Using On-Line Parameter Estimation to Improve Efficiency of IPM Machine Drives

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1 Usng On-Lne Paamete Estmaton to Impove Effcency of IPM Machne Dves Hyunbae Km and Robet D. Loenz Dept. of Mech. Eng. and Dept. of Elect. & Comp. Eng. Unvesty of Wsconsn Maon Unvesty Avenue Maon, WI 7 UA Abstact Ths pape pesents a means to mpove the effcency of nteo pemanent magnet (IPM) synchonous machne dves whch can be best mplemented va on-lne self tunng. Wth ths technue an mpoved maxmum toue-peampee tajectoy fo IPM machne can be calculated that ncludes magnetc satuaton. Ths mpoved tajectoy can be shown to mpove effcency. The model-based estmaton algothm s based on measued voltage and cuent and oto poston/velocty. The model has two euatons whee cosscoupled paametes can be elmnated fo the obustness of paamete estmaton. Paamete estmaton s mpoved by combnng the model wth a closed loop obseve. Ths algothm s sutable fo on-lne estmaton. The pefomance of ths algothm s llustated by expementaton. The vecto contolle usng ths algothm contols moto toue accuately unde any load and speed. I. ITRODUCTIO Pemanent magnet (PM) synchonous machnes ae wdely used fo hgh effcency dve applcatons. Inteo pemanent (IPM) synchonous motos have magnets mounted nsde the oto. Ths geometc chaactestc povdes seveal advantages [, ]. Fst, the oto s mechancally obust fo hgh speed opeaton because the magnets nsde oto ae potected and contaned by the oto on. econd, the nheent salency,.e. the dffeence between -axs and d- axs nductance, benefcally changes both the agap toue poducton and the feld weakenng chaactestcs. To take full advantage of these popetes, the contolle would deally have accuate machne paametes. Appopate contol metho ae eued to utlze those advantages n the constant toue and constant powe egon. Maxmum toue-pe-amp contol has been ntoduced to mpove toue poducton n the constant toue egon. The maxmum toue-pe-amp. tajectoy was calculated usng fxed paametes. Wth ths tajectoy, the toue command s conveted to s and comman fo a synchonous fame cuent egulato [-]. Only L satuaton effect was consdeed fo the calculaton of the tajectoy [8]. s Cuent command was dectly calculated fom the output of the PI speed contolle fo achevng maxmum toue-pe-amp. wthout consdeng paamete vaatons [, 7]. A smple Ths wok was funded pmaly by the Wsconsn Electc Machnes and Powe Electoncs Consotum n suppot of CPE and made use of CPE ERC haed Facltes suppoted by atonal cence Foundaton unde Awad umbe EEC model based on measung the L dependence on -axs cuent was developed to mpove toue poducton [9]. Most metho fo mpovng toue poducton ae senstve to machnes paametes. Unfotunately, stato esstance and pemanent magnet flux vay wth moto tempeatue []. The d and axs total nductance, L d and L ae known to depend on agap flux []. In actual applcatons, on-lne paamete estmaton fo L d and L s eued to acheve maxmum toue-pe-amp. contol. Most of paamete estmaton appoaches ae based on measuements that ae not ch enough to estmate all paametes fo nducton machnes and IPMs. The low chness n the measuement lea to a vey senstve o llcondtoned paamete estmaton poblem. In ode to ovecome the ll-condtonng, some estmaton algothms based on ecusve least suae (RL) metho have been poposed []. The schemes estmate the emanng paametes by fxng ll-condtoned paametes to po estmates, yeldng some mpovement n paamete estmaton. Also, seveal estmaton metho based on adaptve contol theoy have been poposed [-]. Howeve, most of the paamete estmaton schemes have dffculty n ovecomng the lmtatons of the low chness of measuements and the nteacton of estmated paametes fo any load and speed condtons. Genetc algothms (GAs) ae based on stochastc off-lne optmzaton (seach) algothms. Paametes of nducton machnes have been successfully dentfed by utlzng Genetc algothms [7,8]. The pupose of ths pape s to pesent a novel appoach whch can ovecome these lmtatons by totally decouplng each paamete n the model. The valdty of the poposed method s vefed by both smulaton and expementaton. Also, the pape demonstate how the ncluson of satuaton n the maxmum toue-pe-ampee tajectoy yel mpoved effcency wth hghe values of fundamental cuent. II. IPM MACHIE MODELIG I ROTOR REFERECE FRAME The model of the IPM machne n the oto efeence fame s outlned fo the development of the adaptve paamete estmaton method. The machne model s epesented by ().

