal basis functions of theform:

0-7803-7031-7/01/$10.00 (C) 2001 IEEE

0-7803-7173-9/01/$10.00 © 2001 IEEE 115

(~J,k(f)= 2j/2 )p2Jt–k, j,kcz

yj,k(t) = 2J’2 ( )y2~t –k, j,kez

(3)

(4)

where the parameter j controls the dilation or compressionof the function in time scale and amplitude. The parameterk controls the translation of the function in time. z is the setof integers.

Wavelet system may or may not have compact support.Compact support means that the wavelet system has finitenumber of nonzero coefficients. A wavelet system withcompact support allows wavelets to localize in both timeand frequency, so only is dealt with here. Severaltechniques have been used in the literature to create waveletsystems, These include cubic splines, complexexponentials, and parameter-space constructions. Once awavelet system is created, it can be used to expand afunction f(t)in terms of the basis functions:

where the coefficients c(l), and d(j, k) are calculated byinner product as:

(6)

(7)

If the wavelet system has compact support and an upperlimit is placed upon the degree of dilation j, then theexpansion equation becomes:

(8)

The expansion coefficients c(l) represent the approximationof the original signal ~(t) with a resolution of one point perevery 2J points of the original signal. The expansioncoefficients d(j, k) represent details of the original signal atdifferent levels of resolution. These coefficients completelyand uniquely describe the original signal and can be used ina way similar to the Fourier transform. The wavelettransform then is the process of determining the values ofc(1) and d(j,k) for a given f(t)and wavelet system. Theexpansion equation naturally leads to a recursive algorithmfor the wavelet transform, given certain assumptions. First,the function f(t)is taken as a sequence of discrete pointssampled at 2’ points per unit interval. These points can be

viewed as the inner product of @and ~(t). That is, the samplepoints are approximation, or c(l) coefficients, of thecontinuous function ~(t). This allows c(l) and d(j, k) terms tobe calculated by direct convolution of ~(t) samples with thecoefficients h~and g~.

It was discovered in [10] the wavelet transform can beimplemented with a specially designed pair of FiniteImpulse Response (FIR) filters called a “Quadrature MirrorFilters” (QMF) pair. QMFs are distinctive because thefrequency responses of the two FIR filters separate the highfrequency and low frequency components of the inputsignal. The dividing point is usually halfway between O Hzand half the data sampling rate (the Nyquist frequency).The outputs of the QMF filter pair are decimated (ordesampled) by a factor of two; that is, every other outputsample of the filter is kept, and the others are discarded. Thelow-frequency (low-pass) filter output is fed into anotheridentical QMF filter pair. This operation can be repeatedrecursively as a tree or pyramid algorithm, yielding a groupof signals that divides the spectrum of the original signalinto octave bands with successively coarser measurementsin time as the width of each spectral band narrows anddecreases in frequency.

The tree or pyramid algorithm can be applied to thewavelet transform by using the wavelet coefficients as thefilter coefficients of the QMF filter pairs as shown in [11].The same wavelet coefficients are used in both low-pass andhigh-pass (actually, band-pass) filters. The low-pass filtercoefficients are associated with the h~ of the scaling function#t). The output of each low-pass filter is the c(l), orapproximation components, of the original signal for thatlevel of the tree. The high-pass filter is associated with the

g~ of the wavelet function Y(t).The output of each high-pass filter is the d(j,k), or detail components, of the originalsignal at resolution 2J. The c(l) of the previous level are usedto generate the new c(l) and d(j, k) for the next level of thetree. Decimation by two corresponds to themultiresolutional nature of the scaling and waveletfunctions. The reverse wavelet transform essentiallyperforms the operations associated with the forward wavelettransform in the opposite direction [12].

In wavelets applications, different basis functions havebeen proposed and selected. Each basis function has itsfeasibility depending on the application requirements. In theproposed scheme, the Daubechies-4 (db4) wavelet [10]served as the wavelet basis function for the detection andclassification of faults as well as for the estimation of thevoltage and current phasors. The db4 FIR filter coefficientsare given in Table 1.

