Power Quality Analysis Using Wavelet Transform: A Review

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1 ISSN (Olie) : ISSN (Prit) : Iteratioal Joural of Iovative Research i Sciece, Egieerig ad Techology Volue 3, Special Issue 3, March Iteratioal Coferece o Iovatios i Egieerig ad Techology (ICIET 4) O st & d March Orgaized by K.L.N. College of Egieerig, Madurai, Tail Nadu, Idia Power Quality Aalysis Usig Wavelet Trasfor: A Review V. Kuar #, S. K. Gawre #, T. Kuar #3 # Departet of Electrical Egieerig, MANIT, Bhopal, Idia. # Departet of Electrical Egieerig, MANIT, Bhopal, Idia. #3 Departet of Electrical Egieerig, MANIT, Bhopal, Idia. ABSTRACT With a icreased use of oliear loads, sesitive electroic equipets ad variable frequecy drives power quality has becoe a proiet issue these days. The developet of ew ethods for detectio classificatio ad aalysis of power quality is a ajor cocer ow a day. This paper presets a literature review of the applicatio of wavelet trasfors i the detectio ad aalysis of power quality. The sigal uder aalysis is ofte polluted by oises, uder this situatio the extractio of features becoes a difficult tas, especially whe the oise preset i sigal has high frequecy spectru which overlap with the frequecy of fault. I this paper the de-oisig ethods are discussed. This review also presets the use of wavelet i other fields of power syste ad advatages of wavelet trasfor over other sigal processig tools. KEYWORDS power quality; wavelet trasfor; ultiresolutio aalysis; de-oisig; discrete wavelet trasfor I. INTRODUCTION I the idustrialized world, due to cotiuous icrease i sources of disturbace which occurs i itercoected power grids, the electric power syste suffers fro uwated variatio i the voltage ad curret sigals [, 48-5]. These uwated variatios i curret ad voltage sigal leads to poor power quality []. The sources of disturbaces i ay power syste etwor are large uber power sources, power electroic devices such as iverters ad coverters, ad oliear loads. Electric power has poor power quality if it has voltage sag, voltage swell, haroics, trasiets etc. Power quality is the set of costraits of electrical properties that allows electrical syste to fuctio i iteded aer without sigificat loss of its perforace or life. The power quality proble causes syste equipet s alfuctioig (partial or coplete failure of power syste equipets) [39,40] which ca be very costly for ed users so i order to iiize power quality evets, it ecessary to idetify the evets through power quality detectio ad classificatio syste. No-statioary disturbaces are the ajor cause of alfuctioig of electrical equipets. Power quality detectio requires the feature extractio fro the iput disturbace sigal.feature extractio is very iportat part of power quality aalysis. A brief survey o the ethods for power quality evets classificatio is doe i [3, 4] New ad powerful tools for aalysis are curretly available. Sigal processig tools is used for the feature extractio of power sigal. Wavelet aalysis has bee prove to be a effective sigal processig tool for the detectio ad aalysis of power sigals but other sigal processig tools such as Fourier trasfor, S-trasfor, tie-tie trasfor, higher-order statistics have also bee used to fid out other saliet features. Traditioally, Fourier trasfor is used for appig sigal fro tie doai to frequecy doai by decoposig the sigal ito various frequecy copoets, but i Fourier trasfor the tie iforatio of trasiets is copletely lost [5]. To overcoe this liitatio of Fourier trasfor shorttie Fourier trasfor (STFT) techique is used [6]. STFT is the techique which ca be used oly for statioary sigal where the frequecy does ot chages with tie but due to liitatio of fixed widow width STFT caot recogize the sigal dyaics property of a o-statioary sigal. These drawbacs of Fourier trasfor ad STFT is overcoe by wavelet trasfor. Wavelet trasfor ca be applied for statioary as well as o-statioary sigals ad provides tie-frequecy iforatio of sigal siultaeously [5, 44]. I [6,3] ethod for the detectio ad localizatio of PQ Copyright to IJIRSET 30 M.R. Thasehar ad N. Balaji (Eds.): ICIET 4