2 é v ù v s û = é s -ω L é ù ω L d s û ù s û é whee P: numbe of pole L d : total d-axs stato nductances (= L md L ld ) L : total -axs stato nductances (= L m L l ) λ pm : pemanent magnet flux lnkage (= L md I f ) : stato d-axs cuent n oto fame : stato -axs cuent n oto fame s ù û ω λ pm () Electomagnetc toue can be expess as follows: T e = P [λ pm s (L d -L ) s ] () Feld algnment toue (λ pm ) s poduced by nteacton s between d-axs magnet flux and -axs stato cuent n (). nce IPM machne has salency (L >L d ), eluctance toue ((L d -L ) s ) s poduced as the cuent-nduced magnet flux along L d and L nteacts wth othogonal cuent s components. II. AALYI OF ALIECY AD ATURATIO FOR IPM MACHIE A. IPM alency Chaactestcs B. Measued atuaton Effects fo IPM motos Fgues and show measued d and -axs nductances fom a commecal IPM moto. The paametes wee measued by usng an off-lne estmaton method. Fo ths machne, the -axs nductance s about thee tmes the d-axs nductance. Ionsatuatoneducestheagapfluxdensty, causng IPM machnes to demonstate nonlnea nductance. The effect of the satuaton fo -axs nductance s geate than that fo the d-axs, compang Fg. wth. Ld [mh] 8 Magntude of [A] Fg.. Measued total d-axs stato nductance as a functon of d-axs cuent n the oto fame L [mh] Magntude of Fg.. Measued total -axs stato nductance as a functon of -axs cuent n the oto fame Pemanent Magnet shaft stato oto symmetcal -phase stato wndngs oto -axs axs magnetc flux oto d-axs daxs magnetc flux III. IPM TORQUE COTROL WITH ATURATIO COMPEATIO A. Maxmum Toue-pe-Ampee Tajectoy usng omnal Paametes Fgue shows constant toue loc and maxmum touepe-ampee tajectoy calculated by usng fxed nomnal paametes whee T eb s base toue. Fg.. IPM machne magnetc flux paths Fgue shows the magnetc flux paths fo the d and -axs of a fou-pole oto. The on tbuton nomally used fo mbeddng magnets nsde the oto poduces salency n the IPM machne. The d-axs magnetc flux passes though the physcal agap as well as the two bued magnets that act as a lageseesagap. The-axsmagnetcfluxpassesonly though the steel pole peces. Theefoe, the -axs nductance s lage than the d-axs nductance and salency esults, whch mpacts electomagnetc toue poducton. T eb T eb T eb T eb T eb Max. T/A Tajectoy w/o atuaton [A] Fg.. Constant toue loc and maxmum toue-pe-ampee tajectoy usng nomnal paametes.

