Active power filter improvement by new DC link for power quality enhancing

Transcription

1 Lonardo Elctronc Journal of Practcs and Tchnologs ISSN Issu 6, January-Jun 015 p Actv powr fltr mprovmnt by nw DC lnk for powr ualty nhancng Hamdrza GOLSHANI *, Sayd Mohammad SHARIATMADAR Islamc Azad Unvrsty Nargh Branch, Thran, Iran E-mals: * Corrspondng author, phon: , Abstract Actv Powr Fltrs (APFs) ar on of th dvcs whch could b appld for mprovng th Powr Qualty (PQ) ndcs such as harmoncs, unbalancs and voltag flckr. Th most mportant topcs n dsgnng APFs ar thr corrct control and spcally sutabl DC capactor control for aforsad paramtrs mprovmnt. So n ths papr, a nw DC voltag lnk s dvlopd by combnng th fuzzy and PI control approachs nto th prdctv control structur. Th prsntd DC lnk conssts of a Fuzzy-PI Controllr (FPIC). So, ths paramtrs ar modfd by mnmzng th rrors btwn th DC lnk output and rfrnc voltag. Fnally, th output sgnal s addd to two rfrnc currnt achvd by ncorporatng th p- thory. Ths mthod can almost mprov th all PQ paramtrs such as harmonc, flckr, unbalancs, powr factor, tc. To tst th APF n th worst condtons, an actual powr systm wth nonlnar loads s consdrd. Th ams of ths papr ar a nw DC lnk of actv powr fltr, powr ualty mprovmnt basd on fuzzy logc controllr. Kywords Actv Powr Fltr; DC Voltag Capactor; p- thory 177

2 Actv powr fltr mprovmnt by nw DC lnk for powr ualty nhancng Introducton Hamdrza GOLSHANI, Sayd Mohammad SHARIATMADAR Th prolfraton of lctronc non-lnar loads such as swtch mod powr convrtrs, powr lctroncs opratd adjustabl spd drvs, fluorscnt lamps, arc furnacs, wldng upmnt and othr non-lnar loads n domstc, commrcal and ndustral nstallatons has producd a srous concrn n th fld of lctrc powr ngnrng du to dstorton wavform and voltag dsturbanc n th powr ntworks. Th dstorton wavform conssts of harmonc, ntr-harmonc, voltag flckr, nos and notch. Also, voltag unbalancs, transnts and short and long tm phnomna as sag and swll voltag ar classfd n th dsturbanc catgory. Th compnsaton for ths paramtrs bcoms ncrasngly mportant both for utlts and ndustrs to fd thr snstv upmnt wth a sutabl powr ualty, thrby avodng malfuncton and loss of rvnu. Actv Powr Fltrs (APFs) ar prsntly th most vrsatl and ffctv upmnts to confront th challng of rducng dsturbancs and dstortons n powr systm. Thy ar applcabl of compnsatng th mntond phnomna such as harmoncs, unbalancs, voltag flckr, tc., provdd that thr control systm s appropratly dsgnd. Hthrto, dffrnt mthods hav bn prsntd such as Instantanous Powr Thory (IPT) [1-3], Drct Applcaton of th Instantanous Powr Thory (DAIPT) [4,5], Synchronous Rfrnc Fram Controllr (SRFC) [6-9], p- Thory (pt) [10-1] and combnd mthods [13, 14]. Th nstantanous powr thory s usd to dtct ractv and harmonc currnt componnts and to dtrmn propr compnsatng currnt componnts to fd back to th systm. It has bn provd wth ffctv opraton and good prformanc undr balancd voltag sourc condtons. Ths mthod has bn wll-dvlopd [14] for th purpos of ln currnt compnsaton. Ths dvlopmnt s also known as actv fltr n powr lctroncs tchnology. Howvr, whn th voltag sourc s manngfully unbalancd, grat rrors may b rsultd from calculaton formula by drct applcaton of th nstantanous powr thory [3]. Rvwng systm prformanc usng th nstantanous powr thory, t s dffcult to oprat ffcntly undr unbalancd thr-phas voltag sourcs [5] to achv ractv and harmonc currnt compnsaton. Th SRFC mthod s basd on postv, ngatv sunc and dc bus voltag that at frst, load currnt harmoncs ar xtractd n th d- rfrnc fram by postv sunc synchronous rfrnc fram thn, fundamntal ngatv sunc load currnt and a DC bus voltag controllr to rgulat APF DC bus voltag ar takn out by ngatv sunc [10]. 178

