Dynamic Analysis of three Voltage Source Power Converters supplying Squirrel Cage Induction Machines

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Eugenia McKinney
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1 ntentionl Confeence on Powe Syte Tnient PST 2003 in New Olen, USA Dynic Anlyi of thee Voltge Souce Powe Convete upplying Squiel Cge nduction Mchine F.D. Knello, N.D. Htzigyiou Dept. of Electicl nd Copute Engineeing, Ntionl Technicl Univeity of Athen, Zogfou, 5773, Geece (e-il: Abtct n thi ppe, the dynic nlyi of thee of the ot poiing type of voltge ouce convete, i tudied. The convete upply quiel cge induction chine nd they eploy hyteei cuent contol, voltge pce vecto odultion nd inuoidl pule width odultion (SPWM), epectively. Detiled odel fo the electicl dive e ued, llowing the tudy of thei behvio in bod bndwidth. The peented odel e developed uing Mtlb code nd Siulink. ndiect field-oiented contol i ued fo the egultion of the otting peed nd the tto flux. The hyteei cuent contolle i copoed of thee independent pe phe cuent contolle. DC ide i conideed idel it i ued tht the contol yte intin the dc voltge t it efeence vlue. The opetionl chcteitic of the exined vible peed chee e tudied uing thei epone to tep chnge of the lod toque nd the efeence peed. Keywod Contol, PWM, vecto contol, induction chine, pce vecto, hyteei cuent contol, honic, witching fequencie.. NTRODUCTON The ecent evolution in powe electonic [],[2], the ocited new odultion technique nd the icopoceo [3],[4], fcilitted the ppliction of ophiticted contol technique enuing bette opetionl chcteitic of the vible fequency dive. AC induction chine dive now cope fvobly to DC oto dive, on conidetion uch powe to weight tio, cceletion pefonce, intennce, opeting envionent nd highe opeting peed without echnicl coutto. Cot nd obutne of the chine nd contol flexibility e often eon fo chooing induction chine dive in ll to ediu powe nge ppliction. Field-oiented nd toque contol [3]-[5],[7] technique ende the induction chine poibly the in choice fo vible peed dive in the futue. n typicl induction oto dive, the powe convete eve to convet the upplied enegy into fo uited fo the opetion of the oto. The powe convete condition the powe deliveed to the oto in oe deied nne diected by the contolle. The piy function of the contolle i to tnlte the cond vlue nd feedbck ignl to contol ignl fo opeting the convete. nvete type cn be divided into two bod ctegoie by the ouce chcteitic of thei dc link: voltge o cuent ouce invete. Mot of tody ll induction oto dive ue voltge ouce pule-width-odultion (PWM) [5],[6],[8] invete tht llow fo both gnitude nd fequency of it output voltge to be chnged electoniclly. The function of the pule-width odulto i to tnlte the odultion wvefo into tin of witching pule fo the invete. n the following, the dynic nlyi of thee of the ot poiing type of voltge ouce convete, i tudied. The convete upply quiel cge induction chine nd they eploy hyteei cuent contol [6],[9], voltge pce vecto odultion, inuoidl pule width odultion (SPWM), epectively. The hyteei cuent contolle i copoed of thee independent pe phe cuent contolle. ndiect field-oiented contol [3],[6],[9]- [] i ued fo the egultion of the otting peed nd the tto flux. Two P contolle e ued fo the tcking of the optil dq-xi cuent. n ce of ttiony fe P egulto co-coupling te i vey ueful. n the peent tudy ynchonou fe P egulto i ued. n ce of the convete eploying hyteei technique the tcking of the cuent efeence doe not equie the ue of P contolle. The in dvntge of thi ethod i the ccute tcking of the cuent efeence nd conequently it high dynic pefonce. Mot of the publihed odel of electicl dive conide only the fundentl