SENSORED and SENSORLESS CONTROL OF PERMANENT MAGNET SYNCHRONOUS MOTORS USING MATRIX CONVERTERS

Transcription

1 SENSORED and SENSORLESS CONTROL OF PERMANENT MAGNET SYNCHRONOUS MOTORS USING MATRIX CONVERTERS A. Aas and D. Saltve *Dept. d'engnyea Electònca. Unvestat Poltècnca de Catalunya. C. Colom Teassa. Catalunya. Span. Abstact: Ths pape nvestgates the nfluence of the powe convete on the pefomance of Suface Mounted Pemanent Magnet Synchonous Moto Dves, whch employ Hgh Fequency Voltage Injecton to acheve low speed contol. The effects of IGBT voltage dop, deadtme and deadtme compensaton on poston estmaton ae dscussed and the use of Matx Convete s poposed to educe these effects. Space Modulaton Poflng technque s used to fuhe mpove the estmated angle. Expemental esults demonstate the emakable pefomance of the sensoless speed contol employng the Matx Convete and the contbutons of the Space Modulaton Poflng technque. Keywods: Sensoless Contol, Pemanent Magnet Synchonous Moto, Matx Convetes. 1. INTRODUCTION The avalablty of hghe-stength magnet mateals, mpoved powe swtches, and new ntegated ccuts ae povdng the ngedents fo new Pemanent Magnet Synchonous Machnes (PMSM) and dve confguatons, wth mpotant commecal mplcatons. The PMSM have the potental to eplace the nducton moto n a numbe of ndustal, commecal and domestc vaable speed applcatons. The contol of synchonous AC machnes eques the knowledge of the oto poston and speed fo feld oentaton and closed loop speed and poston contol. Roto shaft sensos ae usually ftted addng to the total cost of the dve and educng ts elablty. Nevetheless, sensoless at zeo speed s stll a challenge, especally fo the Suface Mounted Pemanent Magnet Synchonous Machnes (SMPMSM), whee the magnet salency s athe small. Fo ths eason extensve eseach has beng caed out to develop sensoless stateges. Methods, based on the model of the machne n whch the back EMF s ntegated to detemne the lnkage flux, have been successfully mplemented [1]-[3]. Howeve, all these technques fal at low speed due to lack of a elable back-emf estmate devng fom ntegato dft and nceasng senstvty to eos n the paamete estmaton. A second type of sensoless stategy sutable fo zeo and low speed opeaton s the so called njecton method [4]-[7]. In ths method HF voltage (o cuent) sgnals ae njected nto the machne temnals. The poston dependent nductance causes modulaton n the esultng HF cuent (voltage) that gve the poston nfomaton. Ths technque has been epoted fo hgh salency machnes such SR motos and bued magnet PM machnes [8]-[1]. In suface mounted PM machnes, chaactesed by small salency, the technque has been ted [11] usng the salency ceated by man flux satuaton, but opeaton was only possble at low loads. Futhe poblems fo poston estmaton ase fom the use of standad nvetes fo powe conveson. The convete non-lneates such as deadtme, devce voltage dop and cuent clampng at zeo cuent values [12]-[15] cause dstoton n the poston estmates. In ecent yeas thee has been much development of the dect AC-AC convete-matx Convete [16]-[17], and t s clamed that ths can poduce an output wavefom fee of the nfluence of voltage dops and deadtme delays,.e. behaves as an deal lnea voltage convete [16] [17]. The wok pesented n ths pape compaes the use of a Matx Convete and a conventonal Voltage Souce Invete n a low speed sensoless SMPMSM dve, whch uses HF voltage njecton to obtan the poston estmate. Expemental esults demonstate the excellent pefomance of the Matx Convete speed sensoless contol system. 2. HIGH FREQUENCY INJECTION FOR SENSORLESS CONTROL An AC synchonous machne s sad to be salent f the stato nductance measued n the decton of the 89

