Modified Direct Torque Control for Single-phase Induction Motor Drives

Transcription

1 Modifid Dirct Torqu Control for Singl-phas Induction Motor Drivs THANATCHAI KULWORAWANICHPONG and TAWAT CHUCHIT Powr Systm Rsarch Unit School of Elctrical Enginring Suranar Univrsity of Tchnology Univrsity Avnu, Nakhon Ratchasima THAILAND Abstract: - This papr illustratd a modifid stratgy of dirct torqu control for singl-phas induction motors. Th proposd stratgy was basd on classical six-sctor hystrsis-typ dirct torqu control schm dvlopd by using stator rfrnc fram. Th modification mad in this papr ld to two control stratgis calld modifid six and twlv sctors, rspctivly. A switching tabl was drivd basd on th voltag vctors gnratd by th thr-lg two-phas invrtr topology. Simulations wr carrid out and prformanc analysis was prsntd. Ky-Words: - Singl-phas induction motor drivs, Dirct torqu control, Hystrsis control, Six-sctor basd DTC, Twlv-sctor basd DTC Introduction Thr-phas induction motors hav bn incrasingly important for industrial lctric motor applications. It should not that thr still xist DC motors in som limitd applications,.g. motors for vhicls. Apart from a larg-siz lctric motor driv, singl-phas induction motors ar commonly usd in houshold lctric motor applications. Ths applications typically consum th powr of a fractional hors powr up to around tn hors powrs. Although most lctric appliancs rquir a fw amount of kilo-watt input, minimizing powr losss during thir opration givs a grat bnfit rsulting in nationwid lctric nrgy usd by housholdrs. In gnral, singl-phas motors ar controlld by a thyristor-phas controllr or a variabl rsistor. This is quit simpl, but it is not fficint in trms of nrgy consumption. To achiv this goal, complx control stratgy cannot b avoid as long as ac machins ar involvd. On of widly-usd control schms is variabl-voltag, variabl-frquncy (VVVF) []. It can b applid for motor control in many forms. Howvr, this control stratgy dos not guarant minimum loss opration. Thrfor, adjustabl frquncy and voltag of th powr supply is mor flxibl and can lad to mor conomical opration of houshold lctric appliancs. Ovr half a cntury, stady-stat analysis of induction motors has bcom a powrful tool to charactriz thir prformancs [-4]. It is fairly good in dscribing stady-stat bhaviors. For simpl control whr accuracy and prcision ar not that much important, any stady-stat modl is modrat. Howvr, nowadays, a vry accurat torqu-spd control of induction motors via th spac phasor thory, calld vctor control [,6], is incrasingly rquird by industris [7,8]. Howvr, thr also xists som simpl control tchniqu that can giv good prformancs in rsponss. On of thm is Dirct Torqu Control (DTC). It givs outstanding faturs of fast torqu rspons and simpl control structur. Control of induction motor drivs basd on dirct torqu control givs a fast rspons following th torqu command. In fact, this control tchniqu is not nw. Thr is a thousand of works publishd on wll-known intrnational journals and confrncs spcially thos of th thr-phas induction motor drivs. Also, thr xist som articls dscribing th stratgy of dirct torqu control for a singl-phas induction motor. In this papr, a modifid DTC was proposd in ordr to nhanc singl-phas induction motor driv prformancs. Th basic structur of invrtr circuit is givn in Fig.. It consists of thr lgs with six switchs as sam as thos of th thr-phas voltag sourc invrtr. V dc s s 4 s s3 s s 6 M IM Fig. Invrtr circuit topology for singl-phas induction motor drivs This papr was dividd into six sctions. Sction is a brif rviw of singl-phas induction motor modling A ISSN: Issu 9, Volum 8, Sptmbr 9

