EFFICIENCY OPTIMIZATION OF INDUCTION MOTOR DRIVES

Transcription

1 Naučno-stučn spozju Engtska fkasnost ENEF 03, Banja Luka,. 3. novba 03. gon Ra po pozvu EFFICIENCY OPIMIZAION OF INUCION MOOR RIVES Banko Blanuša, Faculty of Elctcal Engnng, Rpublka Spska, Bosna an Hzgovna Sloboan N. Vukosavć, Faculty of Elctcal Engnng Blga, Sba Abstact -h pap scbs th ost coonly us tho fo ffcncy optzaton of nucton oto vs (IM). Spl stat contol, Mol bas an Sach contol. hy hav bn analyz an pont out goo ss an awbacks of vy tho. An algoth fo ffcncy optzaton of IM that wok n poc clos cycl opaton cycls an known opatng contons s also psnt. h us algoth s bas on th tchnu of ynac pogang. hs ol s plnt n vcto contol nucton oto v. Sulatons an xpntal tst a pfo. Rsults a psnt n th pap.. INROUCION Scntfc consatons psnt n ths pap a lat to th thos fo pow loss nzaton n nucton oto vs. h nucton oto s wthout oubt th ost us lctcal oto an a gat ngy consu. h-phas nucton otos consu 60% of nustal lctcty an t taks consabl ffots to pov th ffcncy []. h vast ajoty of nucton oto vs a us fo hatng, vntlaton an a contonng (HVAC). hs applcatons u only low ynac pfoanc an n ost cass only voltag souc nvt s nst btwn g an nucton oto as chapst soluton. h classcal way to contol ths vs s constant V/f ato an spl thos fo ffcncy optzaton can b appl [-3]. Fo th oth s th a any applcatons wh, lk lctcal vhcls, lctc ngy has to b consu n th bst possbl way an us of nucton otos n such applcaton us an ngy optz contol statgy [4]. h voluton of th pow gtal cocontolls an vlopnt of pow lctoncs nabls applyng not only thos fo nucton oto vs (IM) contol, lk vcto contol o ct tou contol, but also vlopnt of ffnt functons whch ak vs o obust an o ffcnt. On of th o ntstng algoth whch can b appl n a v contoll s algoth fo ffcncy optzaton. In a convntonal sttng, th fl xctaton s kpt constant at at valu thoughout ts nt loa ang. If achn s un-loa, ths woul sult n ovxctaton an unncssay copp losss. hus n cass wh a oto v has to opat n w loa ang, th nzaton of losss has gat sgnfcanc. It s known that ffcncy povnt of IM can b plnt va oto flux lvl an ths tho has bn povn to b patculaly ffctv at lght loas an n a stay stat of v. Also flux ucton at lght loas gvs lss acoustc nos v fo both convt an achn. Fo th oth s low flux aks oto o snstv to loa stubancs an gas ynac pfoancs [5]. h publsh thos anly solv th pobl of ffcncy povnt fo constant output pow. Rsults of appl algoths hghly pns fo th sz of v (Fg. ) (Abahasn t al.,998) an opatng contons, spcally loa tou an sp (Fgs. an 3). Effcncy of IM changs fo 75% fo low pow 0,75kW achn to o thn 95% fo 00kW achn. Also ffcncy of v convt s typcally 95% an o. Fg. Rat oto ffcancs fo ABB otos (catalog ata) an typcal convt ffcncy. Fg. Masu stana oto ffcncs wth both at flux an ffcncy optz contol at at chancal sp (. kw at pow). hat s obvous, convt losss s not ncssay to cons n ffcncy optal contol fo sall vs. Bst sults n ffcncy optzaton can b achv fo a lght loas an stay stat of v. Functonal appoxaton of th pow losss n th nucton oto v s gvn n scon scton. Basc concpts statgs fo ffcncy optzaton of nucton oto v what nclus ts chaactstcs, avantags an awbacks a scb n th scton. Iplntaton of on tchnu fo ffcncy optzaton of IM bas on fuzzy logc, B-

