hybrid signal processing and machine intelligence techniques for detection, quantification and...

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Engineering Applications of Artificial Intelligence 22 (2009) 442–454

Contents lists available at ScienceDirect

Engineering Applications of Artificial Intelligence

0952-19

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/engappai

Hybrid signal processing and machine intelligence techniques for detection,quantification and classification of power quality disturbances

B.K. Panigrahi a, P.K. Dash b,�, J.B.V. Reddy c

a Department of Electrical Engineering, IIT, Delhi, Indiab Center for Research in Electrical, Electronics and Computer Engineering, College of Engineering, D-75 Maitrivihar, Bhubaneswar, Orissa 751023, Indiac Department of Science and Technology, New Delhi, India

a r t i c l e i n f o

Article history:

Received 28 September 2007

Received in revised form

1 September 2008

Accepted 3 October 2008Available online 1 December 2008

Keywords:

Power quality disturbances S-transform

Wavelet transform

Feature extraction

Support vector machine

Multi-class pattern recognition

76/$ - see front matter & 2008 Elsevier Ltd. A

016/j.engappai.2008.10.003

esponding author. Tel.: +91674 2301306.

ail address: [email protected] (P.K. Da

a b s t r a c t

This paper presents an advanced signal processing technique known as S-transform (ST) to detect and

quantify various power quality (PQ) disturbances. ST is also utilized to extract some useful features of

the disturbance signal. The excellent time–frequency resolution characteristic of the ST makes it an

attractive candidate for analysis of power system disturbance signals. The number of features required

in the proposed approach is less than that of the wavelet transform (WT) for identification of PQ

disturbances. The features extracted by using ST are used to train a support vector machine (SVM)

classifier for automatic classification of the PQ disturbances. Since the proposed methodology can

reduce the features of disturbance signal to a great extent without losing its original property, it

efficiently utilizes the memory space and computation time of the processor. Eleven types of PQ

disturbances are considered for the classification purpose. The simulation results show that the

combination of ST and SVM can effectively detect and classify different PQ disturbances.

& 2008 Elsevier Ltd. All rights reserved.

1. Introduction

In recent years, power quality (PQ) has become a significantissue for both utilities and customers. PQ issues (Bollen) and theresulting problems are the consequences of the increasing use ofsolid-state switching devices, non-linear and power electronicallyswitched loads, unbalanced power systems, lighting controls,computer and data processing equipments as well as industrialplant rectifiers and inverters. These electronic-type loads causequasistatic harmonic dynamic voltage distortions, inrush, pulse-type current phenomenon with excessive harmonics and highdistortion. A PQ problem usually involves a variation in theelectric service voltage or current, such as voltage dips andfluctuations, momentary interruptions, harmonics and oscillatorytransients causing failure or mal-operation of the power serviceequipment. Hence to improve PQ, fast and reliable detection of thedisturbances and the sources and causes of such disturbancesmust be known before any appropriate mitigating action can betaken.

However, in order to determine the causes and sources ofdisturbances, one must have the ability to detect and localizethese disturbances. In the current research trends in PQ studies,wavelet transform (WT) (Daubechies, 1990; Mallat, 1989; Meyer,

ll rights reserved.

sh).

1992; Santoso et al., 1996a, b; Ribeiro, 1994) is widely used inanalyzing non-stationary signals for PQ assessment. Its adequacyfor this particular application was further confirmed by otherauthors (Ribeiro and Rogers, 1994; Pillay and Bhattacharjee, 1996;Angrisani et al., 1998a). Wavelet-based online disturbance detec-tion for PQ applications is discussed in Karimi et al. (2000) andMokhtari et al. (2002). Although WT has been extensively used forthe detection of PQ disturbances, the effect of electrical noise isnot adequately considered in many of the cases. A de-noisingscheme has been proposed in Lu and Huang (2004) for enhancingwavelet-based PQ monitoring system. Recently a hybrid algorithmusing both WT and short-time correlation transform (STCT) (Yangand Liao, 2001) has been presented for the detection andclassification of PQ disturbances.

In order to identify the type of disturbance present in thepower signal more effectively, several authors have presenteddifferent methodologies based on combination of WT andartificial neural network (ANN). Using the multiresolution proper-ties of WT (Zang et al., 2003; Santoso et al., 1997a, b; Gaouda et al.,1999, 2002), the features of the disturbance signal are extracted atdifferent resolution levels and are used to train different ANNalgorithms. By this method, it is possible to extract importantinformation from a disturbance signal and determine the type ofdisturbance that has caused a PQ problem to occur. Gaing (2004)demonstrated the classification of seven types of PQ events byusing wavelets and probabilistic neural network (PNN). Energydistribution at 13 decomposition levels of wavelet and time

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duration of each disturbances are taken as features and these 14features are applied to PNN for classification with increasedmemory and computational overhead due to the large number offeatures. Moreover, the PQ signals considered here do not containany noisy data which generally do not happen in practice. Haibo(He and Starzyk, 2006) presented a self-organizing learning arraysystem based on WT for the classification of seven types of PQproblems. Here, 11 decomposition levels of wavelets are used forthe classification and also, 22 types of wavelets are tested to geteffective classification by a particular type of wavelet.

Like WT, S-transform (ST) (Stockwell et al., 1996; Pinnegar andMansinha, 2003a) is a powerful signal processing technique,which explores the possibility of better time�frequency repre-sentation of a signal. It is an invertible time�frequency spectrallocalization technique that combines elements of WT and short-time Fourier transform (STFT). The ST uses an analysis windowwhose width scales inversely with frequency thereby providing afrequency-dependent resolution. It has been successfully appliedin many fields of research like power signal disturbances, seismicsignal analysis, biomedical signal processing, etc. (Livanos et al.,2000; McFadden et al., 1999; Dash et al., 2003).

