A Control Strategy for Combined Series-Parallel Active Filter System under Non-Periodic Conditions

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1 Euroe ssoiio for he Develome of Reewle Eergies, Evirome d Power Quliy Ieriol oferee o Reewle Eergies d Power Quliy (IREPQ 9) Vlei (Si), 5h o 7h ril, 9 orol Sregy for omied SeriesPrllel ive Filer Sysem uder NoPeriodi odiios M. Ur, S. Ozdemir d E. Ozdemir Eleril Eduio Derme ehil Eduio Fuly, Koeli Uiversiy 48, Umuee, urkey Phoe/Fx umer:96 75 / :96 emil: mur@koeli.edu.r, sozsl@koeli.edu.r, eozdemir@koeli.edu.r sr. I his sudy, geerlized oive ower heory sed orol sregy is roosed for hse 4wire omied SeriesPrllel ive Filer (SPF) sysem usig hreedimesiol (D) Se Veor Pulse Widh Modulio (SVPWM). he SPF sysem osiss of Series ive Filer (SF) d Prllel ive Filer (PF) omiio oeed ommo Dire urre (D) lik for simuleous omesig he soure volge d he lod urre. he geerlized oive ower heory ws lied i revious sudies for he PF orol, i his sudy he heory is used for he SPF sysem orol uder osiusoidl d oeriodi urre d volge odiios. he losed loo orol lgorihm for he roosed SPF sysem hs ee desried o dire orol of filerig erforme y mesurig soure urres d lod volges for he PF d he SF, reseively. he roosed orol sregy hs ee verified y simulig he SPF sysem i Ml/Simulik evirome. eriod of he urres is o equl o he eriod of he lie volge [], []. I his er, he geerlised iseous oive ower heory is used for he SPF sysem uder osiusoidl d oeriodi lod urre d soure volge odiios. he SPF sysem osiss of kok oeio of SF d PF wih ommo D lik. While he PF omeses urre quliy rolems of lod d regulig of D lik, he SF omeses volge quliy rolems of uiliy [], [4]. he sysem ofigurio of he SPF sysem is show i Fig.. v S v SF v L i S i L i PF Key words Hrmois, ule, reive ower omesio, oeriodi, ive filer, DSVPWM. L S Soure v S i S v SF i L v L N /N i PF R SF SF PF R PF L SF L PF L L L L Nolier lods. Iroduio he lrge use of olier lods d ower eleroi overers hs iresed he geerio of osiusoidl d oeriodi urres d volges i eleri ower sysems. Geerlly, ower eleroi overers geere hrmoi omoes whih frequeies h re ieger mulilies of he lie frequey. However, i some ses, suh s lie ommued hreehse hyrisor sed reifiers, r fures d weldig mhies, he lie urres my oi oh frequey lower d higher h he lie frequey u o he ieger mulile of lie frequey. hese urres ier wih he imede of he ower disriuio sysem d disur volge wveforms Poi of ommo oulig (P) h ffe oher lods. hese wveforms re osidered s oeriodi, lhough mhemilly he urres my sill hve eriodi wveform, u i y eve, he VD SF PF SPF Sesiive lods Fig.. Sysem ofigurio of he SPF sysem. I hse wire sysems, oveiol SVPWM mehod, whih is sed o αβ le, hs ee widely used o redue riles d o ge fixed swihig frequey. I his sudy, he DSVPWM sheme is used for orollig he SPF sysem, whih uses wo leg 4wire Volge Soure Iverer (VSI) euse he zero sequee omoes mus e orolled [5]. I he losed loo orol sheme of he roosed SPF sysem, soure urres d lod volges re mesured d filerig erforme is orolled direly. he SPF sysem rovides miimum hrmois of hese urres d volges. hs://doi.org/.484/reqj7.4 4 RE&PQJ, Vol., No.7, ril 9