3 = = s é T e () P[λ pm (L d -L ) ] Maxmum toue-pe-ampee s an mpotant chaactestc fo IPM moto effcency. The maxmum toue-pe-ampee tajectoy can be found by takng the devatve of (),.e. the magntude of cuent vecto n d-axs wth espect to the cuent n the d-axs. The tajectoy s the closest path fom the desed toue to the ogn n Fg.. The dashed lnes epesent constant ated toue fo gven values of cuent. B. Real Maxmum Toue-pe-Ampee Tajectoy consdeng atuaton Maxmum toue-pe-amp s functon of L d, L and λ pm. Wth ths calculaton, λ pm s assumed to be constant. As shown n ecton II, L d and L change nonlnealy wth nceasng cuents. Theefoe, the tajectoy of Fg., calculated by usng fxed nomnal values, s not the actual maxmum toue-pe-ampee tajectoy fo the IPM machne. The actual maxmum toue-pe-ampee tajectoy ncludng on satuaton should be calculated by usng measued paametes as they vay wth opeatng condtons. Fgue shows constant toue loc and the maxmum toue-pe-ampee tajectoy ncludng on satuaton as expementally measued. ù û toue. The d- axs cuent (, ) can be appoxmated by d ode cuve fttng. =AT e BT e CT e D () s =ET e FT e GT e H () whee A, B, C, D = [.9, -., -.,.9] E, F, G, H = [., -.889,.9, -.]. These smple appoxmatons (, ) can be used as cuent command as a functon of toue fo cuent egulato. [A] Measued Cuve Fttng 7 Te [m] Fg.. d-axs cuent fo max. T/A Tajectoy wth satuaton as a functon of toue. Measued Cuve Fttng T eb T eb T eb Max. T/A Tajectoy w/ atuaton [A] Fg.. Constant toue loc and maxmum toue-pe-ampee tajectoy ncludng satuaton. If off-lne paamete estmaton method s used to obtan paametes fo a ange of opeatng condtons, ths tajectoy can be calculated. Howeve, ths s computatonally ntensve because of the non-lneaty of the satuaton. uch calculatons ae usually uneasonable n eal tme. C. Cuent as functon of Toue Maxmum Toue-pe- Ampee Tajectoy wth atuaton Fgue and 7 shows d- axs cuent fo maxmum toue-pe-amps tajectoy wth satuaton as a functon of Te [m] Fg. 7. -axs cuent fo max. T/A tajectoy wth satuaton as a functon of toue. D. Compason of Maxmum Toue-pe-ampee Tajectoy wth and wthout atuaton Fgue 8 shows the advantage of ncludng satuaton n the maxmum toue-pe-ampee tajectoy. Te [ m] 8 Max. T/A Tajecotoy w/ atuaton Max. T/A Tajecotoy w/ atuaton [A] Fg. 8. Real constant toue loc and maxmum toue-pe-ampee tajectoy consdeng satuaton.

4 Wth low magntudes of cuent, thee s not much dffeence between the two tajectoes. Wth hghe cuents the satuaton tajectoy shows a notceable mpovement n toue poducton when satuaton s ncluded. Fgue 9 shows pecentage ncease n toue compang the tajectoy wthout satuaton and the tajectoy ncludng satuaton. Ths fgue clealy demonstates the advantage of ncludng satuaton n the maxmum toue-pe-ampee tajectoy. Toue [%] b max [A] Fg. 9. Impoved toue poducton usng maxmum toue-pe-ampee tajectoy ncludng on satuaton IV. DEIG OF THE O-LIE PARAMETER ETIMATIO A. Poposed Estmaton cheme The model euatons fo effcent and compact paamete estmaton can be obtaned by elmnatng devatve tems, whch ae zeo at steady state. The coespondng oto fame models fo the estmaton fo and d-axs nductances ae: s -v = ^L ω () s v s - s s - ω λ pm = ^L d ω (7) The elmnaton of devatve tems s motvated by seveal concens. Fst, sepaatng the estmaton of L fom that of L d hasbeenfoundtoleadtobette-behavedestmates. The estmated paamete fom one model s totally ndependent of the dynamcs of the othe model. Anothe advantage s to educe senstvty to nose, whch s amplfed though dffeentaton. Includng the dffeentaton tems n () and (7) can make the model fo paamete estmaton unstable. tato esstance and flux lnkage ae ncluded n these models. Resstance ( s ) and pemanent magnet flux (λ pm ) can be assumed constant because the paamete vaaton s