Modllng n ttony f fnc of ngl nd two-ph ndcton chn ncldng th ffct of on lo nd gntng flx tton M.opc Hln Unvty of chnology, botoy of Elctochnc.O. Box 3 FIN-5-HU, Fnlnd Fx 35 9 5 99 E-l: Mc.opc@ht.f V. Nvpc Unvty olthnc Bcht Dptnt of Elctcl Engnng Spl. Indpndnt 33, RO-77, Ron E-l: vln@tp.ltch.pb.o ABSRAC h pp d to n gnl odl fo ltng th ngl nd two-ph ndcton chn opton. h objctv of th odl to pdct oto pfonc pt ch toq, nd oto pd. h odl ncld pntton of both n nd xly wndng n ttony fnc f nd lo th ffct of co lo nd th tton of th n flx pth. A notbl ft of th odl th tchnq d fo pntng th dffnt lvl of tton n th both x of gntton. h dvlopd odl tbl fo lton nd odllng th tdy-tt nd tnnt opton of th ngl nd two-ph ndcton chn o cct. Kywod: odllng, ngl-ph, two-ph ndcton chn, on lo, tton, vcto contol INRODUCION Dffnt odn contol tchnq ppld to dc th pct of pt vton on th dv pfonc. Ion lo nd flx tton ong th n c of th pt vton fo ngl o two-ph ndcton oto. Dffnt fo th th-ph ndcton chn wth ytcl ffct, th ffct dffnt fo th q nd d x, d to th nyty of th chn. h pp dvotd to th odllng of ch chn wth nclon of th on lo nd tton ffct tht cn b flly copntd, bc thy cognd by th contol yt. h ph focd on thod of nng th ffct n ngl o two-ph ndcton chn dv. h popod two contol yt: oto flx nd tto flx ontd contol two-ph ndcton oto dv. MAHEMAICA MODE h dvlopd odl bd on vl pton, gnlly ccptbl ttd n []: Only th fndntl pc-honc coponnt of th gp flx dtbton condd. Ung th pton tht th nq dtnct gntton cv long ch of th two othogonl x of th chn ncld gntc-flx tton ffct. No ppoton d. h dvlopd odl th followng ndctnc: tdy-tt, dffntl nd dync (cocoplng gntng ndctnc n [] nd [3]. A non-ln to tht octd wth th totl tto flx lng odl co lo. Snc th tto wndng of th nytcl two-ph ndcton chn not dntcl, th only fnc f wth contnt pt th ttony on. In d-q coodnt, th chn odl dcbd follow ccodngly to Fg. (th lt of ybol gvn n Annx I: Stto voltg qton v v R p ( p ( M A R p ( p ( Roto voltg qton R l p ω p (3 q R p ω p ( Flx qton: l ( (5 df q ( ( q d (7 ( q d ( ( (9 d df q ( ( ( Cnt qton: q d ( ( df d q d (3 A th chn nytcl, th t vton of th gntton flx n d-q x : d d d d d d d d d d d q d d q df q d q d q d q d d d (
d q d d q d q d q d q q q d d d d Now, f th ntodcd th notton: d d dd d dync ndctnc n x d d q d dync ndctnc n x q d d ttc ndctnc n x d q ttc ndctnc n x q q h ndcd voltg n th gntng bnch bco: q (5 d d d d d q d ( d q d q d d q (7 d q wh th ndctnc t dcbd by th lton: d q d ( dd d co ρ ( ( dd d n ρ (9 ( co ρ ( q q ( q n ρ ( q ρ ctn ( d h lctogntc toq : ( q ( d ( df ( (3 J pω B ω ( h chn pt cn b nd xpntlly thogh clcl thod, o thotclly by FEM coptng. h vl of th tnc d to odl on lo nd fo tndd no-lod tt, t ft wth nodl pply of td fqncy, nd thn wth WM pply of td fqncy. h tt d fo nng th dct pont on th gntng cv of th chn. h ld poc of nng th pt pntd n [] nd []. Und tnnt conon, th Eq. ( ( dcb th pfonc of th ngl o two-ph ndcton chn. h tt-vbl fo of th voltg qton wll b: v --- v --- R M l (/ ω - fq R f,q q R A l ω - Fg.. R R f,d fd d h d-q x ngl nd two-ph ndcton chn qvlnt cct wth on lo nd n flx tton ncldd A p x Bx x wh: [,,,,, df ] [,, ],, q A RM B ω q q q RA ω d d d d q ot q R ot q ω ( q d d d ( ( ot ω ( ot d R q q q ω R R (5- ( d d ( d (7 q ω d R df ( h bov odl vfd by copng ltd wth xpntl lt. ROOR FUX ORIENED CONROED WO- HASE INDUCION MACHINE A th tto wndng of th ngl-ph ndcton oto nblncd, th vcto contol pncpl hv to b plntd n pcl wy. h chn pt dff fo x d to x q. h wvfo of th lctogntc toq dontt th nblnc of th yt. Evn fo ql pltd, othogonl tto cnt nd, th toq contn oclltng t. Fo Eq.(3, t cn b obvd tht th pnt dffnt vl fo fd gntng ndctnc. In [] th w popod o lton btwn th tto cnt n od to lnt th oclltng t fo toq xpon. Howv, th lton vld only n ln conon (nglctng
tton nd on co lo. Ftho, th bov ntond odl plntd ng non-fd qvlnt cct, whch p o coplctd nt of gntng, tl ndctnc fo tto nd oto. A nw lton fo th toq coptton, cn b nd, by ng Eq. (7-(, n Eq. (3: wh: l l df q d q q d d (9 (3 A d, n qvlnt toq xpon to tht q of th ytc chn, wthot oclltng t n tdy tt, cn b obtn by pong th followng conon: (3 d (3 q Aft o coptng nplton, t lt: d ( (33 Fo Eq. (3, ( nd (7-(, on cn obtn th dync lton tht lt th oto flx to th tto cnt: p ω q (3 p ω d (35 wh: ; R R In n bty fnc f, th oto flx of ngl-ph ndcton chn cn now b dvd : ( (3 d p ω ω ω ω (37 d p ( wh ω ngl pd of th bty fnc f. Bd on th dvd oto flx odl, th oto fld ontd contol yt cn b dptd to ngl-ph ndcton chn. h chn qton n th oto flx fnc f, cn now b obtnd by ng th contnt conon fo oto flx fld ontton contol. h ltnt qton follow: ω q (3 d p (39 wh th oto flx pltd, ω ω - ω, nd ω th ngl pd of th oto flx vwd fo th tto. h toq xpon n oto flx ontd contol yt bco: d ( SAOR FUX ORIENED CONRO OF HE WO- HASE INDUCION MACHINE h toq xpon dpndng on tto flx nd cnt : d q q d q d d h bov lton cn b plfd follow: q ( ( Ully, th tto wndng hv dntcl confgton, nd dff only thogh nb of tn nd th of th copp w. h n to btwn th lg ndctnc of th n nd xly tto wndng ql to th q tn to (. Conon fo th tto cnt bco nd nd Eq. ( cn b -wttn : ( (3 h dync lton fncton of tto cnt nd flx dcbd follow: p ω σ p 3 ω σ wh ω ω σ σ p p ( (5
σ d ( q /( d ( q d ( q d ( q S S Fo n bty fnc f, th copondng dync qton ly ddctbl by btttng th ω t wth ω -ω. Bd on th vcto odl gvn bov, t cn b ppld th fld ontd pncpl to contol th tto flx of th ngl o two-ph ndcton chn. h followng qton obtnd: ( (7 ( p σ p (9 ω σ Extnc of th tton ffct nd co lo n th chn cn b ncldd n ch nn tht th toq nd flx podcton n th chn govnd olly by tto cnt. It h to b ntond tht n tto flx ontd contol opton, th chn pnt tdy-tt pll-ot toq tht lt th tbl optng gon. EXERIMENA AND SIMUAED RESUS Expntl vlon of th popod odl w d on cpcto n ngl-ph ndcton oto, th pt of whch hown n Annx II. Fg. lltt th toq lp chcttc of th oto wth both tto wndng ngd (no n cpcto w connctd. Wth ybol o dnotd th d pont of th cv. A good cccy of th odl cn b obvd. Fth nly of th oto d by lton of lod opton n two c: nol cpcto n ngl-ph ndcton oto, nd vcto contolld ngl-ph ndcton oto, wthot nnng cpcto. D to pc ltton, only fw lton lt pntd. Fg 3, ddctd to n cpcto oto nd Fg 5, to vcto contolld oto, pctvly. wo potnt povnt ld thogh vcto contol opton: gnfcnt dcng of th pltng coponnt toq of th oto, nd dcyd pd ocllton bot th fnl optng pont. oq (N 3 oq (N - - -.5.5.5 t (c Fg. 3. Sltd toq-t vton fo two ph ndcton oto wth n cpcto oq (N - - - pd (ot/n Fg.. Sltd toq-pd vton fo two-ph ndcton oto wth n cpcto. oq (N -.5.5.5 t (c Fg. 5. Sltd toq-t vton fo vcto contolld twoph ndcton oto oq (N.5.5.5 - Fg.. -.5...3..5..7..9 oq-lp chcttc (-clcltd, o d lp pd (ot/n Fg.. Sltd toq-pd vton fo vcto contolld twoph ndcton oto