Although a lot of research studies have been reported for thedetection and classification of PQ disturbances, the objective ofdetecting the disturbance in noisy environment and correctlyclassifying the nature of disturbance is still a challenging one. Thispaper aims to propose the powerful digital signal processingtechnique, ST (Stockwell et al., 1996), for the detection of the PQdisturbance both in normal and noisy environment. The superiorproperties of ST can provide significant improvement in thedetection of PQ disturbances (Dash et al., 2003). As ST is able toextract the three important features of a power signal: (i)fundamental component of the signal (i.e., either 50 or 60 Hz);(ii) frequency content of the signal; and (iii) the stationary phaseof the signal, we are inspired to use these three features of thedisturbance signal for accurate classification of the PQ distur-bance. Inspired by the different intelligent techniques available forclassification purpose, we have used the support vector machine(SVM) as a power signal pattern classifier.

2. S-transform

WT addresses the problem of resolution by introducing adilation (or scale) parameter d. The continuous WT (CWT) W(t,d)of a function y(t) is given as

Wðt; dÞ ¼Z 1�1

yðtÞwðt � t; dÞdt (1)

where W(t,d) is the scale replica of a fundamental wavelet.The spectral information in the signal y(t) is extracted through thecorrelation or convolution with W(t,d). The dilation parameter d

determines the width of the wavelet W(t,d), and thus controls theresolution. The WT is displayed in state space defined by thedilation d and translation t. The spectral information of the signaly(t) can be obtained from the state space representation. Stock-well et al. (1996) proposed a new windowed Fourier transformcalled the ST, as an extension to the ideas of the Gabor transformand the WT. The ST of a signal x(t) is defined as

Sðt; f Þ ¼Z 1�1

xðtÞgðt� tÞ expð�j2pftÞdt (2)

where

gðtÞ ¼1

sffiffiffiffiffiffi2pp exp �

t2

2s2

� �(3)

and

sðf Þ ¼ 1

jf j(4)

Combining Eqs. (2)–(4) gives

Sðt; f Þ ¼Z 1�1

xðtÞ jf jffiffiffiffiffiffi2pp exp �

ðt� tÞ2f 2

2

!expð�j2pftÞdt (5)

The normalization factor of ðjf j=ffiffiffiffiffiffi2ppÞ ensures that when

integrated over all t, S(t,f) converges to X(f), the Fourier transformof x:Z 1�1

Sðt; f Þdt ¼Z 1�1

xðtÞ expð�j2pftÞdt ¼ Xðf Þ (6)

It is clear that x(t) can be obtained from S(f,t). Thus, the ST isinvertible.

In Eq. (2), S denotes the ST of x, which is a continuous functionof time t and the frequency is denoted by f; and the quantity t is aparameter, which controls the position of the Gaussian window onthe t-axis. The scaling property of the Gaussian window is similarto that of the scaling property of continuous wavelets, becauseone wavelength of the Fourier frequency is always equal to onestandard deviation of the window. The ST, however, is not a WT,because the oscillatory part of the ST is provided by the complexFourier sinusoid, which does not translate with the Gaussianwindow when t is changed. As a result, the shapes of the real andimaginary parts of the ST change as the Gaussian windowtranslates in time. True wavelets do not have this propertybecause their entire waveform translates in time with no changein shape. Thus, the ST is conceptually a hybrid of short-timeFourier analysis and wavelet analysis, containing elements of bothbut falling entirely into neither category.

The ST has an advantage in that it provides multiresolutionanalysis while retaining the absolute phase of each frequency.This has led to its application for detection and interpretation ofevents in time series in a variety of disciplines. In this expressionof ST, the scalable Gaussian window (the product of ðjf j=

ffiffiffiffiffiffi2ppÞand

the real exponential) localizes the complex Fourier sinusoid,giving the ST analyzing function (the term in braces in Eq. (5)). TheCWT provides time resolution by translating its whole analyzingfunction (the wavelet) along the time axis. The ST is differentbecause only the amplitude envelope of the analyzing function(the window) translates; the oscillations are given by the fixedFourier sinusoid, which does not depend on t. Since the localoscillatory properties of the analyzing function determine thephase of the local spectrum, the ST can be considered as having‘‘fixed’’ phase reference. The fixed-phase reference gives the STsome advantages over WTs.

The inverse ST is given by

yðtÞ ¼

Z 1�1

Z 1�1

Sðt; f Þdt� �

ei2pft df (7)

and S(t,f) is complex and it is represented as

Sðt; f Þ ¼ Aðt; f Þeiyðt;f Þ (8)

where A(t,f) ¼ |S(t,f)| is the amplitude of the S-spectrum andy(t,f) ¼ arctan(Im[S(t,f)]/Re[S(t,f)]) is the phase of the S-spectrum.The phase of S-spectrum is an improvement on the WT in that theaverage of all the local spectra does indeed give the same result asthe Fourier transform.

The ST is a linear operation on the signal y(t). If additive noiseis added to the signal y(t), it can be modeled as ynoisy(t) ¼y(t)+Z(t). The operation of the ST leads to

SfynoisyðtÞg ¼ SfyðtÞg þ SfZðtÞg (9)

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B.K. Panigrahi et al. / Engineering Applications of Artificial Intelligence 22 (2009) 442–454444

As reported in Pinnegar and Mansinha (2003b), the S-spectrumof Gaussian white noise varies as

ffiffiffiffiffijf j

p, thereby noise peaks have

larger amplitude at higher frequencies on the S-spectrum. Hence,to have a better performance at noisy conditions, the Gaussianwindow width varies as

ffiffiffiffiffiffiffiffiffiffiffi1=jf j

pinstead of (1/|f|). Thus, the time

average of the resulting S-spectrum tends to vary asffiffiffiffiffiffiffiffiffiffiffi1=jf j4

p, which

leads to smaller noise peaks at high frequencies. As seen fromEq. (9) since the S-spectrum of the noisy signal is the sum of theS-spectrum of the signal and S-spectrum of the noise, the effect ofnoise can be eliminated by a soft threshold technique.

