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2 Etimatio of Power Sytem Harmoic Uig Hybrid RLS-Adalie ad KF-Adalie Algorithm B.Subudhi ad P.K.Ray Departmet of Electrical Egieerig atioal Ititute of echology, Rourkela, Idia Abtract hi paper preet combied RLS-Adalie (Recurive Leat Square ad adaptive liear eural etwor ad KF-Adalie (Kalma Filter Adalie) approach for the etimatio of harmoic compoet of a power ytem. he eural etimator i baed o the ue of a adaptive perceptro compriig a liear adaptive euro called Adalie. Kalma Filter ad Recurive Leat Square algorithm carry out the weight updatig i Adalie. he etimator track the igal corrupted with oie ad decayig DC compoet very accurately. Adaptive trackig of harmoic compoet of a power ytem ca eaily be doe uig thee algorithm. he propoed approache are teted both for tatic ad dyamic igal. Out of thee two, the KF-Adalie approach of trackig the fudametal ad harmoic compoet i better. Keyword-Harmoic Etimatio; Adaptive Liear eural etwork(adalie); Dicrete Fourier raform(df); Fat Fourier raform(ff); I. IRODUCIO Due to the itroductio of electroically cotrolled load, the harmoic ditortio i power ytem voltage ad curret waveform i icreaed. Damped high-frequecy traiet are geerated due to frequetly witchig o ad off of power emicoductor at poit of voltage ad curret waveform. So voltage ad curret waveform of a ditributio or a tramiio ytem are ot pure iuoid, but may coit of fudametal frequecy, harmoic ad high frequecy traiet. Alo may of power ytem load are dyamic i ature which implie time varyig amplitude of the curret waveform o provide the quality of the delivered power, it i importat to kow the harmoic parameter uch a amplitude ad phae. hi i eetial for deigig filter to elimiate or reduce the effect of harmoic i a power ytem [4]. So may algorithm have bee propoed to evaluate the harmoic [-, 4-9, -]. I order to get the voltage ad curret frequecy pectrum from dicrete time ample, mot frequecy domai harmoic aalyi algorithm are baed o the dicrete Fourier raform (DF) or o the fat Fourier traform (FF). However, thee two method uffer leakage effect []. Although other method, icludig the propoed algorithm i thi paper, uffer that problem, ad thi i due to exitig high-frequecy compoet i the meaured igal, but trucatio of the equece of ampled data, whe oly a fractio of the equece of a cycle exit i the aalyzed waveform, boot leakage problem of DF method. So the eed for ew algorithm that proce the data, ample-byample, ad ot a widow of data a i DF ad FF, i of importace. Becaue thee method proce data ample-byample, looig oe or more ample create le leakage problem tha DF ad FF. Kalma Filter [6,,, 4-] i oe of the robut algorithm for etimatig the magitude of iuoid of kow frequecie embedded i a ukow meauremet oie. But thi algorithm caot track abrupt or dyamic chage of igal ad it harmoic. Recetly, may reearcher adopt Artificial Itelligece techique [] for harmoic etimatio. Dah et al. [4] ue a algorithm baed o a adaptive eural etwork, which how better trackig capability of dyamic amplitude a to that of claic Kalma filterig approach. I that algorithm, the weight are updated uig Widrow-Hoff delta rule. A etimatio of harmoic parameter i a oliear problem, Qidwai ad Betayeb [- ] ue Geetic algorithm (GA), a a heuritic ad tochatic global earchig algorithm for thi purpoe. hi method provide excellet reult but mai diadvatage i that i take more time for covergece. II. PROPOSED ALGORIHM Let u aume the voltage or curret waveform of the kow fudametal agular frequecy a the um of harmoic of ukow magitude ad phae. he geeral form of the waveform i y( A i( t ) A exp( ( () Where, i the umber of harmoic. fudametal frequecy; ( i the additive oie; A exp( f ; i the i the probable decayig term. he dicrete time verio of Eq. () ca be repreeted a y( A i( k ) A exp( k) ( () Where, i amplig period. Approximatig decayig term uig firt two term of aylor erie a y A A k () f /9/$6. 9 IEEE ECO 9

