Detection, Localization, And Classification of Power Quality Using Discrete Wavelet Transform

8/12/2019 Detection, Localization, And Classification of Power Quality Using Discrete Wavelet Transform

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Alexandria Engineering Journal

Alexandria Engineering Journal, Vol. 42 (2003), No. 1, 17-23 17 Faculty of Engineering, Alexandria University, Egypt

Detection, localization, and classification of power qualitydisturbances using discrete wavelet transform technique

Mahmoud El-Gammal, Amr Abou-Ghazala and Tarek El-ShennawyElectrical Eng. Dept., Alexandria University, Alexandria, Egypt

Modern spectral and harmonic analysis is based on Fourier based transforms. However,these techniques are less efficient in tracking the signal dynamics for transientdisturbances. Consequently, The wavelet transform has been introduced as an adaptabletechnique for non-stationary signal analysis. Although the application of wavelets in thearea of power engineering is still relatively new, it is evolving very rapidly. The applicationof the wavelet transform in detection, time localization, and classification of power qualitydisturbances is investigated and a new identification procedure is presented. Differentpower quality disturbances will be classified by a unique energy distribution patternbased on the difference of the discrete wavelet coefficients of the analyzed signal and apure sine wave. Verification of the proposed algorithm was done by simulating differentdisturbances and analyzing the results.

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Keywords: Wavelet transform, Non-stationary signals, Power quality, Disturbanceidentification

1. Introduction

Power Quality is an issue of increasingconcern both to the utilities and theircustomers. A power quality problem can bedescribed as any variation in the electricalpower service, such as voltage sags andswells, interruptions, transients, harmonics,notches, and fluctuations, resulting in miss-operation or failure of end-use equipment. Toanalyze these electric power system distur-bances, data is often available as a form of asampled time function that is represented by a

time series of amplitudes. When dealing withsuch data, the Discrete Fourier Transform(DFT) based approach is most often used. Theimplementation of the DFT by variousalgorithms has been constructed as the basisof modern spectral and harmonic analysis.

The DFT yields frequency coefficients of asignal, which represents the projection oforthogonal sine and cosine basic functions.Such transforms have been successfully

applied to stationary signals where the proper-ties of the signals do not vary with time.However, for non-stationary signals, anyabrupt change may spread all over thefrequency axis. Consequently, the Short TimeFourier Transform (STFT) uses a (time-frequency) window to localize -in time- sharptransitions is used for non stationary signals.However, the STFT uses a fixed time-frequency window, which is inadequate for thepractical power system disturbances encoun-tering a wide range of frequencies. Under thissituation, the Fourier techniques are less

efficient in tracking the signal dynamics. Therefore, an analysis adaptable to non-stationary signals is required instead ofFourier-based methods.

The Wavelet Transform (WT) technique,recently proposed in the literature as a newtool for monitoring power quality problems [1],has received considerable interests in fieldssuch as signal processing, voice commun-ications, and image compression [2,3]. The WT


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18 Alexandria Engineering Journal, Vol. 42, No. 1, January 2003

is well suited to wide-band signals that maynot be periodic and may contain bothsinusoidal and non sinusoidal components.

This is due to the ability of wavelets to focuson short time intervals for high frequencycomponents and long time intervals for lowfrequency components.

This paper introduces an approach thatutilizes the wavelet multi-resolution signaldecomposition in the detection, localization,and classification of power quality distur-bances. Programs to simulate disturbancessuch as short duration voltage variations; in-cluding sags, swells, and interruptions, harm-onics in a power system, notches, andcapacitive switching transients are allformulated in MATLAB code according to IEEE

standards [4]. Detection and Localization areperformed in the wavelet domain rather thanthe time domain or the frequency domain.Different power quality disturbances will beclassified by a unique energy distributionpattern according to Parsevals theorem ratherthan constructing time-frequency picture ofthe distorted signal and comparing the energydistribution of the distortion at differentfrequency bands and at certain time [5].

