Particle Swarm Optimized Fuzzy Controller for Indirect Vector Control of Multilevel Inverter Fed Induction Motor

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Marion Owen
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1 Patcl Swa Optzd Fuzzy Contoll fo Indct Vcto Contol of Multlvl Invt Fd Inducton Moto Sanjaya Kua Sahu,T. V. Dxt and D.D. Na 3 Elctcal Engnng, Bhla Insttut of Tchnology Dug, Chhattsgah49, Inda Elctcal Engnng, Saguja Unvsty Abkapu, Chhattsgah-497, Inda 3 Elctcal and Elctoncs Engnng, Chhattsgah Insttut of Tchnology Rajanandgaon, Chhattsgah-49445, Inda Abstact Th Patcl Swa Optzd (PSO) fuzzy contoll has bn poposd fo ndct vcto contol of nducton oto. In ths poposd sch a Nutal Pont Clapd (NPC) ultlvl nvt s usd and hystss cunt contol tchnqu has bn adoptd fo swtchng th IGBTs. A Madan typ fuzzy contoll s usd n plac of convntonal PI contoll. To nsu btt pfoanc of fuzzy contoll all paats such as bshp functons, noalzng and d-noalzng paats a optzd usng PSO. Th pfoanc of poposd contoll s nvstgatd und vaous load and spd condtons. Th sulaton sults show ts stablty and obustnss fo hgh pfoanc dvs applcatons. Kywods: Multlvl Invt, Hystss Cunt Contol, Patcl Swa Optzaton (PSO), Fuzzy Logc Contoll (FLC).. Intoducton Th phas nducton otos a wdly usd n th ndustal pupos bcaus thy show btt pfoanc dung havy loads as wll as cost ffctv. Howv th dawbacks assocatd wth nducton oto a ts nonlna bhavou, contollablty and ts coplxty n dvlopng athatcal odl []. By vcto contol o fld ontd contol (FOC) thoy, nducton oto can b contolld lk a spaatly xctd dc oto. As a sult fld and toqu of th nducton achn can b contolld ndpndntly by anpulatng th cospondng fld ontd quantts. Th a two thods of vcto contol - dct and ndct vcto contol [] [3]. In ths pap th ndct contol thod s adoptd, wh th slp angl, th d-axs and q-axs stato cunts n synchonous fnc fa a coputd fo th toqu and oto flux and usd fo vcto contol. A ult-lvl nvt s a pow lctonc ccut bult to synthsz stppd appoxaton of a snusodal wav output voltag o cunt fo a nub of DC voltags [4]. Th ultlvl nvts gand th attnton n ndustal dv applcaton du to followng fatus [5]: a) Ipovs th wavfo qualty as th lvl of nvt ncass. b) Rducs th sz and atng of flt coponnts. c) Hgh ffcncy du to low swtchng fquncy. d) Low dv/dt acoss swtchs and gnat low dstotd output voltags. ) Daw nput cunt wth vy low dstoton. f) Gnat sall coon-od voltag whch ducs th stss n th oto bangs. Th sval ultlvl nvt topologs a: Th Nutal pont clapd (NPC) nvt, Flyng Capacto Invt (FCI), and Cascad H-Bdg (CHB) nvt [6]. Th NPC nvts a vy popula fo hgh voltag and hgh pow applcatons. Thotcally, NPC topology wth any nub of lvls can b alzd. But so of th pobls lk coplxty of swtchng algoth, voltag unbalanc acoss capactos, voltag clapng qunts, and ccut layouts hav lts on th lvl n pactcal ultlvl nvts [7]. In an N-lvl NPC, ach phas lg conssts of pow swtchs, clapng dods. Th DC bus qus bulk capactos. Th ln voltag has Lvls. At any gvn t th a (N-) swtchs n ach lg whch a n ON stat. Voltag atng of ach of th dvc s assud to b( ). In cnt yas, Fuzzy logc has gd as an potant atfcal ntllgnc tool to chaactz and contol a syst, whos odl s not known o ll dfnd. Ths pap nvolvs th dvlopnt of novl thodology to optz th pfoanc of Madan typ fuzzy logc contoll basd on a p dfnd objctv functon. Th pdfnd objctv functon s optzd by optzng th noalzaton paat, dnoalzaton paat and th bshp functons of th Fuzzy logc contoll. Rcntly, th has bn a hug ntst n th Patcl Swa Optzaton (PSO) du to ts gat potntal as an