2 using spac phasor thory. Sction 3 illustrats a basic DTC usd as rfrnc. Sction 4 prsnts th modifid DTC proposd in this papr. Rsults and discussion ar in Sction. Th last sction, Sction 6, is conclusion. Singl-phas Induction Motor Modl d λ ds = ri ds ds + v ds (3) d s s s λ qr = ri r qr + ωλ r dr (4) d s s s λ dr = ri r dr ωλ r qr () By rarranging () () basd on flux linkag and currnt rlations of th singl-phas induction motor, th stat-spac modl, in which stator and rotor currnts, and rotor spd ar stat variabls, can b formd. d [ x ] = [ A ][ x ] + [ B ][ u ] (6) [ y] = [ C][ x] (7) Fig. Winding alignmnt of a singl-phas motor Singl-phas induction motors can b charactrizd by svral diffrnt modls. Th spac-phasor approach [,4] is th mthod usd in this papr. With this modl, motor currnts, torqu and spd can b obsrvabl. Th spac-phasor modl is vry complicatd and nds mor spac for xplanation. Howvr, in this papr only a brif dscription is prsntd as follows. Fig. dscribs winding alignmnt of a singl-phas induction motor consisting of main and auxiliary windings with thir inducd voltags and currnts. As shown in th figur, a stationary rfrnc fram which is along th axis of th main stator winding is dfind and usd for mathmatical analysis throughout this papr. It is ssntial to inform that all quantitis spcially on th rotor nd to b transfrrd to th stator axis. This can b prformd by using th following transform matrix. V V s qr s dr cos θr = sin θ r r sin θr v θ r cos r v qr dr () Th suprscripts s and r indicat th rfrnc axis in which th variabl blongs to. Th dynamic machin modl for a singl-phas induction motor with squirrlcag rotor in a stationary rfrnc can b xprssd as follows []. d λ qs = ri qs qs + vqs () Whr [ ] s s T = qs ds qr dr ω r x i i i i [ u] = [ v v T ] T qs ds L [ y] = [ i i ] T qs ds [ A] = [ G] [ M] [ B] = [ G] [ N] C = [ ] [ ] Llqs + Lmq Lmq L lds Lmq Lmq + G = Lmq L lr + Lmq Lmq L lr + Lmq rqs r ds Xm r X r [ M ] = Xm X r r s s B m αi dr αi qr Jm [ N ] = J m P Lmq Xm = ωr Lmq, X r = ωr ( L lr + Lmq ), α = J m ISSN: Issu 9, Volum 8, Sptmbr 9

3 s s s s i, i, i, i, λ, λ, λ, λ ar th currnt and flux qs ds qr dr qs ds qr dr linkag of th stator and rotor windings. L, L, L ar lqs lds lr th lakag inductancs of th stator and rotor windings. L is th stator-rotor mutual inductanc. r, r, r ar mq qs ds r th stator and rotor rsistancs. All variabls and paramtrs ar rfrrd to th stationary main-winding rfrnc. J m is motor s momnt of inrtia and B m is damping cofficint. Applying a numrical tim-stpping mthod to solv a st of diffrntial quations, motor currnts, angular spd and position can b calculatd numrically. u 3 () u () u () 7 4 q s u () u () u () d s 3 Dirct Torqu Control Schms A Basic dirct torqu control [9] is givn in Fig. 3. Invrtrs prformd by following th command gnratd by using th control block diagram in Figur. u () u () 6 Fig. 4 Spac vctor for invrtr control λ srf T rf T dλ dt α 3. Principl of Classical DTC A simpl dirct torqu control utilizs a control stratgy basd on appropriat hystrsis bands for torqu and flux rgulation. Torqu and flux rrors ar fd to th invrtr optimal switching tabl. This tabl looking-up is usd to synthsiz a switching squnc for govrning th voltag sourc invrtr as shown in Fig.. λ s Fig. 3 Basic dirct torqu control Schms λ srf dλ With this control stratgy, stator flux and lctromagntic torqu ar both calculatd by using th mathmatical modl givn in th prvious sction. According to () and (3), stator flux linkags can b stimatd by intgrating ths quations as xprssd in (8) and (9). Eq. () givs th xprssion of torqu stimation. Rsults from this calculation will b compard with flux and torqu rfrncs. Th rrors ar intrprtd by looking up a providd switching tabl for commanding th voltag sourc invrtr [9-]. ( ) λ = qs v r i (8) qs qs qs ( ) λ = ds v r i (9) ds ds ds P T = ( i λ i λ qs ds ds qs) () For singl-phas invrtr-fd induction motors, a classical spac vctor tchniqu similar to that of thrphas invrtr-fd induction motors. It consists of six unsymmtrical non-zro vctors and two zro vctors as shown in Fig. 4. T rf T λ s dt Fig. Classical dirct torqu control Schms Th rlationship btwn th voltag vctors and flux variation whn stator rsistanc drop nglctd is givn by th following quation. v dλ α s = () s Th abov quation shows that th applid voltag spac vctor producs a stator flux variation which has th sam dirction of th voltag spac vctor and amplitud which is proportional to th voltag and tim intrval for which th voltag vctor is applid. Fig. 6 shows th possibl dynamic locus of th stator flux and its variation with rspct to th chosn VSI stats. In Fig. 7, th stator flux rvolvs in a dirction of th slctd voltag vctor. Thrfor, rduction of th stator flux magnitud can b mad by choosing a voltag vctor of ISSN: Issu 9, Volum 8, Sptmbr 9