voltge coponent fo the tudy of ft tnient. n thi ppe detiled nd fully petic odel fo the powe electonic nd the induction chine e ued, llowing the tudy of thei behvio in bod e of witching fequencie. The peented odel e developed uing Mtlb code nd Siulink tht futhe fcilitte the ccute deign nd evlution of the exined chee. The epone of the exined vible peed chee in the extee ce of iultneou tep chnge of the lod nd the efeence peed, i tudied. Uing the eult obtined the opetionl chcteitic of the popoed vible peed chee e evluted. ult eltive with the pectl denity of the electognetic toque e obtined. Thee eult cn be ued in ode to detect poible echnicl eonnce. The popgted honic to the tto cuent tht epeent chine ohic loe e lo clculted.. MODEL OF THE M DRVE n thi ection the detiled odel of the M, the contol yte nd the odultion technique e biefly eviewed. The connection of the induction chine to the gid i chieved vi voltge ouce convete ccde, hown in Fig., in ode to contol the ective powe exchnged

2 ntentionl Confeence on Powe Syte Tnient PST 2003 in New Olen, USA between the netwok nd the electicl chine nd lo to povide vible peed ode of opetion. Electicl Gid Fig. DVS convete ccde M Contol Syte A. nduction Mchine Model nduction chine e epeented by the fouth ode odel expeed in the bity efeence fe [0],[2]. Uing geneto convention fo the tto cuent the dqtto nd oto voltge e given by u = ω Ψ + p d d d q Ψ d u = + ω Ψ + pψ () u q d u q q = 0 = ( ω -ω ) Ψ + pψ d = 0 = + ( ω -ω ) Ψ + pψ q Whee d p =, ω ο i the be cyclic fequency, ω i ω o dt the otting peed of the bity efeence fe nd ubcipt {d}, {q}, {}, {} denote d,q-xi, tto, oto, epectively. The fluxe e elted to the winding cuent by the following eqution, Ψ d q d q d = Χ i + Χ i Ψ = X d i q + X d q i Ψ = X + X (2) Ψ = X q q + X The equivlent of the n elticlly connected e [0] cn be optionlly ued fo iulting the echnicl yte of the electicl dive. n the epoted iultion the following iple eqution of the echnicl yte i dopted. dω J = Tel Tl k ω (3) dt Whee ω i the ngul otting peed, J i the ineti nd k i the dping fcto. Subcipt {}, {el}, {l} denote oto, electognetic nd echnicl lod, epectively. B. M Contol The geneto contol yte conit of two jo loop, one fo the oto otting peed nd the othe fo the d d q d q d T el Tlod oto flux linkge. n Fig.2 the poduction of the peed nd flux efeence fo lod toque nd eued otting peed i hown. The field wekening nd lod peed chcteitic togethe with low p filte (T= ec) e ued. The eued lod ignl i led to the lod optil otting peed chcteitic, which poduce the input ignl to low-p filte of ec tie-contnt. The output of the low-p filte i fed next input to the otting peed contolle. So optil pefonce i chieved by tcking the optil otting peed. At high lod the contol chee ipoe contnt otting peed. A entioned befoe, the deied electognetic toque i chieved by the ppliction of field-oienttion contol chee. T lod Lod-Speed ω ω ef Chcteitic T ω Field Wekening λ ef + Fig.2 Poduction of the peed nd flux efeence Knowing the vlue of the deied electognetic toque T e, the q-xi cuent coponent in the field-oiented fe i given by the eqution [3],[0], e q 4 L T = (4) 3PL ' e ' e λ d Supecipt {}, {e} denote the efeence vlue nd the field oiented fe, epectively. t i lo known tht, when popely oiented, the lip peed nd the dq-xi cuent coponent in the field oiented fe e elted [3],[0], e q ω = ω e ω = (5) e L d Roto flux cn be contolled by egulting d. Given oe deied level of the oto flux, the deied vlue of the d-xi cuent coponent cn be obtined fo [3],[]: e + L p e d = λ (6) d L C. ndiect Field-Oiented Voltge Contol The deied dq-xi voltge in the field-oiented fe e tditionlly obtined fo the fouth ode odel of the induction chine. The only dwbck of thi contol chee i tht it equie ccute knowledge of the chine pete. t i coonly ued with on-line pete dptive technique fo tuning the vlue of the pete ued in the indiect field contolle, enuing in thi wy ucceful opetion. A odifiction of the ethod led to the ue of two P contolle fo the tcking of the optil dq-xi cuent [3],[6],[3]-[5]nd it i e 2