3 Lonardo Elctronc Journal of Practcs and Tchnologs ISSN Issu 6, January-Jun 015 p Th combn mthod has a good prformanc to mprov th powr ualty phnomna n th worst condton [3]. Ths mthod s composd of thr man parts: computaton of rfrnc currnts, rgulaton of dc capactor voltag, and producton of frng pulss. In th mntond mthod, th actv fltr control systm s stablshd upon th combnaton of th synchronous dtcton mthod and p- thory [11]. In th all control mthods, a DC rgulator s appld for adjustng to a spcfc condton that APF can sutablty mprovs th powr ualty n th powr systm. Thrfor, ths part of APF control s sgnfcantly mportant. Ths papr s appld th combnd control basd on [3], and formulatd th appropratd dc capactor voltag dpndnt upon Fuzzy-PI Controllr (FPIC) and a Fuzzy Prdctor (FP). Aftr th fuzzy logc was ntroducd as a modl of a human thnkng n ordr to rmov th gap btwn th prcson of math and th mprcson of th ral world, th fasblty of t for controllng dynamc systms was rcognzd and ths mthod s uckly dvlopd and ts applcaton n dffrnt control systm s ncras n latr yars. Also, som applcatons of fuzzy logc ar n dffrnt controllrs as PID controllrs whch call fuzzy PID (FPID) [15-1]. Th analyss of som drct acton FPID controllr structurs ar nvstgatd n [15]. To dvlop th FPID, A robust fuzzy-pid control schm s suggst by unfyng an optmal fuzzy rasonng nto a wll-dvlopd PID typ of control framwork [16]. In th nxt, a FPID controllr s dvlopd by frst dscrbng th dscrt-tm lnar PID control law and thn gradually drvng th stps ncssary to ncorporat a fuzzy logc control mchansm nto th modfcatons of th PID structur [17]. A functon-basd valuaton approach s rcommndd for a systmatc study of FPID lk controllrs addrssng smplcty and nonlnarty ssus and A BIBO (boundd-nput boundd-output) stablty analyss of a FPID control was gvn. Thn a fuzzy prdctv controllr basd on th fuzzy optmzaton fram for mult objctv satsfacton problms ar suggstd and th mthods for ffctv optmzaton n fuzzy modl prdctv control hav bn compard n [18-1]. Brfly, n ths papr, at frst an APF s dsgnd basd on combnd mthod [3]. Thn, to mprov th control systm, th fuzzy PI s prsntd for stablzng and ncrasng spd opraton of that. In ths mthod, th rror trms to fuzzy nstad of multplyng wth th scalar PI gans. Th FPIC paramtrs ar adjustd by mnmzng a projctd cost functon that pnalzs th sum of th suard rrors btwn th plant outputs and rfrnc trajctors. In th applcaton part, an dntcal FPI controllr of th adaptaton part s usd to 179

4 Actv powr fltr mprovmnt by nw DC lnk for powr ualty nhancng Hamdrza GOLSHANI, Sayd Mohammad SHARIATMADAR control th actual plant. Th adjustd paramtr valus ar transfrrd to ths dntcal controllr at ach tm stp. Now, th APF must b tstd at th worst condtons, hnc, th powr systm wth nonlnar load s consdrd. Ths load can gnrat th harmoncs, unbalancs, fluctuatons and tc. n powr systm and th APF dsgnd should mprov thos paramtrs. Th APF opraton s compard wth APF n [3] to analyz proposd control. Matral and mthod Actv powr fltr dsgn Th sngl ln dagram (SLD) of a supplyng sourc of nonlnar load wth th APF s shown n Fgur 1. In ths fgur, bus 1 ndcats th pont of common couplng (PCC), whch s th supplyng bus of nonlnar load such as rctfrs and compnsatd wth APF. Th dvss ar also connctd to th PCC through th transformr T S, (HV/MV). In ths fgur, X Lsc s th short crcut ractanc at bus PCC. Fgur 1. Powr systm wth APF and EAF loads In Fgur 1, th APF transformr, T APF (MV/LV), conncts th compnsator to powr systm. Th purpos of applyng ths transformr s to rduc th voltag lvl on th APF for mplmntaton. Th usd APF s composd of sx nsulatd-gat bpolar transstors (IGBT) 180

