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1 Ctato: jayaulasoorya, Jaaa V., Putrus, Gham ad Ng, Chog 2005 Fast orecursve extracto o dvdual harmocs usg artcal eural etwors. IEE Proceedgs: Geerato, Trasmsso ad Dstrbuto, p ISSN Publshed by: IET URL: < Ths verso was dowloaded rom Northumbra Research L: Northumbra Uversty has developed Northumbra Research L NRL to eable users to access the Uversty s research output. Copyrght ad moral rghts or tems o NRL are retaed by the dvdual authors ad/or other copyrght owers. Sgle copes o ull tems ca be reproduced, dsplayed or perormed, ad gve to thrd partes ay ormat or medum or persoal research or study, educatoal, or ot-or-prot purposes wthout pror permsso or charge, provded the authors, ttle ad ull bblographc detals are gve, as well as a hyperl ad/or URL to the orgal metadata page. The cotet must ot be chaged ay way. Full tems must ot be sold commercally ay ormat or medum wthout ormal permsso o the copyrght holder. The ull polcy s avalable ole: Ths documet may der rom the al, publshed verso o the research ad has bee made avalable ole accordace wth publsher polces. To read ad/or cte rom the publshed verso o the research, please vst the publsher s webste a subscrpto may be requred.

2 Fast No-Recursve Extracto o Idvdual Harmocs Usg Artcal Neural Networs J.V. jayaulasoorya, BSc, PhD G.A. Putrus, BSc, MSc, PhD, CEg, MIEE correspodg author C.H. Ng, BSc Power ad Cotrol Research Group School o Egeerg Uversty o Northumbra at Newcastle Ellso Buldg Newcastle upo Tye NE1 5RD UK Tel Fax

3 Fast No-Recursve Extracto o Idvdual Harmocs Usg Artcal Neural Networs Idexg terms: Harmocs, Harmoc extracto, Artcal Neural etwors Abstract No-lear loads, whch cause harmoc dstorto, are creasgly beg used electrcal power systems. Ths s causg a major cocer ad real-tme harmoc motorg electrcal power systems has become mportat. May applcatos such as harmoc motorg ad lter desg eed techques or ast extracto o dvdual harmoc compoets. The tme lmtatos ad computatoal complexty assocated wth covetoal techques mae t appealg to vestgate ew techques or harmoc extracto. Ths paper presets a ovel techque based o artcal eural etwors ANN or ast extracto o dvdual harmoc compoets. It uses the o-lear mappg capabltes o ANNs to accurately estmate dvdual harmoc compoets o a dstorted sgal. The proposed algorthm was mplemeted o a real-tme hardware platorm ad tested. Results show that the Artcal Neural Networ based Harmoc Extractor ANNHE s sgcatly aster ad less computatoally complex tha covetoal techques.

4 1. Itroducto The assumpto that the electrcal supply at the customers' mas s a set o balaced susodal voltage sources s ever ully reached practce. The susodal shape o the voltage waveorms gets deormed due to the low o curret sgals other tha those at udametal requecy, whch are mostly geerated by o-lear loads coected to the system. These steady-state perodc waveorms, whch deorm the supply sgal, are termed as harmocs. Harmocs power systems cause losses, coveece ad sometmes serous problems to the cosumer as well as to the power system [1-4]. Recet ew years have wtessed rapd growth harmoc voltages ad currets jected to the power system due to the creased utlsato o o-lear loads. I addto, devces employg hgh requecy swtchg, such as swtch mode power supples SMPS televsos, computers ad compact luorescet lghtg add a sgcat level o harmocs to the supply system. Although voltage dstorto at the trasmsso level s typcally much less tha 1.0 percet, ths dstorto creases closer to the load pot. At some loads, the curret waveorm wll barely resemble a se wave. As a result, harmoc dstorto s more proouced at the dstrbuto level. The eects o creasg harmoc levels electrcal power systems have trggered several ssues regardg the qualty o the supply. Oe such ssue s adaptato o harmoc stadards such as G 5/4 Lmts or harmocs the UK electrcty supply system[4], to set lmts o the harmoc polluto. Accordg to these stadards, the ed users must lmt the harmoc currets jected to the power system. These stadards requre that cosumers should mata the harmoc curret geerated by

