Control Algorithm for Shunt Active Power Filter using Synchronous Reference Frame Theory

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1 World Acadmy o Scnc, Engnrng and chnology Inrnaonal Jornal o Elcrcal and Comr Engnrng Vol:, No:, 9 Conrol Algorhm or Shn Acv Powr Flr ng Synchrono Rrnc Fram hory Conalva J. Mgwa, Bda J. Kndy and Bakar M.M. Mwnywwa, Inrnaonal Scnc Indx, Elcrcal and Comr Engnrng Vol:, No:, 9 wa.org/pblcaon/4688 Abrac h ar rn a mhod or obanng h drd rrnc crrn or Volag Sorc Convrr (VSC) o h Shn Acv Powr Flr (SAPF) ng Synchrono Rrnc Fram hory. h mhod rl on h rormanc o h ProoronalIngral (PI) conrollr or obanng h b conrol rormanc o h SAPF. o mrov h rormanc o h PI conrollr, h dback ah o h ngral rm nrodcd o comna h wndng hnomnon d o ngraor. Ung Rrnc Fram ranormaon, rrnc gnal ar ranormd rom a b c aonry ram o d q roang ram. Ung h PI conrollr, h rrnc gnal n h d q roang ram ar conrolld o g h drd rrnc gnal or h Pl Wdh Modlaon. h ynchronzr, h Pha Lockd Loo (PLL) wh PI lr d or ynchronzaon, wh mch mha on mnmzng dlay. h ym rormanc xamnd wh Shn Acv Powr Flr mlaon modl. Kyword Pha Lockd Loo (PLL), Volag Sorc Convrr (VSC), Shn Acv Powr Flr (SAPF), PI, Pl Wdh Modlaon (PWM) I. INRODUCION HE vr ncrang o owr mcondcor wchng dvc n owr ly or DC moor, comr and ohr mcrorocor bad qmn ca harmonc n lcrc owr ym. Harmonc may ca ro roblm ch a xcv hang o lcrc moor and malncon o nv lcronc gadg. Flrng o harmonc can b cd by ng hr av or acv owr lr. radonally, av lr hav bn d or harmonc mgaon ro. Acv lr hav bn alrnavly rood a an adqa alrnav o lmna harmonc crrn gnrad by nonlnar load a wll a or racv owr comnaon. Varo conrol mhod wh varo conrol rag a d n [][], [45] wr mlmnd or mnmzng harmonc n h lcrc owr nwork. Howvr, o da h hn acv owr lr ll C. J. Mgwa wh h Darmn o Elcrcal and Comr Sym Engnrng, Unvry o Dar alaam, anzana ( hon: ; ax: 477/49; mal: mgwaj4@gmal.com ). B.J. Kndy, wh h Darmn o Elcrcal and Comr Sym Engnrng, Unvry o Dar Salaam, anzana. (mal: bjkndy@dm.ac.z ). B. M. M. Mwnywwa wh h Elcrcal and Comr Sym Engnrng Darmn, Unvry o Dar Salaam, anzana, (mal: bakary_mwnywwa@dm.ac.z). xnvly d. Acv Powr Flr con o Volag Sorc Convrr orang a rlavly hgh rqncy o gv h o whch d or cancllng low ordr harmonc n h owr ym nwork. Wh Shn Acv Powr Flr, crcal ar nvolv gnraon o h rrnc gnal d o gnra gang gnal or h VSC. Fg. how Block Dagram o PWM Conrolld VSC orad a APF. hrha AC load Low Pa Flr Magnd Adjmn Crrn nor Hgh Pa Flr L Conrollr L VSC hrha AC ym I U Gang gnal PWM Modlaor Fg. Block Dagram o PWM Conrolld VSC orad a APF C Svral conrol mhod nvolvd n gnrang rrnc gnal hav bn d n [][4] among hm bng h Synchrono Rrnc Fram mhod. Many conrol rag hav bn rood, or xaml n [4][5] d abo akng car o dlay whch whn no akn car o, may ca h conrollr o b nabl hnc h whol ym bcomng nabl. Howvr, whr conrol concrnd, h ngral comonn o h PI conrollr