3 ntentionl Confeence on Powe Syte Tnient PST 2003 in New Olen, USA depicted in Fig. 3. n ce of ttiony fe P egulto co-coupling te i vey ueful. n the peent tudy ynchonou fe P egulto i ued, hown in Fig. 3. D. ndiect Field-Oiented Cuent Contol uing Hyteei Technique n ce ndiect Field-Oiented Cuent Contolled M uing hyteei cuent contol the P cuent Contolle do not pply. The exct tcking of the efeence vlue of the tto cuent i chieved by the ppliction of hyteei cuent contolle, which i decibed in oe detil in ubection G. Thi ethod enue high dynic pefonce but give ie to the poble of the highe witching fequencie nd the genetion of ubhonic coponent. t doe not lo dequtely enue the intennce of the cuent inide the hyteei bnd xiu eo of twice the hyteei bnd occu on ndo bi. Ι q ω ef ω P λ T el V q Ι d P Ι q P V d Ι d V d Clcultion of, d q, ω V q V d qd0 Cuent Contol bc V PWM U t ) U ( t ) = 3U / 2 (7) ( b Thi i le thn wht i obviouly poible when e.g. the phe α nd b e witched to U =U d /2 nd U b =-U d /2, epectively. n thi ce, the xiu line-to-line voltge would equl U d. The foeentioned ethod opete t contnt cie fequency, while the fundentl fequency i peitted to vy. The witching fequency i then nonpeiodic in pinciple nd the coeponding Fouie pect e continuou contining fequencie lowe thn the lowet cie idebod. Thee honic e undeied nd poduce lowfequency toque honic [6]-[8] tht y tiulte eonnce in the echnicl tniion tin of the dive yte. A ynchoniztion between the cie fequency nd the contolling fundentl void thee dwbck. A eduction of the honic ditotion cn be chieved by dding zeo-equence wvefo to the inuoidl efeence ignl. F. Spce Vecto Modultion The pce vecto odultion technique [6],[8],[9] diffe fo the foeentioned ethod in tht thee e not epte odulto ued fo ech the thee phe. nted. the coplex efeence voltge vecto i poceed whole. The witching vecto nd the voltge efeence e hown in Fig.4 [6],[8]. Alo the boundie between the contollble nge, the ix-tep opetion nd oveodultion e hown in the e figue. d M MODEL V q U 3 U 2 Fig. 3 ndiect field-oiented voltge contolle E. Sinuoidl Pule Width Modultion Thi ethod eploy individul cie odulto in ech of the thee phe [5],[6],[8],[0]. The efeence ignl U, U b, U c of the phe voltge e inuoidl in the tedy tte, foing yeticl thee-phe yte. They e obtined fo the efeence vecto U, which i plit into it thee phe coponent U, U b, U c. Thee copto nd tingul cie ignl U c, which i coon to ll thee-phe ignl, genete the logic ignl U, U b, nd U c tht contol the hlf-bidge of the powe convete. Thi ethod doe not fully utilize the vilble DC voltge. The xiu vlue of the odultion index, 0.785, i eched t point whee the plitude of the efeence ignl nd the cie becoe equl. The xiu line-to-line voltge plitude in thi opeting point i U 4 U α U 0 U 7 U 5 U 6 U Fig. 4 Voltge efeence nd witching-tte vecto The efeence vecto U i pled t fixed fequency 2f. The pled vlue U(t ) i then ued to olve the eqution: 2 f ( tu + tbu t0 = t tb 2 f b ) = U ( t ) (8) Whee U nd U b e the two witching-tte vecto 3