5 Lonardo Elctronc Journal of Practcs and Tchnologs ISSN Issu 6, January-Jun 015 p swtchs and on DC capactor. Among many rasons n usng IGBT, th hgh spd n swtchng and lack of ncssty of commutaton crcuts ar mportant. Th structur of th proposd control systm for th APF s llustratd n Fgur. Ths control s basd on combnaton of p- thory and nw DC voltag lnk by FPIC mthod. Accordng to ths fgur, th convrtd vctors of voltag and currnts ar usd n a - systm as follows n ordr to comput th nstantanous actv and ractv powrs n powr systm: Fgur. Proposd control systm of APF Th nstantanous ar calculatd as follows [3]: = p (1) Thrfor, + = + = p p p () whr: p; ; p; p p + = + = + = + =. It should b notd that th actv powr s transfrrd through componnts p, p and componnts and do not hav any rol n ths powr transportaton. Thrfor, th rfrnc currnts for th 181

6 Actv powr fltr mprovmnt by nw DC lnk for powr ualty nhancng Hamdrza GOLSHANI, Sayd Mohammad SHARIATMADAR ractv powr compnsaton (th man componnt and harmonc componnts) ar calculatd as follows: r r = 1 0 Whn th currnts and voltags ar snusodal and balancd, both th p and powrs wll b of constant valus. Howvr, wth harmoncs or mbalancd currnts, th p and powrs ar no longr constants, and thy can b xprssd as follows [3]: whr, p = p + p (4) = + p = pω + phω = + ω hω p, : Actv and ractv powrs rlvant to non harmonc and balancd currnts; p, : Actv and ractv powrs rlvant to th harmonc and currnt ngatv componnts; p ω, ω : Actv and ractv powrs rlvant to th ngatv componnt of a thrphas currnts; p h ω, h ω : Actv and ractv powrs rlvant to th harmonc componnts of a thr-phas currnts. In ordr to mprov th powr ualty ndcs n powr systms, dffrnt paramtrs can b dfnd to crat rfrnc currnts, as shown n Tabl 1. Tabl 1. Th lst of paramtrs appld n th APF control Dfntons Th usd varabls n th control systm Th goal of compnsatng pc c Compnsatng for harmoncs and balancng th p currnt Compnsatng for th man componnt of th 0 ractv powr Compnsatng for th unbalancd currnt and th ω man componnt of th ractv powr p + ω Compnsatng for harmoncs, unbalancd currnt p and th ractv powr Compnsatng for harmoncs and flckr of th p + (r / x) voltag p (3) 18

7 Lonardo Elctronc Journal of Practcs and Tchnologs ISSN Issu 6, January-Jun 015 p Basd on th avalabl dfntons n ths tabl, th majorty of th powr ualty ndcs n powr systms can b st n allowabl rangs. Th scond part ncluds th DC capactor voltag rgulator of APF. Aftr calculaton of ncpnt currnts, th DC capactor voltag must b kpt at a constant lvl for th propr opraton of th APF. Consdrng E.(5), f th capactor voltag s constant, th actual powr valu xchangd btwn th capactor and th powr systm n stabl condtons wll b zro. v dca = 1 [v 3 dc (t) + v dc (t T ) + v x dc (t T x )] (5) Δ = C (v v ) / (6) dc dc rf dca I Δdc = 3V T jcp = jm x, j a, b, c (7) whr, ν dca s avrag DC voltag, T x, samplng tm, Δ dc rfrnc voltag, I cp, currnt pak that s n phas wth th voltag., rurd nrgy to achv th Howvr, undr transnt condtons, th capactor voltag changs, and th actv powr s thus xchangd wth th systm. Thrfor, ths powr should b ncludd n th control systm n such a way that th capactor voltag rmans stabl. In Fgur, th capactor voltag producs th rror sgnal () aftr bng compard wth th rfrnc voltag. Ths sgnal and ts drvaton produc th sgnal (I cp ) aftr passng through a proportonal-ntgral controllr (PIC) n srs wth a lmtr. Ths controllr has smpl structurs and robust prformancs and th dscrt-tm PI controllr s dfnd n th ncrmntal form as blow: u(k) = u(k 1) + K P K IT ((k) (k 1)) + ((k) + (k 1) whr K P, K I ar th proportonal and ntgral gans, rspctvly, T s th samplng prod, u s th output of th PI controllr, and k s th dscrt tm ndx. Th rror trm ( =r-y) s dfnd as th dffrnc btwn th rfrnc nput (r) and th actual voltag of DC lnk (y). Now, by dfnng th followng rror trms E.(11) can b smplfd th PIC uaton: (k) P = (k) (k 1) (9) (8) 183