3 ow Eq. () become y( A i( k ) A A k ( (4) he oliearity arie i the model i due to phae of the iuoid. Bettayeb ad Qidwai ued GA for etimatig phae of the harmoic. Although uig GA for etimatig phae alleviated the metioed problem but due to itroductio of GA, the algorithm become low ad caot be ued a a olie etimator. I thi paper a fat eural etwork called Adalie i ued. he weight of the adalie i updated uig Recurive Leat Square ad Kalma Filter algorithm. For etimatio amplitude ad phae Eq.(4) ca be rewritte a [ A i( k )co A co( k )i ] y( () A A k ( k ) Fig. Block diagram of Adalie hi equatio give a idea of uig a adaptive liear combier compriig a eural etwork called Adalie to etimate the phae of the harmoic. he block diagram of the Adalie i how i fig. he iput to the Adalie i x ( [i( co(... i( t ) co( t] (6) he weight vector of the Adalie W ( [ Wk ( ) W (... W ( W ( W ( W ( ] (7) i updated uig Recurive Leat Square Algorithm a x x x... x W W W W ( k ) W ( K( k ) ( k ) (8) Error i meauremet i ( k ) y( k ) k ) W( (9) he gai K i related with covariace of parameter vector Weight updatio W y^( y( e e( K( k ) P( k )[ ( k ) P( k )] () he updated covariace of parameter vector uig matrix iverio lemma P( k ) [ I K( k ) k ) ] P( () akig ome iitial value for the etimate at itat t iitialize thee equatio. A the choice of iitial covariace matrix i large it i take P=I where i a large umber ad I i a quare idetity matrix. he weight vector of the Adalie i updated uig Kalma Filter Algorithm a G( P( k / k ) ( P( k / k ) Q) () G i the Kalma gai, x i the obervatio vector, P i the covariace matrix, Q i the oie covariace of the igal. So the covariace matrix i related with Kalma gai with the followig equatio. P ( k / P( k / k ) G( P( k / k ) () So the updated etimated tate i related with previou tate with the followig equatio. W ( k/ W( k/ k) Gk ( )( y( W( k/ k)) (4) After the updatig of weight vector uig RLS or KF algorithm, amplitude, phae of the fudametal ad th harmoic parameter ad decayig parameter are derived a A ( W W ) () W ta (6) W A W (7) W W (8) Becaue W A co( ) A i( )... A co( ) A i( ) A A ] (9) [ III. SIMULAIO RESULS AD DISCUSSIOS A. Static igal corrupted with radom oie ad decayig DC compoet. he power ytem igal ued for the etimatio, beide the fudametal frequecy, cotai higher harmoic of the rd, th, 7th, th ad a lowly decayig DC compoet []. hi kid of igal i typical i idutrial load compriig power electroic coverter ad arc furace []. y(. i( t 8 ).i(t 6 ) (). i(t 4 ). i( 7t 6 ).i(t ). exp( ( he igal i corrupted by radom oie (.rad( havig ormal ditributio with zero mea ad uity variace. Fig. ad how v. ECO 9

4 etimated igal uig ad method repectively. It i ee from the fig. that ad etimated igal almot matche with each other i both the cae. Fig. 4 how the comparative etimatio of fudametal amplitude of igal uig both ad method. I cae of, etimated amplitude ocillate betwee.47 p.u. to.p.u. but etimate fudametal amplitude a. p.u. Fig. provide a comparative etimatio of third harmoic compoet of igal uig the above two method. I the etimatio uig, durig firt few iitial time period etimatio i. p.u. after that it ettle aroud. p.u. KF-Adalie etimate third harmoic amplitude a. p.u. Fig.6 how the etimated reult of th harmoic amplitude uig both the algorithm. RLS-adalie etimate it betwee.9 to. p.u. havig more ocillatio durig iitial time period. But the etimated value of fifth harmoic compoet uig KF-Adalie i. p.u. Fig. 7 give the etimated reult of 7 th harmoic compoet of igal uig the two algorithm. RLS-Adalie etimate it aroud. p.u. but ocillatio varie from.4 to.6 p.u. KF-Adalie etimate 7 th harmoic compoet a.49 p.u. which i more accurate. Fig. 8 provide a comparative etimatio of th harmoic compoet of igal uig