Indirect Vector Control of Induction Motor

Transcription

1 Pocdng of th 6th WSEAS Intnatonal Confnc on Sulaton, Modllng and Optzaton, bon, Potugal, Sptb 4, 6 98 Indct Vcto Contol of Inducton Moto AEXANDU ONEA VASIE HOGA MACE ĂŢOI Dpatnt of Autoatc Contol and chncal Infoatc Dpatnt of Elctc Dv "Gh. Aach" chncal Unvty of Iaş Bd. Mangon. 53A, 66 Iaş OMANIA al: aona@ac.tua.o, hoga@tua.o, ato@tua.o Abtact: h pap pha a oluton fo nducton oto pd contol. h pap pnt a vcto contol odl of nducton achn wth fou paat only. h an advantag of th nu nub of paat odl cont n th aunt poblt of th. h paat ult unvocally fo th dntfcaton pocdu. h nu nub of paat odl pv th dynac bhavo of th oto. h odl nz th unctanty of th odl paat. h ndct vcto contol tuctu wa foulatd accodng to th odl, ulatd wth MAAB, and plntd wth a floatngpont DSP poco. h xpntal ult how good tannt and tadytat pfoanc. h accuacy of th ult gvn by th pcon of th oto odl ud. KyWod: nducton oto, vcto contol, paat taton, ytcal odl, aytcal Γ. Intoducton Squlcag nducton oto a pl low cot and obut lctcal achn. Fo th a of t contuctv plcty th achn antnanc f, and t ud n hotl nvonnt wthout odfcaton. h pncpl of toqu gnaton n th nducton achn la wth th on of th d.c. achn. Unfotunatly th laty wa not hghlghtd bfo 7. h on of th aon of th vcto contol tchnqu dvlopnt aft th pod. h thoy of th pac vcto allowd to plfy and to cop th xpon of th lctoagntc toqu. h dlvd a a vcto poduct btwn th an actv cunt and a actv cunt n a pcfc coodnat yt. h abnc of th autonoou nducto dvc and th lac of oto cunt aunt nca th coplxty of th contol tuctu. h contol tuctu ut allow catng n th achn an quvalnt pannt agntc though th contol of oto flux, and th dcouplng btwn th flux and th lctoagntc toqu. h why th athatcal odl ud hav to dcb wth th hght pobl accuacy th opatng of th achn n both tadytat and tannt g. In th dct vcto contol ch th flux poton aud o tatd on th ba of th flux coponnt n th tato coodnat. In th ndct contol ch th flux poton nd ndctly though th oto pd and th lp taton. h abnc of th oto flux poton no and th ablty to opat at low pd ha ncad th populaty of th ndct contol tatgy. obutn of th oluton adoptd vy potant, nc o paat can chang a a functon of t o ay b unnown. Sval odn nonlna contol thod ud n th contol a potd n th ltatu a fdbac lnazaton tchnqu o obut tchnqu bad on vaabl tuctu yt. An analy of val contol algoth n th fld howd a vaty of coputatonal and ntfacng pobl. So autho val that th apl at a low a hundd of μ a oftn qud to nu dynac pfoanc. hfo a powful pocng unt qud. wo ntfac cla can b condd: poc ntfac and u ntfac. Poc ntfac th ot qutng n t of hadwa ouc, whl th u ntfac tongly oftwa dpndnt. Mot of th ndutal oluton fo dgtal dv contol a clod yt, and do not allow to th u to odfy th contol algoth o to bd nw upplntay functon. h yt a not uful fo ach. Pap potng unvty ach val a poo xpntal actvty o only ulaton ult a pntd. h pap focu on an ndct vcto contol oluton plntd on an xpntal tup buld n th chncal Unvty Gh. Aach, Jay. h xpntal ult w obtand wth a oftwa pacag calld DMCDS (Dgtal Moton