can lad o ngraor wnd rlng no nably o h conrollr and hnc oor rormanc o h hn acv owr lr. In ordr o mrov rormanc, h ar rn a mhod o cvly comna h wnd o h ngral rm o h PI conrollr. I an ngraor anwnd crc. An xra dback ah rovdd by ng o o h araor modl and ormng an rror a h drnc bwn h mad acaor o and h conrollr o c dng h rror back o h ngraor hrogh an arora gan. h rror gnal zro whn h acaor no arad. Emha lacd on choong h gan, ha hold b larg nogh ha h anwnd crc k n o h ngraor mall ndr all rror condon. h rormanc o h rood mhod xamnd wh an acv lr mlaon modl and h rl ar comard wh h SAPF who anwnd chm. Inrnaonal Scholarly and Scnc Rarch & Innovaon () 9 8 cholar.wa.org/7689/4688

2 World Acadmy o Scnc, Engnrng and chnology Inrnaonal Jornal o Elcrcal and Comr Engnrng Vol:, No:, 9 Inrnaonal Scnc Indx, Elcrcal and Comr Engnrng Vol:, No:, 9 wa.org/pblcaon/4688 ABLE I NOMENCLAURE L, L Ln ndcanc, lr ndcanc I V, Dc crrn, volag, Load crrn, harmonc crrn lad harmonc a, b c hrha crrn,, Comonn crrn n dq ram d q v, ar, vbr vcr hrha rrnc volag K, K Prooronal conan, ngral conan Error gnal c, Conrollr o, acaor o, Ingral m conan, rackng m conan D Anaralll dod, D, Swch, n, z Pov ral, ngav ral and nral on rcvly. arg o rqncy Arbrary o ha II. HARMONIC CURREN REFERENCE o g h rrnc harmonc crrn, r h load crrn mard. h load crrn con o ndamnal comonn and harmonc comonn h. Ung h band a lr, wh arora co rqnc h ndamnal crrn xracd rom h mard ym load crrn. Ung comaraor, a hown n Fg., h load crrn comard o h ndamnal comonn and h rror h rrnc harmonc gnal. l Banda lr Fg. Harmonc rrnc xracon whr h = ha hb hc, h nanano magnd o h hr ha harmonc crrn. l = load crrn and = ndamnal comonn o h load crrn. h coordna rom a hrha a b c aonry coordna ym o h d q roang coordna ym a hown n Fg. b ax π c ax π π a ax β ax π α ax q ax Fg. Rrnc Fram ranormaon π d ax h ranormaon moran bca n d q rrnc ram h gnal can cvly b conrolld o g h drd rrnc gnal. ranormaon mad n wo : Fr a ranormaon rom h hrha aonry coordna ym o h woha ocalld α β aonry coordna ym don. Load crrn and volag a Pon o Common Colng (PCC) ar ranormd o α β coordna. h hrha gnal wh maxmm volag V m, a dgr aar rom ach ohr a gvn by (): h gnal = V co π co π co abc m () n h a b c aonry ram roang abc wh h rqncy o n radan /c. h gnal n α β aonry ram ar oband ng (). Fg. 4 how h rrnc gnal calclaon ng h Synchrono Rrnc Fram hory. h drd conrolld gnal oband ar d or PWM roc o gnra h wchng gnal or h VSC. III. REFERENCE FRAME RANSFORMAION Rrnc Fram ranormaon h ranormaon o Inrnaonal Scholarly and Scnc Rarch & Innovaon () 9 8 cholar.wa.org/7689/4688