both the algorithm. RLS-Adalie etimate it betwee.9 to. p.u. with it ocillatio aroud. p.u. but KF-Adalie etimate it a.p.u. Amplitude i p.u im e i ec. Fig.4 Etimatio of amplitude of fudametal compoet of igal Amplitude i p.u im e i ec. Fig. Etimatio of amplitude of third harmoic compoet of igal. e tim ated... Amplitude i p.u Amplitude i p.u S am ple o. Fig. Actual ad Etimated value of igal uig.. etim ated im e i ec. Fig. 6 Etimatio of amplitude of fifth harmoic compoet of igal.6 Amplitude i p.u Amplitude i p.u Sam ple o. Fig. Actual ad Etimated value of igal uig ime i ec. Fig. 7 Etimatio of amplitude of eveth harmoic compoet of igal ECO 9

5 Amplitude i p.u..... Phae i deg ime i ec. Fig. 8 Etimatio of amplitude of eleveth harmoic compoet of igal S am ple o. Fig. Etimatio of phae of third harmoic compoet of igal Phae i deg Amplitude i p.u Sam ple o. Fig. 9 Etimatio of amplitude of compoet of igal S am ple o. Fig. Etimatio of phae of fifth harmoic compoet of igal Phae i deg Amplitude i p.u Sam ple o. Fig.4 Etimatio of phae of eveth harmoic compoet of igal im e i ec. Fig. Etimatio of amplitude of alpha of igal Fig. 9 how the comparative etimatio of compoet of igal uig both the algorithm. Etimated value of igal uig KF-Adalie i.496 p.u. but it value uig RLS- Adalie varie from.49 to. p.u. ad it ettle at.49 p.u. Fig. give the etimated reult of alpha uig both the algorithm ad it how that etimatio uig KF-Adalie i more accurate Phae i deg S am ple o. Fig. Etimatio of phae of eleveth harmoic compoet of igal -4 x.. Phae i deg MSE S am ple o. Fig. Etimatio of phae of fudametal compoet of igal im e i ec. Fig.6 Etimatio of MSE of tatic igal 4 ECO 9

6 Amplitude i p.u im e i ec. Fig. 7 Etimatio of rd harmoic compoet of igal durig amplitude chage Fig. - how the trackig of the fudametal, rd, th, 7 th ad th harmoic compoet of igal i preece of radom oie ad decayig DC compoet uig RLS-Adalie ad KF-Adalie method. I the above etimatio proce, KF- Adalie i tued optimally by properly chooig the covariace ad oie covariace matrice. he time required for trappig the fudametal ad harmoic i approximately. ec. ( ample) for RLS-Adalie method but KF- Adalie trap the fudametal ad harmoic compoet iitially with more correct etimatio. Fig.6 how the comparative etimatio of Mea Square Error (MSE) of igal uig the two algorithm. From the figure, it i foud that, MSE performace i cae of KF- Adalie i comparatively better tha RLS-Adalie method. Fig.7 how the trackig of rd harmoic compoet of igal, whe it amplitude uddely chage from. p.u. to.6 p.u. at. ec. From the fig., it i ee that both the method track the rd harmoic compoet but trackig by KF-Adalie i comparatively better. B. Harmoic Etimatio of a Dyamic Sigal o examie the performace of RLS-Adalie algorithm i trackig harmoic ad it robute i rejectig oie, a time-varyig igal of the form y( {. a( }i( t 8 ) {. a ( }i( t 6 {. a ( }i( t 4 ) ( i ued where:.i f t.i f t () a a.i f t.i f t a.i f t.i f ) () () t (4) f. Hz f. Hz. f 6. Hz. ad radom oie ( i ame a i the cae of tatic igal.fig.8 ad 9 how the v. etimated value of igal uig RLS-Adalie ad KF-Adalie repectively. I both the cae ad etimated value cloely matche with each other. Fig. - how the trackig of fudametal, rd ad th harmoic compoet of amplitude of a dyamic igal uig both RLS-Adalie ad KF-Adalie method. I all the three cae RLS-Adalie provide ocillatory etimatio but KF-Adalie provide more accurate ad coitet performace. Fig ad 4 how the trackig of fudametal ad rd harmoic compoet of phae of a dyamic igal uig both the method. Both the method etimate correctly but KF-Adalie performace i better havig egligible ocillatio. Fig. provide a comparative performace of Mea Square Error (MSE) of igal. KF-Adalie performace i lightly better i MSE aalyi. Amplitude i p.u etim ated Sam ple o. Fig.8 Actual ad Etimated waveform of dyamic igal uig Amplitude i p.u etim ated Sam ple o. Fig.9 Actual ad Etimated waveform of dyamic igal uig Amplitude i p.u im e i ec. Fig. Etimatio of amplitude of fudametal compoet of dyamic igal Amplitude i p.u im e i ec. Fig. Etimatio of amplitude of third harmoic compoet of dyamic igal ECO 9