2 atfcal nual ntwoks an tou sv contol a psnt n fouth scton. Fg 3. Masu stana oto ffcncs wth both at flux an ffcncy optz contol at lght loa (0% of at loa). Effcncy optz contol fo clos-cycl opaton of hgh pfoanc IM s psnt n ffth scton. h athatcal concpt fo coputng optal contol, bas on th ynac pogang appoach, s scb. At th n, concluson suass th sults achv, plntaton possblts an ctons of futh sach n ths fl.. FUNCIONAL APPROXIMAION OF HE POWER LOSSES IN HE INUCION MOOR RIVE h pocss of ngy convson wthn oto v convt an oto las to th pow losss n th oto wnngs an agntc ccut as wll as conucton an coutaton losss n th nvt. h ovall pow losss (P tot ) n lctcal v conssts of convt losss (P nv ) an oto losss (P ot ), whl oto pow losss can b v n copp (P Cu ) an on losss (P F ) (Un & Na, 008): Ptot = Pot Pnv (). Pot = PCu PF Convt losss: Man consttunts of convt losss a th ctf, C lnk an nvt conuctv an nvt coutaton losss. Rctf an C lnk nvt losss a popotonal to output pow, so th ovall flux-pnnt losss a nvt losss. hs a usually gvn by: nv nv s nv ( ) P = R = R, () wh,, a coponnts of th stato cunt s n, otatonal syst an R nv s nvt loss coffcnt. Moto losss: hs losss consst of hystss an y cunt losss n th agntc ccut (co losss), losss n th stato an oto conuctos (copp losss) an stay losss. At nonal opatng pont, th co losss a typcally -3 ts sall thn th coop losss, but thy psnt an loss coponnt of a hghly loa nucton oto vs [6]. h an co losss can b ol by [7]: P F h = c Ψ ω c Ψ ω, (3) wh s agntzng flux, ω supply funcy, c h s hystss an c y cunt co loss coffcnt. Copp losss a u to flow of th lctc cunt though th stato an oto wnngs an ths a gvn by: Cu s s p = R R, (4) h stay flux losss pn on th fo of stato an oto slots an a funcy an loa pnnt [6]. h total sconay losss (stay flux, skn ffct an shaft stay losss) usually on't xc 5% of th ovall losss. Consng also, that th stay losss a of potanc at hgh loa an ovloa contons, whl th ffcncy optz s ffctv at lght loa, th stay losss a not cons as a spaat loss coponnt n th loss functon. Foal osson of th stay loss psntaton n th loss functon hav no pact on th accuacy algoth fo on-ln optzaton [6]. Bas on pvous consaton, total flux pnnt pow losss n th v a gvn by th followng utaton: Ptot = ( Rnv Rs ) ( Rnv Rs R ) cω chω. (5) Effcncy algoth woks so that flux n th achn s lss o ual to ts nonal valu: n, (6) wh n s nonal valu of oto flux. So lna xpsson fo oto flux can b accpt: R R = L, (7) t L L wh Ψ =L n a stay stat. Expsson fo output pow can b gvn as: P out =ω, (8) wh s postv constant, ω angula sp, oto flux an actv coponnt of th stato cunt. Bas on pvous consaton, assupton that poston of th oto flux s coctly calculat, coponnt of oto flux s ual 0 (Ψ Q =0) an laton P n =P tot P out,output pow can b gvn by th followng uaton: P = a b c ω c ω ω, (9) n wh a=r s R nv, b= R s R nv R,, c =c an c =c h. Input pow shoul b asu an xact P out s n n o to acu coct pow loss an avo couplng btwn loa pulsaton an th ffcncy optz. otal pow losss can b calculat as ffnc btwn nput an output v pow: Ptot = Pn Pout, (0) wh Pn = Vc I c () s nput v pow an Pout = ω () s output v pow. Vaabls V c an I c a voltag an cunt n C lnk. Elctoagntc tou s known vaabl n a v an sp ω s asu o stat. So, w can calculat pow losss wthout knowlg of oto B-