3 World Acadmy o Scnc, Engnrng and chnology Inrnaonal Jornal o Elcrcal and Comr Engnrng Vol:, No:, 9 PICONROL Inrnaonal Scnc Indx, Elcrcal and Comr Engnrng Vol:, No:, 9 wa.org/pblcaon/4688 [ A ]= = V αβ m co π co π co h ax a, b, and c ar xd on h am lan and ar π radan. β arad rom ach ohr by α ar orhogonal ax wh h α ax bng ynchronzd wh h a ax o a b c lan and h β ax bng orhogonal o hα ax. αβ n () ll roang wh h rqncy o radan/cond. o lmna h rqncy, a rhr akn, a ranormaon rom h α β aonry coordna ym o h d q roang coordna ym rormd ng () a b c co B = n n co Eqaon () agnd ch ha whn mlld by αβ, h α β coordna whch ar n aonry ram achv h am rqncy a ha n d q roang ram a gvn n (4) co n α [ A ] [ B ] β co n n co PLL () () dq = αβ (4) v d q or dacal qacal K K K K n( A B) = n Aco B co An B A B ε,n( A B) = A B onrolld qconroll d co n In ynchrono rrnc ram PI bad conrollr, ngraor ar d o lmna h ady a rror o h DC comonn o h d q coordna o h rrnc gnal. In accordanc o h d q ram hory, h crrn harmonc ar rrnd a DCcomonn n hr corrondng rrnc ram and h ngraor lmna h ady a rror o ach harmonc comonn. Ung h Park ranormaon, rrnc gnal ar convrd r no α β aonry ram, hn no d q roang ram. h PI conrollr d o lmna h ady a rror, and hnc achvng h drd conrolld rrnc gnal. h algorhm rhr carrd a orward, whr h volag rrnc gnal n d q roang ram convrd back no a b c aonry ram, h rrnc gnal or h Pl Wdh Modlaon (PWM). h nvr ranormaon rom d q roang ram o a b c aonry ram achvd ng (5) [ ] Fg. 4 Block dagram o rrnc gnal calclaon or h PWM B v [ A ] v α β [ B] [ B ] [ A] = (5) abc dq. va r vb r vc r co = n PWM n co IV. HE PROPORIONAL INEGRAL (PI) CONROLLER h PI conrollr vry moran ar or h SAPF. I con o rooronal rm and ngral rm. Wh h lmn, h b conrol rormanc o h SAPF oband. PI oc on h drnc (rror) bwn h roc varabl (PV) and h on (SP), h drnc bwn harmonc crrn rrnc gnal h and h lr crrn. In h ar h PI conrollr ha bn mlmnd. PI conrollr algorhm nvolv wo ara aramr; h Prooronal and h Ingral. h Inrnaonal Scholarly and Scnc Rarch & Innovaon () 9 84 cholar.wa.org/7689/4688

4 World Acadmy o Scnc, Engnrng and chnology Inrnaonal Jornal o Elcrcal and Comr Engnrng Vol:, No:, 9 Inrnaonal Scnc Indx, Elcrcal and Comr Engnrng Vol:, No:, 9 wa.org/pblcaon/4688 Prooronal val drmn h racon o h crrn rror; h Ingral drmn h racon bad on h m o rcn rror. h wghd m o h wo acon d o adj h roc o h lan. By "nng" h wo conan n h PI conrollr algorhm, h PI conrollr can rovd conrol acon dgnd or cc roc rqrmn. h xbook vron conrol qaon or h rooronal l ngral (PI) a gvn n (6), a xrd n [5]. ( ) = k k ( τ ) dτ (6) Wh h conrollr ranr ncon a xrd n (7) k Dc ( ) = k (7) k, k ar h rooronal and ngral gan. h ron o h conrollr can b dcrbd n rm o h ronvn o h conrollr o an rror, h dgr o whch h conrollr ovrhoo h on and h dgr o ym ocllaon. Fg. 5 how PI conrollr congraon r K K/ c araon Fg. 5 PI conrollr who anwnd chm lan o A. Ingraor Wnd A conrollr wh ngral acon combnd wh h acaor ha bcom arad can gv ndrabl c. I h conrollr rror o larg ha h ngraor ara h acaor, h dback ah wll b brokn bca h acaor wll rman arad vn h roc o chang. h ngraor bng nabl ym may hn ngra o a vry larg val. h c