2 flux L d s dffeent to the nductance measued n the decton of the toque poducng axs L q. Ths dffeence s caused by asymmety n the oto desgn, as n the case of synchonous eluctance and nteo magnet PM machnes and/o by man flux satuaton, as n suface mounted PM machnes. The α-β model of a synchonous PM machne n the stato efeence fame ncludng the salency s gven by equaton (1). It can be seen that due to the salency, the elaton between the stato voltage and cuents, o nductance matx, s a functon of the oto poston. vα Rs α s = vβ Rs b ψ α Ls Ls cos(2θ ) = ψ β Ls sn(2θ ) ψ α s ψ β L cos( ) s sn(2θ ) α θ ψ m L cos(2 ) s Ls θ β sn( θ ) whee the nductances ae as follows: Lq L L d q Ld Ls = Ls = (2) 2 2 To extact the poston nfomaton contaned n the nductance matx of equaton (1), the HF otatng voltage vecto gven by equaton (3) s added to the stato voltages [12] as shown n Fg1. v v = v α β ω = ˆ sn( t) V cos( ωt) If the njecton fequency ω >> ω e ; whee ω e s the synchonous exctaton fequency, the nduced HF cuents n the stato wndngs ae gven by equaton (4). (1) (3) poston sgnals at base band, as gven n equaton (6). The angle 2θ can be then extacted dectly by an ac tangent (atn). α _ pos β _ pos ω* I1 cos(2θ ) I1 sn(2θ ) Id*= - PI - - PI PI s dq α β v α θ v β VSI MC dq α β Angle estmato 3 2 Fg 1. Sensoless speed contol stuctue wth the hf voltage njecton. (6) SMPMSM In a SMPMSM the salency s small and not pefectly snusodal, whch has two majo effects fo the applcaton of the voltage njecton stategy. Fst the level of useful poston sgnal s small and the dstoton n the HF cuents due to the nvete s non-lneaty.e. dead tme becomes sgnfcant. Second, the salency s not snusodally dstbuted and futhemoe t s shape and phase shft wth espect to the oto poston wll be load dependent [11]. Ths wll poduce hamoncs n the poston sgnals n equaton (6) and n tun wll poduce angle estmaton eos. α β ω Hadwae BP Flte I α I β j ω t Synchonous Flte HP Flte j 2ωt Ialpha I beta 2θ -1 δ tan Fg 2.. Synchonous flte fo demodulaton of hf cuents. = α β I I cos( ωt) I1 cos(2θ ωt) sn( ω t) I sn(2θ ω ) 1 t (4) 3. CONVERTER NON-LINEAR CHARACTERISTICS whee I Vˆ L L L ω s = ; d q V Ls I = ˆ 1 (5) L L ω d In equaton (4) t can be seen that only the negatve sequence component, popotonal to the salency value, contans oto poston nfomaton. To extact ths useful sgnal fom the total hgh fequency cuent the synchonous flte of Fg.2 s mplemented. The Band Pass Flte emoves the fundamental component fom the HF component. The fst otaton of coodnates tansfoms the HF cuents to a otatng fame synchonous wth the voltage njecton, convetng the postve sequence cuent nto DC. Theefoe, by means of a hgh pass flte t can be completely emoved. Fnally, a otaton back attached to the fame synchonous wth the negatve sequence poduces the q Among the convete non-lnea chaactestcs, the most mpotant ones, especally when usng such a sensoless technque, ae dead tme and zeo cuent clampng. These non-lneates ntoduce a dstoton on the HF cuents and, theefoe, n the fnal estmated oto poston. Seveal methods have been epoted to compensate these non-lneates. Howeve, none of them can completely ovecome the effects [14] [15] Voltage Souce Invete. Fg. 3 shows the typcal wavefom pattens fo the conventonal VSI dung commutaton of one-leg. Note the effect of the dead tme ntoduces an uncetanty fo the voltage output (shown n dotted aea n Fg. 3) dung the whole dead tme (td). The cuent decton s needed to know exactly whch ant-paallel dode wll conduct dung the dead tme and consequently to know 9