3 paats an pow loss calculaton s npnnt of th oto paat changs n th wokng aa. 3. SRAEGIES FOR EFFICIENCY OPIMIZAION OF IM Nuous scntfc paps on th pobl of loss ucton n IM hav bn publsh n th last 0 yas. Although goo sults hav bn achv, th s stll no gnally accpt tho fo loss nzaton. Accong to th ltatu, th a th statgs fo alng wth th pobl of ffcncy optzaton of th nucton oto v []:. Spl Stat Contol (SSC),. Loss Mol Contol (LMC) an 3. Sach Contol (SC) 3.. Spl Stat contol h fst statgy s bas on th contol of on of th vaabls n th v [], [8] (Fg.4). hs vaabl ust b asu o stat an ts valu s us n th fback contol of th v, wth th a of unnng th oto by pfn fnc valu. Slp funcy o pow facto splacnt a th ost oftn us vaabls n ths contol statgy. Whch on to chos pns on whch asunt sgnals s avalabl []. hs statgy s spl, but gvs goo sults only fo a naow st of opaton contons. Also, t s snstv to paat changs n th v u to tpatu changs an agntc ccut satuaton. Fg. 4. Contol aga fo th spl stat ffcncy optzaton statgy. 3. Loss Mol Contol In th scon statgy, a v loss ol s us fo optal v contol [8], [6](Fg. 5). hs algoths a fast bcaus th optal contol s calculat ctly fo th loss ol. Fg. 5 Block aga fo th ol bas contol statgy. But, pow loss olng an calculaton of th optal opatng contons can b vy coplx. hs statgy s also snstv to paat vaatons n th v. 3.3 Sach Contol In th sach statgy, th on-ln pocu fo ffcncy optzaton s ca out [0], [], [] (Fg. 6). h on-ln ffcncy optzaton contol on th bass of sach, wh th stato o oto flux s cnt n stps untl th asu nput pow sttls own to th lowst valu s vy attactv. Sach statgy thos hav an potant avantag copa to oth statgs. It s copltly nsnstv to paat changs whl ffcts of th paat vaatons caus by tpatu an satuaton a vy xpss n two oth statgy. Bss all goo chaactstcs of sach statgy thos, th s an outstanng pobl n ts us. Whn th loa s low an optal opatng pont s foun, flux s so low that th oto s vy snstv to loa ptubatons.also, flux convgnc to ts optal valu sots can b to slow, an flux nv achs th valu of nal losss thn n sall stps oscllats aoun t. Fg. 6. Block aga of sach contol statgy. h a hyb thos [5], [3] whch cobn goo chaactstcs of two optzaton statgs SC an LMC an t was nhanc attnton as ntstng soluton fo ffcncy optzaton of contoll lctcal vs. 4. MOERN ECHNIQUE FOR EFFICIENCY OPIMIZAION OF IM Pow loss ol s vy attactv, bcaus t s fast an agntzng flux whch gvs nu pow losss can b calculat ctly fo loss ol. Bas on xpsson (8), (9) an (0) pow losss can b xpss n ts lat to, an ω s as follows P tot, b (, ) = ( a c L ω c L ω ) ω (3) ( L ). Assung absnc of satuaton an spcfyng slp funcy: ω s = ω ω =. (4) pow loss functon can b xpss as functon of cunt an opatonal contons (ω, ): P tot (,, ω ) = ( a c L ω c L ω ) ( c ω c ) L c ( ) ( L ) b. Bas on uaton (4), t s obvous, th stay-stat optu s aly foun bas upon th loss functon paats an opatng contons. Substtung α= (5) B-3

4 ( a c L ω c L ω ) L b an γ = c valu of cunt whch gvs nal losss s: γ LMC =. (6) α If th losss n th v w known xactly, t woul b possbl to calculat th optal opatng pont an contol of v n accoanc to that. Fo th followng asons t s not possbl n pactc [0]:. Evn though ffcncy optzaton coul b calculat xactly, t s pobably that ltaton n coputaton pow n nustal vs woul ak ths possbl.. A nub of funantal losss a ffcult to pct: stay loa, on losss n cas of satuaton changs, copp losss bcaus of tpatu s tc. 3. u to ltaton n costs all th asuabl sgnals can not b acu. It ans that ctan uantts ust b stat whch natually las to an o. 4. Paats n th loss ol a vy snstv to tpatu s, agntc ccut satuaton, skn ffct an so on. Fo abov nton asons t s pactcally to calculat pow losss on th bass of loss ol. Sach algoths o not u th knowlg of oto paats an ths a applcabl unvsally to any oto. So th a vy ntnsv sach of ths thos, spcally on acac lvl. Sach algoths a usually bas on th followng thos [4]. 