2 volutonay algoth, whch s basd on th socal bhavou of flocks of bds and schools of fsh [8].Snc t s populaton basd and slf adaptv, t has gand an ncasng populaty as an ffcnt altnatv to th gntc algoth (GA) n solvng optzaton pobl. Sla to oth populaton-basd optzaton thod such as th GA, th PSO algoth stats wth ando ntalzaton of a populaton of ndvduals n th sach spac. Each patcl n th sach spac s adjustd by ts own flyng xpnc and th oth patcls flyng xpnc to fnd th global bst soluton at ach gnaton [8]. Ths pap poposs an plntaton of th PSO thod fo an off-ln tunng of th noalzaton paat, d-noalzaton paat and bshp functons of th fuzzy contoll.. Th-Lvl NPC Invt Th th-lvl NPC nvt wth two DC lnk capactos C and C n ss and a nutal pont O s shown n Fg... Modlng. Inducton Moto Th th-phas squl cag nducton oto athatcal quatons n synchonous otatng fnc fas a as follows [] [3]: V R p () Wh, ds s ds ds qs V qs Rsqs pqs ds () R p ( ) (3) d d q R p ( w w ) (4) q q d L L (5) ds s ds d L L (6) qs s qs q L L (7) d d ds L L (8) q q qs And lctoagntc toqu 3 P T L ( qsd dsq ) (9) d w dt () dw T j B w Tl dt () Fg. Th Lvl NPC Invt Tabl : Swtchng Lvls n a Th-Lvl NPC Invt th S S S 3 S 4 Pol voltag V o ON ON OFF OFF V dc / OFF ON ON OFF OFF OFF ON ON / Each phas of th th-lvl NPC nvt has two pa of swtchng dvcs S, S and S 3, S 4 n ss, wh a, b, c phass. Th cnt of ach pa s clapd to th nutal of th DC lnk capactos though th clapng dods D, D, D 3, D 4, D 5 and D 6. Tabl I nuats th swtchng stats fo th sconducto dvcs fo th th - phas of ths nvt. In Tabl-, th swtchng sybols +, and - spctvly dnot that th th -phas tnal s connctd to th postv bus, th nutal pont and th ngatv bus. V dc.3 Th-Lvl Hystss Cunt Contoll Fg. : Th-Lvl Hystss Swtchng Sch An analytcal soluton of dffnt ultlvl PWM tchnqus fo th-lvl NPC has bn psntd [9], []. Aong ths tchnqus, th hystss band s usd vy oftn bcaus of ts splcty of plntaton, fast

3 spons cunt and obust stuctu [], []. Hystss band contoll s usd to tack th ln cunt fncs. Th cunt os btwn th fnc and asud cunts a usd to dvlop th vald swtchng stats n ach nvt lg by th hystss band contoll. a+h a+δ a a-δ a- h Vdc/ Actual Cunt Rfnc Cunt -Vdc/ Vdc/ -Vdc/ 3: Th-Lvl Hystss Cunt Contol Dad Zon Hystss Band Fg. To dvlop a swtchng sch fo th th-lvl nvt, th zo voltag lvl should b appld only at appopat nstants. Th swtchng logc ust nsu that th s no succssv tanston btwn V dc and V dc stats, as ths wll ncas th fquncy of swtchng. A dad zon δ s ncssay n th hystss band h, to avod swtchng towads two-lvl sch, bcaus of fnt saplng at of o. Wthout th dad zon, whn th o bcos zo and s not dtctd, th oppost polaty of focng functon follows, sultng n a twolvl sch. Howv, th ntoducton of dad zon ncass th tackng o and has to b chosn to a nu valu, dpndng on th bst saplng spd that can b achvd [3]. If U psnts th nput stat to b appld, psnts o ( ) and c psnts th chang n a a o th swtchng logc s govnd by quaton () If thn U fo h U fo U fo h and c U fo h and c Els f thn U - fo - h U fo - U fo - - h and c U - fo - - h and c () Th abov logc psntd n Fg. and Fg.3, tacks fnc cunt th n th low band (though and + stats) o n th upp band (though and - stats). HU, ans th swtch stat s V dc / ; U ans th swtch stat s ; andu, ans th swtch stat s V dc /. Slaly th b-phas and c-phas swtchng functon fo th th-phas voltag souc nvt can b obtand..4 Indct Vcto Contol Th ndct vcto contol s a tchnqu that contols th dynac spd of Inducton oto. Unlk dct vcto contol, n ndct vcto contol, th unt vctos a gnatd n an ndct ann. Fg.4 s th phaso daga that xplans th fundantal pncpl of ndct vcto contol. Th d s q s axs a fxd on th stato and d q axs a fxd on th oto whch otats at a spd. Synchonously otatng axs d q a otatng ahad of d q axs by th postv slp angl sl cospondng to slp fquncy. Thus sl (3) dt ( ) dt sl Fo dcouplng contol q o pq and d.substtutng th abov condton n quatons (3), (4), (7) and (8). s V ds V s s V qs V ds sl s ds V qs s s qs ds qs d (q-d, s) Stato Rfnc fa (q-d, ) Synchonous fnc fa (q-d, ) Roto fnc fa Fg. 4: Phaso daga of Indct Vcto Contol pncpl R Lqs sl L (4) 3 P L T qs L (5) qs L T 3 PL (6) L [ p ] (7) L R ds Th quatons (4-7) a usd to poduc an adquat fld ontaton. Ths quatons could b popagatd to th st pont vaabls [4].