4 th tabl in which th stator flux is rducd. Th possibl global locus is dividd into six diffrnt sctors as signald by th discontinuous lin. Accordingly a six sctor lookup tabl is drivd as givn in Tabl. u 4 () 4 u 3() u () u () 6 3 u 7() u () 6 u () Fig. 6 Classical DTC and its switching vctors α (4) α () Δλs α(3) q s λ srf α (6) λ + Δλ srf s P 3 α () u 3u u P P u 43 P u 4 u () u 3 u 6 α() Fig. 7 Locus of th stator flux vctors basd on th classical DTC according to th six voltag vctors Fig. 7 illustrats th stratgy of controlling th magnitud of th stator flux vctors within th hystrsis band of Δ λs. From th figur, th circl is dividd into six sctors. At a particular tim sampling, th stator flux vctor is locatd on which of th six sctors. Each sctor corrsponds with six voltag vctors givn at th top right cornr. To forc th stator flux vctor rvolving within th hystrsis band, on of th six voltag vctors u u d s that yilds th bst dirction of riding on th dash circl must b chosn. Tabl Switching tabl for classical DTC sctor dλ dt u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u u From Tabl, th summary of voltag vctor slction is prsntd according with th nd for changing th stator flux and torqu valus. Although six vctors ar normally mntiond, thr ar totally ight voltag vctors, whr th two lft ar zro vctors. In this papr, to control th stator flux magnitud uss th stratgy of two-lvl flux hystrsis. It consists of two cods for th flux chang. dλ = is for flux incrmntal whil dλ = rprsnts th flux rduction as givn in th tabl. Th following quations dscrib th dtrmination of th flux chang basd on th twolvl flux hystrsis. dλ = if λ λ Δλ s srf s dλ = if λ λ + Δλ s srf s () (3) Equation illustrats th cas such that th stator flux is locatd insid th innr circl, th lowr limit. In this cas, th flux must b incrasd. This givs dλ =. In th sam mannr, Equation 3 illustrats th cas such that th stator flux is locatd outsid th outr circl, th uppr limit. In this cas, th flux must b dcrasd. This givs dλ =. Manwhil, whr th stator flux is rgulatd, th inducd torqu is also controlld by th six voltag vctors. Th torqu chang can b classifid into thr valus. dt = is to incras th torqu. In th opposit dirction, dt = mans to rduc th torqu. Unlik th flux chang, th torqu rror control is basd on th stratgy of thr-lvl hystrsis. dt = is usd for which of rgulating th torqu lvl. Ths can b summarizd by (4) - (7). ISSN: Issu 9, Volum 8, Sptmbr 9