3. Detection of PQ disturbances using time–frequencytransforms

The proposed approach is applied to detect, localize andclassify signal patterns in electrical power networks. The signalpatterns considered for this application include:

(i)
Decrease in fundamental voltage signal magnitude knownas sag.
(ii)
Increase in fundamental voltage signal magnitude known asswell.
(iii)
Complete collapse of the voltage signal amplitude known asinterruption.
(iv)
Oscillatory voltage or current transients of low and highfrequency due to capacitor switching.
(v)
Voltage spikes. (vi) Notches occurring in the voltage signal due to the power
electronics control.
(vii) Harmonics, or sag with harmonics, or swell with harmonics.
(viii)
Voltage flicker.
0 100 200 300

–1

0

1

Sample number

Mag

nitu

de

Fig. 2. Swell signal (–), magnitude contour ( � � � � ) and phase contour (- � - � -).

3.1. ST-based detection

The proposed ST is applied to a variety of PQ disturbancesignals described above, for detection and quantification of theevent. WT has been successfully applied to detect the PQdisturbance signal. Although, WT is able to detect the disturbance,it is very difficult to quantify the disturbance level from thedecomposition level itself. In this section we have presented someof the results of ST to detect and quantify the PQ disturbance.

The output from the ST is an N�M matrix called the S-matrixwhose rows pertain to frequency and whose columns pertainto time. Each element of the S-matrix is complex valued. TheS-matrix can be represented in a time–frequency plane similar tothat of the WT. The ST performs multiresolution on a time-varyingpower signal, as its window width varies inversely withfrequency. This gives high time resolution at high frequency andhigh-frequency resolution at low frequency. The useful informa-

Sample number

Nor

mal

ized

fre

quen

cy

0 100 200 300

0.1

0

0.2

0.3

0.4

Mag

nitu

de

Fig. 1. (a) ST contour of voltage sag (50%). (b) Sag signal (–),

tion related to magnitude, phase and frequency of the signal isderived from the S-matrix for the detection, quantification andclassification of various PQ signals. The magnitude contour is thelocus of the maximum value of the S-matrix at a particular time(sample). To determine the phase from the S-matrix, the regionsof maximum amplitude are determined and the correspondingphase at these points is calculated. The phase so obtained is calledstationary phase of the signal. The frequency content of the signalis also derived from the S-matrix and presented as frequencycontour.

The signals are simulated using MATLAB (2000). The numberof samples per cycle of the AC voltage waveform is chosen to be64, and hence the sampling frequency is (64�50) i.e. 3.2 kHz. Todemonstrate the detection capability of ST, we have simulated themost frequently occurred PQ phenomena, i.e., voltage sag andvoltage swell. Fig. 1(a) represents the ST contour of voltage sag(50%), which gives a visual inspection of the voltage sag. InFig. 1(b), the sag signal is plotted along with the magnitudecontour (dotted) and phase contour (dash-dotted). It is observedfrom the figure that the magnitude contour detects the voltagesag as well as it also nearly quantifies the voltage sag as 50%. Asthis is voltage sag with no phase jump the phase contour shows astraight line around zero. The onset and offset of the phasecontour is only at the initiation and recovery of the sag event.Fig. 2 represents a voltage swell without any phase change and it

is also noted that the ST is able to detect and quantify the swell(50%). Fig. 3 represents voltage sag associated with a phase jumpof p/10 rad. It is noted that the magnitude contour derived fromthe ST matrix detects and quantifies the sag and the phase contouralso detects and quantifies the phase change.

It is very important for the PQ studies as well as for theprotection point of view to extract the change in fundamentalmagnitude of the signal. As in a realistic power system study, theharmonic injected to the system varies with the amount of non-linear load switched on to the system, the harmonic content in the

0 100 200 300

–1

–0.5

0.5

Sample number

0

magnitude contour ( � � � � ) and phase contour (- � - � -).

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power signal may be time varying. For fault studies we are mainlyinterested in the change in fundamental magnitude of the voltageas well as the current. To demonstrate the effectiveness of the STto extract any change in the fundamental component, some of theresults are presented here. Fig. 4 shows a signal where theharmonic content (3rd harmonic 20%, 5th harmonic 10% and 7thharmonic 5%) is fixed throughout the six cycles (384 samples), butthere is a drop in magnitude (50% sag) in the fundamental. It isnoted that the ST magnitude contour detects and quantifies thischange. Fig. 5 shows a signal where the fundamental magnitudeis constant (1), but contains some time-varying harmonic. Thusthe ST magnitude contour does not show any change.

0 100 200 300

–1

–0.5

0

0.5

1

Sample number

Mag

nitu

de

Fig. 3. Sag signal with a phase jump (–), magnitude contour ( � � � � ) and phase

contour (- � - � -).

0 100 200 300

–1

–0.5

0

0.5

1

Sample number

Mag

nitu

de

Fig. 4. Sag with harmonic (–), magnitude contour ( � � � � ) and phase contour (- � -

� -).

Sample number

0 100 200 300

–1

–0.5

0

0.5

1

Mag

nitu

de

Fig. 5. Time varying harmonic (–), magnitude contour ( � � � � ) and phase contour

(- � - � -).

To demonstrate the ability of ST to detect the voltage violationsin the presence of noise, we have simulated the voltage sag andswell in the presence of noise of signal-to-noise ratio (SNR) 20 dB.It is observed that the ST magnitude contour is able to detectthese voltage violations accurately and the results are reported inFigs. 6 and 7, respectively.