5 ther loads below some speced values. To adequately deal wth the harmoc dstorto electrcal power systems, ad to comply wth the above recommedatos, t s o the utmost mportace to motor the harmoc levels. Covetoal techques used or harmoc motorg employ ether requecy doma or tme doma harmoc extracto techques. Dscrete Fourer Trasorm DFT ad Fast Fourer Trasorm FFT are usually used or calculatg the harmoc cotet o a perodc sgal. Although the FFT s ast terms o computg speed, t eeds data pots sampled over oe cycle o the sgal to accurately calculate the harmoc compoets. Thereore, the tme requred to extract the harmoc compoet depeds o the udametal requecy o the sgal beg aalyzed. Ths s a major drawbac whe aalysg sgals wth low requeces. Sce the udametal requecy o electrcal power system sgals s 50 Hz or 60 Hz typcally, harmoc extracto taes 20 ms or ms, respectvely. Also, the perverso o FFT or DFT would yeld accurate results, due to ptalls such as alasg, leaage ad pcet ece eect [5]. I addto, the FFT ca be cosdered as a more geeral approach to harmoc extracto, where all the harmoc requecy compoets wth the bad-wdth o the sgal s calculated. Ths maes the FFT processor hardware more expesve as more computatoal power s requred. However, may applcatos, such as harmoc motorg, may requre extracto o a lmted umber o dvdual harmocs. For a example, may cases oly the 5th ad 7th harmocs are o terest as the levels o other harmoc compoets are sgcatly low. Tme doma techques or harmoc extracto maly uses dgtal lter techques such as Ite Impulse Respose IIR lters. Although, these ca be used to extract

6 dvdual harmoc compoets, the rpple ad tme delay herted these lters mae them less appealg. Also, practcal dcultes mplemetg the deal lter characterstcs mae the desg process o these lters much more complcated. More recet research eorts revolve aroud proposg alteratve techques or harmoc extracto. The dgtal recursve measuremet scheme or o-le tracg o power system harmocs proposed by Grgs et al [6] uses a Kalma Ftler KF to estmate the harmoc compoets. It s reported that the method preseted s capable o tracg harmocs eve wth tme varyg ampltudes. I ths method, the dstorted sgal s state space modelled wth harmoc compoets as state varables. The, a KF based techque s appled to estmate the harmoc compoets. The KF algorthm s more accurate tha the FFT ad t s also capable o extractg dvdual harmocs. However, oe o the major drawbacs o ths method s that the KF has to be ormulated or all possble requeces expected. Omsso o ay requecy compoet at the ormulatg phase o the KF wll lead to accurate results. Also, ths method eeds correct deto o state equatos, measuremet equatos ad covarace matrces. The "subspace" methods such as m-orm method ad Proy method are dscussed by Leoovcz et al [7]. It has bee show that the m-orm method could be eectvely used or parameter estmato o dstorted sgals ad Proy method could also be appled or estmatg the requeces o sgal dstorto. However, the computatoal complexty o these methods s much more tha that o the FFT whlst the tme tae or harmoc extracto s smlar. The use o ANNs or real-tme harmoc motorg has bee the ocus o may researchers [8-11]. ANNs provde smple ad straghtorward techques or selectvely tracg dvdual harmoc

7 compoets. However, all these methods the ANN s ot used ts pure orm, where a put s ed to the ANN ad a output s tae. Rather, they use the trag algorthm o ANNs, whch recursvely estmate the harmoc compoets. Due to the recursve ature o harmoc estmato, results publshed so ar dcate sgcatly slower respose, eve less tha the FFT. Also, the eed or susodal waveorm geerators at deret requeces maes the hardware realsato more complex. Ths paper proposes a method based o eed orward ANNs, whch s sgcatly aster tha the FFT. Also, t requres less computatoal power allowg t to be mplemeted eve o low-ed mcrocotrollers, whch reduces the hardware mplemetato costs sgcatly. ANNs bascally use addto ad multplcato operatos, whch ca be mplemeted more easly o mcrocotrollers, as compared to calculato o se ad cose uctos the FFT ad calculato o matrx verso the Kalma Flter. 2. Formulato o the ANN 2.1 Artcal Neural Networs ANN A eed orward mult-layered ANN ca be cosdered as a lexble mathematcal structure whch s capable o detyg complex o-lear relatoshps betwee put ad output data sets. For these reasos ANN models have bee oud useul ad ecet, partcularly problems or whch the characterstcs o the process are dcult to descrbe usg mathematcal equatos. ANNs are powerul objects havg erece ad geeralsato capabltes; act, a ANN that has bee traed wth a represetatve umber o examples o a gve process s able to extrapolate states ot preset example data set.