elatvely much smalle than and d-axs eactance. Also, voltage domnates at hgh feuences n the paamete estmaton models. The affect of the stato esstance can then be neglected at hgh feuences. Fgue shows an on-lne paamete estmaton scheme fo IPM machnes based on () and (7). v ω s s v s ω λ pm ω ˆs ˆs D D LPF LPF * * d,nom K s d,nom K d s Fg.. On-lne IPM machne paamete estmaton The oto fame models () and (7) ae used fo estmates, whch ae constant at steady state and whch nclude the effect of satuaton. The sgnals fom the models contan PWM tansents. Unwanted hgh feuency components can be flteed out though a low pass flte as shown. The data though the flte wll act as the command fo a smple closed loop obseve, whch mpoves estmaton n the pesence of tansent nose. The obseve feedfowad uses the nomnal values of L and L d to mpove paamete estmaton dung statup tansents. B. mulaton Results Fg. shows estmated paametes fo poposed adaptve paamete estmaton scheme fo constant and vayng toue mode opeatons. s [A] L [mh] L d [mh] s d -.. L e L.. Ld e Ld.. Tme [sec] Fg.. Estmated paamete fo adaptve paamete estmaton scheme basedonmrac. The smulaton was been done wth measued nomnal paametes as shown n Table I. Both opeatons utlzed a

5 Hz suae wave toue command that s conveted to the coespondng and d axs cuent n the oto fame usng the nomnal maxmum toue-pe-amp tajectoy. Fom the fgue t s appaent that good tackng chaactestcs fo both L and L d ae shown wthout paamete estmaton eo. V. EXPERIMETAL REULT The estmaton method was tested wth the IPM moto whose paametes ae gven n Table I. Table I IPM Test Moto Paametes Paamete Value Max. Toue 7.. m Max. peed pm R. Ω L Ld. mh.7 mh λpm.88 Wb J 99. kg m - Poles Fgue shows the block dagam of the toue contolle ncludng the maxmum toue-pe-ampee tajectoy whch ncludes on satuaton. Functons () and () ae used to convet the toue comman to -d cuent comman along the functons () and (). A oto fame PI cuent egulato s used to contol cuent. Coss couplng wth the paamete dependency s decoupled pecsely by usng ^L and ^L d fom the poposed on-lne paamete estmaton scheme. * T e Max. T/A ncludng atuaton ω * * s On-Lne Paamete Estmaton d Cosscouplng Decouplng Cuent Regulato * v ds ds * v * v s ds j e θ s* v s* v s PWM VI LPF& Coodnate Tansfom Encode Fg.. Toue contolle based on maxmum toue-pe-ampee tajectoy ncludng satuaton. Fgue shows the expemental test setup, whch conssts of dual moto and load dves, DP, and PC. The swtchng and samplng ates of the hadwae system s 8 khz. Expemental esults llustate the convegence capablty of the on-lne paamete estmaton scheme. A ectangula wave toue command wth the feuency of about, Hz poduces the two dffeent levels of cuent, whch ae shown n Fg. and. θ Intel Pentum based PC *, [A] * s, ^Ld [mh] ^L [mh] DP D/A A/D PWM Cuent Feedback Gate gnals Osclloscope Poston Feedback Test Dve Fg.. Expemental test setup. APEX Moto Analog peed Command -.. * s s * d s d s Load Dve Electocaft Moto Tme [sec] Fg.. Expementally estmated total -d axs nductance fo two dffeent stato -d axs cuents. Fo both condtons, the estmated and d-axs nductance convege vey fast to easonable values (Fg., ). The estmaton esponse shown used decoupled models and closed loop obseves. Compang the estmated paametes wth the system dentfcaton esults of Fg. and, the poposed on-lne scheme s vefed. The esults fom on-lne paamete estmaton scheme ae consstent wth that fom system dentfcaton, usng the off-lne method. It can be seen that the estmated paametes fo hgh cuent levels become smalle due to on satuaton, whch s expected.