2. The proposed algorithm

The wavelet analysis procedure adopts awavelet prototype function, the analyzingwavelet or the mother wavelet. Temporalanalysis is performed by shifting a contracted,high-frequency versions of the mother wavelet,while frequency analysis is performed withdilated, low-frequency versions of the samewavelet. Any signal can be represented interms of a wavelet expansion or series (similarto Fourier series) using coefficients in a linearcombination of the wavelet functions atdifferent scales. The selection of the motherwavelet is not a trivial issue. Different motherwavelets exist with various characteristics.Success of a given wavelet basis in aparticular application does not mean that thisset is efficient for other applications [6].

Let (t) represents the mother wavelet as afunction of time, then the daughter waveletsare generated from the mother wavelet bymeans of scaling and translation as shown ineq. (1):

0).(s ),s

t (

s

1(t) s, >

= (1)

Where S is the scaling parameter, used to

perform stretching and compression opera-tions on the mother wavelet, and is thetranslation parameter, used to obtain the timeinformation of the signal to be analyzed. Inthis way, a family of scaled and translatedwavelets is created and serves as the base, thebuilding blocks, for representing the signal [7].

The Continuous Wavelet Transform (CWT) fora signal X(t ) is defined as follows:

dt ) s

t ( * .x(t)

s

1) CWT(s,

=

+

. (2)

It is noted that the CWT must be defined interms of the mother wavelet. That is, one doesnot merely discuss the wavelet transform of afunction, one must discuss the wavelettransform of a function with respect to aparticular mother wavelet. Let x(t) be thesignal to be analyzed. Once the motherwavelet is chosen, the computation starts withs =1 and the continuous wavelet transform iscomputed for all values of s. For convenience,the procedure will start from scale s=1 andwill continue for the increasing values of s,i.e., the analysis will start from high frequen-cies and proceeds towards low frequencies.

This first value of s corresponds to the mostcompressed wavelet. It should be as narrow asthe highest frequency component that existsin the signal. As the value of s increases, thewavelet dilates. As a result, for every scale andfor every time interval, one point of thetranslation-scale plane is computed. Thecomputations at one scale construct the rowsof the translation-scale plane, and the compu-tations at different scales construct the

columns of the translation-scale plane.It is necessary to discretize the CWT fordigital computational purposes. The main ideaof the discrete wavelet transform DWT is asfollows: A time-scale representation of a digitalsignal is obtained using digital filteringtechniques. Filters of different cutoff frequen-cies are used to analyze the signal at differentscales. The decomposition of the signal intodifferent frequency bands is simply obtained


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Alexandria Engineering Journal, Vol. 42, No. 1, January 2003 19

by successive high pass and low pass filteringof the time domain signal. After the filtering,half of the samples can be eliminated bysubsampling [8]. This constitutes one level ofdecomposition. This decomposition halves thetime resolution since only half the number ofsamples now characterizes the entire signal.However, this operation doubles the frequencyresolution, since the frequency band of thesignal now spans only half the previousfrequency band, effectively reducing theuncertainty in the frequency by half.

The DWT of the original signal is obtainedby concatenating all coefficients starting fromthe last level of decomposition. Fig. 1illustrates this procedure with three decom-position levels [9]. Any change in the

smoothness of the signal can be detected andlocalized at the finer resolution levels. As faras detection and localization are concerned,the first finer decomposition levels of thedistorted signal are normally adequate todetect and localize this disturbance.

However, the other coarser resolutionlevels are used to extract more features thatcan help in the classification process.

The proposed classification process de-pends on Parseval's theorem , which statesthat: "The energy that a time domain signalcontains is equal to the sum of all energies

concentrated in the different resolution levelsof the corresponding wavelet transformedsignal". This can be mathematically formu-lated as follows:

.N

1k

N

1k

J

1i

N

1k

2 ) k ( i d

2 ) k ( J a

2 ) k ( f =

=

=

=

+=

(3)

The left-hand side of eq. (3) expresses thetotal energy of the discrete time domain signal

f, N is the number of samples. The right-handside of the equation consists of two parts; theenergy concentrated in the level J of theapproximated version of the signal (a) + Theenergy concentrated in the detailed versions ofthe signal d , from level 1, to level J .