2 disturbaces i both tie ad frequecy doai was proposed. II. POWER QUALITY PROBLEMS AND CAUSES Power quality is a critical issue i power syste [8]. There are the various causes of power quality probles i power syste etwor which havig ultiple sources of supply, o liear loads ad electroic equipets [36, 38]. The rectificatio of power quality proble will reduce the ris of iterruptio ad failures of power supply. The utilizatio of a cobiatio of advaced sigal processig techiques ad real-tie oitorig process for idetificatio of failig of copoets facilitates aiteace ad reduces uscheduled outages. I [37] DSP tool is ipleeted for the iproveet of power quality i distributio syste. The iportat steps which are to be used for itigatio, of power quality probles, are as follows. ) Cotiuous oitorig of differet power syste quatities, ) Detectio, idetificatio ad categorizatio of power quality related disturbaces. 3) Fidig out probable causes of the idetified probles. 4) Autoatic rectificatio of the probable causes. Followig figure shows the various power quality probles ad their causes. III. SIGNAL PROCESSING TOOLS A. Short-Tie Fourier Trasfors I ay applicatios especially i tie frequecy aalysis of sigal, stadard Fourier trasfor is ot adequate because Fourier trasfor of the sigal does ot cotai ay of the local iforatio. I order to eliiate this weaess of Fourier trasfor, i 946 Deis Gabor (physicist ad egieer) first itroduced widowed Fourier trasfor also ow as Short Tie Fourier trasfor (STFT). The power syste geerally taes a rough estiate of the o-periodic ad tie-varyig variatios. Also for iforatio such as evaluatig duratio, severity ad localizatio of disturbace propagatio, there is a dead for both tie ad frequecy aalysis ethods. Short-tie Fourier trasfor (STFT) is a sigal processig tool used for aalysis, i frequecy doai, of sigals but it is ost suitable for the sigals which are statioary ad periodic. It ca be used for o statioary sigal but operate i fixed widow size to focus a certai period of tie, which ca trace the agitude variatios oly up to soe extet so o- statioary sigals are difficult to aalyze with shorttie Fourier trasfor [7, 8, 9,0] although it ca extract the spectral iforatio fro the sigal. I [] author used both Fourier trasfor as well as wavelet trasfor for characterizig the evets. Eve though the STFT has a Power Quality Aalysis Usig Wavelet Trasfor: A Review fixed frequecy resolutio for all frequecies oce the size of widow is chose, it gives a easier iterpretatio i ters of haroics. I [] author has used hybrid of wavelet-fourier algorith for haroic aalysis of sigal. I [7] author has doe the aalysis of voltage disturbace i tie ad frequecy doai ad with the experietal result proved that wavelet trasfor is better tha shorttie Fourier trasfor. B. Discrete STFT For the tie-frequecy aalysis of o-statioary sigals Discrete Short-Tie Fourier Trasfor (STFT) is applied. Discrete STFT decoposes tie-varyig sigal ito tie-frequecy doai copoets hece it provides the tie-evolutio of each sigal copoets. Give a sigal the discrete STFT for frequecy bad at tie is defied as jw jw X ( e ) x( ) w( ) e Copyright to IJIRSET 3 M.R. Thasehar ad N. Balaji (Eds.): ICIET 4 () I equatio above, w / N represets frequecy (i radias) N = uber of frequecy bads w () represets the selected widow size of S, S N whe sigal recostructio is required. So equatio () is equivalet to jw ~ jw X( e ) e X( w ) () I equatio () ~ jw X ( w ) x( ) w( ) e x( ) h ( ) Is the Kth coplex badpass filter s output with ipulse respose ad the cetral frequecy f jw ( ) w( e (3) h ) f fs N (Hz) Where =0,,..,N- (4) Discrete STFT i equatio () ca be see as lowpass represetatios of badpass filter output. Every badpass filter has a equal badwidth deteried by the widow selected. For Haig widow of size S, the badwidth of the badpass filters ca be give as 4 fs B (Hz) (5) S With a proper selectio of size of widow, discrete STFT is able to detect ad aalyze trasiets i a voltage disturbace. It has bee also see that STFT is ore suitable tha wavelet filters for the aalysis of voltage disturbace data. C. Wavelet Trasfor Cocept of wavelet started to appear i early 980 s as a sigal processig tool. Wavelet theory provided ew ethod for decoposig a fuctio or sigal ito various frequecy copoets, ad the study each copoet with a resolutio atch to its scale. A wavelet is a sall wave, its eergy is cocetrated i tie to give a tool