2 . Geerlized Noive Power heory he geerlised oive ower heory [6] is sed o Fryze s heory of oive ower/urre [7] d is exesio of he heory roosed i [8] [9]. Volge veor v() d urre veor i() i hse sysem, v ) [ v ( ), v ( ), v ( )], () ( i ) [ i ( ), i ( ), i ( )]. () ( he iseous ower () d he verge ower P() is defied s he verge vlue of he iseous ower () over he vergig iervl [, ], h is ( ) v ( ) i( ) v ( ) i ( ), () P( ) ( τ ) dτ. (4) he vergig ime iervl e hose rirrily from zero o ifiiy for omesio of eriodi or oeriodi wveforms, d for differe s, he resulig ive urre d oive urre will hve differe hrerisis [6]. he iseous ive urre i () d oive urre i () re give (5) d (6). P( ) i ( ) v ( ) (5) V ( ) i ( ) i( ) i ( ) (6) I (5), volge v () is he referee volge, whih is hose o he sis of he hrerisis of he sysem d he desired omesio resuls. V () is he orresodig rms vlue of he referee volge v (), h is V ( ) v ( τ ) v ( τ ) dτ. (7) he iseous oive ower () d he verge oive ower P () is defied over he vergig iervl [, ], h is ( ) v ( ) i ( ) v ( ) i ( ), (8) P ( ) ( τ ) dτ. (9) he defiiios i he iseous oive ower heory re ll osise wih he sdrd defiiios for hreehse fudmel siusoidl sysems d re vlid i vrious ses, suh s siglehse sysems, osiusoidl sysems, d oeriodi sysems s well, y hgig he vergig iervl d he referee volge v () []. I his heory, ll he defiiios re iseous vlues; herefore, hey re suile for relime orol.. DSVPWM lgorihm I his er, he DSVPWM lgorihm is uilized for orollig he SPF sysem, whih uses wo leg 4 wire VSI. he swihig veors of he leg 4wire VSI re show io D le i Fig.. he eigh swihig veors re disriued i he αβ se d he zero swihig veors V d V 7 re i oosie direios. Sie here is zero xis i he D se, wo zero swihig veors e used ideedely o orol he zero sequee volge [5]. e V 4 V V V 7 V V 5 V 6 zero lh Fig.. Swihig veors i D se. he iseous volge e rsformed o he αβ D se y usig (). v v v α β / / / / V / v / v / v () he referee veor i he αβ D se e wrie s, V R ( k) i. vα j. vβ k. v. () Oe he referee veor V R hs ee deermied, i e refleed he αβ le s show i Fig. o deide whih seor d whih ive swihig veors re o e seleed [5]. V 4 αβ xis V αβ V 7 βxis V V αβ V 5 αβ V 6 αβ V Rαβ V R V αβ αxis Fig.. DSVPWM mehod i he leg 4wire VSI. hs://doi.org/.484/reqj7.4 4 RE&PQJ, Vol., No.7, ril 9

3 wo zeroswihig veors V d V 7 wih differe effeive imes d 7 syhesize he refleio of he referee veor i he zero xis. log wih he differe swihig fuios, he referee se veor V R (k) is reseed i le I. LE I. Swihig fuios d swihig volge se veors S S S V R Swihig veors V ( i. j. k.( )). d V 6 V ( i. j. k.( )). d V 6 V ( i.( ) j. k.( )). d V 6 V ( i.( ) j. k.( )). d V 4 6 V ( i.( ) j.( ) k.( )). d V 5 6 V ( i. j.( ) k.( )). d V 6 6 ( i. j. k.). Vd V 7 ( i. j. k.( )). V d V I Fig., he referee volge veor V R is loed i seor i whih he four swihig ses (V, V 7, V d V ) re dje o he referee veor. he effeive swihig ime of eh swihig veor, wihi PWM swihig eriod, s, e oied from equio (), () [5]. V. V. V. V 7. 7 V R. s () 7 s () he seleed swihig veors e lied i sequee oimized o redue swihig loss or hieve eer volge ol Hrmoi Disorio (HD). Symmeril sequeig gives he lowes HD ouu, due o he f h ll swihig veors re rrged symmerilly []. So his sequeig mehod is hose i his er. I symmeril sequeig sregy, he swihig sequee is rrged s V V V V 7 V 7 V V V. Fig. 4 shows he sequeig of swihig ses for ime eriod of s for seor I. v v v s. s 7 7 Fig. 4. PWM swihig ime sequee. 4. orol of he SPF Sysem I his sudy, he SPF sysem, whih hs wo leg 4 wire VSI, uses geerlised oive ower heory sed urre d volge orol wih he DSVPWM sheme.. Volge orol sregy Volge orol lok digrm is show i Fig. 5. he osiusoidl, uled d/or oeriodi lod volges (v L, v L, v L ) is lied o Phse Loked Loo (PLL) irui d fudmel osiive sequee urres (i, i, i ), used s referee urre i () d he sme hse wih he fudmel osiive sequee lod volge (v L, v L, v L ) d uiy mliude re oied. Effeive vlue of referee urre I () is I i ( ) ( τ ) i ( τ ) dτ (8) (4)(7) show he equios ivolved i he lulio of swihig ime of eh ivolved swihig veor for referee veor hes i seor I. s ( ) vrα ( ) vrβ (4) Vd v L Phse Loked Loo (PLL) i Refere Volge lulio v SF* v L PI D SVPWM v D SF Swihig Sigls v s Rβ (5) Vd vr s ( ) / (6) V 7 d s ( ) (7) 7 Fig. 5. Volge orol lok digrm. he verge ower luled give (4) y usig his referee urres d soure volges. Desired siusoidl lod volges (v L, v L, v L ) s omesio referee volges (v SF*, v SF*, v SF* ) of SF, is derived y usig (9) from mliude d hse gle of fudmel osiive sequee omoe of he lod volges. Referee volge is omred lod hs://doi.org/.484/reqj7.4 4 RE&PQJ, Vol., No.7, ril 9