5 Countr-clockwis dirction: dt = if T T Δ T (4) rf dt = if T T () rf Clockwis dirction: dt = if T T Δ T (6) rf dt = if T T (7) rf It should not that th slction of hystrsis band-wih is th ky. Too small band-wih may caus loss of controllability. 3. DTC With Diffrnt Sophisticatd Tabls Improvmnt of dirct torqu control can b carrid out in many diffrnt ways. Th followings ar som. Tabl Switching tabl for modification DTC sctor dλ dt u u u u u u u u u u u u u u u u u u 4 4 u u u u u u 4 4 u u u u u u u u u u u u Twlv-sctor In both classical DTC and modifid DTC thr ar two stats pr sctor that introduc ambiguity and hnc cannot b usd. In ordr to utiliz all six activ stats pr sctor th stator flux locus is dividd into twlv sctors instad of six. This novl stator flux locus is introducd in Fig. 9. Th look up tabl for -sctor DTC is as prsntd in Tabl 3.. Six-sctor of diffrnt zons: In this instad of having th first zon sctor from -4 to., it will b from to 4 as givn in Fig. 8. that th stats V and V4 ar not usd in th classical DTC bcaus thy can incras or dcras th torqu at th sam sctor dpnding on th position. In th modifid DTC, V and V ar th stats not usd. Howvr, now th ambiguity is in cas of flux instad of torqu as it was in Classical DTC which maks us inclind towards modifid DTC as th main point is to control th torqu. Tabl shows modifid DTC lookup tabl for all its six sctors. u 3() u () u 4 () u 3() u 7() u () u () u () u () u () Fig. 9 Twlv-sctor DTC and its switching vctors u 4() u 7() u () u () 6 u () Fig. 8 Modifid DTC and its switching vctors u () Tabl 3 Switching tabl for twlv-sctor DTC sctor dλ dt u u u u u u u u u u u u u u u u u u 4 4 u u u u u u 4 4 u u u u u u u u u u u u ISSN: Issu 9, Volum 8, Sptmbr 9

6 dλ dt sctor u u u u u u u u u u u u - u u u u u u 4 4 u u u u u u 4 4 u u u u u u u u u u u u Simulation Rsults To vrify th ffctivnss of th proposd DTC, th stator flux was assumd to b rgulatd at.8 Wb whil th lctromagntic torqu was controlld accordingly as follows. T =. N.m for s t. s rf T =. N.m for. s t. s rf T =. N.m for. s t. s rf T =. N.m for. s t. s rf T =. N.m for. s t 3. s rf Th tst [3] was challngd by thr diffrnt stratgis of th switching tabl: i) classical six-sctor DTC of Tabl ii) modifid six-sctor DTC of Tabl iii) twlv-sctor DTC of Tabl 3. It nots that paramtrs of th tst systm can b obtaind in [4]. Th tst was dividd into thr cass. Each cas rprsntd th chang in sampling tim or th hystrsis band-wih. Also, ach of which was prformd th stator flux rgulation and th torqu control as givn abov by th thr switching tabls. All th thr tst cass wr illustratd as follows. 4. Tst : Sampling tim = μs Hystrsis flux =. Hystrsis Torqu =. Torqu(Nm) Spd(rpm) Rsponss of Dirct Torqu Control Schms Tim(s) Fig. Rsponss of th classical DTC cas Spd(rpm) Torqu(Nm) Rsponss of Dirct Torqu Control Schms Tim(s) Fig. Rsponss of th modifid DTC cas By applying th thr diffrnt switching tabls of DTC for singl-phas induction motor drivs with hystrsis control of a spcifid rror band, rsults of currnt, torqu and flux rsponss can b shown in Fig., and for th classical DTC, modifid six-sctor DTC and twlv-sctor DTC, rspctivly. ISSN: Issu 9, Volum 8, Sptmbr 9