As voltage sag, swell, momentary interruptions are thecommon PQ phenomena generally associated with the change inmagnitude of the signal. But for the harmonics and transients, thefrequency information of the signal plays an important role forthe classification purpose. To demonstrate the efficacy of the STin extracting the magnitude phase and frequency contour, atransient signal is simulated and the signal is presented inFig. 8(a). In this figure itself, the magnitude contour and phasecontour is plotted. It is observed that the magnitude contour is astraight line having a value of 1 and the phase contour is a straightline with a value of 0. This indicates that the amplitude and phaseof the fundamental component in the transient signal is alwaysmaintained at 1 and 0, respectively. The ST matrix contour ispresented in Fig. 8(b), which clearly indicates the presence ofhigh-frequency components during a specific period of time. Thus,it is observed that only from the magnitude contour and the phasecontour it is difficult to characterize the transient signal as thesame type of magnitude and phase contour will be obtained froma normal undisturbed signal with magnitude 1 and phase angle01. Hence, as it is known that the transient is a high-frequencyphenomenon, the frequency contour obtained from the ST matrixshows a peak at the high-frequency zone. This is demonstrated inFig. 8(c). All the above-mentioned contours (magnitude, phaseand frequency) are discussed in Section 3 and the plots of the

0 100 200 300

–1

–0.5

0

0.5

1

Sample number

Mag

nitu

de

Fig. 6. Sag with noise (SNR 20 db) (–), magnitude contour ( � � � � ) and phase

contour (- � - � -).

0 10 20 30

–1

0

1

Sample number

Mag

nitu

de

Fig. 7. Swell with noise (SNR 20 db) (–), magnitude contour ( � � � � ) and phase

contour (- � - � -).

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0 0.50

0.5

1

Normalized frequency

Mag

nitu

de

Sample number

Nor

mal

ized

fre

quen

cy

0 2000

0.1

0.2

0.3

0.4

0 200

–1

–0.5

0

0.5

1

Sample number

Mag

nitu

de

Fig. 8. (a) Transient (–), magnitude contour ( � � � � ) and phase contour (- � - � -). (b) ST contour. (c) Frequency contour.

0 50 100 150 200 250 300 350 400 450 500–1

0

1

2

3spike

s-transform contours

0 50 100 150 200 250 300 350 400 450 5000

0.10.20.30.4

0 50 100 150 200 250 300 350 400 450 500–1

0

1notch

s-transform contours

0 50 100 150 200 250 300 350 400 450 5000

0.2

0.4

Fig. 9. (a) ST contour of spike. (b) ST contour of notch.


contours for different PQ signals are shown in Figs. 1–8. Fig. 9(a)and (b) depicts ST contours for voltage spike and notch,respectively, clearly localizing the PQ events. Fourteen types ofPQ disturbances are simulated and the features of all the types ofdisturbances are extracted from the S-matrix apart from peakmagnitude and change of phase. These features are summarizedin the following section.

Feature extraction is done by applying standard statisticaltechniques to the contours of the S-matrix as well as directly onthe S-matrix. These features have been found to be useful fordetection, classification of the PQ disturbance signals. The powersignal is normalized with respect to a base value, which is thenormal value without any disturbance. The features are specifiedas follows:

Feature 1: Energy of the magnitude contour. (Magnitudecontour corresponding to the maximum magnitude of the S-matrix at each sample, hence it reflects the fundamental of thesignal.)Feature 2: Energy of the frequency contour. (This reflects thefrequency content of the signal—particularly for harmonic andtransients.)Feature 3: Standard deviation of the Phase contour.

The next section outlines some of the basic concepts of WT usedfor feature extraction of the non-stationary PQ disturbancesignals.

3.2. WT-based detection

The discrete wavelet transform (DWT) is a special case of theWT that provides a compact representation of a signal in time and

frequency that can be computed efficiently. The DWT is calculatedbased on two fundamental equations: the scaling function f(t),and the wavelet function c(t), where

fðtÞ ¼ffiffiffi2p X

k

hkfð2t � kÞ (10)

cðtÞ ¼ffiffiffi2p X

k

gkfð2t � kÞ (11)

The scaling and wavelet functions are the prototype of a class ofortho-normal basis functions of the form

fj;kðtÞ ¼ 2j=2fð2jt � kÞ; j; k 2 Z (12)

cj;kðtÞ ¼ 2j=2cð2jt � kÞ; j; k 2 Z (13)

where the parameter j controls the dilation or compression of thefunction in time scale and amplitude. The parameter k controlsthe translation of the function in time. Z is the set of integers.

Once a wavelet system is created, it can be used to expand afunction f(t) in terms of the basis functions

f ðtÞ ¼Xl2Z

cðlÞflðtÞ þXJ�1

j¼0

X1k¼0

dðj; kÞcj;kðtÞ (14)

The expansion coefficients c(l) represent the approximationof the original signal f(t) with a resolution of one point per every 2J

points of the original signal. The expansion coefficients d(j,k)represent details of the original signal at different levels ofresolution. c(l) and d(j,k) terms can be calculated by directconvolution of f(t) samples with the coefficients hk and gk, whichare unique to the specific mother wavelet chosen. The WT yieldscertain features that are essential for classifying PQ events andthey are summarized as follows.

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WT can be implemented with a specially designed pair of FIRfilters known as quadrature mirror filters (QMFs pair). QMFs aredistinctive because the frequency response of these two FIR filtersseparates the high- and low-frequency components of the inputsignal. The tree or pyramid algorithm can be applied to the WT byusing the wavelet coefficients as the filter coefficients of the QMFfilter pairs as shown in Fig. 10. In WT multiresolution algorithmwavelet coefficients mentioned above are used for both low-pass(LP) and high-pass (HP) filters. The LP filter coefficients areassociated with the scaling function, and the HP filter is associatedwith the wavelet function. Fig. 10 shows the tree algorithm of themultiresolution WT for a discrete signal sampled at 3200 Hzgiving approximate and detailed outputs. In wavelets applications,different basis functions have been proposed and selecteddepending on the application requirements. Daubechies waveletfamily is one of the most suitable wavelet families in analyzingpower system transients and in the present work; and ‘‘db5’’wavelet has been used as the wavelet basis function for PQdisturbance detection and classification. The filter coefficients forthe ‘‘db5’’ mother wavelet are obtained using MATLAB WaveletTool Box as

LO_D ¼ 0:0033 �0:0126 �0:0062 0:0776 �0:0322 �0:2423 0:1384 0:7243 0:6038 0:1601

HI_D ¼ �0:1601 0:6038 �0:7243 0:1384 0:2423 �0:0322 �0:0776 �0:0062 0:0126 0:0033

LO_R ¼ 0:1601 0:6038 0:7243 0:1384 �0:2423 �0:0322 0:0776 �0:0062 �0:0126 0:0033

HI_R ¼ 0:0033 0:0126 �0:0062 �0:0776 �0:0322 0:2423 0:1384 �0:7243 0:6038 �0:1601

The energy at each decomposition level is calculated using thefollowing equation as

EDi ¼XN

j¼1

jDijj2; i ¼ 1;2; . . . ; l

EAl ¼XN

j¼1

jAijj2 (15)

where i ¼ 1,2,y,l is the wavelet decomposition level from level 1to level l; and N the number of coefficients of detail orapproximate at each decomposition level.