2 Pocdng of th 6th WSEAS Intnatonal Confnc on Sulaton, Modllng and Optzaton, bon, Potugal, Sptb 4, 6 99 Contol Dvlopnt Shll dvlopd alo n th chncal Unvty Gh. Aach. Indct vcto contol oto fld ontd of nducton achn h analy of vcto contol tuctu hghlght val poblt to contol th ntantanou valu of th lctoagntc toqu of th nducton achn. Bcau th quaton that dcb th achn bco gnfcantly l coplcatd whn th fnc othogonal fa ynchonou and ynphac wth th oto flux, alot all pactcal ch u th typ of ontaton []. h poton of oto flux can b tatd dctly o ndctly. h ft typ an th u of tanduc o flux tato. h ndct taton ch of th oto flux poton nu a good bhavou n all pd ang, and thy a th coon oluton n pactc. h nducton achn quaton n th flux coodnat fa can b wttn a follow: d u jω d j( ω ω ( d J p ( x D Sbol u,, dnot voltag, cunt, and flux lnag, pctvly, oto pd ω, laag nductanc a dntfd wth ndx σ, ndx dnot paat and vaabl aocatd wth agntzng flux, ndx dnot paat and vaabl aocatd wth th tato,and ndx fo paat and vaabl aocatd wth th oto. Indc uppcpt dnot th fa ynchonou wth th fnc flux. If th poton of th oto flux nown and th coodnat fa yphac wth th on, thn d ; q ( and ( can b wttn a follow. d q d; ωl ; p Ψ q (3 q q θ ω ω p d d ud σ d ωσ q (4 d q uq σ q ωσ d ω On th ba of th quvalnt odl of vcto contolld nducton achn, th quaton of th dcouplng and pfoanc gulato can b coputd. Eq. (4 ud to dgn cunt gulato and th dcouplng gulato of th coand voltag. ang nto account only th dψ pannt agntc tat, q. (4 bco: dd ud σ d ωσq (5 d q uq σ q ωd h contol tuctu bad on th nv dynac odl of th nducton achn au nowldg about fv paat of th achn:,,, ş h paat of th achn a uualy tablhd wth th hotccut and no load tt of th nducton achn. h valu of th tato and oto lag nductanc dffcult to obtan bcau fo th tt data pobl to n only th u of th paaat Σσ, but not ach on of th. h tt tandad cond val pcal dtbuton of th paat: h quvalnt ccut ncopltly pcfd bcau th valu of th tato and oto lag nductanc hav not unqu valu. h odn paat taton thod allow to coput wth hgh accuacy fou paat aocatd to th nducton oto odl: th paat of th tato ccut (,, th t contant of th oto, and th global laag coffcnt σ [],[3]. If th dgn now th valu of th tato laag nductanc σ, th oth paat can b coputd a follow. σ ; ;σ ; (6 ( σ h u of th laag nductanc of th achn contant [4]. A good appoxaton of th tato laag nductanc σ [5]: σ σ (7 h appoxaton allow coputng th oto laag nductanc a:

3 Pocdng of th 6th WSEAS Intnatonal Confnc on Sulaton, Modllng and Optzaton, bon, Potugal, Sptb 4, 6 σ σ σ (8 4( σ h valu of th ato of tato laag nductanc and th oto laag nductanc dfnd a: σ ( σ σ < (9 σ σ h a ca whn th ato can not chaactz wll nough th laag n th tato and th oto of th nducton achn. A btt appoach to b th u of a nu nub of paat whch can dfn th tannt lctoagntc tat and can b ctd wthout appoxaton. 3 Squlcag nducton oto copact odl h odl of th qulcag nducton oto ha a dg of fdo bcau oto voltag null (u. h a pobl th obtan val odl whch a ngtcally quvalnt wth th clacal ytcal odl of th achn. h nducton achn can b alatd wth a tanfo. hn a tun ato can b xpland n th a ann a th tun ato ud fo a tanfo. h clacal quvalnt ccut of th achn obtand wth th nw tat vaabl: ' N ' N ' N u u ; ; N N ( N and paat ' N ' N ; σ σ N N ' N ; ( N h odl copltly chaactzd by fv paat. Bcau th nducton oto qulcag, th tun ato α N N can b chon abtaly and any oth valu that nu th pow nvaanc allowd xcpt o. A o gnal odl of th nducton oto ult fo q. ((, wth th nw vaabl dfnd n ( and th paat dfnd n (3. ' g ' Ψ g ; Ψ ( α α ' ' ' α ; α ; α (3 h phao quaton ( can b wttn n a atcal fo: ( ω ( ω p j p j u ( ( ω p j ( ω ω p j p j (4 ( p j( ω ω It dfnd a atx (5 α h allow wtng th quvalnt odl of th oto (6. ( p jω α ( p jω u ( ( p jω α ω α ( (6 ω ' p j p j ( ( p jω ω h tuctu of th quvalnt odl pntd n Fg.. u ( σ ( α(p jω α (p jω ( α σ ( α α(p jω ' p jω α p j( ω ω Fg.. h gnalzd phao ccut of th qulcag nducton oto h tun ato atx (5 do not odfy th nput pdanc at th oto tnal. h quvalnt ccut gnat th a toqu and pd fo th a nput gnal. So aabl popt can b obtand wth aytc quvalnt ccut by choong appopat valu fo α. A tv ccut obtand whn α chon to vanh oto laag nductanc n th phao gnalzd ccut. α α (7 Fo th patcula ca, th facto α yld: α. (8 h nw aytcal Γ odl copltly pcfd by fou paat (9 and pntd n Fg ; 4 5; σ 4 σ 5 σ 5; 4 5 (9 5 5 u ( σ σ (p jω (p jω p jω p j( ω ω Fg.. h quvalnt aytc quvalnt ccut. '