- qs R L sl L (8) qs L T (9) 3 PL L [ p ] () ds L R If t s accptd that th oto flux st pont s constant thn ts dvatv s zo and th abov quaton s splfd as ds () L Usng th abov quatons th block daga of

4 - qs R L sl L (8) qs L T (9) 3 PL L [ p ] () ds L R If t s accptd that th oto flux st pont s constant thn ts dvatv s zo and th abov quaton s splfd as ds () L Usng th abov quatons th block daga of ndct vcto contol of nducton oto dv s as shown n Fg.5. Rfnc spd + Spd contoll (G) T Estaton of,, ds qs sl ( G ) sl + + ds qs Tansfoaton ( q, d, ) ( a, b, c) ( G ) 3 abc Th-Lvl u Th- abc Hystss Lvl Cotoll abc 78V Invt Fg. 5: Block daga of Indct Vcto Contol of IM It contans th pncpal blocks, G usd as spd ds contoll, G usd fo staton of,, andg 3 usd fo cunt co-odnat tansfoaton (q, d, ) to (a, b, c). 3. Fuzzy Logc Spd Contoll Th spd contoll block G s poposd to b a Madan typ fuzzy contoll havng fv blocks naly noalz, fuzzf, nfnc chans, d-fuzzf, and d-noalz as shown n Fg.6. [5]. c Noalz Fuzzf Infnc Mchans Knowldg Basd ul Nw Fuzzy Paats By PSO qs D-Fuzzf Fg. 6: Block Daga of Fuzzy Contoll 3. Noalz and D- noalz sl V abc D-Fuzzf du shown n Fg. Th o s th dffnc btwn th fnc spd and th actual oto spd. Input t t t () ( ) ( ) ( ) Input c( t) ( t) ( t ) (3) Wh, s th actual spd and s th fnc spd. Two noalzaton paats (k, k ) fo nputs (, c) and on d-noalzaton paat (k 3 ) fo output (du) a dfnd. In noalzaton pocss th nput vaabls a scald n th ang of (-, +) and n dnoalzaton pocss th output valus of fuzzy contoll a convtd to a valu dpndng on th tnal contol lnt. Th dtnaton of noalzaton and dnoalzaton paats of fuzzy contoll s potant fo syst stablty. 3.Fuzzf and D-fuzzf Th fuzzf pocsss th csp nput valus (, c) and convt th nto fuzzy valus. Also th fuzzy valus obtand n fuzzy nfnc chans a convtd to csp output (du) valu by a d-fuzzf. H, a tangula fuzzy bshp functon s dfnd fo ach nput and output valus by svn clusts. Fo svn clusts n th bshp functons, svn lngustc vaabls a dfnd as: Ngatv Bg (), Ngatv Mdu (NM), Ngatv Sall (NS), Zo (Z), Postv Sall (PS), Postv Mdu (PM), Postv Bg (PB). Fg. shows th bshp functons usd to fuzzfy two nput valus (, c) and d-fuzzfy output (du) of th alzd fuzzy contoll. Th pak o botto ponts of th bshp functons to b tund a a and a fo o (), b and b fo chang n o (c) and c and c fo output (du). Thfo th dsgn of fuzzy contoll qus th optzaton of nn paats (k, k, k 3, a, a, b, b, c, c ). NM a NM b NM NS a NS b NS () Z PS PM PB ( c) ( du) Z a a Z PS PM PB b b PS PM PB In closd loop contol syst th us of o () and th chang n o (c) as contoll nput s a unvsal appoach. Thfo th fuzzy contoll has two nputs, o and chang n o (, c) and on output (du) as c c c c Fg. 7: Mbshp functons of Inputs and output