4. Rosnbock Mtho 0.5 h flux s chang gaually n on cton f (ΔP tot <0).Whn algoth tcts chang of pow losss (ΔP tot >0), flux s chang n oth cton, untl th u accuacy s achv: k = ; ΔPγ < 0 ( n ) = kδ ; k =, wh k = ; ΔPγ > 0 ΔP tot (n)= P tot (n)- P tot (n) an Δ(n)= (n)- (n). hs tho s spl, but flux convgnc can b to slow. 4. Popotonal Mtho o acclat flux convgnc to ts optal valu s possbl to us not only th sgn of th consu pow, but also th oul of th nput pow. hs can b xpss by: ( n ) = k sgn( Δ ), wh k s postv nub. hs algoth psnts convgnc pobls an oscllatons f k s constant valu. Btt sults a obtan f k s a nonlna functons vayng wth syst contons. 4.3 Gant Mtho hs algoth s bas on th gant ctons sach thos, usng th gant of th nput pow. h gant s coput usng a st o ln appoxaton. ( n ) = k Pγ. hs pobl has pobls aoun th optu flux u to ffculty to obtan a goo nucal appoxaton of th gant. 4.4 Fbonacc Mtho hs tho conssts of saplng th nput pow of th oto wokng at ffnt fluxs a functon Fbonacc s ss. 4.5 Sach Mthos Bas on Fuzzy Logc Sach contoll s us ung th stay stats of v. Bas on xpsson (9) t can b conclu that functon of pow loss s nonlna. Also contoll of ffcncy povnt shoul follow known uls. hs a asons why fuzzy logc s oftn us n alzaton of ffcncy optzaton contoll. hs obtans fast an soothly convgnc of flux to th valu whch gvs nal pow loss fo a gvn opatng contons. ypcal SC optzaton block s shown n Fg. 7 [5]. Input vaabl n optzaton contoll s v nput pow (P n ), whl output vaabl s nw valu of agntzaton cunt ( * ). Fuzzy contoll s vy spl an t contans only on nput an on output vaabl. Scalng factos, nput gan P g an output gan I g a calculat followng th nxt xpsson [5]: P I g g = P = I P tot _ no totlmc * n LMC, (7) wh P tot_no s pow loss fo nonal flux, an P tot_opt s pow loss fo optal flux valu calculat fo loss ol, I n s nonal an * LMC s optal agntzng cunt fn by (6). Fg. 7. SC ffcncy optzaton contoll. 4.6 ou Rsv Contol n Sach Mthos fo Effcncy Optzaton On of th gatst pobl of LMC thos s ts snstvty on loa ptubaton, spcally fo lght loas whn th flux lvl s low. hs s xpss fo a stp ncas of loa tou an thn two sgnfcant pobls appa: - Flux s fa fo th valu whch gvs nal losss ung tansnt pocss, so tansnt losss a bg. - Insuffcncy n th lctoagntc tou las output sp to convg slow to ts fnc valu wth sgnfcant sp ops. Also, oscllatons n th sp spons a appa. hs a coon pobl of thos fo ffcncy optzaton bas on flux ajustng to loa tou. Sp spons on th stp chang of loa tou (fo 0.5 p.u. to. p.u.), fo nonal flux an whn LMC tho s appl, s psnt n th fg. 8. Sp ops an slow sp convgnc to ts fnc valu a o xpos fo LMC tho. hs a asons why tou sv contol n LMC tho fo ffcncy optzaton s B-4

5 ncssay. Mol of ffcncy optzaton contoll wth tou sv contol s psnt n fg. 9 [6]. Optal valu of agntzaton cunt s calculat fo th loss ol an fo gvn opatonal contons (6). Fuzzy logc contoll s us n tnaton of Δ, on th bass of th pvously tn tou sv (Δ ). Contoll s vy spl, an th s on nput, on output an 3 uls. Only 3 bshp functons a nough to scb nflunc of tou sv n th gnaton of opt. 4.7 Sach Mthos Usng Nual Ntwoks o fn contol cobnaton that las to th nu pow nput pont an atfcal nual ntwok (ANN) bas sach algoth can b ploy to opat as an ffcncy optz. On typcal ANN sach contol block appl fo ct tou contoll IM s psnt n Fg. 0 [4]. Also, sla tho can b appl fo vcto contoll IM [4]. Fg. 0 ANN ffcncy optz. Fg. 8 Sp spons on th stp loa ncas fo nonal flux an whn LMC