8 A ANN cossts o smple processg elemets ow as euros. The puts to the ANN are weghted ad processed by each euro. Itally, a eural etwor has to be traed usg a set o put data represetg possble puts to the etwor ad the desred output data. I ths process, the weght o each euro s adjusted to mmse the output error. Ater trag, uow put data ca be preseted to the eural etwor ad correspodg output data are obtaed. I ay gve applcato, selecto o approprate parameters as put ad output o the etwor s the ey to the success ad optmal perormace o the eural etwor. Thereore, the case o power system harmoc extracto, the rst tas would be to ormulate the problem ad the selecto o a sutable set o put ad output parameters. 2.2 Problem ormulato A voltage or curret sgal st that s dstorted wth harmocs ca be modelled as: N 0 s t V s t 1 where V ad are the ampltude ad phase agle o the th harmoc compoet, respectvely. The proposed system samples the sgal st at a samplg requecy s ad the tme dscrete sgal S s obtaed, where 0, 1, 2,... etc. The, M tme delayed samples rom S are ed to the ANN as show Fgure 1. Thereore, the put to the ANN s a colum vector gve by: S{ M 1} S{ M 2 }... S 1 S T 2 A mmal value or M s desred, as t wll determe the tme tae to extract the harmoc. However, t should be large eough to gve the ANN a sucet umber o puts ad hece mproved accuracy.

9 The output o the ANN, Y, s a ucto o the put vector ad the weghts assocated wth euros. Thereore, Y, 3 The desred output o the ANN, d Y, s the extracted th harmoc compoet ad s gve by: s d V Y s 4 The output error s, Y Y d, s V s 5 Least Mea Square LMS algorthm used or trag ANNs s based o a approxmate steepest descet procedure. I ths method, the adjustmet to the th weght s estmated by usg the partal dervatve o the squared error wth respect to the th weght. That s [12]: 2 old ew 6 where s a parameter used or tug the learg process typcally s betwee 0 ad 1. Substtuto rom equato 5 equato 6 yelds: 2, s s old ew V,, s 2 s old ew V 7 The terato s cotued utl reaches a predetermed error goal.

10 2.3 Implemetato o the ANN A multlayer eed orward ANN wth 5 euros at the put layer ad 1 euro at the output layer s mplemeted as show Fgure 1. The ANN s traed usg a sgal cotag tme-varyg 3 rd, 5 th, 7 th, 11 th ad 13 th harmoc compoets. Also, the trag sgal was cotamated wth 1% r.m.s. whte ose ad the udametal requecy o the sgal also vared the rage Hz order to mae the ANN robust or ose ad requecy varatos ecoutered typcal power systems. The sgal to be aalysed s sampled at 6400 Hz, whch s oud to be sucet to all the sgcat harmoc compoets up to th 64 harmoc. Separate ANNs were traed or extractg each dvdual harmoc compoet. Expermets revealed that whe the umber o put samples M 31, the ANN does ot reach the set error goal o Thereore, M s set to 31 where the ANN coverged to the set error goal. he the ANN was tested wth data whch are deret rom the data used or trag, results produced were accurate. Ths problem was aalysed ad deted as the "over ttg" problem assocated wth ANNs [12]. Ths problem results whe weghts are coverged to local mma durg the terato o equato 7. To resolve the problem, a addtoal output Y s troduced as show Fgure 2, whch esures that the weghts coverge the correct drecto. Let, ad, Y, 8 Y d V cos 9 s