3 Power Quality Aalysis Usig Wavelet Trasfor: A Review for aalysis of trasiets, o statioary, tie varyig pheoeo which geerally occurs i the power syste etwor. Wavelet has ability to allow siultaeous tie ad frequecy aalysis of a sigal with a flexible atheatical foudatio [47]. Fig shows the wave (siusoid) oscillatig with costat aplitude i tie iterval t, thus this wave will posses ifiite eergy ad i case of wavelet as the Fig shows the eergy is fiite ad cocetrated aroud a poit. Figure. Sie Wave Figure. Daubechies Wavelet Ψ D0 This is ot a ew idea. Approxiatio usig superpositio of fuctios has existig for a log tie. I early 800's J. Fourier gave the cocept of Fourier trasfor to superpose sie ad cosies to represet other fuctios. However, i wavelet aalysis, the scale we use plays a very iportat role[]. Wavelet algoriths process data at differet scale. If we observe a sigal with a large widow, we ca otice gross features. Siilarly, if we loo a sigal with a sall widow, we could otice sall features. The result i wavelet aalysis is to see both the sall as well as large features of a sigal or fuctio. This aes wavelet a ore useful ad iterestig tool i sigal aalysis. For approxiatio of irregular sigals, sies ad cosies which coprise the bases of Fourier aalysis was ot very satisfactory. These sies ad cosies fuctios are o-local (stretch over ifiite iterval). Therefore they give poor result i approxiatio of sharp spies. Wavelets are well suited for approxiatio of data with sharp discotiuities. I wavelet aalysis, sigal broe ito a series of local basis fuctios called wavelets, which are scaled ad shifted versios of the origial (or Mother) wavelet [5]. Wavelet trasfor ca be classified i three differet ways ow as the wavelet series, cotiuous Wavelet Trasfor ad discrete Wavelet Trasfor. I wavelet series ethod appig, of a fuctio of cotiuous variable ito a sequece of coefficiets, is doe. I cotiuous WT, each wavelet is created by perforig scalig ad traslatio operatios i a other wavelet. Mother wavelets are oscillatig fuctio with a fiite eergy ad average value of zero, i.e. ( t) dt 0, where (t) is the R other wavelet [45], ay wavelet fuctios aed as other wavelets. The wrog choice of other wavelet ay lead to poor results as they have differet properties. Soe of the popular wavelets are Haar, Morlet, Coiflet, Sylet ad Daubechies. These wavelet fuctios are used accordig to the applicatio, db4 is frequetly adopted wavelet i power quality applicatios [8]. I [46] series of wavelet applicatio i uerical aalysis has bee perfored. The sigal ca be represeted i ters of wavelet fuctio ad scalig fuctio as j / j f ( t) c ( ) ( t ) d ( ) ( t ) (6) Where c j d j j j represets level scalig coefficiet, represets j level wavelet coefficiet, represets scalig fuctio, (t) represets wavelet fuctio, j ca be ay higher level wavelet trasfor ad t is tie. The wavelet coefficiets represet the iforatio which is cotaied i various frequecy bads of a sigal. The pea agitude, the ea value, square agitude, the stadard deviatio, the etropy of these coefficiets at the differet resolutio levels are cooly used agitudes proposed i the literature as characteristic features for the detectio ad aalysis of power quality evets i power systes [3]. Pea ad square agitude, stadard deviatio ad ea value of wavelet coefficiets are proposed for aalysis of voltage evet [4-3]. The coefficiets of the CWT with the Morlet wavelet fuctio for detectio ad localizatio purposes are used i [6,7]. I [30, 3] wavelet trasfor ad SVM is used for developet of algorith for autoatic classificatio of power quality evets. I [3] a approach for power quality disturbace classificatio usig Wavelet Trasfor (WT) ad Hidde Marov Model (HMM) is proposed. I [6, 33] by usig wavelet trasfor ad S-trasfor the disturbaces i grid coected distributed geeratio syste is aalyzed. I [35] adjusted Haar wavelet fuctio is used for aalysis of power syste disturbaces. I [60] wavelet j Copyright to IJIRSET 3 M.R. Thasehar ad N. Balaji (Eds.): ICIET 4

4 trasfor has bee used for recogizig overvoltage i a power syste etwor. D. Cotiuous wavelet trasfors The cotiuous wavelet trasfor (CWT) of a cotiuous sigal ca be expressed as CWT x( a, b) * x( t) ( t dt a, b R a 0 a, b ) Where, * * t b a, b( t) (8) a a x (t) is sigal to be aalyzed, (t) is other wavelet fuctio, a is scalig paraeter ad b is traslatio paraeter [5]. The other wavelet is chose to provide a prototype for all widows i the process. All the widows used for the dilated, copressed ad shifted are the versios of the other wavelet. ulie Fourier Trasfor, CWT has a ability to create a tie- frequecy represetatio of a sigal which offers very good tie ad frequecy localizatio. I other words, CWT divides a cotiuoustie sigal ito a equal tie itervals ad equalfrequecy itervals. I CWT, sigal is ultiplied with wavelets, sae as STFT ad the