Table 1. db4 FIR filter coefficients

k h, ~o -0.0106 -0.2k304

1 0.0329 0.71482 0.0308 -0.6309

3 -0.1870 -0.0280

4 -0.0280 0.1870

5 0.6309 0.03086 0.7148 -0.03297 0.2304 -0.0106

0-7803-7031-7/01/$10.00 (C) 2001 IEEE

0-7803-7173-9/01/$10.00 © 2001 IEEE 116

Ill. PROPOSED WAVELETS DISTANCE

PROTECTION ALGORITHM

In order to investigate the applicability of the proposedwavelet transform distance protection algorithm, a

simulation of transmission line model for different faultlocations and different loading conditions is done. Faultsimulations were carried out using PSCAD. The simulatedpower network is shown in Fig.1. The network consists oftwo areas connected by a transmission line. Thetransmission line was modeled as a distributed parametersline, representing a 225km long 240kV ideally transposed

transmission line with impedance, ZL=(4.15 + J84.66)f2.The three phase voltage and current signals at the relaylocation, which is at bus “A’, are sampled at 960Hz (16samples/fundamental power cycle). These six signals arethen filtered using a pre-band-pass filter with cut-offfrequency 80Hz to attenuate the dc component. The output-filtered signals are the input to the proposed waveletdistance protection algorithm.

G1 A T. Line B G2Zh

240kV, 225km

Sources X/R=60

Fig. 1 Transmission line model system

The proposed technique is divided into two sections:

1) The first section is the detection of the fault byobserving the output of the high-pass filter (details) of thefirst decomposition level. This decomposition level has theability to detect any disturbances in the original signalwaveform. Fig. 2 shows an example for an original currentwaveform during a fault and the output of the high-passfilter (D 1) of the first decomposition level. It is clear that thefault moment has been detected easily by thisdecomposition. By passing all three phase currents andvoltages at the relay location through the wavelet firstdecomposition level, it is possible to detect and classify thefaulty phase(s). The data window length till the moment offaul~ detection is half a cycle (8 samples).

Oriaina!current smal

01Detail (Dl)

*Eog

-010 20 40 60 80 100 120 140 160 180

Fig.2 Original current waveform and D1 during a fault

2) The second section of the algorithm is the estimationof the fundamental frequency voltage and current phasors. Itcan be done by observing the output of the low-pass filter atthe second decomposition level, Theoretically, Thefrequency band of the fundamental frequency should beobtained from the fourth level of decomposition, and thisrequires a very long data window, which is not possible tobe applied on line. The second level of decomposition givesa very good approximation for the phasors. At this level thehigh frequencies in the signal are eliminated by the high-pass filters of the first and second decomposition levels andthe DC component has already been eliminated by pre-band-pass filtering the signal. The data window length forestimating the phasors before the fault is half a cycle (8samples). However, at the moment of fault detection, thelast half cycle data window is kept and it starts to increaseby one new sample until it reaches a full cycle (16 samples)and then it continues with this window length. This isequivalent to an adaptive data window, and gives theadvantage of fast clearance to the near faults, while thefaults at the end of the line need about% to one full cycle tobe classified. The estimation of the phasors is based oncapturing the peak of each signal (magnitude), and locatingits position from the beginning of the data window (phase).For each new sample, the impedances for ground and phasefaults that are seen by the relay at “A” are calculated usingthe well-known equations:i- For phase to ground faults

vz phase = ~

phase(9)

Pha.w(l)+ Iphaw(x + K(o) Zpha,, (o)

, K(o)=ZL(o)/zL(l)

where Vp,,,,,,,is the estimated phase voltage phasor, 1,,.,,(1),1,,,,,,,,(2),1,,.,.(0), are the positive, negative, and zero sequenceestimated phase currents respectively, and K(O) is the ratiobetween the zero sequence to the positive sequenceimpedance of the protected transmission line.

ii- For phase faults (example: phase “a” to phase “b”fault)

where V,,, and V~are the estimated voltage phasors, l., and Ibare the estimated current phasors.