s appl. Fg. 9. Block fo ffcncy optzaton wth tou sv contol. If tou sv s suffcnt thn Δ 0 an ths block has no ffct n a tnaton of opt. Oppostly, cunt (agntzaton flux) ncass to obtan suffcnt sv of lctoagntc tou. wo scalng blocks a us n ffcncy contoll. Block IS s us fo noalzaton of nput vaabl, so sa contoll can b us fo a ffnt pow ang of achn. Block OS s us fo output scalng to ajust nflunc of tou sv n tnaton of LMC an obtan ust copos btwn pow loss ucton an goo ynac spons. Input v pow s asu an ffnc btwn two succssv stps s calculat. Rsult ΔP n (k) s on nput vaabl n atfcal nual ntwok. It s scal to th noalz ntval [0 ] n nput scalng block IS. Scon nput vaabl s last stp of stato flux ΔΨ σ (k-). h nual ntwoks has two nputs, on output, an two hn lays, of 4 an nuons spctvly. h tanng was on off-ln, by connctng th ANN n paalll wth an aaptv stp nu sach syst. Output vaabl of ffcncy contoll s nw stp of stato flux ΔΨ s (n). Also, t s noalz to ntval [-,] an ts scalng to al valu s plnt n output scalng (OS) block. Stay stat of th syst s tct n scon pat of ffcncy optzaton block whch nput s chancal sp ω (n). If stay stat s tct optzaton block s nabl an output s Ψ s(n)=ψ s (n). Avsly, flux s st to th valu gvn by flux waknng block an Ψ s(n)=ψ 0 s(n) 4.8 Hyb tho fo ffcncy optzaton Hyb tho cobns goo chaactstcs of two optzaton statgs SC an LMC [6, 7]. It was nhanc attnton as ntstng soluton fo ffcncy optzaton of contoll lctcal vs. ung tansnt pocss LMC s us, so fast flux changs an goo ynac pfoancs a kpt. Sach contol s us fo ffcncy optzaton n a stay stat of v. Elctcal v wth block fo ffcncy optzaton s shown n Fgu. Elctc v s suppl fo th pay pow ntwok 3x380V. hs voltag s ctf an th voltag an cunt n C lnk a su. h v nvt s cunt gulat (CR) voltag th-phas nvt. Rfnc an asu an coponnts of stato cunt a kpt n th cunt contolls. hs B-5

6 contolls a alz n otatonal, coonat syst as a lna PI contoll. Outputs of contoll a an coponnt of stato voltag. hs voltags a tansfo (B tansfoaton) n th-phas fnc voltags v * a, v * b, v * c. hs voltags a scal an la to PWM oulato, wh contol sgnals of nvt swtchs a gnat. hs v woks as sp contoll v. Sp fnc an asu sp a l nto sp contoll. Sp contoll s alz as PI contoll n ncntal fo, wth popotonal coffcnt n a fback local banch. h output of sp contoll s fnc valu of lctoagntc tou. Rfnc valu of stato cunt coponnt s tn n a block fo ffcncy optzaton an coponnt of stato cunt vcto on th bass of stato cunt vcto coponnt an lctoagntc tou fnc. Poston of oto flux vcto s tn n nct vcto contol block (IVC). Fg.. Ovall popos block aga of ffcncy optzaton contoll n IM. Hyb ol fo ffcncy optzaton conssts fo 3 blocks, LMC, SC an Stay stat contol (SSC) block. LMC s us ung tansnt stats caus of xtnal sp o tou an [5]. Optal contol ( * LMC, * LMC) s calculat ctly fo loss ol fo a gvn opatonal contons what obtans pow loss optzaton an goo ynac pfoancs. SC s us n a stay stat fo a constant output pow. On th bass of sp fnc an asu sp, SSC block fns ts output an contols swtchs (Fg.). If tansnt stats s tct, LMC s actv an ts outputs a fowa to nct vcto contol (IVC) block an cunt gulatos. Whn stay stat s tct n SSC block, last valu of agntzng cunt ung tansnt stat s us as statng pont fo sach algoth A. Loss ol contoll B-6 Optal contol calculaton n LMC fo a gvn opatonal contons s scb at th bgnnng of Scton 4. Expsson fo coponnt of stato cunt a fn by uatons (6). hs tho s snstv to paat changs u to tpatu changs an agntc ccut satuaton, what consuntly las to o n a cunt fncs calculaton. So, algoth fo paat ntfcaton s always actv, an paats n th loss ol a contnuously upat (Fg.). B. Sach contoll Sach algoth s us n stay stat, whch s tct n th SSC block. Eo that xsts btwn th cunt fnc that s gnat n th LMC ol an n th Sach ol appas as a consunc of nvt an stay losss whch a not nclu n th ol. h