Thus, for an l level decomposition the feature vector adopted isof length l+1 and is denoted by (Gaing, 2004)

Feature ¼ ½ED1;ED2;ED3; . . . ;EDl;EAl� (16)

HP

LP

HP

LP

Signal

3200 Hz

800-1600 Hz

0 - 800 Hz

Fig. 10. Comparison of disturb

3.3. Comparison of WT and ST for noisy PQ signals

It is observed that both the ST and WT are able to detect theinitiation and end of the disturbance in a pure signal veryaccurately, where as WT fails to detect the disturbance in noisyenvironment unlike the ST-based detection. The classificationaccuracy in both the cases are practically the same when thesignal is not corrupted with noise or the noise level is lowlike SNR ¼ 50 dB. For noisy signals the performance of WTdeteriorates considerably whereas the performance of ST issatisfactory.

In this section, a comparison between ST and WT is carriedout for the detection of PQ disturbances in noisy environments.This result is demonstrated in Fig. 11. Another set of practicaldata obtained from the laboratory setup by initiating capacitor-switching transient also demonstrates the effectiveness ofthe ST over WT for detection of the transient event as shownin Fig. 12. The ST output clearly shows the detection andlocalization of the transient event whereas the WT output issusceptible to noise and may produce a wrong conclusion aboutthe event.

4. Classification of PQ disturbances using SVM

The SVM has been applied in this study as the classifier todiscriminate PQ disturbance patterns. The SVM is a new universallearning machine proposed by Vapnik (1998), and Cortes andVapnik (1995). SVMs represent novel learning techniques thathave been introduced in the structural risk minimization (SRM)and in the theory of VC bounds. It creates a model with aminimized VC dimension (measure of complexity of the model).The developed theory (by Vapnik) shows that when the VCdimension of the model is low, the expected probability of error islow as well, which means good performance on previously unseendata (good generalization).

SVM overcomes some of the drawbacks of ANNs like localminimum, over learning and the difficulties in choosing the

HP

LP

D1

D2

D3

D4

0 - 400 Hz

400 - 800 Hz

0 - 200 Hz

200 - 400 Hz

ance detection using WT.

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0 200 400 600 800 1000 1200 1400–1

0

1Signal

0 200 400 600 800 1000 1200 1400–0.05

0

0.05Wavelet decomposition level 1 (D1)

0 200 400 600 800 1000 1200 14000

0.5

ST magnitude contour

Fig. 12. Wavelet decomposition structure.

0 200 400 600

–1

–0.5

0

0.5

1

Sample number

Mag

nitu

de0 200 400 600

–0.02

–0.01

0

0.01

0.02

Sample numberM

agni

tude

of

D1

0 200 400 600–0.02

–0.01

0

0.01

0.02

Sample number

Mag

nitu

de o

f D

1

0 200 400 600–1

–0.5

0

0.5

1

Sample number

Mag

nitu

de

Pure signal Noisy signal (SNR=30dB)

ST WT

Fig. 11. Comparison of detection of transient (capacitor switching) using WT and ST.


network structure. Some of the properties of SVM are:

(i)
solid theoretical foundation (ii) regularized method yielding good generalization and
(iii)
stable solution of quadratic optimization problem.
4.1. Binary classification

Suppose we have N samples, each consisting of a pair of data:an input vector xiARd, i ¼ 1,2,y,N and a class label yiA{+1,�1} foreach vector. These data pairs form the training set.

For linearly separable case, the data points will be correctlyclassified by

hw � xii þ bXþ 1 for yi ¼ þ1 (17)

hw � xii þ bp� 1 for yi ¼ �1 (18)

Inequalities (17) and (18) be combined into one set of inequality.

yiðhw � xi þ biÞ � 1X0; i ¼ 1; . . . ;N (19)

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0.4 0.6 0.8 1 1.2 1.40

0.05

0.1

0.15

Feature 1

Feat

ure

3

Normal

Sag

Sag (Ph change)Swell

Swell (Ph change)MI

Fig. 13. Feature 1 vs. feature 3.


SVM finds an optimal separating hyperplane with the max-imum margin by solving the following optimization problem:

Minðw;bÞ

1

2wTw subject to : yiðhw � xi þ biÞ � 1X0 (20)

Using Lagrangian and Kuhn–Tucker theory, we can transformthe problem into the dual problem as

Maxa

QDðaÞ ¼XN

i¼1

ai �1

2

XN

i;j¼1

aiajyiyjhxi � xji

subject to : aiX0; i ¼ 1; . . . ;N andXN

i¼1

aiyi ¼ 0 (21)

To find the optimal hyperplane, the dual Lagrangian QD(a) mustbe maximized with respect to non-negative Lagrange multipliersai. The solution a*i for the dual optimization problem determinesthe parameters w* and b* of the optimal hyperplane. Thus, weobtain a hyperplane of the form

f ðx; a�; b�Þ ¼XN

i¼1

yia�i hxi � xi þ b�

¼Xi2sv

yia�i hxi � xi þ b� (22)

The data samples for which the aia0 are the support vectors.For solutions with real-time data, usually only a small percentageof the training data turn out to be support vectors.