trasfor is coputed idividually for differet parts of the tie-doai sigal. I [8] CWT ad Morlet wavelet fuctio are used for the oise rejectio, i cobiatio with ultiresolutio sigal decopositio ad recostructio with db6 are used for detectio ad estiatio of the duratio ad aplitude respectively of the power disturbace. Visual detectio of power quality evets i the tie frequecy plae is doe i [9-0]. CWT is ot frequetly used because of its coputatio coplexity [4]. E. Discrete Wavelet Trasfors Discrete wavelet trasfor (DWT) uses the discrete values of the sigal i tie doai. Matheatically the expressio for DWT ca be give as t b oao a, b( t) (9) a ao o Where ad are the itegers which cotrols the wavelet dilatio ad traslatio respectively, ao is a fixed dilatio step paraeter which should be always greater tha oe ad b is the positio paraeter, it s value o should be ore tha zero. Paraeters ad cotai the set of positive ad egative itegers. The scale-locatio of the sigal i the tie-frequecy-doai is deteried by usig equatio (0) give below Power Quality Aalysis Usig Wavelet Trasfor: A Review (7) /, x( t) ao ( ao t bo ) doai ca be deteried oly after calculatio of all Copyright to IJIRSET 33 M.R. Thasehar ad N. Balaji (Eds.): ICIET 4 T (0) Where, the values of T are the scale-locatio grid of the sigal i tie frequecy doai accordig to idexes ad. I power quality aalysis, the discrete wavelet trasfor is sufficiet to classify the power quality probles. It coverts a tie doai discrete sigal to its correspodig wavelet doai. This process is called sub-bad codificatio, which is doe by applyig digital filter techiques. I theory sigal processig, filterig a give sigal f eas aig a covolutio of this sigal. DWT evaluatio has two stages show i Fig 3 f() dt h d () g d () y h () y g () Figure 3. Sub-bad Codificatio of a Sigal The f sigal is passed through a low-pass ad a highpass digital filter h d () ad g d () respectively. Half of the sigal saples are the eliiated which is idicated by. DWT evaluatio ivolves two steps. I first step the wavelet coefficiets are deteried. These obtaied coefficiets represet the sigal i the wavelet doai. I the ext step, the obtaied wavelet coefficiets are used for calculatig approxiatio as well as the detailed versio of origial sigal, i differet levels of resolutios, i the tie doai are doe. Output of first level decopositio of sigal is first level wavelet coefficiet of approxiatio ad of detailed versio, which are y h () ad y g () respectively. These coefficiets are ow as ca ( ) ad cd ( ) respectively. Ad ca be stated as followig ca ( ) f ( ). hd ( ) () cd ( ) f ( ). g d( ) () Whe these sigals pass through aother low pass digital filter the secod level wavelet coefficiet of approxiatio ad of detailed versio ca be obtaied they ca be writte as ca ( ) ad cd ( ) respectively. This process will cotiued up to - i order to calculate to calculate the level approxiated ad detailed wavelet coefficiets. Wavelet trasfor i tie

5 Power Quality Aalysis Usig Wavelet Trasfor: A Review wavelet coefficiets. This is obtaied by the process ow as rebuildig the correspodig wavelet coefficiets, alog the differet resolutio levels. Thus we get the approxiated ad the detailed versio of the sigal, ca j () ad cd j () respectively, ad correspodig wavelet spectru is also obtaied [3]. I [4] author has presets a approach, usig the discrete wavelet trasfor (DWT) aalysis, which is able to provide the detectio ad tie locatio of power quality probles.[4] presets DWT based power quality idex. I [43] the use of DWT i low frequecy applicatio of power syste has bee proposed. The low frequecy i power syste ay lead to blacout. I [4] DWT is used presets a approach which is able to provide the detectio, tie locatio ad the idetificatio of power quality proble i which the sigal is first decoposed i wavelet trasfor. Later, usig the obtaied wavelet coefficiets, feature extractio is doe ad a Artificial Neural Networ is developed for classificatio of the power quality disturbaces. F. Multiresolutio aalysis Multiresolutio aalysis techique of wavelet is used i aalysis of wavefors ad iages [5-56]. Wavelet fuctios ad scalig fuctios are used as buildig blocs to decopose ad recostruct the sigal at differet resolutios i Multi Resolutio Aalysis (MRA). I MRA two filters schee is utilized i each level, i which oe is low pass filter ad aother is high pass filter show i figure below, Co() h() C() c() d() g() d() h() g() Figure 4. Multi resolutio Aalysis The copoet obtaied after level MRA aalysis level will be iitial sigal for MRA level. This sigal is the passed through low pass filter ad high pass filter. The filter s output are the high frequecy copoet i level as relatio i eq.