7 Spd(rpm) Torqu(Nm) Rsponss of Dirct Torqu Control Schms Tim(s) Fig. Rsponss of th twlv-sctor DTC cas Fig. 3 of th classical DTC cas Fig. 4 of th modifid DTC cas As can b sn, th rsults showd that two proposd DTC schms can b usd to rgulat both flux and torqu mor accurat than thos controlld by th classical DTC. This can b xplaind by visualizing stator flux trajctory of th motor du to th opration for all thr cass as shown in Figs Fig. of th twlv-sctor DTC cas Th rsults rvald that th modifid six-sctor DTC (Tabl ) gav th bttr rspons in both stator flux and torqu than th classical schm spcially in transint stats. Howvr, th prformanc can b furthr improvd by applying th twlv-sctor DTC. It is du to th numbr of sctors. Th twlv-sctor DTC consists of mor choics to command th VSI input. Thrfor, optimal switching commands can b variously synthsizd. 4. Tst : Sampling tim = μs Hystrsis flux =. Hystrsis Torqu =. In this tst, th thr diffrnt switching tabls of DTC for singl-phas induction motor drivs wr still usd. Th hystrsis band-wih of th flux and torqu was st as thos of th tst whil th sampling tim was smallr. With th smallr sampling tim, th classical DTC was unabl to control th inducd torqu following th command. Thus, its rsults wr not prsntd. Th rsults of currnt, torqu, spd and flux rsponss of th two lft can b shown in Fig. 6 and 7 for modifid six-sctor DTC and twlv-sctor DTC, rspctivly. In addition, th stator flux trajctory of th two DTC was also givn in Figs 8 9. ISSN: Issu 9, Volum 8, Sptmbr 9

8 Spd(rpm) Torqu(Nm) Rsponss of Dirct Torqu Control Schms Tim(s) Fig. 6 Rsponss of th modifid DTC cas Fig. 8 of th modifid DTC cas Spd(rpm) Torqu(Nm) Rsponss of Dirct Torqu Control Schms Tim(s) Fig. 7 Rsponss of th twlv-sctor DTC cas As can b sn, whn th sampling tim was rducd, th stator flux locus was smoothr in cas of th modifid six-sctor schm. At this tst, th diffrnc was not significant. It indicatd that th choic of sampling tim is ssntial in ordr to achiv good prformancs Fig. 9 of th twlv-sctor DTC cas 4.3 Tst 3: Sampling tim = μs Hystrsis flux =. Hystrsis Torqu =. In this tst cas, th thr diffrnt switching tabls of DTC for singl-phas induction motor drivs wr still usd. Th hystrsis band-wih of th flux and torqu was st to diffrnt valus whil th sampling tim was hld as th tst cas. With th smallr sampling tim, th classical DTC was still unabl to control th inducd torqu following th command. Thus, its rsults wr not prsntd in this cas. Th rsults of currnt, torqu, spd and flux rsponss of th two lft can b shown in ISSN: Issu 9, Volum 8, Sptmbr 9

9 Fig. and for modifid six-sctor DTC and twlvsctor DTC, rspctivly. In addition, th stator flux trajctory of th two DTC was also givn in Figs Spd(rpm) Torqu(Nm) Rsponss of Dirct Torqu Control Schms Tim(s) Fig. Rsponss of th modifid six-sctor DTC cas Spd(rpm) Torqu(Nm) Tim(s) Rsponss of Dirct Torqu Control Schms Fig. Rsponss of th twlv-sctor DTC cas As can b sn, whn th hystrsis band-wih was changd, th stator flux locus was smoothr in cas of th twlv-sctor schm whil th rsult from th modifid six-sctor was not as good as that of th twlv-sctor schm. At this tst, th diffrnc was clarly diffrnt. It indicatd that th choic of bandwih is also anothr ssntial factor in ordr to achiv good prformancs Fig. of th modifid DTC cas Fig. 3 of th twlv-sctor DTC cas Conclusion This papr prsntd a modifid six-sctor basd DTC and a twlv-sctor basd DTC for singl-phas induction motor drivs. Looking-up tabl basd switching control stratgy of th invrtr was providd. Tst was conductd to prform th stator flux and torqu rgulation. As a rsult, th modifid six-sctor basd DTC and th proposd twlv-sctor basd DTC gav satisfactory rsults and this confirmd th ffctivnss of th proposd DTC schms. In addition, from which satisfactory rsults choics of sampling tim and hystrsis band-wih ar two ky factors in ordr to gain good prformancs. ISSN: Issu 9, Volum 8, Sptmbr 9