4 Pocdng of th 6th WSEAS Intnatonal Confnc on Sulaton, Modllng and Optzaton, bon, Potugal, Sptb 4, 6 h laag nductanc ha th valu σ 4 5 ( 5 and th global laag coffcnt df 5 4 σ ( h oto t contant of th nw odl ( 4 5 h dnot a dynac bhavo quvalnt wth th on of th odl wth fv paat. Fnally th paat of th odl a unvocal nd on th ba of th tatd paat of th oto ( ˆ, ˆ, ˆ, σˆ. ( ( σˆ ˆ 4 ˆ ;4 ˆ ;4 σˆ ˆ ;σ 4 σˆˆ ;4 (3 ˆ 4 Indct vcto contol of nducton oto h nu nub of paat odl of nducton oto ud fo a vcto contol tuctu. On th pupo th dcouplng gulato ut b dgnd tang nto account th nw tat vaabl and th nw dfnd paat. Wth (, (3 and (8, th phao odl fo ( bco: d u jω d j( ω ω Ψ 4 ( ( 4 4 p 4 ( 4 x In th fnc fa ynchonou wth th oto flux phao, th phao quaton n catzan coodnat a: d d 4 ωl q (5 4 p 4q dd ud d σ4 ωσ4q (6 d q uq q σ4 ωd h quvalnt odl a nonlna poc wth two nput ( d, q and two coupld output (Ψ,. h dcouplng gulato obtand wth th nv odl of th achn. h lad to a fdfowad tuctu pntd n Fg.4. d q θ Ψ ω l ω p Fg.3. h nducton oto odl n th oto flux fa p ( ( p d q J Fg. 4. Stuctu of th dcouplng gulato h tanf functon of th actv coponnt not a pop on, and, fo pactcal plntaton placd wth d (7 ( h actv potcton of th goup nvtoto ald though th lt of th cunt coponnt, ± q ax, whch gnat th toqu. h dcouplng of th tato cunt allow a cacad contol tuctu l th on ud fo DC oto pd contol. h optal pd gulato paat can b obtand wth th polplacnt thod. h nv odl ud fo cunt fnc valu lad thotcally at an ovall yt wthout dynac. In tadytat (7 bco: d Ψ (8 ˆω l