6 *, [A] * s, ^Ld [mh] ^L [mh] d s s * s d * s Tme [sec] Fg.. Expementally estmated total -d axs nductance fo two dffeent stato -d axs cuents. VI. COCLUIO A maxmum toue-pe-ampee tajectoy that ncludes the effect of satuaton can poduce moe toue and mpoved effcency fo IPM dves. The on-lne estmaton method poposed s smple and has a compact executon. The estmated paametes (L d, L ) ae ndependent of each othe. Closed loop obseves cause mpoved esponse and elable paamete estmaton fo constant and tansent toue opeatons. Off-lne paamete dentfcaton metho eue specal connectons, eupment, and opeaton. The poposed onlne paamete estmaton technue eues no such tems. The poposed on-lne paamete estmaton scheme can estmate the paametes fo all opeatng anges. These estmated paametes can be used to calculate the maxmum toue-pe-ampee tajectoy ncludng satuaton. REFERECE [] B.K. Bose, A Hgh-Pefomance Invete-Fed Dve ystem of an Inteo Pemanent Magnet ynchonous Machne, IEEE Tans. on Ind. Appl., vol., pp , ep./oct [] B.K. Bose, P.M. zezesny, A Mcocompute-Based Contol and smulaton of an Advanced IPM ynchonous Machne Dve ystem fo Electc Vehcle Populson, IEEE Tans. on Ind. Elect., vol., pp. 7-7, 988. [] T.M. Jahns, G.B. Klman, T.W. eumann, Inteo Pemanent-Magnet ynchonous Motos fo Adjustable-peed Dves, IEEE Tans. on Ind. Appl., vol. IA-, pp , July/Aug. 98. [] T.M. Jahns, Flux-Weakenng Regme Opeaton of an Inteo Pemanent-Magnet ynchonous Motos Dves, IEEE Tans. on Ind. Appl., vol. IA-, pp. 8-89, July/Aug. 98. [].R. MacMnn, T.M. Jahns, Contol Technues fo Impoved Hgh- peed Pefomance of Inteo PM ynchonous Motos Dves, IEEE Tans. on Ind. Appl., vol. 7, pp. 997-, ep./oct. 99. []. Momoto, M. anada, Y. Taketa, Wde-peed Opeaton of Inteo Pemanent-Magnet ynchonous Motos wth Hgh-Pefomance Cuent Regulato, IEEE Tan. on Ind Appl.,vol.,pp.9-9,Jul/Aug 99. [7] J. Km,. ul, peed Contol of Inteo Pemanent Magnet ynchonous Moto Dve fo the Flux Weakenng Opeaton, IEEE Tans. on Ind. Appl., vol., pp. -8, July/Feb [8] J.Wa,T.M.Jahns, AewContolTechnuefoAchevngWde constant Powe peed Opeaton wth an Inteo PM Altenato Machne, Rec. of IEEE Ind. Appl. ocety Conf.,pp.87 8,. [9]. Momoto, T. Ueno, M. anada, A. Yamagwa, Effects and Compensaton of Magnetc atuaton n Pemanent Magnet ynchonous Moto Dves, Rec. of IEEE Ind. Appl. ocety Ann. Conf. pp. 9, 99. [] B. neyes, D.W. ovotny, T.A Lpo, Feld-Weakenng n Bued Pemanent Magnet AC Motos Dves, IEEE Tans. on Ind. Appl., vol. IA-, pp. 98-7, Ma./Ap. 99. [] T. ebastan, Tempeatue Effects on Toue Poducton and Effcency of PM Motos usng dfeb magnets, Rec. of IEEE Ind. Appl. ocety Conf., pp. 78-8, 99. [] M. Vélez-Reyes, G.C. Veghese, ubset electon n Identfcaton, and Applcaton to peed and Paamete Estmaton fo Inducton Machnes, Poc. of the th IEEE Confeence on Contol Applcatons, Albany Y, ep. 8-9, 99. [] H. Kubota, K. Matsuse, T. akano, DP-based peed Adaptve Flux Obseve of Inducton Moto, IEEE Tans. on Ind. Appl., Vol. 9, o., pp. -8, Ma./Ap. 99. [] H. ugmoto,. Tama, econday Resstance Identfcaton of an Inducton-Moto Appled Model Refeence Adaptve ystem and Its Chaactestcs, IEEE Tans. on Ind. Appl., Vol. IA-, o.,, pp. 9-, Ma./Ap [] R.D. Loenz, D.B. Lawson, "A mplfed Appoach to Contnuous On- Lne Tunng of Feld Oented Inducton Machne Dves", IEEE Tans. on Ind. Appl., Vol, o., pp. -, May/Jun., 99. [] P.Y. Chung, M. Dölen, H. Km, R.D. Loenz, "A Contnuous-Tme Obseve to Estmate Electcal Paametes of Inducton Machnes", Rec. of IEEE Ind. Appl. ocety Ann. Conf, pp. 9-, ep./oct.. [7] P.Y. Chung, M. Dölen, H. Km, R.D. Loenz, "Paamete Identfcaton fo Inducton Machne Dves by Contnuous Genetc Algothms, Intellgent Engneeng ystem Desgn though Atf. eual etwoks, C.H. Dagl et al. (E.), vol., pp. -, AME Pess, Y,. [8] Alonge F., D lppolto F., Feanta, G., and Ramond, F. M., Paamete Identfcaton of Inducton Moto Model usng Genetc Algothms, Poc. of IEEE Contol Theoy and Applcatons, vol., pp. 87-9, ov., 998.