3 the output voltage. Moeove, any dead tme compensaton technques, such as the one based on the edge shftng, should be appled to compensate such uncetanty [14] [15]. T3 t d1 t c t d2 Vdc D1 Va td ( VA < V B ) T4 V B D2 Fg. 3 Voltage Souce Invete tmng dagam showng typcal devce sequencng wth commutaton fom uppe to lowe swtches Matx Convete. Altenatvely, the MC commutaton pocess s dffeent when compaed to the VSI. Fg. 4 shows the MC geneal scheme and one of ts bdectonal swtch between two dffeent phase lne nputs V A and V B and the output. V A Va ( V A > V B ) Fg. 5. Fou step swtchng commutaton stategy fom swtch A to swtch B and fo postve cuent. Notce how the output voltage changes dependng on the nput voltages. Typcal tme fo the effectve dead tme (t c ) whee thee s voltage uncetanty s just of 2ns, whch s much lowe than the equvalent tme fo the VSI. Moeove, the edge shftng technque s nheent to the cuent based commutated MC, snce the cuent dectons ae always known. Hence, the tmng obtaned fo the same commutaton as Fg. 5 but fo negatve cuents s as Fg. 6 llustates. t d1 V A t c t d2 V B T3 V C VA D1 V I V b V c - LOAD ( VA < V B ) ( V A > V B ) T4 Fg. 6. Fou step swtchng commutaton stategy fom swtch A to swtch B and fo negatve cuent. Notce how the edge of all sgnals have been shfted compaed to Fg. 5. V A V B D2 D5 4. SPACE MODULATION PROFILING VB D3 T3 Fg. 4. Top: Matx Convete scheme wth voltage and cuent polates. Down: Matx Convete topology between two nputs and one output. The commutaton fom voltage phase nput V A to voltage phase nput V B when the cuent s postve s beng studed. The swtchng tmng dagam when the well establshed fou commutatons step s appled s llustated n Fg. 5 [16][17]. T4 D4 D6 To acheve good sensoless oto poston contol the accuacy of the oto poston estmaton needs to be mpoved futhe. In ths wok ths s done by means of Space Modulaton Poflng (SMP). The peodcty of the eo wth oto poston can be exploted to mpove the oto poston estmaton. In the pesent wok, the coecton of the salency poston sgnals I alpha and I beta athe than the dect coecton of the angle estmaton s favoued. The coecton of the poston sgnals has been caed out fo ndvdual hamoncs, the method havng the advantage of only equng the ampltude and phase (only two values) pe each hamonc to be cancelled. Ths appoach s sutable when only a small numbe of hamoncs ae to be suppessed. To compensate fo poston sgnals wth 91

4 eos of a che spectum, such as those poduced by any emanng nvete non-lneates and any geometcal asymmety n the SMPMSM, the SMP technque poposed n [18] s bette suted Commssonng of the SMP. In the commssonng pocess, the pofle of expected dffeences between salency poston sgnals I alpha, I beta and the deal values ae calculated and stoed n the SMP tables. The sgnal pocessng fo extacton of the pofles s pefomed off-lne. In ths eseach the commssonng pocess s undetaken wth the SMPMSM dve opeated n sensoed toque contol. The speed s contolled at an abtay value of 6 pm by the load dve, esultng n 3 Hz exctaton fequency and 6 Hz fundamental salency poston sgnals. The data s captued at a fx ate of 1/3 khz dung 6 seconds (2 samples). Smla data captues ae epeated fo dffeent toque cuent efeences fo the whole load ange, fom 1 A to 1 A n ntevals of.5 A. The pofle s ceated fo each ndvdual toque level. The fundamental component of the salency poston sgnal s extacted by naow Buttewoth band pass flte cented at 6 Hz and the spectal contents of the poston sgnals lmted to 6 Hz by a low pass flte. The data s appled backwads and fowads to the fltes usng the fltflt Matlab command to acheve a non-causal fltes that peseve the sgnals phase. The dffeence between both sgnals s calculated and stoed as a functon of the oto poston. Ths s done by dvdng the complete oto evoluton nto a dscete numbe of ntevals (6 was used n ths wok), all the eo measuements coespondng to the same angle nteval ae aveaged to poduce the typcal eo fo that poston. Appoxmately 5 samples pe poston nteval, coespondng to 1 dffeent evolutons have been used n the calculaton of each aveage. Ths sgnal pocessng s epesented n the flow dagam of Fg. 7. I alpha I beta 2f e f Non-causal fltes θ Inteval = 1 to 6 Σ n SMP tables Ibeta I alpha Fg. 7. Sgnal pocessng flow dagam fo the poflng of the salency. The poflng pocedue s epeated fo the data obtaned wth the dffeent toque efeences geneatng the twodmensonal SMP tables shown as sufaces n Fg. 8. I alpha I beta Estmated oto poston 9 Estmated oto poston Fg. 8. SMP tables 4.2. Load phase shft compensaton The use of the SMP tables allows the extacton of the fundamental component of the poston sgnal, enablng the estmaton of the salency poston δ. Unde no load ths poston concdes wth the oto flux decton, o d axs. Unde load, the stato satuaton s nfluenced by the stato cuents and wll poduce a shft of the salency elatve to the oto flux axs, poducng an offset between the estmated angle and the actual oto poston. In machnes wth a salency domnated by oto geomety ths shft s neglgble. Nevetheless, when satuaton nduced salency s beng tacked as n SMPMSM, the shft of the salency becomes sgnfcant and has to be taken nto account to acheve good oentaton. Ths phase shft s also quantfed dung the commssonng pocess by aveagng the phase dffeence between the salency angle δ and the measued oto poston θ fo each load value. Because the salency s nfluenced by the stato flux, the dynamc of the phase shft can be appoxmated by the dynamc of the stato cuent. Theefoe, the phase compensaton can be pefomed usng the measued value of sq o, f the commanded value s used nstead, a flte s appled to emulate the dynamcs of the q-axs cuent loop. Ths second altenatve s pefeed because t esults n a smoothe sgnal fee fom the components at njecton fequency; the same toque cuent estmaton s used to addess the SMP tables. Fnally the complete oto poston estmaton ncludng the SMP and the satuaton shft table s shown n Fg. 9. Hee the demanded toque cuent sq * and the estmated oto poston angle θˆ ae used to addess θ sq sq θ the SMP tables to obtan the coectng quanttes I alpha and I beta., whch ae subtacted fom the demodulated aw poston sgnals I alpha and I beta and the esult flteed to obtan the coected salency poston sgnals I alpha 92