(5)-(6). h c c (5) g c d (6) I [3] the author proposed a wavelet Multi-Resolutio Aalysis (MRA) techique based odel which was used to decopose the sigal ito various details ad approxiatio sigals, ad uique features fro the st, 4th, 7th ad 8th level detail are obtaied as criteria for classifyig the type of disturbace occurred. G. Applicatio of wavelet trasfor i other fields of power syste Wavelet trasfor has bee ipleeted i followig several fields of power syste i last few years Power quality Power syste protectio Power syste trasiets Partial discharge Load forecastig Power syste easureets. Measuree t % Partial discharge 4% Load forecastig 3% others % Power Syste Protectio 36% Let the sigal c ( ) is discrete tie sigal scattered i 0 two levels. This sigal is filtered ito low frequecy copoet level ( c ( ) ) by usig low pass filter ( h () ) ad ito high frequecy copoet level ( d ( ) ) by usig high pass filter ( g () ). This sigal is the passed through dow saplig this ca be show by the relatio give i eq.(3)-(4). h c c 0 (3) g c d 0 (4) g() ad h() are high pass ad low pass filters respectively. Trasiets % Power Quality 3% Figure 5. Wavelet based Applicatios i Power Syste(Publicatios) IV. DE-NOISING I power quality aalysis, the sigal captured, for idetifyig the types of disturbace, is ofte polluted by haroics ad oises. The presece of oises i the sigal creates a proble i the feature extractio of the sigal ad it becoes a very difficult tas whe the Copyright to IJIRSET 34 M.R. Thasehar ad N. Balaji (Eds.): ICIET 4

6 Power Quality Aalysis Usig Wavelet Trasfor: A Review existig oise has high frequecy spectru. Geerally the disturbaces i power syste has high frequecy spectru therefore if the oises preset i the sigal also has high frequecy spectru the the frequecy of both, the oise ad the fault or disturbace, will overlap with each other ad it becoe difficult to idetify the disturbace. To overcoe this difficulty ad to iprove the perforace of the syste a suitable de-oisig schee to be icorporated ito the syste so that the classificatio syste becoe worable eve i a oisy eviroet [33, 34]. I [9] the author tested the perforace of his proposed ethod i differet oisy eviroets, differet levels of oises with the sigal to oise ratio (SNR). The overall accuracy of classificatio capability of proposed ethod was foud 95.8%. I [34], it is clear that if the sigals are cleared fro oises, the start ad ed of the disturbaces ca be easily detected due to variatio i aplitude of the DWT coefficiets about those particular poits ad the duratio of occurrece ca the be deteried. I [57] author has give a overview of wavelet based threshold ethods for de-oisig of power sigal. I [58] author has proposed two stadard statistical hypotheses test-based de-oisig procedures for power quality iproveet. I [59] author has proposed a de-oisig approach to detectio of trasiet disturbaces i a oisy eviroet i power quality oitorig syste. V. CONCLUSION This paper presets coprehesive survey o the developet of techologies used i power quality aalysis, which is the ajor area of research i the field of power syste. For detectig ad characterizig power syste disturbaces wavelet based systes have bee foud to be ore robust ad effective. Fro the aalysis of the literature it ay be cocluded; Oe of the proisig issues i field of power quality is developet of high speed autoatic syste for the idetificatio, detectio ad classificatio of disturbace. The differet techiques of wavelet are used to build ew odels for aalysis of power quality evets. Thus the scope for future applicatios icludes olie oitorig, fault classificatio ad real tie cotrol syste. REFERENCES [] I. Huter, Power quality issues: a distributio copay perspective, Power Egieerig Joural, vol. 5, o., pp , April 00. [] M.H.J. Bolle, what is power quality? Electric power Systes Research, vol. 66, o., pp. 5-4, 000. [3] C.H. Ki, R. Aggarwal, Wavelet trasfors i power systes: part geeral itroductio to the wavelet trasfors, Power Egieerig Joural, pp. 8-07, 000. [4] C.S. Burrus, R.A. Gopiath, H. Guo, Itroductio to wavelets ad wavelet trasfors: a prier, New Jersey: Pretice Hall, 998. [5] A. A. Abdelsalaa, A. A. Eldesouyb, A. A. 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