calld ngraor wnd hr ar vral way o avod ngraor wnd. In h ar a mhod o cvly comna h wnd o h ngral rm o h PI conrollr rnd. A mhod or anwnd llrad In Fg, 6. In h ym an xra dback ah rovdd by ng h o o h acaor modl and ormng an rror a h drnc bwn h mad acaor o and h conrollr o c and dng h rror back o h ngraor hrogh h gan a hown n Fg. 6. h rror gnal zro whn h gnal no arad. Whn h acaor arad h xra dback r o mak h rror gnal qal o zro. h man ha h ngraor r o ha h conrollr o a h araon lm. h ngraor h r o an arora val wh h m conan, whch calld h rackng m conan r K / / / c araon Fg. 6 PI conrollr wh anwnd chm lan o Whn h conrol gnal ara, h ngraon a n h conrollr rac h ror a. h rackng m conan h dgn aramr o h anwnd. Common choc o a xrd n (8) = (8), ar h ngral m conan and rackng m conan I <, hn h ngraor a I () bcom nv o h nanc whn, a gvn n (9) K( τ) ( τ) I( ) = dτ ( τ) dτ V. PHASE LOCKED LOOP (PLL) h PLL crc wh h PI conrol chm conrol h ocllaon rqncy o h VCO wh h m o a volag rooronal o h rror gnal and a volag rooronal o h m ngral o h rror gnal a hown n Fg 7. Pha Dcor ε PI Flr PI VCO Fg 7 Convnonal PLL Whn h orc or ynchronzaon,.. h ha o h n gnal rqncy o h PLL lo, a conrol volag corrondng o a drnc bwn h n gnal rqncy and h lrnnng rqncy o h VCO m b mmorzd a h o volag gnal o an ngraor o a o manan h o rqncy o h VCO d abnc o h n gnal. hror h PI conrol chm o h (9) Inrnaonal Scholarly and Scnc Rarch & Innovaon () 9 85 cholar.wa.org/7689/4688

5 World Acadmy o Scnc, Engnrng and chnology Inrnaonal Jornal o Elcrcal and Comr Engnrng Vol:, No:, 9 Inrnaonal Scnc Indx, Elcrcal and Comr Engnrng Vol:, No:, 9 wa.org/pblcaon/4688 convnonal PLL rovdd wh h cond ngraor whch hl o mnmz dlay ha may ac ynchronzaon n Fg 8 [6]. PI Flr Pha Dcor ε PI VCO Dcr m ngraor Fg 8. PLL wh addonal ngraor VI. SINUSOIDAL PULSE WIDH MODULAION (SPWM) SCHEME SPWM chm d o drmn h wchng nan o h VSC or h ro o mananng In/O lnary cally or Acv Powr Flr Alcaon. Fg. 9 how h bac rncl o SPWM a d n [7]. All modlaon chm n rncl am o cra ran o wchd l whch hav h am ndamnal volcond avrag (.. h ngral o h volag wavorm ovr m) a a arg rrnc wavorm a any nan. hr ar vral way n whch wchng nan can b dcdd, a h am m mananng h mnmm harmonc conn or h wchd wavorm. In h ar naral amlng d, whr h wchng nan ar drmnd by h nrcon o h carrr wavorm and h rrnc wavorm. h mor common orm o narally amld PWM a ranglar carrr nad o awooh carrr o comar agan h rrnc wavorm. Narally amld PWM comar a low rqncy arg rrnc wavorm V r (ally a nod) agan a hgh rqncy carrr wavormv r. Fg. 9 how on ha lg o an nvrr drvn by a ranglar wav carrr. h ha lg wchd o h r DC ral whn h rrnc wavorm grar han h ranglar carrr and o h lowr DC ral whn h carrr wavorm grar han h rrnc wavorm. V z load V n D D. v r. M co( ) Fg. 9 Dobldg narally amld PWM wh hal brdg (on ha lg) volag orc convrr h rrnc wavorm xrd a = M co( ) = M co y (9) v r