The above concepts can also be extended to the non-separablecase, i.e., when a data point does not satisfy inequality (19).Positive slack variables xi, i ¼ 1,y, N can be introduced toquantify the non-separable data in the defining condition of thehyperplane:

yiðhw � xii þ bÞ þ xi � 1X0; xiX0 (23)

In terms of these slack variables, the soft margin hyperplane isdefined by {w,b} that minimize the functional:

1

2wTwþ C

XN

i¼1

xi (24)

subject to the constraints (23).The dual of the quadratic optimization problem (24) can be

formulated as follows:

Maxa

QDðaÞ ¼XN

i¼1

ai �1

2

XN

i;j¼1

aiajyiyjhxi � xji

subject to : 0paipC; i ¼ 1; . . . ;N andXN

i¼1

aiyi ¼ 0 (25)

The hyperplane decision function is the same as in Eq. (22).Kernels are used for learning non-linear decision surfaces by

mapping data into higher feature space as x-f(x). Kernel is afunction that calculates the inner product in some feature space as

Kðx1; x2Þ ¼ hfðx1Þ �fðx2Þi

Following are the two common kernel functions used in SVM

Polynomial kernel : Kðx1; x2Þ ¼ ðhx1 � x2i þ 1Þd (26)

Gaussian kernel : Kðx1; x2Þ ¼ expð�kx1 � x2k2=ð2s2ÞÞ (27)

Detailed discussion on SVMs can be found in Cherkassky andMulier (1998).

4.2. Multi-class classification

SVMs were originally designed for binary classification. How toeffectively extend it for multi-class classification is still an

ongoing research issue. The earliest used implementation forSVM multi-class classification is the one-against-rest method (Linand Hsu, 2002). It constructs k-SVM models where k is thenumber of classes. The ith SVM is trained with all of the examplesin the ith class with positive labels and all other examples withnegative labels. The ith SVM solves the following problem:

minðwi ;bi ;xi

Þ

1

2ðwiÞ

Twi þ CXN

j¼1

xijðw

iÞT

ðwiÞTfðxjÞ þ bi

X1� xij; if yj ¼ i

ðwiÞTfðxjÞ þ bip� 1þ xi

j; if yjai

xijX0; j ¼ 1; . . . ;N (28)

Now class of x is determined by the decision function, which hasthe largest value i.e.,

class of x � arg maxi¼1;...;k

ðwiÞTfðxÞ þ bi

� �(29)

Another major approach is the one-against-one method (Linand Hsu, 2002). This method constructs k(k�1)/2 classifiers whereeach one is trained on the data from two classes.

For training data from the ith and jth classes, the followingbinary classification problem is to be solved:

minðwij ;bij ;xij

Þ

12 ðw

ijÞTwij þ C

Ptxij

t ðwijÞ

T

ðwijÞTfðxtÞ þ bij

X1� xijt ; if yt ¼ i

ðwijÞTfðxtÞ þ bijp� 1þ xij

t ; if yt ¼ j

xijj X0

(30)

If sign ((wij)Tf(x)+bij) says x is in the ith class then one adds votefor the ith class. Otherwise, the jth class is increased by one. Thenwe predict x is in the class with largest vote. This voting approachis called the Max-Wins strategy.

The third algorithm considered here is the directed acyclicgraph SVM (DAGSVM). The training phase of DAGSVM (Platt et al.,2000) is same as the one-against-one method. However, in thetesting phase, it uses a rooted binary acyclic graph with k(k�1)/2internal nodes and k leaves. Each node is binary SVM of ith and jthclasses. Given a test sample x, starting at the root node, the binarydecision function is evaluated. Then it moves to either left or rightdepending on the output value. Therefore, we go through a pathbefore reaching a leaf node, which indicates the predicted class.

Finally, we have considered fuzzy SVM (FSVM) for our analysis.The training phase of FSVM (Abe and Inoue, 2002) is same as theone-against-one method. To solve the problem of unclassifiable

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regions, fuzzy membership functions are introduced on thedirection orthogonal to the optimal separating planes. The inputsample x belongs to the class with the maximum degree ofmembership.

5. Simulation results using synthetic PQ signals using SVM

Fourteen classes (C1–C14) of different PQ disturbances de-scribed in Section 3 are taken for classification and they are asfollows:

C1- normalC2- pure sag

0.8 0.9 1 1.1 1.2

0.12

0.14

0.16

0.18

0.2

Feature 1

Feat

ure

2

Sag

Swell

Sag harmonic

Swell harmonic

flicker

Notch

Spike

Transient


0.8 0.9 1 1.1 1.2

0.12

0.14

0.16

0.18

0.2

Feature 1

Feat

ure

2

Sag

Swell

Sag harmonic

Swell harmonic

flicker

Notch

Spike

Transient (LF)


Feature 1

0.9 0.95 1 1.05 1.10.11

0.12

0.13

0.14

Feat

ure

2

Fig. 16. Feature 1 vs. feature 2 of 5 classes (these class

C3- pure swellC4- sag with phase changeC5- swell with phase changeC6- momentary interruption (MI)C7- harmonicsC8- sag with harmonicC9- swell with harmonicC10- flickerC11- notchC12- spikeC13- transient (low frequency)C14- transient (high frequency)

The waveforms of the above-mentioned PQ disturbances aresimulated using MATLAB Toolbox and are shown in Figs. 1–9. Thetotal duration of the signal considered is of 10 cycles (640 samplepoints). Different voltage sag of duration starting from 3 cycles to6 cycles are simulated having sag magnitude varying from 0.15 to0.9. Similarly, different voltage swell of duration starting from 3cycles to 6 cycles are simulated having swell magnitude varyingfrom 1.05 to 1.8. For the simulation of the pure harmonicwaveform we have considered the 2nd, 3rd, 5th and the 7thharmonic components of different percentages varying from 5% to25% of the fundamental in a variety of possible combinations.Similar type of sag and swell as mentioned for pure sag and swellare created in these harmonic signals to get the sag with harmonicand swell with harmonic signal. For the simulation of the flickersignal, the flicker frequency is varied from 5 to 20 Hz and theflicker magnitude is varied from 0.05 to 0.25, modulated with afundamental signal of 50 Hz and magnitude 1. The notch and spikesignals are simulated for various notch and spike width andmagnitude (depth). The low-frequency transients are simulatedwith a transient frequency range of 200–500 Hz, whereas for high-frequency transients the frequency range was 500–1200 Hz.Hence, taking the above-mentioned parameters of variousdisturbances 1400 signals are simulated for the 14 differentclasses.