4 volges d lied o DSVPWM d hus SF swihig sigls re oied. P( ) v ( ) i ( ) (9) I ( ) I V N Noeriodi N Soure i I V N i I V N I V N i LL N Noeriodi Lods. urre orol sregy Rsf sf Rf f he verge ower luled give (4) y usig soure urres d fudmel osiive sequee (v L, v L, v L ) lod volges over he vergig iervl [, ]. Desired siusoidl soure urres (i S, i S, i S ) re derived y usig (5). lso, he ddiiol ive urre i () required o mee he losses i () is drw from he soure y regulig he D lik volge v D o he referee V D. Prooriol Iegrl (PI) oroller is used o regule he D lik volge v D. hus, he omesio referee urres (i PF*, i PF*, i PF* ) of PF is oied. he referee urres re omred soure urres o relize he losed loo orol sheme. he, usig DSVPWM oroller, PF swihig sigls re oied. urre orol lok digrm of he SPF sysem is show i Fig. 6. he SPF sysem Ml/Simulik lok digrm is show i Fig. 7. i i S v L V D * ( ) vl[ K P ( VD vd ) K I ( VD vd ) d] () v D Refere urre lulio v S PI i PF i X i PF* PI v L Fig. 6. urre orol lok digrm. 5. Periodi urre d Volge D SVPWM PF Swihig Sigls For omesio of eriodi urres d volges wih fudmel eriod, usig omesio eriod h is mulile of / is eough for omlee omesio [6]. I his sudy, hse soure volge omoes is give i le II. hse RL loded yrisor reifier d hse R loded diode reifier i eh hse oeed hse 4wire ower sysem. hyrisor reifier firig gles re. LE II. hse soure volge omoes Fudmel Ule (%) Hrmois (%) 5 Hz V 7,5 5 5,5,5 vl is Vd ulses vl SF orol Lsf g v v g Lf ulses Vd is is vl Vd Vd PF orol Fig. 7. he SPF sysem Ml/Simulik lok digrm. Disree, s e6 s. Fig. 8 demosre he simulio resuls for he eriodi urre d volge omesio. hse soure urre d lod volge is siusoidl d led d eurl urre elimied fer omesio. le III shows summry of mesured omoes. vs(v) vl(v) il() is() inl() ins() () hse soure volge wveforms () hse lod volges fer omesio () hse lod urre wveforms (d) hse soure urres fer omesio (e) Lod eurl urre wveforms (f) Soure eurl urre fer omesio. Fig. 8. Periodi volge d urre omesio..45 hs://doi.org/.484/reqj7.4 4 RE&PQJ, Vol., No.7, ril 9

5 LE III. Summry of mesured vlues uder eriodi urre d volge odiio HD (%) RMS () HD (%) RMS (V) Lod urres (I L ) 8,97 9,8 9,4 65, 8,5 8, 8,59 47, Soure Volges (V S ),, 6,96 6,5 6,5 67,7 Soure urres (I S ) 4,4 4,48 4,4 7,74 7,78 74, Lod Volges (V L ),,, 9, 9, 9,5 6. NoPeriodi urre d Volge. Suhrmoi urre d volges he suhrmoi urres re (frequey lower h fudmel frequey) yilly geered y ower eleroi overers. he mi feure of hese oeriodi urres is h he urres my hve reeiive eriod. Whe he fudmel frequey of he soure volge is odd mulile of he suhrmoi frequey, he miimum for omlee omesio is / of he ommo eriod of oh f s d f su. Whe f s is eve mulile of f su, he miimum for omlee omesio is he ommo eriod of oh f s d f su [6]. I his sudy, hse soure volge d lod urre omoes re give i le IV. Suhrmoi urre d volge omesio simulio resuls re show i Fig. 9. he suhrmoi omoe e omleely omesed y hoosig.5, d he soure urres d lod volges re led d siusoidl. ddiiolly, he eurl urre omoe is omesed. LE IV. hse soure volge d lod urre vlues Prmeers Fudmel Suhrmoi Freq. (Hz) 5 urres 5 % Volges V %. Sohsi oeriodi urres d volges he r fure lod urres my oi sohsi oeriodi urres (frequey higher h fudmel frequey u o ieger mulile of i). heoreilly, he eriod of oeriodi lod is ifiie []. he oive omoes i hese lods o e