5 and I beta. The salency angle 2 δ s obtaned by dect tan -1 extacton fom quotent of ths sgnals. Fnally as ndcated n ths Fg. 9, the salency angle θ δ s coected fo the satuaton shft dependng on the efeence toque cuent sq * to obtan the oto poston estmatonθˆ. α-axs SMP β-axs SMP I beta I alpha I beta - I' beta I alpha - * sq : tan -1 θ Cuent loop nomnal dynamc I'alpha ^ sq Phase compensaton table ^ 2θδ.5 Angle Dscmnaton θ ^ θ δ - ^ θ the zoom and the FFT befoe and afte the SMP, espectvely. I alpha, I beta [A] Sampled Poston Sgnals Fg. 1. Poston sgnals befoe SMP compensaton unde full load fo MC..2 Compensated Poston Sgnals Fg. 9. SMP and phase shft coecton fo oto poston estmaton. 5. EXPERIMENTAL RESULTS I' alpha, I' beta [A] Expemental esults have been caed out closng the speed and cuent loops of the SMPMSM, as Fg. 1 shows. A hf voltage of 3 volts and 1KHz has been njected n ode to estmate the oto poston angle. Table I. Specfcatons of SMPMSM, VSI and Matx Convete PMSM Rated powe / Numbe of 3.8kW / 6 poles Nomnal speed / Rated toque ad/s / 12.2Nm Rs / Ld / Lq / Salency.5Ω / 4.35mH / 5.9mH /.73 VSI Swtchng devce 12V, 5 A, IGBT Tun on / tun off / dead tme 4ns / 8ns / 2 µs dode / IGBT voltages dops 2V / 3V Matx Convete Swtchng devce 12V, 35 A, IGBT Tun on / tun off / dead tme 4ns / 8ns / (1.2.5) µs dode / IGBT voltages dops 2V / 3V Unde full load, the contbuton of the SMP s much cleae and consequently the wost pefomance s gven by MC wthout SMP. Agan, the MC wth SMP acheves the best pefomance constanng the Angle eo wthn less than 5 electcal degees. Theefoe, the best speed esponse s obtaned as well wth the MC wth SMP. A deepe analyss s done n the MC wth SMP system, whee the contbuton of the SMP s clealy shown. Fg. 1 shows the poston sgnals befoe the SMP and Fg. 11 afte the SMP. In ode to do the compason n the fequency doman, a zoom of both sgnals s caed out an ts FFT calculated. Hence, Fg. 12 and 13 show Fg. 11. Poston sgnals afte SMP compensaton unde full load fo MC. I alpha, I beta [A] Ampltude [A] Ampltude [A] Sampled Poston Sgnals Sampled Alpha Poston Sampled Beta Poston Fequency [Hz] Fg. 12. FFT of the poston sgnals befoe SMP compensaton. 93

6 I' alpha, I' beta [A] Ampltude [A] Compensated Poston Sgnals Compensated Alpha Poston Roto speed [pm] Roto angle [elec degees] Fg. 15. Roto speed and oto angle unde Sensoless Speed evesal Contol wth SMP Ampltude [A] Compensated Beta Poston Fequency [Hz] Fg. 13. FFT of the poston sgnals afte SMP compensaton. Fg.14 shows the speed evesal fom 3pm to 3pm unde sensoless speed contol wthout SMP, wheeas Fg15. shows the same test but wth SMP. Note how the contol of the SMPMSM s good enough not only n steady state but also dung the tansent. The angle estmaton, theefoe, s good enough to acheve such a sensoless speed contol. Fom Fg 14 t mght be seen, howeve, a small oscllaton n the speed esponse. Ths s due to moto coggng (whch acts as a petubaton on the speed loop and hence the I q demand). In Fg. 15 t mght be obseved how the ncluson of the SMP educes such oscllaton. Roto speed [pm] CONCLUSIONS The use of the Matx Convete, nstead of the conventonal Voltage Souce Invete, fo Hgh Fequency Injecton Sensoless fo Suface Mount PMSM Dves, has been pesented. The man advantages ae outlned. The mnmsaton of the nonlnea chaactestcs, such as voltage dop and moe mpotantly dead tme and cuent clampng, allows the Matx Convete to acheve a much moe lnea chaactestc and consequently to mpove the oveall sensoless pefomance. Expemental esults demonstate the supeo behavo of the poston estmaton when usng a Matx Convete. The Space Modulaton Poflng technque s used to futhe mpove the angle estmaton. Fnally, sensoless speed contol s acheved and ts expemental esults shown. 