5 Chang n Eo (c) In ths wok th cnt of gavty o cntod thod s usd fo d-fuzzfcaton. As a sult th contol ncnt s obtand by th quaton [6]. H da (4) du A d s th dstanc btwn th fuzzy st and th s aa valu of th fuzzy st. cnt, A 3.3 Knowldg Bas and Infnc Mchans Th ul dfnton s subjctv and basd on xpt s knowldg and xpncs. It stablshs th latonshp btwn outputs wth nputs [7]. Fo th syst wth two nputs and svn bshp functons n ach lads to foty nn cobnaton of ths nputs, n whch th a foty nn uls. Th uls a lk: R. If = and c = Thn du s o R. If = and c = NM Thn du s o... R49. If = PB and c = PB Thn du s PB Th uls a psntd by a atx calld atx nfnc shown n Tabl. A fatu of th ul bas usd s th syty acoss th dagonal. Ths fatu occus n systs wh th physcal bhavos of th syst xhbt syty, whch s consstnt n cas of spd contol of Inducton, oto. Th dvlopd fuzzy logc uss th nfnc thod fo ach ul gvn by th laton du n ( ), ( c) ;,,...49 (5) Tabl : Fuzzy Lngustc Rul Tabl Eo () NM NS Z PS PM PB NM NS Z NM NM NS Z PS NS NM NS Z PS PM Z NM NS Z PS PM PB PS NM NS Z PS PM PB PB PM NS Z PS PM PB PB PB PB Z PS PM PB PB PB PB Thfo, th sultng bshp functon s gvn by du ax ( du), ( du),... 49( du) (6) 4. Fuzzy Logc Spd Contoll Basd on Patcl Swa Optzaton 4. Patcl Swa Optzaton Patcl Swa Optzaton s a populaton basd stochastc optzaton tchnqu, nspd by socal bhavou of bd flockng o fsh schoolng. In PSO syst th ndvduals calld patcls, fly aound n a ultdnsonal sach spac and chang th poston wth t. Dung ts flght, ach patcl adjusts ts poston accodng to ts own xpnc and accodng to th xpnc of nghboung patcl. Th poston o valu cospondng to ts own xpncs calld P bst and cospondng to th xpnc of nghboung patcl s calld G bst. Th sach fo th optal poston advancs as th patcls vlocts and postons a updatd. Th ftnss of ach patcl s poston and taton s calculatd usng a p dfnd objctv (ftnss) functon and th vlocty of ach patcl s updatd usng th P bst and G bst, whch w pvously dfnd. Th vlocty of th patcl can b odfd by th followng quaton. v ( n ) ( n) v ( n) C ( n) P bst x ( n) C ( n) G bst x ( n) (7) Wh, v ( n ) s th vlocty of th patcl at taton n, v ( n ) s th vlocty of th patcl at taton (n + ), ( n) and ( n ) a ando nubs wth unfo dstbuton n th ntval [, ], ( n) s th ontu o ntal wght constant gvn by [8] ax ( n) n ax n nax (8) H n ax s th axu nub of taton, ax and n a th axu and nu wghts spctvly. Appopat valus of ax and n a.9 and.4 spctvly [9]. Th valus C and C a two postv constants psnt th socal and cogntv acclatons fo th P bst and G bst postons, spctvly. Vayng ths paats has th ffct of vayng th stngth of th pull towads th two bsts. Valus of CC an that both th cogntv and socal acclatons a absnt, and patcls kp ovng at th cunt spd untl thy ht a bounday of th sach spac (assung no nta) [].Wth C and C, ach patcl sachs fo th bst poston n ts nghbouhood, and placs th cunt bst poston f th nw poston s btt []. Howv, wth C and C, th nt