The proposed classification method is doneusing unique patterns. The difference be-tween the discrete wavelet coefficients of theanalyzed signal and a pure signal at each levelwill be computed, and the result will bedivided by the total energy of the correspond-ing pure signal for normalization purposes,and then multiplied by 100 to have apercentage ratio as shown in eq. (4):

100 * energy total

) pure ( energy ) i ( energy ) i ( dif %

= . (4)

Where i is the wavelet transform level. Theunique pattern is then plotted with thepercentage difference as the y-axis, and theresolution level as the x-axis. The energy ofthe distorted signal will be partitioned atdifferent resolution levels in different waysdepending on the power quality problem athand; hence, each power quality problem is

characterized by a unique energy distributionplot.

3. Applications

Detection, localization and identification ofdisturbances are done by simulating,according to IEEE standards [4], differentdisturbance signals and analyze these signalsusing MATLAB graphic user interface toolbox

Fig. 1. Multiple decomposition of wavelet analysis.


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(for detection and localization) using Daub4mother wavelet and 12 resolution levels [6].Identification is done using our proposedmethod formulated as a MATLAB code. 18different disturbances were simulatedincluding voltage sags at different durationsand magnitudes, i.e, 4 cycles, 50%, capacitorswitching at 1000 Hz, notches, voltage swellsat different durations and magnitudes,harmonic contents, and a combination of theabove [10]. Three cases (sag at 4 cycles, 50%,swell at 6 cycles, 120% and capacitorswitching at 1000 Hz) are shown in figs. 2, 3and 4.In all the studied cases, the maximum energydistribution occurs at the tenth level ofresolution, which corresponds to around 50

Hz. This is determined by the number ofsamples representing the signal. The firstresolution levels of decompositions of figs 2-a,3-a, 4-a hardly show any non-zero coefficientsdue to absence of frequency components atthese high frequencies. Higher resolutionlevels, corresponding to lower frequencies,start to pick up the disturbance. Figs. 2-a, 3-ashow the start and the end of a transientphenomenon. This could be attributed to ashort duration disturbance; sag, swell, or aninterruption. However, we still need furtherinformation for precise identification. Fig. 4-a

shows the start of a transient phenomenonthat decays gradually with time. This may givesense to some sort of discharging or decayingtransient, involving capacitor energization.Figs. 2-b, 3-b show the standard energydistribution among various decompositionlevels of the detailed versions of test signal.

The decomposition starts with the highestfrequency tending to capture any transientvariation or discontinuity of the signal, as westep up with the resolution levels, the waveletstretches trying to pick up lower frequencies.

The bulk energy is concentrated in the 7 th through the 11 th levels. After this level, thewavelet dilates more and more to search forany sub-power frequencies, which obviouslydo not exist. Referring to figs 2-b, 3-b, thepercentage energy deviation from a pure sinewave, in case of sag or swell, is proportional tothe magnitude and the duration of the sag orswell respectively. This suggests anidentification patterns for these disturbances.

For fig. 4-b, we have a peak at the fifthresolution level (corresponding to 1000 Hz),identification of the frequency can be used tolocate the switching source.

Fig. 2-a. Wavelet analysis of the sagged wave, 4 cycles,50%.

Fig. 2-b. Energy distribution among various resolutionlevels compared with pure sinewave (upper plot).

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i t

Scale


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Fig. 3-a. Wavelet analysis of the swelled wave, 6 cycles,120%.

Fig. 3-b. Energy distribution among various resolutionlevels compared with pure sinewave (lower plot).

Figs. 5-a, 5-b could be used as a classificationpattern for notching, furthermore, the numberof tics could be counted, and we can revealthat this is the result of a 6 or a 12 pulseconverter, moreover, the firing angle of thethyristor could be anticipated from the timeseries corresponding to the wave length (20

msec ~ 360 ~ 1000 sample points in ourprocedure). Figs. 6-a and 6-b (lower plot) showknee or peak other than the tenth level. Thisis the area of high order harmonics

Fig. 4-a. Wavelet analysis of capacitor switching wave, at1000 Hz.