10 6 Acknowldgmnt Th authors would lik to acknowldg th financial support of th rsarch grant (MRG89) sponsord by th Thailand Rsarch Fund, during a priod of this work. Rfrncs: [] P.C. Kraus, Analysis of Elctric Machins, McGraw-Hill, 987. [] N. Nawngrnd, C. Sukcharon, T. Kulworawanichpong, Simulation of Singl-Phas Induction Motor Drivs with Non-sinusoidal Powr Supply. Th WSEAS Transactions on Systms, Issu, Vol, pp. 9-34, 6 [3] R. Krishnan, Elctric motor drivs modlling, analysis and control, Prntic-Hall, [4] S. Rawkul, T. Kulworawanichpong, S. Sujitjorn, Paralll -Connctd Singl -Phas Induction Motor:Modlling and Simulation, Th WSEAS Transactions on Circuits and Systms, Issu 3, Vol, pp [] J.W.L. Nrys, A. Hughs & J. Corda, Altrnativ implmntation of vctor control for induction motor and its xprimntal valuation, IEE Procdings- Elctric Powr Applications, 47(),, pp [6] M. Yano & M. Iwahori, Transition from slipfrquncy control to vctor control for induction motor drivs of traction applications in Japan, Th th Intrnational Confrnc on Powr Elctronics and Driv Systms, 3, Saitama, Japan, pp. 46. [7] S. Shinnaka, S. Takuchi, A. Kitajima, F. Eguchi & H. Haruki, Frquncy-hybrid vctor control for snsorlss induction motor and its application to lctric vhicl driv, IEEE 6 th Annual Applid Powr Elctronics Confrnc and Exposition,, Yokohama, Japan, pp [8] M. Bnhaddadi, K. Yazid & P. Khaldi, An ffctiv idntification of rotor rsistanc for induction motor vctor control, Proc. IEEE Instru. and Mas. Tch. Conf., 997, Ottawa, Canada, pp [9] P. Vas, Snsorlss Vctor and Dirct Torqu Control, Oxford Univrsity Prss,998. [] Y.V.Siva Rddy, M.Vijayakumar and T. Brahmananda Rddy, Dirct Torqu Control of Induction Motor Using Sophisticatd Lookup Tabls Basd on Nural Ntworks, AIML Journal, Jun 7. [] F.A.S. Nvs, E.B.S. Filho, J.M.S. Cruz, R.P. Landim, Z.D. Lins, A.G.H. Accioly, Singl-phas induction motor drivs with dirct torqu control, Th 8 th Annual Confrnc on IEEE Industrial Elctronics Socity (IECON),. [] R. d F. Campos, L.F.R. Pinto, J.d Olivira, A.Nid, L.C.d Marqus, A.H.d Souza, Singl- Phas Induction Motor Control Basd on DTC Stratgis, IEEE Intrnational Symposium on Industrial Elctronics (ISIE 7), 4-7 Jun 7. [3] T. Kulworawanichpong and T. Chuchit, Improvd dirct torqu control for singl-phas induction motor drivs, Th 9 th WSEAS Intrnational Confrnc on Powr Systms, 3 Sptmbr 9, Budapst, Hungary, pp. 7. [4] N. Nawngrnd and T. Kulworawanichpong, Voltag-dpndnt paramtr rfinmnt for singlphas induction motors using gntic algorithms, Th WSEAS Transaction on Systm and Control, Vol. 4, Issu, pp. 4 4, 9 ISSN: Issu 9, Volum 8, Sptmbr 9