4 ntentionl Confeence on Powe Syte Tnient PST 2003 in New Olen, USA djcent in pce to the efeence vecto U. The olution of eqution (8) e the epective on-dution t α, t b, nd t ο of the witching-tte vecto U, U b, U o : t t t b 0 3 = 2π f = 2 f U 2 3 = U 2π f t ( t )(co ( t t ) in α b α in α ) 3 The ngle α in thee eqution i the phe ngle between the efeence vecto nd U. Thi technique in effect vege the thee witchingtte vecto oνe ub-cycle intevl t o = /2f to equl the efeence vecto U (t ) pled t the beginning of the ub-cycle. t i ued in Fig. 4 tht the efeence vecto i locted in the fit 60 o ecto of the coplex plne. The witching-tte vecto djcent to the efeence vecto e then U nd U 2. A the efeence vecto ente the next ecto, U 2 nd U 3, copoe the efeence voltge vecto. Hving coputed the on-dution of the thee witching-tte vecto tht fo one ubcycle, n dequte equence in tie of thee vecto ut be deteined next. The zeo vecto i edundnt. t cn be eithe foed U ο (---) o U 7 (+++). U ο i pefeed when the peviou witching-tte vecto i U, U 3 o U 5 while U 7 will be choen following U 2, U 4, U 6. Thi enue tht only one hlf-bidge need to coutte t tnition between n ctive witching-tte vecto nd the zeo vecto. Hence, the iniu nube of couttion i obtined. G. Hyteei Cuent Contol The behvio of thi kind of contolle cn be explined in te of coplex plne witching dig hown in Fig. 5 [6]-[8]. The witching line e locted t ditnce h, equl to the hyteei bnd, fo the tip of the cuent efeence vecto. The entie dig ove with the cuent efeence vecto with it cente eining fixed t the tip of the vecto. b-xi A- qd c-xi B+ C+ A+ C- B- h h h h Fig. 5 Switching dig -xi (9) The typicl o expected behvio of the contolle i to confine opetion to the inteio, hexgonl egion of the witching dig. Thu, wheneve the cuent eo touche one of the witching line, tht invete leg i witched diving the cuent eo in tht leg in the oppoite diection. Note, howeve, tht the cuent eo cn be cied to one of the witching line by otion of the cuent vecto qd o by otion of the cuent efeence vecto qd nd the ttched witching dig. Thu, the itution occu, whee, fo exple, the (A-) witching line i encounteed with the invete in the tte (+,b-,c-). The yte i then effectively hot-cicuited nd cn "cot" out to the tip of the witching dig befoe new witching of the invete occu. Duing thi peiod the oto i effectively "out of contol" ince the exct tjectoy i deteined only by the oto pete nd the intenl E.M.F. t thi condition nd not by the pplied voltge. Hence, n eo of 2ΔΙ, twice the expected vlue equl to the hyteei bnd, cn occu on n lot ndo bi. Thi poble cn be ovecoe by incopoting econd thehold tht ene when the boundy i being eched with the invete in tte tht would poduce hot-cicuited condition nd voiding thi ode. One of the in dwbck of thi ethod i tht thee i tendency to lock into liit cycle of high fequency witching which copie only nonzeo voltge vecto. Clocking nd contolling the witching fequency cn eedy thi. Alo the odultion poce genete ubhonic inceing the echnicl tee nd the poibility of undeible echnicl eonnce. The cuent eo i not tictly liited while the xiu ovehoot i twice the width of the hyteei bnd.. RESULTS n thi ection the eult obtined by the iultion of the foeentioned odel e given. The induction chine i ued to opete with contnt lod of 0.5 p.u. At t=0.5ec tep chnge of the lod fo 0.5 p.u. to 0.7 p.u. occu. t i ued tht thi lod tep chnge i followed by n identicl chnge of the efeence peed. The tep chnge of the efeence peed nd the epone of the thee exined electicl dive e hown in Fig. 6. The oto ineti i elected ll o tht ft chnge of the oto peed e poible. t hould be teed tht the ll ineti ende toque nd peed eonnce -becue of the honic poduced by the powe convete- oe poible. t i obviou fo Fig. 6 tht the epone of the thee exined electicl dive e vey tifying. Afte bout 0.5 ec tedy tte i eched. The penent peed eo i zeo due to the ue of P contolle. Howeve the powe convete uing voltge pce vecto odultion peent the llet ovehoot nd it i the le ocilltoy. n Fig 7-9 the cuent pce vecto tjectoie e hown. Thi i wy to evlute the PWM chee by viul inpection of the tjectoie of the cuent in the coplex plne. The honic content of tedy tte tjectoy i obeved the devition fo it fundentl coponent, with the fundentl tjectoy decibing 4