8 Actv powr fltr mprovmnt by nw DC lnk for powr ualty nhancng Hamdrza GOLSHANI, Sayd Mohammad SHARIATMADAR I T = ((k) + (k 1)) (10) Th ncrmntal control sgnal s achvd by multplyng ths rror trms wth PI gans. Rgardng to E.(9), (10) can b rwrttn as blow E.(11): Δ u(k) = K P P (k) + K I I (k) (11) u(k) = u(k 1) + Δu(k) Th PIC output shows th xchangd actv currnt pak btwn th APF and th systm. Ths currnt s n phas wth th corrspondng voltag. It can b multpld by th pr-unt voltag and wll b changd nto a snusodal currnt wth an I cp pak that s n phas wth th voltag. Ths sgnal s thn addd to th rfrnc sgnal to produc th fnal rfrnc sgnal. Hnc; most mportant topc n ths part s calculaton of PIC paramtrs. In rgardng to dffrnt paramtrs changs n powr systm wth nonlnar loads, gnral PIC could not mprov th APF. To achv th optmal PIC paramtrs, th fuzzy controllr basd on fuzzy logc mthod s proposd. In a fuzzy logc controllr (Fgur 3), th control acton s dtrmnd from th valuaton of a st of smpl lngustc ruls. Th dvlopmnt of th ruls rurs a thorough undrstandng of th procss to b controlld, but t dos not rur a mathmatcal modl of th systm. Fgur 3. Fnal FPIC Th ntrnal structur of th fuzzy controllr s shown n Fgur 4 (a-b). Hr, th rror and chang of rror c ar usd as numrcal varabls from th ral systm. To convrt ths numrcal varabls nto lngustc varabls, th followng svn fuzzy lvls or sts ar chosn as [15]: ngatv bg (), ngatv mdum (NM), ngatv small (NS), zro (ZE), postv small (PS), postv mdum (PM) and postv bg (). It s dsgnd that svn 184

9 Lonardo Elctronc Journal of Practcs and Tchnologs ISSN Issu 6, January-Jun 015 p fzzy sts for ach nput and output, trangular mmbrshp functons for smplcty s slctd. Th fnal fuzzy logc controllr s shown n Fgur 3. Thrfor, Fgur 4 shows th normalzd trangular mmbrshp functons usd n fuzzfcaton. µ, µ c a) µ IAP Fgur 4. a)error '' and chang n rror 'c'; b)chang n rfrnc currnt b) Th dffrnt ruls ar slctd basd on Tabl. Ths tabl s appld to fuzzy logc controllr bas on stp rspons of PI controllr. Tabl. Control rul tabl c NM NS ZE PS PM NM NS ZE NM NM NS ZE PS NS NM NS ZE PS PM ZE NM NS ZE PS PM PS NM NS ZE PS PM PM NS ZE PS PM ZE PS PM Ths tabl s basd on th thory that n th transnt stat, larg rrors nd coars control, whch rurs coars nput/output varabls; n th stady stat, howvr, small 185

10 Actv powr fltr mprovmnt by nw DC lnk for powr ualty nhancng Hamdrza GOLSHANI, Sayd Mohammad SHARIATMADAR rrors nd fn control, whch rurs fn nput/output varabls. Basd on ths, th lmnts of th rul tabl ar obtand from an undrstandng of th fltr bhavor and modfd by smulaton prformanc. Rsults Th slctd paramtrs for th crcut dagram prsntd n Fgur 1 ar summarzd n Tabl 3. Tabl 3. Th powr systm paramtrs Dffrnt paramtrs Supplyng S SC = 11MVA, V = 0kV, X th = 14.5µΩ, systm f = 50Hz Th load s a rctfr that can chang th Load ts charactrstc: R L = 5.6 and 9.7 Ω, L L = 0 mh. Now, th rsults of th APF dsgn for th nonlnar load ar prsntd and compard wth th stat of bng wthout APF. So, t s assumd that th load s connctd to powr systm and APF s connctd at t = 0.5 sc. Th dffrnt paramtrs of th dsgnd APF ar shown n Tabl. 4. Also ths tabl shows th valus of ordnary PIC ar calculatd by tral and rror mthod. As th valu of hystrss band s slctd to b ual to , th swtchng fruncy s thrfor ual to 10 khz. Ths fruncy corrctly shows th APF capablts. Tabl 4. Th dsgn APF paramtrs Actv Powr Fltr c = 1000µF Hystras Band T = PI Controllr (Scond part) K p = K = By Consdrng Fgur 1 and Fgur, th actual currnt and th computd rfrnc currnt wavforms at dffrnt condtons: wth PIC and FPIC ar shown n Fgur 5(a) and 5(b). In ths fgur, th actual currnt follows th rfrnc currnt n a sutabl mannr by mans FPIC. Th rsultng rror of ths two currnts s about 1.5% at FPIC and 13% at PIC. It should b notd, th PI paramtrs ar ffctv n followng rfrnc currnt. Thrfor th proposd mthod can gnrat th bst rfrnc currnt and th actual currnt follows t 186