7 Amplitude i p.u im e i ec. Fig. Etimatio of amplitude of fifth harmoic compoet of dyamic igal Phae i deg S am ple o. Fig. Etimatio of phae of fudametal compoet of dyamic igal Phae i deg S am ple o. Fig.4 Etimatio of phae of third harmoic compoet of dyamic igal MSE. x im e i ec. Fig. Etimatio of MSE of dyamic igal he performace of the propoed hybrid algorithm are very depedet o the iitial choice of weight vector W ad Covariace matrix P. By uig a optimal choice of weight vector, fater covergece to the true value of igal parameter ca be achieved. After the optimizatio of the weight vector, olie trackig of the chage i amplitude ad phae of the fudametal ad harmoic compoet i preece of oie ad decayig compoet ca be carried out. Both the algorithm track the fudametal ad harmoic igal very well for both tatic ad dyamic igal but the performace of trackig uig KF-Adalie i better tha RLS- Adalie. Both the tatic ad dyamic igal are geerated i MALAB platform. he ued PC had a.46 GHz CPU ad GB RAM. he ame algorithm ca be applied to other area uch a commuicatio chael, telephoe ad other ecrypted igal. IV. COCLUSIOS hi paper preet two ew approache for adaptive etimatio of amplitude ad phae agle of harmoic i a power ytem. he approache are baed o weight vector etimatio of a Adalie uig Recurive Leat Square ad Kalma Filter algorithm. Comparig with RLS-Adalie, imulatio reult reveal improvemet i the performace of propoed KF-Adalie i trackig harmoic parameter eve i preece of white oie ad decayig compoet. REFERECES [] H. Mori, A artificial eural etwork baed method for power ytem voltage harmoic, IEEE ra. PD-7 () 4 49, (99). [] E.A.Abu, Al-Feilat, I.El.Ami, ad M.Bettayeb, Power ytem harmoic etimatio a comparative tudy, Electric Power Sytem Reearch, vol-9, pp.9-97, 994. [] Y..Chag, Y.C.Hieh, C.S.Moo, rucatio effect of FF o etimatio of dyamic harmoic i a power ytem Power Sytem echology,, Proceedig, Iteratioal Power Coferece. Vol., pp. -6, 4-7 Dec.,. [4] P.K.Dah, D.P.Swai, A.Routray ad A.C.Liew, Harmoic etimatio i a power ytem uig adaptive perceptro, IEE Proceedig Geeratio, ramiio ad Ditributio, vol.4, o.6, pp.6-74, ov.996. [].Lobo,.Kozia & H.J.Kogli, Power ytem harmoic etimatio uig Liear Leat Square method & SVD IEE Proceedig Geeratio, ramiio ad Ditributio,vol.48,o.6,pp.67-7, ov.. [6] Steve Liu, A adaptive Kalma filter for dyamic etimatio of harmoic igal i: 8th Iteratioal Coferece O Harmoic ad Quality of Power, ICHQP 98, Athe, Greece, October 4 6, 998. [7] P.K.Dah ad A.Sharaf, A Kalma filterig approach for etimatio of power ytem harmoic, i Proc. rd It. Cof. Harmoic Power Sytem, ahville,, 998. [8].R.Wato, J.Arrillaga, Review Harmoic i large ytem Electric Power Sytem Reearch, vol-66, pp.-9,. [9] S.Mihra, A Hybrid Leat Square-Fuzzy Bacterial Foragig Strategy for Harmoic Etimatio IEEE ra. O Evolutioary Computatio, vol.9, o., February. [] Karre Keedy, Gordo Lightbody & Robert Yacamii, Power ytem harmoic aalyi uig the kalma filter IEEE Power Egieerig Society Geeral Meetig-. [] Ahwii Kumar, Biwarup Da, Jaydev Sharma, Robut dyamic tate etimatio of power ytem harmoic Electrical Power ad Eergy Sytem, vol-8, pp.6-74, 6. [] U. Qidwai, M. Bettayeb, GA baed oliear harmoic etimatio IEEE ra.power Delivery, December 998. [] M. Bettayeb,U.Qidwai, A hybrid leat quare-ga-baed algorithm for harmoic etimatio, IEEE ra. Power Delivery, 8,, April,. [4] Simo Hayki, homa Kailath, Adaptive Filter heory 4 th Editio, Pearo Educatio, 7. [] L. Jug, Sytem Idetificatio-heory for the Uer, d Editio, PR Pretice Hall, Upper Saddle River, J, ECO 9