6 swa s attactd to a sngl pont, G bst. Futho, havng C C causs ach patcl to b attactd to ts own psonal bst poston to a vy hgh xtnt, sultng n xcssv wandng. On th oth hand, C Csults n patcls bng o stongly attactd to th global bst poston, thus causng patcls to ush patuly towads opta []. It s donstatd that th patcl swa s only stabl and guaantd to convg to a stabl qulbu pont f th followng condtons a satsfd []. ( ) 4 C C (9) ( C C) ( n) (3) Howv, whth o not ths pont s actually th global nu cannot b guaantd, and ts accptablty as a soluton should b vfd. Th poston of th patcl at taton n s x ( n ). Th odfd poston at taton ( n ) s gvn by x ( n ) x ( n) v ( n ) (3) 4. Optzaton of Fuzzy Contoll Th Patcl Swa Optzaton s appld to autoat and optz th fuzzy contoll dsgn pocss. Th noalzaton paats (k, k, k 3 ) and th paats of th bshp functons (a, a, b, b, c, c ) a optzd by optzng a poply dfnd objctv o ftnss functon [], [3]. In th contxt of optzaton ou goal s to hav a spd spons wth a shot s t, sall ovshoot and na zo stady stat o. In ths spct a ultpl objctv functon s dfnd as t F dt tdt t (3) Wh, th fst t s th asu of fast dynac spons and th scond t s th asu of stady stat o. Thus th pupos of PSO algoth s to nz th objctv functon. Th PSO basd appoach to fnd th nu valu of objctv functon s as shown n Fg.8. Th nput paats of th poposd PSO algoth a: n, n 3, n 9, C.5, C.5, ax pop va s ax.9, n.4, ( a, a, b, b, c, c), a a, b b, c c, k , k, k3 6, Stall gnaton = and Functon tolanc = 6. Fg. 8: Flowchat of th PSO algoth 5. Sulaton Rsults and Dscusson Coplt sulaton odl fo vcto contolld Inducton oto (IM) dv of th poposd sch s dvlopd usng MATLAB/ SIMULINK. Th oto paats a: Ratd Pow Patd 5HP, Ratd VoltagV 48volt, Ratd Fquncy F 5Hz, Pa of pols P=, Stato Rsstanc Rs.87, Roto Rsstanc R.8, Stato Inductanc Ls.8H, Roto Inductanc L.8H, Mutual Inductanc L 34.7H, Mont of Inta J.66 Kg.. Fg.9 shows th scos of th ftnss functon cospondng to dffnt gnaton n PSO. Th PSO s tnatd at 4 gnatons as th tnaton cta achd. Th tnaton cta of th algoth s th th axu gnatons achd o th wghtd avag chang n th ftnss functon valu ov Stall gnatons s lss than functon tolanc. Th valus of nn paats usd n fuzzy contoll and th optzd valus by patcl swa optzaton a shown n Fg.. Th patcl swa optzd nput and output bshp functons a n Fg..

7 DOM DOM DOM Toqu Dvlopd (N) Toqu Dvlopd (N) Spd Eo (ad/sc) Spd (ad/sc) Stato Cunts(A) Sco Ln Voltag Vab (V) Pol Voltag Vp (V).8 x Bst: Man: Man Sco Bst Sco T(sc) 5-5 Valus of Paats Gnaton..357 Fg. 9: Ftnss Sco vsus Gnaton Fuzzy Paats Patcl Swa Optzd Fuzzy Paats a a b b c c k k k3 Fg. : Convntonal and PS Optzd fuzzy Contoll paats Fg. shows th pol voltag, ln voltag and th ln cunts (stato ln cunts) of th th-lvl nvt und stady stat condton. Th ln cunts a snusodal wth alost nglgbl ppl. Fg.3 shows th spd tackng pfoanc of th oto followng a tapzodal spd fnc. Th spd tackng xpnt s on no load condton. Th oto spd alost tacks th fnc spd n both th dcton. Th ppl contnt n th toqu dung th tanston s copaatvly ducd wth PSO fuzzy contoll as copad to spl fuzzy contoll as shown n Fg.4 NM NS Z PS PM PB Eo ().5 NM NS Z PS PM PB Chang n Eo (c).5 NM NS Z PS PM PB Output (du).5 Fg. : PS Optzd Input Output