Whr M = Modlaon ndx or modlaon dh (.., normalzd o volag magnd) wh rang < M < and = arg o rqncy. Modlaon ndx M xrd n () ˆ M = () d Whr, ˆ,d h ak o h ndamnalrqncy comonn and n volag, rcvly. Nmbr o l, P, gvn a n () P w = () whr, w, ar h ndamnal rqncy and wchng rqncy rcvly Carrr bad mhod, ca low ordr harmonc d o roc ch a ovrmodlaon, whn M and h amlng roc. Drng amlng roc all harmonc whr harmonc nmbr n vn ar canclld o bwn ha lg or all carrr/amlng combnaon. B whn h awooh carrr mhod or aymmrcal rglar amlng d, modlaon roc rodc odd and vn dband harmonc arond ach carrr mll. Sgncan odd dband harmonc rman n h nvrr o wavorm arond h odd carrr mll d harmonc cancllaon bwn h ha lg. Wh ranglar carrr mhod h c or boh naral amlng and aymmrcal rglar amlng o oally cancl h dband harmonc arond h odd carrr mll rom h ll wavorm [7] Smlaon o rov h conc o harmonc cancllng drng amlng roc, whn ng ranglar carrr bad mhod wh Naral Samlng don ng MALAB/SIMULINK owar. Fg how mlaon rl or nglha ll brdg, ng h ranglar carrr mhod. h horcal ha lg a volag harmonc ar hown n Fg. oghr wh h ll o volag n Fg or arclar orang condon o a carrr rao o and modlaon ndx M o.8.. h cancllaon o h odd carrr mll and hr aocad dband can b clarly n. All ll harmonc ar normalzd o V o mak a drc comaron wh h ha lg harmonc. In Fg, wh h ll volag a n, h r carrr gro and h aocad dband ha bn cancld o lavng h cond carrr gro whch can aly b lrd o. Inrnaonal Scholarly and Scnc Rarch & Innovaon () 9 86 cholar.wa.org/7689/4688

6 World Acadmy o Scnc, Engnrng and chnology Inrnaonal Jornal o Elcrcal and Comr Engnrng Vol:, No:, Harmonc Magnd Vo().5.5 Inrnaonal Scnc Indx, Elcrcal and Comr Engnrng Vol:, No:, 9 wa.org/pblcaon/4688 Harmonc Magnd Harmonc Nmbr Harmonc Nmbr Fg Harmonc cra drng PWM roc Scrm o h ha o nral volag Scrm o ln o ln volag MALAB/SIMULINK owar ha bn d o gnra h wchng gnal. Smlaon rl or SPWM roc hown n g. Fg. how h comaron bwn h nodal rrnc volag wh ranglar carrr gnal and Fg how h wchng gnal gnrad a a rl o comaron bwn h carrr gnal and rrnc gnal. Vo().5.5 rrnc gnal carrr gnal m () (c) Fg. PWM Proc VII. SIMULAION RESULS Smlaon bad on MALAB/SIMULINK wr mlmnd o vry h rood Shn Acv Powr Flr wh anwnd chm. h crc aramr o h qvaln owr ym bad on Fg. ar a ollow: Vrm = 8V, V = 45V, L =. mh, L =. mh. h owr convrr wchd a a rqncy o khz. h 5 h, 7 h, and h harmonc wr d o h rood Acv Powr Flr. Ung h Fa Forr ranorm (FF), load crrn and orc crrn wr analyzd o oban h oal Harmonc Doron. Fg, Fg and Fg 4 how wavorm o h ly crrn bor and ar comnaon and h corrondng harmonc cra. h HD bor comnaon.45% and ar comnaon who anwnd chm, HD 4.4%, wh anwnd chm, HD.87% m() Fg. Sorc crrn bor comnaon, Scrm o orc crrn bor comnaon (HD =.45%) Inrnaonal Scholarly and Scnc Rarch & Innovaon () 9 87 cholar.wa.org/7689/4688