7 appl sach algoth s spl. Snc th cunt s vy clos to th valu whch gvs nal losss, sall stp of agntzaton cunt Δ =0.0I n s chosn. Fo two succssv valus of th cunt, pow losss a tn. Sgn of Δ s antan f pow losss a uc. Othws, th sgn of Δ s oppost n th nxt stp: ( ) Δ = ( n ) sgn ΔP ( n ) γ. (8) Whn th two valus of agntzaton cunt an w foun so th sgn of pow loss s chang btwn ths valus nw fnc of cunt s spcf as: =. (9) * SC In ths way, th a no oscllatons of s cunt, a gap flux an lctoagntc tou, whch a chaactstcs of th sach algoth. 5. EFFICIENCY OPIMIZAION OF CLOSE CYCLE OPERAION IM Effcncy povnt of IM bas on ynac pogang (optal flux contol) s an ntstng soluton fo clos-cycl opaton of vs [9]. Fo ths vs, t s possbl to coput optal contol, so th ngy consupton fo on opatonal cycl s nz. In o to o that, t s ncssay to fn pfoanc nx, syst uatons an constants fo contol an stat vaabls an psnt th n a fo sutabl fo coput pocssng. h pfoanc nx s as follows [0], []: N [ x( N) ] L( x( n), u( n) ) J = ϕ n= (0) wh N=/ s, s a po of clos-cycl opaton an s s sapl t. h L functon s a scala functon of x-stat vaabls an u-contol vaabls, wh x(n), a sunc of n-vcto, s tn by u(n), a sunc of -vcto. h ϕ functon s a functon of stat vaabls n th fnal stag of th cycl. It s ncssay fo a coct fnton of pfoanc nx. h syst uatons a: [ x, u ], n = 0.. x( n ) = f N, () an f can b a lna o nonlna functon. Functons L an f ust hav fst an scon vaton on ts oan. h constants of th contol an stat vaabls n ts of ualty an nualty a: [ x, u ] 0, = 0,,.., N C. () Followng th abov nton pocu, pfoanc nx, syst uatons, constants an bounay contons fo a vcto contoll IM n th oto flux ont fnc fa, can b fn as follows: a) h pfoanc nx s [6]: N a = b cω J = n 0 cω. (3) h a, b, c an c a paats n th loss ol of th v. hs paats a tn though th pocss of paat ntfcaton. Roto sp ω an lctoagntc tou a fn by opatng contons (sp fnc, loa an fcton). b) h ynacs of th oto flux can b scb by th followng uaton: s s ( n ) = L, (4) wh =L /R s a oto t constant. c) Constants: k ω =, n n ω ω, ( fo sp) n I n 0, ( fo oto flux) 0. s ax k = 3 p L L, ( fo tou) 0, ( fo stato cunt) (5) I sax s axal apltu of stato cunt, ω n s nonal oto sp, p s nub of pols an Ψ n s nal valu of oto flux. Also, th a constants on stato voltag: 0 v v Vs ax, (6) wh v an v a coponnts of stato voltag an V sax s axal apltu of stato voltag. Voltag constants a o xpss n C than n flont vcto contol. ) Bounay contons: Bascally, ths s a bounay-valu pobl btwn two ponts whch a fn by statng an fnal valu of stat vaabls: ω ( 0) = ω ( N ) = ( 0) = ( N ) = ( 0) = ( N ) n n = f, consng constans n (5) (7) Psnc of stat an contol vaabls constans gnally coplcats vaton of optal contol law. On th oth s, ths constans uc th ang of valus to b sach an splfy th sz of coputaton [9]. Lt us tak th followng assuptons nto account:. h s no satuaton ffct (Ψ Ψ n ).. Supply funcy s a su of oto sp an slp funcy, ω = ω ω s. Roto sp s fn by sp fnc whas slp funcy s usually low an nsgnfcantly nfluncs on total pow loss [] 3. Roto lakag nuctanc s sgnfcantly low than utual nuctanc, L γ <<L. 0, 0, B-7