5 ntentionl Confeence on Powe Syte Tnient PST 2003 in New Olen, USA cicle. Although devition in plitude e eily dicenible, diffeence in phe e of equl ignificnce. t hould be teed tht the honic cuent deteine the coppe loe which ccount fo the jo potion of the chine loe. The voltge pce vecto odulto opete t witching fequency of 4 khz while the inuoidl pule width odulto ue cie ignl of 3.75 khz. The ued hyteei bnd i 5 p.u. of the be cuent. The hyteei cuent technique poduce obviouly the highe honic ditotion. n ce of the hyteei cuent contol chee the ued hyteei bnd, the oto equivlent ectnce nd the dc voltge ffect the witching fequency, nd conequently the cuent honic content. Tuning the peviou pete the cuent honic content cn be optilly djuted. The honic content of the cuent in ce of voltge pce vecto odulto cn be futhe deceed uing n optil odultion ethod [20]-[22]. Rotting Speed (pu) w_spwm w_hytcu wef w_v feence Voltge Spce Vecto Modultion SPWM Hyteei Contol Tie (ec) Fig. 6 feence nd ctul otting peed fo the thee type of convete Voltge Spce Vecto Modultion Fig. 7 Cuent tjectoy of the convete uing voltge pce vecto odultion technique. n Fig. 0 the pectl denitie of the tedy-tte electognetic toque of the thee exined electicl dive e hown. n ce of the hyteei cuent contolle thee pek t 3, 27, 4 Hz occu while the epective pek vlue in ce of voltge pce vecto odulto e 0, 2 nd 28 Hz. n ce of SPWM technique jo pek occu t 35 Hz nd i eult of the ue of non-ynchonized cie nd odultion ignl. The obeved pek depend on the ued witching fequency, hyteei bnd, the pling technique nd obviouly on the ue o not of ynchoniztion technique. The etition of the pek vlue of the electognetic toque pectl denity, i vey ueful undeible echnicl eonnce [6]-[8] cn be voided if the ntul fequencie of the induction chine nd the echnicl dive e known. Hyteei Cuent Contol Fig. 8 Cuent tjectoy of the convete uing hyteei cuent contol. SPWM Fig. 9 Stto cuent tjectoy of the convete uing SPWM odultion technique. Toque Spectl Denity Hyteei Cuent Spce Vecto Modultion SPWM Fequncy (Hz) Fig. 0 Toque pectl denity in the 0-50 Hz fequency e fo the thee powe convete. 5

6 ntentionl Confeence on Powe Syte Tnient PST 2003 in New Olen, USA THD Spce Vecto Modultion SPWM Hyteei Cuent Tie (ec) Fig. THD fo tto cuent ec befoe the ditubnce. n Fig. the THD fcto of the tto cuent i hown in the tie intevl beginning ec befoe the lod nd peed efeence ditubnce. THD i en of evluting the cuent honic content nd conequently the chine coppe loe. V. CONCLUSONS n thi ppe, the dynic pefonce of thee of the ot poiing type of voltge ouce convete, i tudied. The convete upply quiel cge induction chine nd they eploy hyteei cuent contol, voltge pce vecto odultion nd inuoidl pule width odultion, epectively. Detiled odel fo the electicl dive e ued, llowing the tudy of thei behvio in bod bndwidth. The peented odel e developed uing Mtlb code nd Siulink. Vecto contol i ued fo the egultion of the oto peed nd the tto flux. n ce of SPWM nd voltge pce vecto odultion, n indiect field-oiented voltge contolle i pplied. The hyteei cuent contolle i copoed of thee independent pe phe cuent contolle. The opetionl chcteitic of the popoed vible peed chee e tudied howing vey tifctoy dynic epone. The hyteei cuent contolle poduce the highet honic content nd ohic loe een fo cuent tjectoie nd the obtined THD. Uing the tedy tte toque pectl denitie concluion cn be dwn bout poible echnicl eonnce. t i