omleely omesed y hoosig s / or, or eve severl muliles of. hoosig h eriod s my resul i ele oh soure urre d lod volge whih re quie lose o sie wve. If is lrge eough, iresig furher will o yilly imrove he omesio resuls sigifily []. I his work, hse soure volge d lod urre omoes is give i le V. Fig. shows he sohsi oeriodi volge d urre omesio hoosig he eriod s 5. fer omesio, lod volges d soure urres re led d lmos siusoidl wih low HD. I ddiio, soure eurl urre hve ee redued osiderly. he sysem rmeers used for he simulio re give i le VI. vs(v) vl(v) il() is() inl() ins() LE V. hse soure volge d lod urre omoes Prmeers Fud. omoes (%) Freq. (Hz) urres Volges V 7,5 5 5, () hse soure volge wveforms () hse lod volges fer omesio () hse lod urre wveforms (e) Lod eurl urre wveforms (e) Lod eurl urre wveforms (f) Soure eurl urre fer omesio. Fig. 9. Suhrmoi volge d urre omesio. hs://doi.org/.484/reqj RE&PQJ, Vol., No.7, ril 9

6 vs(v) vs(v) vs(v) vl(v) il() il() il() is() inl() ins() () hse soure volge wveforms () hse lod volges fer omesio () hse lod urre wveforms (d) hse soure urres fer omesio (e) Lod eurl urre wveforms (f) Soure eurl urre fer omesio. Fig.. Sohsis oeriodi volge d urre omesio. LE VI. he sysem rmeers Power sysem V S, f s, L s V, 5Hz, 5µH Series rsformer N /N SF filer L SF, R SF, SF mh, Ω, µf PF filer L PF, R PF, PF mh, Ω, µf D us V D,, 8V, 56µF Swihig freq. f SF, f PF khz hse hrisor L L, L D, R D mh, mh, 5Ω hse diode L L, D, R D mh, 47µF, 5Ω 7. olusio I his er, he geerlized oive ower heory, whih is lile o siusoidl or osiusoidl, eriodi or oeriodi, led or uled eleril sysems, is reseed. I hs ee lied o he hse 4wire SPF sysem wih he DSVPWM o ge fixed swihig frequey. he heory is ded o differe omesio ojeives y hgig he vergig iervl. he losed loo orol lgorihm hs ee desried y mesurig soure urres d lod volges i he roosed SPF sysem o dire orol of filerig erforme. he simulio resuls sed o Ml/Simulik sofwre re reseed o show he effeiveess of he SPF sysem for he omesio of vriey of osiusoidl d oeriodi volges d urres i ower sysems. kowledgeme his work is suored y UIK Reserh Fud, (Proje No: 8E8). Referees [] We, E. H. d redes, M., omesio of Noeriodi urres Usig he Iseous Power heory, IEEE Power Egieerig So. Summer Meeig,, [] zreki, L. S., NoPeriodi urres: heir Proeries, Ideifiio d omesio Fudmels, IEEE Power Egieerig So. Summer Meeig,, [] Fuji, H. d kgi, H., he Uified Power Quliy odiioer: he Iegrio of Series d Shu ive Filers, IEEE rs. o Power Eler., (), 998. [4] redes, M., ive Power Lie odiioers, Ph.D. Disserio, ehishe Uiversiä, erli, 996. [5]. Zh,. rulmlm, V. K. Rmhdrmurhy,. Fizer, M. res, N. Jekis, Novel volge se veor PWM lgorihm of hse 4wire ower odiioer, IEEE Power Eg. So.,. 455,. [6] Xu, Y., oler, L. M., Peg, F. Z., hisso, J. N. d he, J. omesiosed Noive Power Defiiio, IEEE Power Eler. Leer, (), 455,. [7] Fryze, S. ive, Reive, d re Power i No Siusoidl Sysems, Przegld Elekro., 7, 9 (i Polish), 9. [8] Peg, F. Z., d oler, L. M. omesio of No ive urre I Power Sysems Defiiios from omesio Sdoi, IEEE Power Eg. So. Summer Meeig,, [9] Xu, Y., oler, L. M., hisso, J. N., mell, J.. d Peg, F. Z., Geerlised Iseous Noive Power heory for SOM, Eleri Power liios, IE, 8586, 7. [] Xu, Y., oler, L. M., hisso, J. N., mell, J.. d Peg, F.Z., ive Filer Imlemeio Usig Geerlized Noive Power heory, IEEE Idusry liios oferee, 6, 56. [] H.Piheiro, F. oero,. Reh. Shuh d e l., Se Veor Modulio for VolgeSoure Iverer: Uified roh, IEON, Idusril Elerois Soiey, IEEE, 8h ul oferee. [] oler, L. M., Xu, Y., he, J., Peg, F. Z, hisso, J. N., omesio of Irregulr urres wih ive Filers, IEEE Power Egieerig Soiey Geerl Meeig,, 788. hs://doi.org/.484/reqj RE&PQJ, Vol., No.7, ril 9