8 4. Elctoagntc tou fnc an sp fnc a fn by opaton contons wthn constants fn n uaton (5). Followng th ynac pogang thoy, Haltonan functon H, nclung syst uatons an ualty constans can b wttn as follows [3]: H ( c ω,, ω, ) = a b c ω S S λ( n ) L μ [ k ]. (8) In a pupos to tn statonay stat of pfoanc nx, nxt syst of ffntal uatons a fn: λ S = λ( n ) c ω c ω b a k μ k μ k λ( n ) =, ω = ω n = 0,,,.., N, = 0 ( ) S L = 0 L wh λ an μ a Lagang ultpls. By solvng th syst of uatons (7) an nclung bounay contons gvn n (3), w co to th followng syst: a 4 λ( n ) = ( n ) =, ω () = ω () k = c ω c ω λ ( ) λ( n ) n = 0,,,.., N. s S 3 b = k s (30) L s L, s (9) Evy sapl t valus of ω (n) an (n) fn by opatng contons s us to coput th optal contol ( (n), (n), n=0,..,n-) though th tatv pocu an applyng th backwa pocu, fo stag n =N- own to stag n =0. Fo th optal contol coputaton, th fnal valu of an λ hav to b known. In ths cas, (N)= n an 5. Expntal sults ϕ λ( N) = = 0. ( N ) Sulatons an xpnts hav bn pfo n o to valat th popos pocu. h xpntal tsts hav bn pfo on th stup whch conssts of: - nucton oto (3 MO, Δ380V/Y0V, 3.7/.A, cosφ=0.7, 400o/n, 50Hz) - ncntal nco connct wth th oto shaft, - PC an SPACE0 contoll boa wth MS30C3 - floatng pont pocsso an pphals, h algoth obsv n ths pap us th Matlab Sulnk softwa, SPACE al-t ntfac an C languag. Hanlng al-t applcatons s on n Contolsk. So copasons btwn algoths fo ffcncy optzaton a a though th xpntal tsts. Expss pobl n ffcncy optzaton thos a ts snstvty to stp ncas of loa o sp fnc, spcally fo low flux lvl. hfo, sp spons on stp ncas of loa a analyz fo LMC an optal flux contol tho. ou loa an sp fnc fo on opatng cycl a shown n Fg. Gaph of pow losss whn nonal flux s appl an optal flux contol an on opatng cycl s psnt n Fg. 3. (9) Fg.. Gaph of sp an loa tou fnc n on on opatng cycl. B-8

9 40 0 pow loss (W) t (s/v) ) t (s/v) b) Fg. 3 Pow losss n on opatng cycl fo a) optal flux b) nonal flux. hat s obvous, fo optal flux contol pow loss ucton s xpss n on opatng cycl 6. Concluson Algoths fo ffcncy optzaton of nucton oto vs a bfly scb. hs algoths can b appl as softwa soluton n contoll lctcal vs, patculay vcto contoll an ct contoll IM. If loa tou has a valu clos to nonal o hgh, agntzng flux s also nonal galss of whth an algoth fo ffcncy optzaton s appl o not. Fo a lght loa thos fo ffcncy optzaton gvs sgnfcant pow loss ucton (Fgs. an 3). h statgs fo ffcncy optzaton, Spl stat contol, Loss ol contol an Sach contol a usually us. LMC an SC a spcally ntst. LMC s fastst thnu but vy snstv to paat vaatons n loss ol of v. Also, calculaton of optal contol bas on loss ol can b to coplx. SC thos can b appl fo any achn an ths a nsnstv to paat vaatons. In any applcatons fux chang to ts optal valu s too slow. So thnus bas on fuzzy logc an atfcal nual ntwoks whch obtans fast an soothly flux convgnc to th valu of nal pow losss a scb. Nw algoth fo ffcncy optzaton of hgh pfoanc nucton oto v an fo clos-cycl opaton has bn popos. Also, pocu fo optal contol coputaton has bn appl. Accong to th pfo sulatons an xpntal tsts, w hav av at th followng conclusons: h obtan xpntal sults show that ths algoth s applcabl. It offs sgnfcant loss ucton (Fg. 3), goo ynac fatus an stabl opaton of th v. So nw thos fo paat ntfcaton n loss ol a LMC vy actual. Also, Hyb tho cobns goo chaactstcs of two optzaton statgs SC an LMC. It was nhanc attnton as ntstng soluton fo ffcncy optzaton of contoll lctcal vs. hs can b vy ntstng fo futh