11 Lonardo Elctronc Journal of Practcs and Tchnologs ISSN Issu 6, January-Jun 015 p wth mnmum rror. Ths ssu shows th dsrd dsgn of th APF control systm by mans proposd mthod. Fgur 6(a) and 6(b) show th powr systm currnt bfor and aftr connctng th APF wth PIC and FPIC rspctvly. Phas-a Phas-b Phas-c Currnt (A) Tm (Sc) a) Phas-a Phas-b Phas-c 0 10 Currnt (A) Tm ( Sc) b) Fgur 5. Actual currnt of APF n a) PIC and n b) Proposd mthod 187

12 Actv powr fltr mprovmnt by nw DC lnk for powr ualty nhancng Hamdrza GOLSHANI, Sayd Mohammad SHARIATMADAR 60 Aftr compnsaton 40 0 Currnt (A) Tm (Sc) a) 50 Aftr compnsaton Currnt (A) Tm (Sc) Fgur 6. Powr systm currnt aftr and bfor compnsaton a) PIC b)fpic b) 188

13 Lonardo Elctronc Journal of Practcs and Tchnologs ISSN Issu 6, January-Jun 015 p As can b sn n ths fgur, th APF can convrt th powr systm currnt to snusodal currnt. By a comparng btwn th Fgur 6 (a) and (b) t can b concludd that th nw DC lnk basd on fuzzy logc mthod has bttr opraton than prvous mthod. Fgur 7 shows th wavform of th DC capactor voltag of th APF wth ts rfrnc. Th DC capactor voltag follows th rfrnc voltag and mprovs th APF opraton. In ths fgur, th rfrnc voltag rror arsng from th proposd mthod s about 0.6% n FPIC and 19% n PIC, whch justfs th sutablty of th proposd control systm. Hnc, t can b argud that th capactor voltag s stablzd vry wll; as a rsult, th stady stat valu of th xchangd actv powr btwn th capactor and th powr systm n prmannt mod wll b zro. Thus, th opraton of th APF control systm s mor dsrabl Voltag (Volt) PI Rgulator Fuzzy Rgulator Tm (Sc) Fgur 7. Capactor voltag at DC lnk wth FPIC and PIC Accordng to rcnt fgurs, P (k) and I (k) changs ar shown n Fgur 8. Fgur 9 shows th curvs of th voltag profl wth and wthout APF n th man bus of th systm (BUS1), wth PIC and FPIC rspctvly. It can b obsrvd that th proposd mthod mprovs th voltag fluctuatons vry wll. 189

14 Actv powr fltr mprovmnt by nw DC lnk for powr ualty nhancng Hamdrza GOLSHANI, Sayd Mohammad SHARIATMADAR p.u 0 p.u Sampls Sampls a) Fgur 8. FPIC rrors n proposd control: a) P (k) and b) I (k) b) 1 Wth APF&Proposd Mthod Voltag Profl (p.u) Wth APF&PIC Wthout APF Tm (Sc) Fgur 9. Voltag fluctuaton changs at BUS1 wth FPIC and PIC APF and wthout APF Th currnt harmonc spctra n th BUS1 of th powr systm (Fgur 1) wth APF, PIC and proposd mthod, and wthout th APF and IEC standard ar dpctd n Fgur 10. Th harmonc spctrum prsntd, basd on th prcntag of th fundamntal componnt, s xprssd for ach harmonc ordr. In ths fgur, th harmoncs of th man bus currnt ar substantally rducd. For xampl, th 5th harmonc wthout th APF was about 35% of th fundamntal componnt and th on wth th PIC-APF t s rducd to 13.6% and wth FPIC- APF s 4.95%. Th THD s ual to 30.1% wthout th APF and s rducd to 13.1% wth th PIC-APF and 5.3% wth proposd mthod. 190