7. ACKNOWLEDGMENT The authos would lke to acknowledge the Secetaía de Estado de Educacón y Unvesdades del Mnsteo de Educacón Cultua y Depote, fom Span, fo suppotng D Anton Aas dung the couse of ths wok and also the economc suppot eceved fom the Mnsteo de Cenca y Tecnología de España fo ealsng ths wok unde the DPI Reseach Poject. Roto angle [elec degees] Fg. 14. Roto speed and oto angle unde Sensoless Speed evesal Contol wthout SMP 8. REFERENCES 1. R. Wu and G. Slemon, A pemanent magnet moto dve wthout a shaft senso, IEEE Tans. Ind. Applcat., vol. 27, no. 5, pp , Sept./Oct G. D. Andeescu, Poston and speed sensoless contol of PMSM dves based on adaptve obseve, n Poc. EPE 99, R. Dhaouad, N. Mohan, and L. Noum, Desgn and mplementaton of an extended Kalman flte fo the state estmaton of a pemanent magnet synchonous 94

7 moto, IEEE Tans. Powe Electon., vol. 6, pp , Sept./Oxt P. L. Jansen, R. D. Loenz, Tansduceless poston and velocty estmaton n nducton and salent AC machnes, IEEE Tans. Ind. Applcat., vol. 31, no. 2, pp , Mach/Apl F. Blaschke, J. van de Bugt, A. Vandenput, Sensoless dect feld oentaton at zeo flux fequency, n Poc. IEEE Ind. Applcat. Soc. Annual Meetng, Oct. 1996, pp M. Schoedl, Sensoless contol of AC machnes at low speed and standstll based on the INFORM method, n Poc. IEEE Ind. Applcat. Soc. Annual Meetng, Oct. 1996, pp J.-I. Ha and S.-K. Sul, Sensoless fled oentaton contol of an nducton machne by hgh fequency sgnal njecton, n Poc. IEEE Ind. Applcat. Soc. Annual Meetng, Oct. 1997, pp M. J. Coley and R. D. Loenz, Roto poston and velocty estmaton fo a salent-plot pemanent magnet synchonous machne at standstll and hgh speeds,, IEEE Tans. Ind. Applcat., vol. 34, No. 4, pp , Jul./Aug S-J. Kang, J-I. Ha and S-K. Sul, Poston contolled synchonous eluctance moto wthout otatonal tansduce, IEEE Tans. Ind. Applcat., vol 35, no 6, pp , Nov./Dec N. Kasa and H. Watanabe, A mechancal sensoless contol system fo salent-pole busheless dc moto wth autocalbaton of estmated poston angles, IEEE Tans. Ind.Electon., vol 47, no. 2, pp , Ap J-H Jang, J-I Ha and S-K Sul, Vecto contol of suface mounted pemanent magnet moto wthout any otatonal tansduce, Poc. IEEE Appled Powe Electoncs Confeence and Exposton (APEC), pp , USA, Mach.4-8, C. Slva, G. A. Ashe, M. Sumne. An HF Sgnal- Injecton Based Obseve fo a Wde Speed Range Sensoless PM Moto Dves Includng Zeo Speed, Euopean Powe Electoncs Conf. EPE Toulouse J. Cho, S. Sul. A New Compensaton Stategy Reducng Voltage/Cuent Dstoton n PWM VSI Systems Opeatng wth Low Output Voltages, IEEE Tans. Industy Applcatons, Vol. 31, No:5, pp 11-18, Septembe/Octobe J. Holtz, J.Quan. Sensoless vecto contol of nducton motos at vey low speed usng a nonlnea nvete model and paamete dentfcaton Industy Applcatons, IEEE Tansactons on, Volume: 38 Issue: 4, Page(s): July-Aug R. Flka, G. A. Ashe, P. Wheele, C. Slva. Analyss of the Influence of Convete Non-lneates on Pefomance of Sensoless Contolled Synchonous PM Machne Algothms, Euopean Powe Electoncs Confeence. EPE Toulouse M. Bland, C. Slva, P. Wheele, L. Empngham. Mnmsaton of Commutaton Delays n Powe Convetes, Euopean Powe Electoncs Confeence. EPE Toulouse P. Wheele, J. Rodguez, J. C. Clae, L. Empngham, A. Wensten. Matx convetes: a technology evew Industal Electoncs, IEEE Tansactons page(s): Volume: 49, Issue: 2Ap N. Teske, G. M. Ashe, M. Sumne, and K. J. Badley, "Encodeless Poston Contol of Inducton Machnes," pesented at EPE Confeence, Gaz, Austa,

8 BLANKED SHEET