IV. SIMULATION RESULTS

The described wavelet transform approach to distanceprotection for transmission lines is applied for the model ofFig, 1, The performed tests include different fault types,different fault locations, and different loading conditions,

0-7803-7031-7/01/$10.00 (C) 2001 IEEE0-7803-7173-9/01/$10.00 © 2001 IEEE 117

1) The first set of tests is carried out with a power angle

of 1(Ydegrees between the two sources, and fault resistance

Rf=O, for different fault locations.Fig.3 shows the impedance calculated at the relay locationfor a single line to ground fault at 50km from the relaylocation. Fig.4 shows the impedance fault trajectory for thisfault, from which one can recognize how fast the faulttrajectory entered the tripping area, It took about 3ms toclassify the fault as an internal fault. Fig. 5 shows theimpedance calculated at the relay location for a double lineto ground fault at 100km, and Fig.6 shows its impedancefault trajectory. It took about 7ms to classify the fault as aninternal fault. Fig.7 shows the impedance calculated at therelay location for a single line to ground fault at 150kmfrom the relay location, and Fig.8 shows its impedance faulttrajectory. It took about 12ms to classify the fault as aninternal fault. This also clarifies the idea of using longerdata window in order to classify the far fault locations.

2) The second set of tests is carried out with a power

angle of 20 between sources, and fault resistance Rf=O, for

different fault locations.Fig. 9 shows the calculated impedance at the relay locationfor a single line to ground fault at the beginning of the linenear bus “A”, and Fig. 10 shows its impedance faulttrajectory. The trajectory entered the tripping zoneimmediately after the fault. Fig. 11 shows the calculatedfault impedance at the relay location for a double line toground fwlt at 50km from the beginning of the line, andFig. 12 shows its fault impedance trajectory. The trajectoryentered the tripping zone after 3ms. Fig. 13 shows thecalculated impedance at the relay location for a phase-to-phase fault at 100km, and Fig. 14 shows its fault impedancetrajectory. The trajectory entered the tripling zone after 8ms.

The results show that wavelet transform enabled thedetection of faults, and estimation of the phasors at the relaylocation. The wavelet distance relay successfully classifiedevery type of fault at any distance.

o0 10 20 30 40 50 60

Tme Samples

Fig,3 Single line to ground fault (A-G) at 50km

Fault trajectory for SLG (A-G) at 50km

R (ohm)

Fig.4 Fault trajectory for single line to ground fault (A-G) at 50km

Double line to around fault 1A-C-G) at 100km. Rf=O

Tme Samples

Flg5 Double Line to ground fault (A-C-G) at 10Okm

R (ohm)

F]g.6 Fault trajectory for double line to ground fault (A-C-G) at 100km

0-7803-7031-7/01/$10.00 (C) 2001 IEEE0-7803-7173-9/01/$10.00 © 2001 IEEE 118

Tme Samples-:20 0 20 40 60 80 100 120 140

R (ohm)

Fig.7 Single line to ground fault (A-G) at 150km Fig. 10 Fault trajectory for single line to ground fault (A-G) at the

beginning of the line

R (ohm) Tme Samples

Fig.8 Fauk trajectory for single line to ground fault (A-G) at 150km Fig. 11 Double Line to ground fault (A-B-G) at 50km

SLG fault (A-G) at the beginning of the line, Fif=O

Tme Samples

Fault trajectow for DLG (A-B-G) at 50km, Rf=O ‘\

j. . . ..II-20 I :

,.: !I

-20 0 20 40 60 80 100 120 140R (ohm)

Fig.9 Single line to ground fault (A-G) at the beginning of the line Fig. 12 Fault trajectory for double line to ground fault (A-B-G) at 50km

0-7803-7031-7/01/$10.00 (C) 2001 IEEE

0-7803-7173-9/01/$10.00 © 2001 IEEE 119

Double line fault (B-C) at 10Okm, Rf=O2500

! ! !! ! ~ -I

o0 10 20 30 40 50 60

Tme Samples

Fig. 13 Double Ltne fault (B-C) at 100km

Fault trajectory for DL,!sak’’@-C) at 100km, Rf=O140, , , ,., . ...’. , I!— 1

‘:20 0 20 40 60 80 100 120 140

R (ohm)