15 Lonardo Elctronc Journal of Practcs and Tchnologs ISSN Issu 6, January-Jun 015 p % of Fundumntal wth out APF wth PIC wth Proposd Mthod Standard THD Harmonc Ordr Fgur 10. Currnt harmoncs ordrs and THD Th advantags of th FPIC-APF dsgn ar: 1. In proposd mthod-apf, th actual currnt of th APF follows th rfrnc currnt at all tms, whch s tru vn f th flckr of th voltag fluctuats randomly. Th rror producd hr s about 1.5% at proposd mthod howvr ths rror s 13% n PIC-APF bcaus of snstvnss PI paramtrs n dsgn routn and thr ffctvnss n gnratng rfrnc currnt and consuntly rducd accuracy n followng t by mans of actual currnt.. By obtanng a constant DC capactor voltag, th ral powr xchang btwn th capactor and th powr systm s zro n all condtons. So, th nw proposd DC lnk n all tm s stabl and ths stuaton lads to th dsrd opraton of th FPIC-APF. 3. Th currnt and voltag harmoncs n th man bus of th powr systm ar compnsatd wth PIC-APF and th THD valu n ths bus s sgnfcantly rducd and s n th IECstandard rang. 4. Th ractv powr n th man bus of th systm rachs almost zro by PIC-APF, and th powr factor s naturally ncrasd n ths bus. Also th FPIC-APF s vry fast than PIC-APF. Th voltag flckr s rducd and s standard. Also and th voltag profl s mprovd at th 1-p.u lvl n th man bus of th systm. 5. Anothr mportant advantag of ths mthod s th possblty of ts actual mplmntaton for th nvstgaton of powr systm opratons. 191

16 Actv powr fltr mprovmnt by nw DC lnk for powr ualty nhancng Concluson Hamdrza GOLSHANI, Sayd Mohammad SHARIATMADAR Th smulaton rsults show that th dsgnd APF s abl to mprov th powr ualty phnomnon and to compnsat th harmoncs n th powr systm. Ths mthod can mplmntd for lctrc dstrbutd ntwork. Also, ths mthod can b usd for nonlnar loads wth ntns changs of charactrstcs. Rfrncs 1. Akag H., Kanazawa Y., Naba A., Instantanous ractv powr compnsators comprsng swtchng dvcs wthout nrgy storag componnts, IEEE Trans. on Industral Applcaton, 1984, 0(3), p Km H., Blaabjrg F., Bak-Jnsn B., Cho J., Instantanous powr compnsaton n thr-phas systms by usng p--r thory, IEEE Trans. on Powr Elctronc, 00, 17(5), p Hooshmand R., Toraban Esfahan M., A nw combnd mthod n actv fltr dsgn for powr ualty mprovmnt n powr systms, Elsvr Journal, ISA Transactons, 011, 50(), p Montro M. I. M., Cadaval E. R., Gonzalz F. B., Comparson of control stratgs for shunt actv powr fltrs n thr phas four wr systms, IEEE Trans. on Powr Elctronc, 007, (1), p Hrrra R. S., Salmron P., Km H., Instantanous ractv powr thory appld to actv powr fltr compnsaton: dffrnt approachs, assssmnt and xprmntal rsults, IEEE Trans. on Industral Elctronc, 008, 55(1), p Mattavll P., Synchronous fram harmonc control for hgh-prformanc AC powr suppls, IEEE Trans. on Industral Applcaton, 001, 37(3), p Escobar G., Stancovc A. M., Mattavll P., An adaptv controllr n statonary rfrnc fram for D-STATCOM n unbalanc opraton, IEEE Trans. on Industral Elctronc, 004, 51(), p

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18 Actv powr fltr mprovmnt by nw DC lnk for powr ualty nhancng Hamdrza GOLSHANI, Sayd Mohammad SHARIATMADAR 18. Hu B. G., Mann G. K. I., Gosn R. G., A systmatc study of fuzzy PID controllrs functon- basd valuaton approach, IEEE Transactons on Fuzzy Systms, 001, 9(5) p Mohan B. M., Snha A., Analytcal structur and stablty analyss of a fuzzy PID controllr, Appld Soft Computng, 008, 8(1), p Flors A., Sáz D., Araya J., Cprano M., Fuzzy prdctv control of a solar powr plant, IEEE Transactons on Fuzzy Systms, 005, 13(1) p Mollov S., Babuska R., Abony J., Vrbruggn H. B., Effctv optmzaton for fuzzy modl prdctv control, IEEE Transactons on Fuzzy Systms, 004, 1(5) p