CONCUSIONS h pp popo n qvlnt cct fo th ngl nd two-ph ndcton chn ncldng ltnoly, bt ndpndnt phnon, th on lo nd th n flx tton. h odl pt n povnt n opton of vcto-contolld ngl nd two-ph ndcton chn. h vcto contol tct tbl fo nytcl twoph ndcton chn y b chod oto o tto flx ontd contol. h odl cn b plntd fo lton by ng th xpntl nd pt o FEM clcltd pt. h tto fld ontd yt cn b dly plntd on th DS bod wth th oto fld contol von, th d th pt. It xpctd tht th tto flx contol hold b o tbl fo low pd pplcton, th oto flx contol yt fl fo hgh-pd pplcton. ANNEX I t of pncpl ybol ω ynchono pd ω oto pd p dffntl opto R M, R A, n, xly tto wndng tnc R oto wndng tnc R fq,d.qvlnt on-lo tnc (d nd q x, n, xly tto lg ndctnc d,q gntng ndctnc (d nd q x l oto lg ndctnc tn to xly/n wndng lctogntc toq J nt of oto, tto flx (d nd q x, oto flx (d nd q x v, tto voltg (d nd q x, tto cnt (d nd q x, oto cnt (d nd q x df, on-lo qvlnt tto cnt (d nd q x ANNEX II Dt of th oto nd lton Rtd otpt pow: 75 W Rtd fqncy: 5 Hz Rtd pd: p Rtd voltg: V Nb of pol: Int:. g Rnnng cpcto: µf/ V. Stto n wndng tnc: 5.35 Ω Stto xly wndng tnc: 3.3 Ω Roto tnc: 3.95 Ω Ion-lo tnc (n d x: 59 Ω Ion-lo tnc (n q x: 7 Ω Stto n wndng lg ctnc:.35 Ω Stto xly wndng ctnc:.5 Ω Roto lg ctnc: 5.5 Ω Mtl ctnc (n d x:.73 Ω Mtl ctnc (n q x:. Ω REFERENCES [] S. D. UMANS, Stdy-tt, lpd-pt odl fo cpcto-n, ngl-ph ndcton oto, IEEE n. Ind. Appl., Vol.3, no., Jn/Fb 99, pp.9-79 [].VAS: Elctcl Mchn nd Dv Clndon, Oxfod, 99 [3].C. KRAUSE, O. WASZYNCHUK nd S.D. SUDHOFF: Anly of Elctcl Mchny, IEEE, Nw Yo, 995 [].VAS: t Etton, Conon Montong, nd Dgno of Elctcl Mchn, Clndon, Oxfod, 993 [5]. VAS: Snol Vcto nd Dct oq Contol Clndon, Oxfod 99 [] M.B.R. CORREA, C.B. JACOBINA, A.M.N. IMA nd E.R.C. DA SIVA: Fld ontd contol of nglph ndcton oto dv, ocdng of IEEE- ESC 9, Fo, Jpn, 99, pp. 99-99 [7] E. EVI: A nfd ppoch to n flx tton odllng n D-Q x odl of ndcton chn, IEEE n. Engy Conv., Vol., no.3, Spt. 995, pp.55 [] I. BODEA nd S.A. NASAR: Unfd ttnt of co lo nd tton n th othogonl x odl of lctc chn, IEE oc., t. B, Vol.3, no., 97, pp. 353-33 [9] X. XU, R. DE DONCKER nd D.W. NOVONY, A tto flx ontd ndcton chn dv n Conf. Rc. ESC, Apl 9, USA, pp. 7-7 [] R. DE DONCKER, F. ROFUMO, M. ASOREI,. FERRARIS, Copon of nvl fld ontd (UFO contoll n dfffnt fnc f n. ow Elct., Vol., no., Mch 995, pp. 5-3 [] NAVRAESCU, V., CRACIUNESCU, A., nd OESCU, M.: - Dct-t ndcton chn thtcl odl fo DS plntton - n Conf.Rc. CIM 9, y 99, Nbg, Gny, pp. 333 [] OESCU, M., JOKINEN,., DEMEER, E., MICU, D.nd V. NAVRAESCU: - Anly of Voltg Rglto fo wo-h Indcton Moto Dv n Conf. Rc. IEEE IEMDC 99, y 999, Sttl, USA, pp. 5-