hown tht echnicl eonnce cn poibly occu t 0, 3 Hz fo voltge pce vecto odultion nd hyteei cuent contol technique. REFERENCES [] Wilon, T.G., The evolution of powe electonic, EEE Tn. Powe Electonic, Vol. 5, no 3, pp , My [2] Chn, C.C., Chu, K.T., An oveview of powe electonic in electic vehicle, EEE Tn. on nd. Electonic, vol. 44 no, pp. 3 3, Feb [3] Novotny D.W., Lipo T.A., Contol nd Dynic of AC chine, Oxfod Pe, New Yok 996. [4] W. Leond, Contol of Electicl Dive, Spinge-Velg, 985. [5] B.K. Boe, Powe Electonic nd AC Dive, Pentice Hll, 986. [6] B.K. Boe, Powe Electonic nd Vible Fequency Dive Technology nd Appliction, EEE Pe, New Yok, 997. [7] El Moucy C., Mende E., Rzek A., Decoupled diect contol fo PWM invete-fed induction oto dive, EEE Tn. nd. Appl., vol. 38, no 5, pp , Sept- Oct [8] J. Holtz, Pule Width Modultion fo Electonic Powe Conveion, Poceeding of the EEE, vol. 82, No. 8, Augut 994. [9] F.D. Knello, N.D. Htzigyiou, The Effect of Vible Speed Wind Tubine on the Opetion of Wek Ditibution Netwok, to be publihed in EEE Tn. Enegy Conveion, vol. 7, no. 4, Decebe [0] Chee-Mun Ong, Dynic Siultion of Electic Mchiney uing Mtlb/Siulink, Pentice Hll PTR, 998. [] F.D. Knello, N.D. Htzigyiou A new popoed Contol Schee fo Wind Tubine uing Neul Netwok, PES Winte Meeting 2002, New Yok. [2] P.C. Kue, Anlyi of Electic Mchiney, McGw-Hill, 986. [3] D.M. Bod nd D.W. Novotny, Cuent Contol of VS-PWM nvete, EEE Tn. nd. Appl., vol. A-2, no. 3, pp , My-June 985. [4] Holtz J., Beye B., Ft cuent tjectoy tcking contol bed on ynchonou pule width odultion, EEE Tn. nd. Appl., 995. [5] Schude C.D., Cddy R., Cuent contol of voltge ouce invete fo ft fou-qudnt dive pefonce, EEE Tn. nd. Appl., vol. A-8, no. 2, pp. 63-7, Mch-Apil 982. [6] Lipo T.A., Kue P.C.. Jodn H.E., Honic toque nd peed pultion in ectifie-invete induction oto dive, EEE Tn. Powe App. Syt., vol. PAS-88, pp , My 969. [7] Tinghu Su, Httoi S., hid M., Hoi T., Suppeion contol ethod fo toque vibtion of AC oto utilizing epetitive contolle with Fouie tnfo, EEE Tn. on nd. Appl., vol. 38, no 5, pp , Sept.-Oct [8] Shotng Chen, Nudui C., Mi S., Contolle-induced pitic toque ipple in PM ynchonou oto, EEE Tn nd. Appl., vol. 38, no 5, pp , Sept.-Oct [9] Nynn G., Rngnthn V.T., Extenion of opetion of pce vecto PWM ttegie with low witching fequencie uing diffeent oveodultion lgoith, EEE Tn. Powe Electonic, Vol. 7, no 5, pp , Sept [20] Kol J. W., Etl H., Zch F. C., nfluence of the odultion ethod on the conduction nd witching loe of PWM convete yte EEE Tn. nd. Appl., vol. 27, no. 6, pp , Novebe-Decebe 99. [2] Ptel H. S., Hoft R.G. Genelized technique of honic eliintion nd voltge contol in thyito convete, EEE Tn. nd. Appl., vol. A-9, no. 3, pp , My-June 973. [22] Buj G. S., ndi G. B., Optil pule width odultion fo feeding AC oto, EEE Tn. nd. Appl., vol. A-3, no., pp , Jnuy-Febuy 977. Autho Biogphie F.D. Knello eceived hi Electicl nd Copute Engineeing degee t Ntionl Technicl Univeity of Athen, in 998. He i PhD tudent in the Electicl Engineeing Deptent of NTUA. Hi eech inteet include powe electonic nd lo odeling nd contol of vible peed wind tubine. N.D. Htzigyiou i Pofeo t Powe Diviion of the Electicl Engineeing Deptent of NTUA. Hi eech inteet include newble, Dipeed Genetion, Dynic Secuity nd A technique. He i ebe of CGRE SCC6 nd enio ebe of the EEE. 6

Analysis of Grid Connected DFIG based Wind Farms for Reactive Power Compensation

Analysis of Grid Connected DFIG based Wind Farms for Reactive Power Compensation Anlyi of Gid Connected DFIG bed Wind F fo Rectie Powe Copention S.Jnthnn Aitnt Pofeo, Deptent of EEE, AMET Unieity, Chenni, Til Ndu, Indi Abtct The popol of thi poject ddee the ectie powe genetion of offhoe