5 Pocdng of th 6th WSEAS Intnatonal Confnc on Sulaton, Modllng and Optzaton, bon, Potugal, Sptb 4, 6 h fdfowad contol tuctu nduc a ltaton of th toqu pon. h tanf functon gvn by ω q, ω, ςω ω d q ς (9 d h pd loop analyzd wth (9. A PI gulato uffcnt n od to nu a null tadytat o. h tuctu of th pd loop gvn n Fg.5a. h lctoagntc t contant a all nough to b nglctd n th odl. h plfd odl of th pd loop gvn n Fg.5b. Nglctng th vcoty coffcnt, D, th tanf functon of th contol yt : v ω z ( z ς vωv ωv ω v v J, pv ς v, Jv p v v p v v v z (3 pv ω ζ ω ω J D (a J D (b Fg.5. Spd contol loop tuctu Nglctng th vcoty coffcnt, D, th tanf functon of th contol yt : ω v ( z z ς vωv ωv v pv v ω v, ς v, z (3 J J v pv h dgn objctv fo th pd gulato to obtan a nu tannt t fo tp nput. Du to th ltd capacty of th toqu pon of th achn, th cutoff fquncy of th loop can not b bgg than th on of th tanf functon (9. If th cutoff fqunc a qual, th paat of th pd gulato a: pv J ; σ v J σ (3 h toqu gnaton chan unddapd. In th ca t dabl to po a cutoff fquncy fo th pd loop uch all than th on of th toqu gnaton chan: ω Bv Kω B ; < K < (3 Eq. (3 can b wtttn wth th coffcnt: K K pv J ; v J (3 σ σ h valu of th coffcnt can b xpntally nd. h contol tuctu can b ud fo cuntfd nvt. If t ud a voltagfd nvt th othogonal coponnt of th tato cunt wll b ndctly contolld though th tato voltag coponnt. wo uplntay loop ut b addd. In th tadytat agntc g, th yt bco th yt dcbd by (6. h tunng of th PI cunt gulato can b don on th ba of th opn loop tanf functon H( K K ; K ; (33 σ h t contant of th lctc ccut,, copnatd wth th ntgal t contant of th PI gulato. H ( ; τ τ K K (34 Fo a pcfc t contant of th cunt loop, th tunng paat of th cunt loop can b coputd: σ K ; σ (35 τad Fnally th coplt contol tuctu pntd n Fg.6. 5 Expntal ult h contol tuctu wa dgtally plntd and ttd. h voltagfd nducton oto wth a PWM nvt ha th nonal paat: PN.5W, UN38V, IN3.8 A, co ϕ.79, N4 v/n, fn5 Hz [8]. h ult w obtand by nucal ulaton wth Matlab, and wth adsp boad C3MCDB [6]. h xpntal ult a pntd n Fg. 74. Fg. 7 how th oto pd, th oto tatd toqu and th valu of th othogonal coponnt of th oto cunt whn th lctc dv not loadd.

6 Pocdng of th 6th WSEAS Intnatonal Confnc on Sulaton, Modllng and Optzaton, bon, Potugal, Sptb 4, ( ( d PI d (, u d u q P (θ θ u A (t u B (t u C (t σ4 p PI ( pv, v p 4 q PI q (, ˆω l ˆω θ d q P (θ θ A (t B (t C (t p Fg.6. h analog contol tuctu v / n t [ ] Fg.7. Spd of th vcto contol nducton oto dv 6 4 A 6 Concluon h nducton oto not a yt copltly obvabl. A a conqunc th ytcal phao ccut can not b copltly pcfd on th ba of th aunt at th oto tnal confgud n a ngl topology. h phao odl ut b foulatd n od to b copltly pcfd wth a nu t of paat. h nw vcto contol ch bad on an aytcal quvalnt odl u only th nfoaton obtand fo th paat dntfcaton xpnt wthout appoxaton t[] Fg.8. h fnc/aud valu of th actv coponnt of th tato cunt 5 5 N t [] Fg.9. h tatd valu of oto lctoagntc toqu A t [] Fg. h fnc/aud valu of th actv coponnt of th tato cunt fnc: [] Va P., Vcto Contol of A.C. Machn. Clandon P, Oxfod, 99. [] Hoga V., Gau I., ăţo M., Indct Paat Etaton of Inducton Moto Bad on Doan Analy. Poc. of th Int. Syp. on Pow Elctonc, NovSad, Yugolava, 465,. [3] Ona A., Hoga V., Daconcu M., Boţan C., Off n Paat Etaton of Inducton Moto Bad on a Multt Scal Appoac: Matoa N., Antonou G. (Ed.. cnt Advanc n Ccut, Syt and Sgnal Pocng, WSEAS P, 75 8,. [4] Ba E., Bnz F., Bolognan S., Buja G., A Fld Ontaton Sch fo CuntFd Inducto Moto Dv Bad on th oqu Angl Clodoop Contol. IEEE an. on Ind. Applcaton, 8, 5, 3844 (99. [5] BnBah., Gatl A., AlHaad M., Auto unng fo Snol AC Moto Dv Syt. IEEE Int. Syp. on Ind. Elctonc, Bld, Slovna, 36737, 999. [6] Ona A, Hoga V., Educatonal Softwa Envonnt fo Moton Contol. Poc. of th IASED 5 th Int. Conf. on Cop. and Adv. chn. n Educaton, ,.