Mbshp Functons of fuzzy contoll T(sc) T(sc) 5 Fg. : Invt Voltags and Cunts T(sc) - 3 T(sc) Fg. 3: Tapzodal Spd Tackng Toqu dvlopd dung tapzodal spd tackng wth Fuzzy Moto Spd Rfnc Spd T(sc) Toqu dvlopd dung tapzodal spd tackng wth PSO Fuzzy T(sc) Fg. 4: Toqu Dvlopd n Tapzodal Spd Tackng Fg. 5 and Fg.6 show th pfoanc of oto fo th constant fnc spd of wth constant load toqu n both fuzzy and PSO fuzzy spd contoll. Th ppl n spd and toqu, whn th oto achvs th fnc spd s naly zo n cas of PSO fuzzy as copad to fuzzy contoll. Fg.7 and Fg.8 show th pfoanc of oto whn th load toqu s suddnly changd fo to and thn fo to at constant fnc spd

8 Toqu(N) Toqu (N) Spd Eo (Rad./Sc) Spd(Rad./Sc) Spd (Rad./Sc) Toqu(N) Toqu (N) Spd Eo (Rad./Sc) Spd(Rad./Sc) Spd (Rad./Sc) Toqu (N) Toqu (N) Spd Eo (Rad./Sc) Spd (Rad./Sc) Spd (Rad./Sc) Toqu (N) Toqu (N) Spd Eo (Rad./Sc) Spd (Rad./Sc) Spd (Rad./Sc) Moto Spd Rfnc Spd T(sc) T(sc) T(sc) Fg. 5: Pfoanc und constant spd and constant toqu wth fuzzy Toqu Dvlopd Load Toqu Moto Spd Rfnc Spd T(sc) T(sc) 4 Toqu Dvlopd Load Toqu T(sc) Fg. 6: Pfoanc und constant spd and constant toqu wth PSO fuzzy Moto Spd Rfnc Spd T(sc) T(sc) Toqu Dvlopd Load Toqu T(sc) Fg. 7: Pfoanc und constant spd and vaabl toqu wth fuzzy Moto Spd Rfnc Spd T(sc) T(sc) 4 Toqu Dvlopd Load Toqu T(sc) Fg. 8: Pfoanc und constant spd and vaabl toqu wth PSO fuzzy Fg.9 and Fg. show th pfoanc of th oto whn th fnc spd s suddnly changd fo to and thn fo to wth a constant load toqu of Fg. and Fg. show th pfoanc of th oto wth vaabl spd and vaabl toqu. Th spd s ncasd fo to and thn dcasd fo to wth a vaabl load toqu. Th load toqu s ncasd fo to and thn t s dcasd to In all ths cass th pfoancs a btt wth PSO fuzzy as copad to fuzzy contoll T(sc) T(sc) Conclusons Fg. 9: Pfoanc und vaabl spd and constant toqu wth fuzzy Fg. : Pfoanc und vaabl spd and constant toqu wth PSO fuzzy Fg. : Pfoanc und vaabl spd and vaabl toqu wth fuzzy Fg. : Pfoanc und vaabl spd and vaabl toqu wth PSO fuzzy Moto Spd Rfnc Spd Toqu Dvlopd Load Toqu Moto Spd Rfnc Spd T(sc) 5 Toqu Dvlopd Load Toqu T(sc) T(sc) - Moto Spd Rfnc Spd Toqu Dvlopd Load Toqu T(sc) T(sc) - Moto Spd Rfnc Spd Toqu Dvlopd Load Toqu T(sc) Th optal fuzzy contoll has bn dsgnd off-ln usng tchnqus of Patcl Swa Optzaton fo ndct vcto contol of ultlvl nvt fd Inducton oto. It achvs good pusut of fnc spd, statng

9 wthout ovshoot and apd jcton of dstubancs wth a low dop-out spd. By copason wth fuzzy logc contoll, t tstfs that ths thod s not only obust, but also can pov dynac pfoanc of th syst. Rfncs [] B. K. Bos, Modn Pow Elctoncs and AC Dvs, Inc. Upp Saddl Rv, NJ-7458: Pntc-Hll PTR Copans,. [] P. Vas, Vcto contol of AC achns, Nw Yok: Clandon, 99. [3] R. Kshnan, Elctc oto dvs odlng, analyss and contol. Nw Dlh: PHI Pvt. Ltd, 3. [4] A. Naba, I. Takahas, and H. Akag, A nutal pont clapd PWM nvt, IEEE Tansacton on Industy Applcatons, Vol. A, No. 7,Spt./Oct 98, pp [5] J. Rodguz, J.