Fig. 4-b. Energy distribution among various resolutionlevels.

Scale

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i t

Scale

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i t


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Fig. 5-a. Wavelet analysis of 6 notch, 30 degree converterwave.


4. Conclusions

Wavelet transform is a powerful tool fornon-stationary signals analysis. It providestime localization of the signal that will have aresolution that depends on the level in whichthey appear. Therefore, it is a good candidatefor detection and localization of short timedisturbances. The standard deviation of thewavelet transform coefficients at differentresolution levels is used in this technique as a

Fig. 6-a. Wavelet analysis of fundamental+5% 3 rd harmonic wave.


feature to classify different power qualityproblems.

A proposed procedure, depending onenergy distribution difference between theanalyzed wave and a pure sine wave, showedexcellent on-line detecting and locatingproperties, plus the ability to fast classifyingthese disturbances in advantage of the currentmethods, which require either an Artificial

Scale

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i t

Scale

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i t


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Neural complementing technique or massiveextra calculations for the standard deviation ofthe wavelet transform coefficients in eachdecomposition level as a characteristic feature.

The main thrust to the wavelet techniqueas shown in this research work is itsdeficiency in handling steady state distur-bances in the wavelet domain. This is mostobvious in the case of harmonic distortions.As a remedy to this problem, combiningFourier analysis and wavelet technique wouldbe the optimum solution. A prescanning of thewaveform by a Fourier analyzer would detectthe harmonic content in the waveform, andtherefore applying the wavelet technique topick non-harmonic distortions.

References

[1] P. F. Ribeiro, Wavelet Transform: AnAdvanced Tool for analyzing Non-Stationary Harmonic Distortions in PowerSystems, IEEE International Conferenceon Harmonics in Power System (ICHPS)VI, Bologna, Italy, pp. 314-320 (1994).

[2] S. Santoso, E. J. Powers, and W. M.Grady, Power Quality Assessment viaWavelet Transform Analysis, IEEE

Transactions on Power Delivery, Vol. 11(2), pp. 924-930 (1996).

[3] S. Huang, C. Hsieh, and C. Huang,Application of Morlet Wavelets toSupervise Power System Disturbances,IEEE Transactions on Power Delivery,Vol. 14 (1), pp. 235-243 (1999).

[4] Recommended Practice in MonitoringElectric Power Quality, IEEE Standard1159 (1995).

[5] A. M. Gaouda, M. M. A. Salama, M. R.Sultan, and A. Y. Chikhani, PowerQuality Detection and ClassificationUsing Wavelet-Multiresolution SignalDecomposition, IEEE Transactions onPower Delivery, Vol. 14 (4), pp. 1469-1176 (1999).

[6] A. Tewfik, D. Sinha, and P. Jorgensen,On the Optimal Choice of a Wavelet forSignal Representation, IEEE

Transactions on Information Theory, Vol.38 (2), pp. 747-765 (1992).

[7] A. Cohen, J. Kovacevic, Wavelets: Themathematical background, proceedings

of the IEEE, Vol. 84 (4), pp. 514-522(1996).[8] S. Mallat, A Theory for Multiresolution

Signal Decomposition: The WaveletRepresentation, IEEE Transactions onPattern Analysis, Vol. 11 (7), pp. 674-693(1989).

[9] M. Vetterli and C. Herley, Wavelets andFilter Banks: Theory and Design, IEEE

Transactions on Signal Processing, Vol.40 (9), pp. 2207-2232 (1992).

[10] T. El-Shennawy, Detection, localization,and classification of power quality

disturbances using discrete wavelettransform techniques, M.Sc. thesis,Alexandria University, Egypt (2002).

Received September 12, 2002Accepted October 8, 2002

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Detection, Localization, And Classification of Power Quality Using Discrete Wavelet Transform