Fig. 14 Fault trajectory for double hne fault (B-C) atl 00km

V. CONCLUSIONS

Use of the wavelet transform in distance protectionrelaying of transmission lines is introduced in this paper.The ability of wavelets to decompose the signal intofrequency bands (multi-resolution) in both time andfrequency allows accurate fault detection as well asestimation of the signal phasor at the fundamentalfrequency. The results show that the proposed techniqueused to introduce wavelets in distance protection isapplicable and encouraging. Various types of faults on thetransmission line can be classified accurately within onecycle according to the fault location. Further studies are inprogress in testing the relay for high resistive ground faultsand line energization.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

V1. REFERENCES

D. V. Coury, and D. C. Jorge “Artificial neural network approach todistance protection of transmission lines”, fEEE Trans. PowerDelivery, Vol. 13, No. 1, January 1998, pp. 102-108.

A, A. Girgis, and R. G. Brown, “Application of Kalman filtering incomputer relaying”, fEEE Trans. on Power Apparatus and Systems,PAS-1 OO(7), July 1981, pp.3387-95,

L L hi , E Styvaktakis, and A, G, Sichanie “ Wavelet transform forhigh impedance fault identification”, Proceeding of the 4“’tntemational conference on advances in power system control,operation and management” Hong Kong, November 1997, pp. 188-191.

D. Wai, and X. Yibin, “A novel technique for high impedance faultidentification”, tEEE Trans. on Power Delivery, Vol. 13, No, 3, July1998, pp. 738-744.

S. Santoso, E. J. Powers, W. M. Grady, and P. Hofmann, “Powerquality assessment via wavelet transform analysis”, fEEE Trans. onPower Delivery, Vol. 11, No. 2, April 1996, pp. 924-930,

D, C, Robertson, 0, I. Camps, J. S. Mayer, and W. B, Gish, “WaveIetand electromagnetic powers ystem transients”, IEEE Trans, on PowerDelivery, Vol. 11, No. 2, April 1996, pp. 1050-1056,

0. Chaari, M. Meunier, and F. Brouaye, “Wavelets: A new tool for

the resonant grounded power distribution systems relaying”, tEEETrans. on Power Delivery, Vol. 11, No. 3, July 1996, pp. 1301-1308,

G. Strang, and T. Nguyen, “Wavelet and filter banks”, Wellesleg-Cambridge Press, 1997.

C. Sidney Burros, and R. A. Gopinath, “Introduction to wavelets andwavelet transforms a primer” , Prentice Hall, 1988,

[10] I. Daubechies, “Ten lectures on wavelets”, Capital City Press, 1992.

[11 ] S. G. Mallat, “A theory for multiresolution signal decomposition: thewavelet representation”, tEEE Trans. on Pattern Analysis andMachine intelligence” Vol. 11, No. 7, July 1989, pp. 674-693,

[12] Mac. A. Cody, “The fast wavelet transform”, Dr. Dobb’s Journal,April 1992.

VI1.BIOGRAPHY

A. H. Osman(SM’01) received his B. SC. and M. SC. inelectrical engineering from Helwan University, Cairo,Egypt in 1991 and 1996 respectively. Currently, he isworking towards a Ph.D. degree at the University ofCalgary, Canada, His areas of interest include powersystem engineering, digital protection relaying, andpower electronics,

O. P. Malik (M’66-SM’69-F87) graduated inelectrical engineering from Delhi Polytechnic, In&la,in 1952, and obtained the M.E. degree in electricalmachine design from the University of Roorkee, India,in 1962. Ju 1965 hereceived the Ph,D. degree from theUniversity of London, England, and D.I.C. from theJmperial College of Science smd Technology, London,or at the University of Calgacy in 1974 and is a faculty

professor emeritus. He is a Fellow of the Institution of Electrical Engineers(London), and a registered professor Engineer in the provinces of Albertaand Ontario, Canada.

0-7803-7031-7/01/$10.00 (C) 2001 IEEE

0-7803-7173-9/01/$10.00 © 2001 IEEE 120