-S. La, and F. Z. Png, Multlvl nvts: A suvy of topologs, contols, and applcatons, IEEE Tansacton on Industal Elctoncs, Vol. 49, No. 4, Aug.. [6] S. La and F. Z. Png, Multlvl convts- a nw bd of pow convts, IEEE Tansacton on Industy Applcatons, Vol. 3, No. 3, May 996, pp [7] X. Yuan and I. Bab, A nw dod clapng ultlvl nvt, IEEE, confnc, 999, pp [8] J. Knndy and R. C. Ebhat, Patcl swa optzaton, Pocdngs of th IEEE Int. Conf. on Nual Ntwoks, Pth, Austala,995, pp [9] M. Kazkowsk and L. Malsan, Cunt contol tchnqus fo th-phas voltag-souc pw convts: A suvy, IEEE Tansacton Ind. Elcton, Vol. 45, No. 5, 998, pp [] A. Shukla, A. Ghosh, and A. Josh, Hystss odulaton of ultlvl nvts, IEEE Tansacton on Pow Elctoncs, Vol. 6, No. 5, May, pp [] J. Zng, C. Yu., Q. Q., Z. Yan., Y. N., B. Zhang, S. Chn, and F. F. Wu., A novl hystss cunt contol fo actv pow flt wth constant fquncy, Elctc Pow Systs Rsach, Vol. 68, 4, pp [] M. Mlosvc, Hystss cunt contol n th-phas voltag souc nvt,zuch: Tchncal Rpot, 3. [3] S. Skanthan, M. Msha, and R. Rao, Ipovd hystss cunt contol of th-lvl nvt fo dstbuton statc copnsato applcaton, IET Pow Elctoncs, Vol., No. 5, 9, pp [4] S. K. Sahu, D. D. Na, and T. V. Dxt, Indct vcto contol of nducton oto usng ANN stato and ANFIS contoll, Intnatonal Jounal of Coput Applcatons, Vol. 66, No. 4, Mach 3. [5] M. N. Uddn, T. S. Radwan, and M. A. Rahan, Pfoancs of fuzzy-logc-basd ndct vcto contol fo nducton oto dv, IEEE Tansacton on Industy Applcatons, Vol. 38, No. 5, Spt./Oct, pp [6] C. C. L, Fuzzy Logc n Contol Systs: Fuzzy Logc contoll Pat and Pat. Nw Dlh: IEEE Pss, 99. [7] Z. Zhao, M. Tozuka, and S. Isaka, Fuzzy gan schdulng of PID contolls, IEEE Tansactons on Systs, Man and Cybntcs, Vol. 3, No. 5, Spt./Oct 993, pp [8] Y. Bkaka and D. B. Attous, Snsolss spd basd on MARS wth tunng of PI spd contoll n FOC of nducton oto dv usng PSO, Wold Acady of Scnc, Engnng and Tchnology, Vol. 6,, pp [9] R. Ebhat. and Y. Sh, Copang ntal wghts and constcton facto n patcl swa optzaton, Pocdng of th Intnatonal Congss on Evaluatonng Coputaton,, pp [] E. AP, Fundantals of Coputatonal Swa Intllgnc. John Wly Sons, 5. [] R. Pz and K. Bhdnan, Patcl swa appoach fo stuctual dsgn optzaton, Coputs and Stuctus, Vol. 85, 7, pp [] V. Donscu, D. Nacsu, G. Gva, and F. Pofuo, A systatc dsgn thod fo fuzzy contoll fo bushlss dc oto dvs, Poc. of th 7th. IEEE Annual Pow Elctoncs Spcalsts Confnc, 996, pp [3] F. D. S. Cadoso, J. F. Matns, and V. F. Ps, A copaatv study of a PI, nual ntwok and fuzzy gntc appoach contolls fo an ac dv, IEEE 5 th Intnatonal Wokshop on Advancd Moton Contol AMC, Coba, 998, pp

Dynamic Modelling and Simulation of Five Phase Induction Motor

Dynamic Modelling and Simulation of Five Phase Induction Motor ISSN (Pnt : 30 3765 ISSN (Onln: 78 8875 Intnatonal Jounal of Advancd Rsach n Elctcal, Elctoncs and Instuntaton Engnng (An ISO 397: 007 Ctfd Oganzaton ol. 4, Issu 4, Apl 05 Dynac Modllng and Sulaton of