sach n ths fl. Ltatu: [] Vukosavc S.N., Contoll lctcal vs - Status of tchnology. In: Pocngs of XLII ERAN Confnc, Vnjacka Banja, Yugoslava, No.,pp. 3-6,998. [] Abahasn F, Psn JK, Blaabjg F: Stat-of-At of optal ffcncy contol of low cost nucton oto vs. In: Pocngs of PESC 96, pp , 996 [3] F. Abahasn, F. Blaabjg, J.K. Psn, P.Z. Gabowsk an P. hognsn, On th Engy Optz Contol of Stana an Hgh Effcncy Inucton Motos n C an HVAC Applcatons, IEEE ansacton on Inusty Applcatons, Vol.34, No.4, pp.8-83, 998. [4] Chs M., Jayaa S., Rashaw R., Rajashkaa K.: Nual ntwok bas ffcncy optzaton of EV v. In: IEEE-IECIN Confnc Rco, pp , 997. [5] Sgak E. S., Stavakaks G.S., Onln Sach Bas Fuzzy Optu Effcncy Opaton n Stay an ansnt Stats fo c an Ac Vcto Contoll Motos, Pocngs of th 008 Intnatonal Confnc on Elctcal Machn, Pap I 90, 008. [6] Vukosavc S.N., Lv E.: Robust SP-bas ffcncy optzaton of vaabl sp nucton oto v, IEEE ansacton of In. Elctoncs (003), Vol. 50, No. 3,pp , 003 [8] Bnbouz M.E.H., Nat Sa N.S., An ffcncyoptzaton contoll fo nucton oto vs, IEEE Pow Engnng Rvw, Vol. 8, Issu 5, pp , 998. [9] Fnanz-Bnal F., Gaca-Caa A., Fau R.: Mol-bas loss nzaton fo C an AC vctocontoll otos nclung co satuaton.in: IEEE ansactons on Inusty Applcatons, (000), Vol. 36, No. 3, 000, pp , 000. [0] Sousa G.C.., Bos B.K., Cllan J.G.: Fuzzy logc bas on-ln ffcncy optzaton contol of an nct vcto contoll nucton oto v., IEEE ansacton on Inustal Elctoncs (995), Vol. 4, No., pp. 9-98, 995. [] Sousa.A., Wlson C.P. Aagao an Sousa G.C..: Aaptv Fuzzy Contoll fo Effcncy Optzaton of Inucton Motos, IEEE ansacton on Inustal Elctoncs, Vol. 54, No.4, pp , 007. [] Ghozzy S., Jlass K., Roboa X.: Engy optzaton of nucton oto v, Intnatonal Confnc on Inustal chnology, pp , 004. [3] Sousa G.C.., Bos B.K., Cllan J.G.: Fuzzy logc bas on-ln ffcncy optzaton contol of an nct vcto contoll nucton oto v., IEEE B-9

10 ansacton on Inustal Elctoncs (995), Vol. 4, No., pp. 9-98, 995. [4] Pyak B., Mono-Egulaz J.A., Pacaula J.: Nual ntwok bas ffcncy optzaton of an nucton oto v wth vcto contol, In: Pocngs of th IECON 0 Inustal Elctoncs Socty, IEEE 00 8th Annual Confnc, Vol., pp. 46-5, 00. [5] Lw Z., Jun L., Xuhu W.: Systatc sgn of Fuzzy Logc Bas Hyb On-Ln Mnu Input Pow Sach Contol Statgy fo Effcncy Optzaton of IM, IPEMC 006. [6] Blanusa B., Matć P., Ivanovc Z, Vukosavc S.N.: An Ipov Loss Mol Bas Algoth fo Effcncy Optzaton of th Inucton Moto v, In: Elctoncs (006), Vol.0, No.., pp. 49-5, 006. [7] C. Chakaboty, Y. Ho: Fast Effcncy Optzaton chnus fo th Inct Vcto- Contoll Inucton Moto vs, IEEE ansacton on Inusty Applcatons, Vol.39. No. 4, pp , 003. [8] Blanuša B., Matć P., okć B.: Nw Hyb Mol fo Effcncy Optzaton of Inucton Moto vs, Pocngs of 5n Intnatonal Syposu ELMAR-00, (IEEE) pp ,00. [9] Lonz, R.. Yang. S.-M.: Effcncy optz flux tajctos fo clos-cycl opaton of flontaton Inucton Machn vs. In: IEEE ansactons on Inusty Applcatons (99), Vol.8, No.3, pp , 99. [0] Bllan R., ynac Pogang, Pnston Unvsty Pss, 957. [] Bayson A. E., Appl Optal Contol,Optzaton, Estaton an Contol, John Wly & Sons, 975. [] Ionl.M., Popscu M., llng S.J., Mll.J.E., Han R.J., McGlp M.I.: On th vaaton wth flux an funcy of th co loss coffcnts n lctcal achns. In: IEEE ansactons on Inusty Applcatons (006), Vol. 4, No. 3, pp , 006. [3] Blanusa B., Sloboan N. V.: Effcncy Optz Contol fo clos-cycl Opatons of Hgh Pfoanc Inucton Moto v, Jounal of Elctcal Engnng, Vol.8/008-Eton: 3, pp.8-88, 008. B-0