11 The adjustmet to the th weght s estmated by usg the partal dervatve o the sum o the squared error wth respect to the th weght as gve by equato old ew 10 where, 2 2 2, cos, s V V E s s 11 Thereore,,,,, 2 d d old ew Y Y 12 The over ttg problem o the ANN s elmated by ths modcato. As a addtoal bous, computato o the ampltude o th harmoc compoet V becomes straght orward as, 2 2 Y Y V 13 It worth potg out that the total harmoc dstorto THD may be calculated usg the r.m.s. values o domat harmoc compoets, as determed by equato 13. Also, a reerece tme s deed, the phase o the harmoc compoet ca be calculated by usg equatos 4 ad Expermetal Results 3.1 Laboratory setup The ANN modules were mplemeted o a dspace DS1103 real-tme hardware platorm cotrolled by Matlab Smul. The test sgals were geerated the laboratory by supermposg ow harmoc compoets o a 50 Hz sgal.

12 Ampltude o the udametal ad the harmoc compoets were chaged ad both the actual ad estmated compoets were measured ad recorded usg TDS3034, 300 MHz Dgtal Osclloscope. 3.2 Extracto o harmoc compoets Fgure 3 shows extracto o the udametal, 5th ad 7th harmocs rom 50 Hz sgals dstorted wth 5 th, 7 th, 11 th ad 13 th harmoc compoets ad 1% whte ose. The sampled sgal, actual compoet ad extracted compoets are llustrated. The results show that the ampltude ad phase o the extracted dvdual harmoc compoets are equal to that o the actual sgal. Also, t ca be see that the ANNHE respose to the chages the dvdual harmoc compoets s relatvely ast. 3.3 Eect o requecy varato The eect o the varato o the udametal requecy o the accuracy o the ANN based harmoc extractor s observed ad aalysed usg smulated data Matlab- Smul platorm. Fgure 4 shows the actual ad estmated 5 th harmoc compoet o a sgal wth a udametal requecy o 51 Hz. To quaty the eect o requecy varato, the percetage r.m.s. error, as deed by equato 14, s used. The % error at deret requeces betwee Hz s gve Fgure 5. v t actual v t estmated Root Mea Square Error % v r.m.s. actual 2 The results show that durg ormal requecy varatos 50 Hz 1%, the extracted harmoc compoet oly slghtly vares rom the actual harmoc compoet.

13 4. Dscusso The ANNHE ad tme doma requecy extracto techques have bee mplemeted Matlab-smul platorm ad respose tme to a step crease o the 5th harmoc compoet o a sgal s aalysed. Two commo tme doma harmoc extracto techques are chose; the IIR lter ad the Kalma lter. The results o extracto usg two types o IIR lters, a Kalma Flter ad the proposed ANNHE techque are preseted Fgure 6, or comparso. The results descrbed ths paper demostrate that the proposed ANNHE techque s capable o accurately extractg harmoc compoets rom a dstorted sgal. I addto, t s show that the proposed method s aster tha other tme-doma harmoc extracto techques cosdered; see Fgure 6. It should be oted that although the respose tme o IIR lters ca be reduced by lowerg the order, the rpple assocated wth them s usually a major cocer [6]. The Kalma lter seems to provde a much aster harmoc extracto tha covetoal IIR lters. However, computatoal complextes such as matrx verso volved KF mae t less appealg or real-tme hardware mplemetato. The recursve ature o ANN based techques proposed the lterature [8-11], results a much slower respose tme e.g. 35 ms [11]. The proposed ANNHE techque s oud to be robust or usual varatos the udametal requecy. However, t s worth otg that IIR lters are more robust to varatos udametal requecy tha the ANNHE techque, as they ca be desged to operate wth a wder badwdth. Nevertheless, ormal varatos the udametal requecy o electrcal power systems are very small 1% whch meas that the techque s capable o provdg adequate perormace wth ths rage.