Based on the feature extraction by the ST method,3-dimensional feature sets for training and testing are constructed.The dimensions here describe the different features derived fromST matrix. All the data sets of features for various classes areapplied to SVM for automatic classification of PQ events.To illustrate the nature of the feature sets for all the 14 classes,Figs. 13–15 are presented here. Fig. 13 illustrates feature 1(magnitude feature) vs. feature 3 (phase feature) for six types ofPQ events (class C1–C6) which mostly vary in magnitude exceptthe two classes for sag with phase change and swell with phasechange. The six types of PQ events described above are sensitive tothe phase changes since they all belong to steady-state dis-turbance category. For transients, spike, notch, etc. phase features

Feature 2

0.12 0.13 0.140.1

0.2

0.3

0.4

Feat

ure

3

Notch

Spike

Trans (LF)

Flicker

Trans (HF)

es are mostly characterized by frequency feature).

ARTICLE IN PRESS


are not that important for classification, and hence they are notused as shown in Figs. 14 and 15. Fig. 14 represents the feature 1vs. 2 for the 7 classes where the features are magnitude andfrequency dependent. Fig. 15 represents the feature 1 vs. feature 2for 9 different classes where the disturbance mostly depends onmagnitude and frequency. It is well visualized that some of theclasses have distinct features, where as some have overlappingfeatures.

Fig. 16 is given as an additional result to demonstrate theeffective feature extraction capability of the ST. The 5 classes asshown in Fig. 16 are mostly having the magnitude of fundamentalin and around 1, but these classes have different frequencycontent and also having phase changes during the occurrence ofthe disturbance.

Table 1 demonstrates the classification result of SVM(DAGSVM) for all the 14 classes. It is observed that theclassification accuracy is 96%.

Table 1Classification results of SVM.

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14

C1 94 1 1 1 2 1

C2 1 95 2 1 1

C3 2 96 1 1

C4 96 1 1 1 1

C5 2 96 1 1

C6 1 1 97 1

C7 1 97 1 1

C8 1 1 96 1 1

C9 1 1 97 1

C10 1 1 96 1 1

C11 1 1 1 1 95 1

C12 1 1 1 97C13 1 1 2 96C14 1 1 1 97

0 100 200 300

0.6

0.8

1

Sample number

0 100 200 300

1

1.1

1.2

1.3

1.4

1.5

Sample number

Mag

nitu

deM

agni

tude

Fig. 17. Comparison of the features of noisy signals (sag with harmonic and sell with har

signal (SNR 20 db), —— GW2 with noisy signal (SNR 20 db).

6. Performance of SVM under noisy environment

In this section, the performance of SVM using either ST-basedor WT-based features are described using synthetic PQ signalsmixed with varying degree of white Gaussian noise.

6.1. SVM using ST-based features

In an electrical power distribution network, the practical dataconsists of noise; therefore, the proposed approach has to beanalyzed under noisy environment. Gaussian white noise iswidely considered in the research of PQ issues. We have obtainedthe noisy signals for all the 14 classes having different SNR. Thethree features as described in the previous section are extractedusing ST.

To demonstrate the feature extraction capability of ST undernoisy conditions we have presented the following results in Fig. 17.The features presented here are for sag with harmonic and swellwith harmonic. We have used the normal Gaussian window,where window width varies with (1/|f|) (represented by GW1) andthe other one, where window width varies with

ffiffiffiffiffiffiffiffiffiffiffi1=jf j

p(repre-

sented by GW2) as discussed in detail in Section 2. It is clear thatthe noise has a very little effect on magnitude contour (on whichfeature 1 depends) and the effect of noise on frequency contour(on which feature 2 depends) is reduced to a great extent.

Features extracted for noisy data consisting of SNR 20, 30 and40 dB and tested with 20, 25, 30, 35 and 40 dB noise levels. Figs. 18and 19 show the representation of training and testing datasamples for sag and transient, respectively. For simplicity, data ofonly two classes are shown. From Figs. 18 and 19, it is quite clearthat a cluster of data (represented within highlighted region thatcorresponds to 25 and 35 dB noise levels) are present duringtesting phase which are not included during training. Theclassification results are shown in Table 2. The overall accuracy

0 0.1 0.2 0.3 0.40

0.1

0.2

0.3

0.4


Mag

nitu

de

0 0.1 0.2 0.3 0.40

0.1

0.2

0.3

0.4

0.5


Mag

nitu

de

monic for different. Gaussian window (GW)) - � - � - GW1, � � � � � GW1 with noisy

ARTICLE IN PRESS

0.70.115

0.12

0.125

0.13

0.135

Feature 1

Feat

ure

2

Untraineddata

Training dataTesting data

0.8 0.9 1

Fig. 18. Training and testing data for sag under noise condition.

0.11 0.12

0.16

0.18

0.2

0.22

Feature 2

Feat

ure

3

Untrained data

Training data

Testing data

0.125 0.13

Fig. 19. Training and testing data for transient under noise condition.

Table 2Classification results of SVM with noisy signal.

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14

C1 90 2 1 1 1 2 1 1 1

C2 93 2 1 1 1 2

C3 3 91 1 2 1 1 1

C4 93 3 1 1 2

C5 2 91 2 1 2 1 1

C6 1 3 2 92 1 1

C7 1 94 2 1 1 1

C8 2 1 2 93 1 1

C9 1 2 2 94 1

C10 2 1 2 91 2 1 1

C11 1 1 1 2 93 2

C12 2 2 2 94C13 1 2 1 1 91 4

C14 1 2 2 3 92

Overall accuracy: 92.3%.