7 World Acadmy o Scnc, Engnrng and chnology Inrnaonal Jornal o Elcrcal and Comr Engnrng Vol:, No:, 9 Inrnaonal Scnc Indx, Elcrcal and Comr Engnrng Vol:, No:, 9 wa.org/pblcaon/4688 Fg. orc ly crrn wh acv owr lr who anwnd, Scrm o ly crrn ar comnaon (HD=4.4%) Fg. 4 orc ly crrn wh acv owr lr wh anwnd, Scrm o ly crrn ar comnaon,( HD =.87%). VIII. CONCLUSION h Shn Acv owr lr wh SRF badpi conrollr wa xamnd n h ar. Ung h SRF hory, h SAPF wh PI conrollr wa modld n wo mod () who anwnd crcry, () wh anwnd crcry. h rormanc o h Shn Acv Powr Flr wh boh rood conrollr crc or rrnc crrn gnraon wr xamnd wh mlaon modl and h rl wr comard. h rl how ha wh boh algorhm h HD m h rcommndd harmonc andard ch a IEEE 59, whr, h on wh h anwnd chm achvd h b rormanc n rm o Acv Flrng. [] C. Qao, K. M. Smdly, hrha Acv Powr Flr wh Und Conanrqncy Ingraon conrol, [] C. Collomb, J. Ln, J. Schonk, (999), Harmonc drbanc n nwork, and hr ramn, Schndr Elcrc Collcon chnq, Cahr chnq no.5, h:// d. Avalabl onln. [4] U. Abdrrahman, R. Ann, L. S. Vrgna, A DSP Conrolld Ronan Flr or Powr Condonng n hrpha Indral Powr, Sym. Sgnal Procng, Volm 8, I, Novmbr, [5] P. Fabana, Pokr and B. Ivo, SnglPha Acv Powr Flr or Drbd Powr Facor Corrcon, PESC. [6] H.J. G, and H.C. Gy, Nw acv owr lr wh ml low co rcr who nd lr, 9 h Annal IEEE Powr Elcronc Scal Conrnc, Vol., 7, 998. [7] F. Hdak, Y. akahro, and A. Hrom, A hybrd Acv Flr or Damng o Harmonc Ronanc n Indral Powr Sym, 9h Annal IEEE Powr Elcronc Scal Conrnc, [8] M. Naar, A. Kamal, D.A. Lo, Nolnar Conrol Sragy Ald o A Shn Acv Powr Flr, Annal IEEE Powr Elcronc Scal Conrnc,. [9] M. Rkonzzaman, and M. Nakaoka, An Advancd Acv Powr Flr wh Adav Nral Nwork Bad Harmonc Dcon Schm, Annal IEEE Powr Elcronc Scal Conrnc,. [] L. SanY, W. ChJ, Combnd comnaon rcr o a ac Var comnaor and an acv lr or nbalancd hrha drbon dr wh harmonc doron, Elcrc Powr Sym Rarch 46, 45, 998. [] A. V. Sankovc, and. A. Lo, A Gnralzd Conrol Mhod or OIn Harmonc Elmnaon or h PWM Boo Rcr ndr Smlano nbalancd In volag and In Imdanc, Annal IEEE Powr Elcronc Scal Conrnc,. [] Y. Y, M.Kazran., V. H. Qnana., A Novl Modllng and Conrol Mhod or hrpha PWM Convrr, Annal IEEE Powr Elcronc Scal Conrnc,. [] C. Poa, B. Sbhahh, D akraj M. Dvan, Hybrd aralll acv/av lr ym wh dynamcally varabl ndcanc US Pan 998 [4] G. Maran, Acv Powr Comnaon o h crrn harmonc bad on h nanano owr hory Darmn o lcrcal Engnrng, Dnara d Jo Unvry o Gala, Domnaca Sr 47, 6Gala Romanakk [5] F. F. Gn, J. D. Powll, A. EmamNan, Fdback Conrol o Dynamc ym, Paron Edcaon. Inc.986, 869 [6] G. Maaaka, S. Yahro, Mhod o ablzng holdovr o a PLL crc US Pan, Novmbr 7, [7] D. G. Holm. Lo, Pl wdh modlaon or owr convrrrncl and racc IEEE r on Powr Engnrng, 49. ACKNOWLEDGMEN h ahor wold lk o acknowldg da/sarec or connd or. REFERENCES [] Boon ck Oo, Advancd Drbon o Dlvr Com Powr, Elcrc Powr Rarch In, Inc. (EPRI), 99. Inrnaonal Scholarly and Scnc Rarch & Innovaon () 9 88 cholar.wa.org/7689/4688