14 5. Coclusos Ths paper proposes a ovel ANNHE to extract harmoc compoets rom a dstorted sgal. The proposed ANNHE s oud to be much aster tha covetoal techques, such as FFT, ad other techques preseted the lterature. The results obtaed show that the proposed ANNHE s robust to ormal varatos the udametal requecy ad ose preset the sgal. The proposed ANNHE s a powerul tool that requres low-cost hardware or real-tme mplemetato. It ca be used or dvdual harmoc extracto may applcatos electrcal power systems. 6. Reereces [1]. IEEE org Group o Power System Harmocs, Power system harmocs: A overvew, IEEE Trasactos: Power Apparatus ad Systems, August 1983, PAS-102, 8, pp [2]. IEEE tas orce o the eects o harmocs o equpmet, Eects o harmocs o equpmet, IEEE Trasactos: Power Delvery, Aprl 1993, PD-8, 2, pp [3]. IEEE tas orce o the eects o harmocs o equpmet, Eects o power system harmocs o power system equpmet ad loads, IEEE Trasactos: Power apparatus ad Systems, September 1985, PAS-104, 9, pp [4]. Egeerg recommedato G 5/4, Lmts or harmocs the Uted Kgdom electrcty supply system, 2000.

15 [5]. Grgs, A.A., Ham, F., A qualtatve study o ptalls FFT, IEEE Trasactos: Aerospace ad Electroc Systems, July 1980, Vol. 16, No. 4, pp [6]. Grgs, A.A., Chag,.B., ad Marram, E.B., A dgtal recursve measuremet scheme or o le tracg o power system harmocs, IEEE Trasactos: Power delvery, Vol. 6, No. 3, 1991, pp [7]. Leoowcz, Z., Lobos, T., Rezmer, J., "Advaced spectrum estmato methods or sgal aalyss power electrocs", IEEE Trasactos: dustral electrocs, Jue 2003, Vol. 50, No. 3, pp [8]. Osows, S, Neural etwor or estmato o harmoc compoets a power system, IEE Proceedg: Geerato, Trasmsso ad Dstrbuto, March 1992, Vol. 139, No. 2, pp [9]. Dash, P.K., Swa, D.P., Routray, A., Lew, A.C., Harmoc estmato a power system usg adaptve perceptros, IEE Proceedg: Geerato, Trasmsso ad Dstrbuto, November 1996, Vol. 143, No. 6, pp [10]. Hartaa, R.K, Rchards, G.G., Harmoc source motorg ad detcato usg artcal eural etwors, IEEE Trasactos o Power Systems, November 1990, Vol. 5, No. 4, pp [11]. La, L.L., Cha,.L., Tse, C.T., So, A.T.P.: "Real-tme requecy ad harmoc evaluato usg artcal eural etwors", IEEE Trasactos: Power Delvery, Jauary 1999, Vol. 14, No. 1, pp [12]. Hay, S, Neural Networs: A Comprehesve Foudato 2d Edto, Pretce-Hall, 1999.

16 7. Lst o Fgures Fgure 1: ANN archtecture used or requecy extracto. Fgure 2: Moded ANN archtecture. Fgure 3: Extracto o the udametal, 5 th ad 7 th harmoc compoets. Fgure 4: Actual ad estmated 5 th ad 7 th harmoc compoet o a sgal wth a udametal requecy o 51 Hz. Fgure 5: R.M.S. error versus requecy Fgure 6: Tme respose to a step crease o 5 th harmoc compoet.

17 1 Z 1 1 Z Z S{ M 1} 1 S S 1 Y Fgure 1: ANN archtecture used or requecy extracto 1 Z 1 1 Z Z S{ M 1} 1 S S 1 Y Y Fgure 2: Moded ANN archtecture

18 c. Extracted udametal compoet Fgure 3a: Extracto o the udametal compoet c. Extracted 5th harmoc compoet Fgure 3b: Extracto o the 5 th harmoc compoet

19 c. Extracted 7th harmoc compoet Fgure 3c: Extracto o the 7 th harmoc compoet Fgure 3: Extracto o the udametal, 5 th ad 7 th harmoc compoets.

20 Extracted 5th harmoc compoet a 5 th harmoc compoet Extracted 7th harmoc compoet b 7 th harmoc compoet Fgure 4: Actual ad estmated a 5 th ad b 7 th harmoc compoet o a sgal wth a udametal requecy o 51 Hz

21 R.M.S. error % * * Fudametal x x 5 th Harmoc o o 7 th Harmoc Frequecy Hz Fgure 5: R.M.S. error versus requecy

22 Fgure 6: Tme respose to a step crease o 5th harmoc compoet a IIR lter o order 2 b IIR lter o order 6 c Kalma Flter d. ANNHE

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