Table 3Comparison of different SVM methods for PQ classification (per 100 training and

100 testing data).

Classification methods Training

time (s)

Testing

time (s)

Accuracy

(%)

DAG SVM 43 4.1 96

1-v-r SVM 178 62 92.5

1-v-1 SVM with Max-Wins testing 42.3 62.8 94.2

Fuzzy SVM 42.5 65 94.2

Multi-layer ANN 130 4.8 90


is 92.3%. Hence, the classification results of SVM are satisfactoryeven if noise levels are different during training and testing.

Table 3 reports the simulation results for PQ disturbanceclassification based on the SVM approach and the method usingANN for classification. From this table it can be observed that,DAGSVM has distinctly higher accuracy over the other alterna-tives.

6.2. SVM performance comparison using ST- and WT-based features

In the following section, a comparative result for theclassification of PQ disturbances using ST and WT is presented.In the previous section, the ST result is reported for both pure andnoisy signals simulated in MATLAB environment. The featureselected for the wavelet is of dimension 9, where each entry in thefeature vector is the energy at the dilation level.

Fig. 20 shows the comparative result of the classificationaccuracy of 14 classes of PQ disturbances using ST and WT. InFig. 21, we have compared the classification of accuracy for twodifferent schemes of WT with that of ST. The following WTschemes are used for comparison of classification accuracy withthat of ST.

Scheme1: ST: In this scheme as explained in Section 4, the threefeatures are taken and are F1, F2 and F3, and thus the feature vectoris of length 3.

Scheme2: WT (with 9 features): In this scheme, the 9 featuresare the energy of the wavelet coefficients at different levels ofdecomposition levels.

Scheme3: WT (with 4 features): In this scheme, the energy ofhigh-frequency components is clubbed into one and the averageenergy of the high-frequency components which appears inD1–D4 is considered as feature 1. Energy of low-frequencycomponents is clubbed into another and the average energy ofthe low-frequency components, which appears in D6–D8 isconsidered as feature 2. The approximate and detail of the levelcontaining the fundamental are the two other features. Thus, thefeature vector is of dimension 4 and is given as

Feature ¼ ½0:25ðED1 þ ED2 þ ED3 þ ED4ÞED5EA5

� 0:333ðED6 þ ED7 þ ED8Þ�

6.3. Experimental verification

In this section, we have demonstrated the applicability of theproposed technique to the practical data. The PQ data are obtainedfrom the laboratory. The laboratory setup is given in Fig. 22. Theelectrical system consists of a source (400 V), which suppliespower through two three-phase lines. Two linear loads compris-ing resistance and inductance elements (static load) and one non-linear load comprising a voltage source converter supplyingpower to a resistive load are used in the laboratory test setup.Different PQ disturbances are simulated by making faults in theline, additional load switching, capacitor switching and varyingthe firing angle of the converter load. The terminal voltagewaveforms are acquired through voltage sensors (LV-20-P). Out-put of the voltage sensor is limited between 710 V to providecompatibility with subsequent signal processing system. Thesesignals are captured by using dSPACE 1104 kit and monitored inthe computer. To get a maximum resolution, the sampling rate hasbeen set to 0.0003125 s. The classification result of the practicaldata is reported in Table 4.

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Comparision of classification accuracy

0102030405060708090

100

1

Class

Eff

icie

ncy

STWT

2 3 4 5 6 7 8 9 10 11 12 13 14

Fig. 20. Comparison of the classification accuracy.

Comparision of classification accuracy

60

65

70

75

80

85

90

95

100

C1 C3 C5 C7 C9C11 C13

Class

Eff

icie

ncy

ST

WT (8features)

WT (4features)

Fig. 21. Comparison of the classification accuracy for three different methods.

230VAC supply

D SpaceElectricalSystem

Electrical SystemPC Induction

Motor

Non Linear Load

Linear Load

LinearLoad

DigitalData

AnalogData

M

~Capacitor

Fig. 22. Laboratory setup to acquire practical PQ data.

Table 4Classification result for practical power quality data.

Class Training/testing

data set

Classification

accuracy with ST

Classification

accuracy with WT

C1 50/20 90 85

C2 50/25 91 87

C3 50/25 92 82

C4 30/10 90 75

C5 30/10 88 70

C6 40/10 93 86

C7 50/20 92 84

C8 40/10 91 85

C9 40/10 92 82

C10 20/5 90 84

C11 40/10 93 85

C12 40/10 92 87

C13 20/5 85 74

C14 40/10 93 88


7. Conclusion

In this paper, an attempt has been made to detect and quantifythe PQ disturbances by extracting efficient features of the powersignals using ST. The features based on magnitude, frequency andphase of the disturbance signal are used to classify the steady-state power signal disturbance events without much effort. In thecase of WT it is difficult to extract these features directly, andhence visual recognition of the disturbance events is not easy as isseen in the case of ST. Further, in the Wavelet analysis some of thefeatures are noise prone (like the energy at dilation level 1 and 2),

and thus a de-noising scheme is necessary to extract thosefeatures accurately. This paper also presents a novel machinelearning technique like support vector machine (SVM) forautomatic recognition of PQ disturbance patterns. The PQ patternrecognition performance of different multi-class SVM learningalgorithms like the k-SVM, FSVM, directed acyclic graph SVM(DAGSVM), etc. is compared along with the ANN-based PQclassifiers. It is observed that amongst the various algorithmsused, DAGSVM correctly classifies the PQ events with a highdegree of accuracy and less training and testing times incomparison to other kernel-based learning techniques and ANN-based methods. A comparison of SVM performance using PQsignal features obtained from ST and WT is also presented in thepaper along with the pattern recognition performance of SVM innoisy environment. From various simulation and experimentalresults, it is concluded that ST-based SVM performs the best incomparison to WT-based SVM under both low and significantnoise in the power signal disturbances, and the classificationaccuracy is higher in the former than the later.

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