Equivalent Circuit Analysis of Interior Permanent Magnet Synchronous Motor Considering Magnetic saturation

Transcription

1 Page 0114 World Electrc Vehcle Journal Vol. 3 - ISSN AVERE EVS24 Stavanger, Norway, May 13-16, 2009 Euvalent Crcut Analyss of Interor Permanent Magnet Synchronous Motor Consderng Magnetc saturaton Jae-Woo Jung 1, Jeong-Jong Lee 1, Soon-O Kwon 1, Jung-Pyo Hong 1, Senor Member, IEEE K-Nam Km 2 1 Department of Automotve Engneerng, Hanyang Unversty, 17 Hangdang-dong, Seongdong-gu, Seoul, Korea, jjw@hanyang.ac.kr, hongjp@hanyang.ac.kr 2 HEV System Engneerng Team, Hyunda&Ka Motors, Jangduk-Dong, Hwaseong-S, Gyeongg-Do, Korea Abstract Generally, desgn of the parts of an automoble s restrcted by space especally components assembled n the engne room. Therefore tracton motor for hybrd electrc vehcle s desgned by nteror permanent magnet synchronous motor (IPMSM). The IPMSM has hgh power densty and effcency because t generates not only magnetc torue but also reluctance torue. However, IPMSM s dffcult to desgn due to magnetc saturaton and lots of analyss methods are reured. Euvalent crcut analyss (ECA) s one of the desgn methods of IPMSM and t s generally used for characterstcs analyss. Usng the ECA, we can calculate the characterstcs uckly. However, ECA can not estmate lne current exactly because of saturaton of magnetc core and flux weakenng control. In order to perform the ECA exactly, calculaton of parameters such as phase resstance, d- and -axs nductance and no-load lnkage flux are mportant. The phase resstance s smply calculated by usng lnear euaton whch s geometrcal problem. However, d- and -axs nductance s nonlnear problem whch s vared wth current level and current angle. Therefore, nonlnear fnte element analyss s necessary. Conventonal ECA s consdered only d- and -axs nductance profle but no-load lnkage flux s consdered as constant value. However, no-load lnkage flux of IPMSM s also vared accordng to current level and current angle smlar wth d- and -axs nductance profle. Therefore, no-load lnkage flux profle whch s calculated case of current level and current angle should be consdered n the ECA. In ths paper, the calculaton method of no-load lnkage flux profle s ntroduced frstly and then characterstc of specfc model s analyzed wth proposed method. The result of lne current from mproved ECA s compared wth expermental result and result of conventonal ECA. Keywords: Euvalent crcut analyss (ECA), Interor permanent magnet synchronous motor (IPMSM), No-load lnkage flux profle 1 Introducton The tracton motor, nverter and battery are manly addtonal parts to compose hybrd electrc vehcle (HEV) and these components reure small volume and hgh effcency. In order to reduce the volume and mprove the effcency of tracton motor, nteror permanent magnet EVS24 Internatonal Battery Hybrd and Fuel Cell Electrc Vehcle Symposum 1

2 Page 0115 World Electrc Vehcle Journal Vol. 3 - ISSN AVERE synchronous motor (IPMSM) s generally appled to tracton motor for HEV because permanent magnets are embedded n the rotor core, IPMSM generates both magnetc torue and reluctance torue by the rotor salency. In order to analyze characterstcs of IPMSM accordng to varaton of parameters, euvalent crcut analyss (ECA) usually appled despte of low accuracy. A lot of researcher s performed to mprove accuracy of ECA such as consderaton of the core-loss resstance or d- and -axs nductance profle accordng to ampltude of lne current and current angle [1]-[4]. However, these methods also nclude error because of no-load lnkage flux nput as a constant value regardless of lne current and current angle. From ths reason, lne current has lttle dfference between measured values and calculated value by ECA especally flux weakenng regon. Ths paper deals wth the mprovement of the ECA by consderng varaton of no-load lnkage flux whch s changed by magnetc saturaton and armature reacton. Lastly, lne current calculated by mproved ECA, conventonal ECA and measured value are compared to verfy the analyss method presented n ths paper. 2 Euvalent crcut analyss Euvalent crcuts for IPMSM based on a synchronous d- reference frame ncludng ron loss are presented n Fgure1. The mathematcal model of the euvalent crcuts s gven as followng euaton [3]. v d v d R a (a) d-axs euvalent crcut R a cd R c c Rc od o v od vo ωl + L d () -axs euvalent crcut o + ωl L dod Fgure1: Euvalent crcut of IPMSM ωψ a Iron loss s consdered by euvalent resstance R c, and the d- and -axs voltages, effectve torue and defnton of current are gven by euaton (1), (2), (3) and (4) respectvely vd od R v a od Ra 1 v = + + o R v c o (1) Ld 0 od + p 0 L o vod 0 ω L od 0 v = o ωld 0 + o ωψ (2) a { ψ ( ) } T = P + L L (3) n a o d od o = + (4) 2 2 e d where, d and s d- and -axs current. cd and c s core loss current. v d and v s d- and -axs nput voltage. R a s a phase resstance and ψ a s lnkage flux per sngle pole. L d and L s d- and -axs nductance, respectvely. P n s the number of pole par and e s lne current. 3 Armature reacton Generally, synchronously rotate reference s appled to descrbe vector dagram of IPMSM. Conventonal ECA s analyzed wth usng constant value of lnkage flux per sngle pole but t s dfferent from real phenomenon because of nonlnear characterstcs of magnetc crcut. In order to mprove ECA, armature reacton and magnetc nonlnearty s consdered n the ECA. Fgure2 brefly shows the varaton of flux densty per sngle pole par. Lne A n the Fgure2 s feld flux densty n the ar-gap whch s generated by PM and Lne B s ar-gap flux densty that s generated by only armature current. The Lne C shows resultant flux densty wth lnear condton. In the Lne C, half of feld flux densty s demagnetzed and the other half of feld flux densty s magnetzed by armature reacton. If magnetc crcut has a lnear characterstc lke electrc crcut, R.M.S value of ar-gap flux densty s always same rrespectve of armature current. However, magnetc crcut has a nonlnear characterstc. Therefore, the half of magnetzed part of flux densty s saturated as shown the Lne D. It means that lnkage flux form PM s vared accordng to nput current level and current angle. In order to consder the nonlnear characterstcs of IPMSM above mentoned, lnkage flux generated by PM may be calculated by FEA accordng to case of current level and current angle. EVS24 Internatonal Battery Hybrd and Fuel Cell Electrc Vehcle Symposum 2

3 Page 0116 World Electrc Vehcle Journal Vol. 3 - ISSN AVERE D Table1: Specfcaton of analyss model 1 B A N PM C S Item Value Unt Note Input voltage 155 V DC DC lnk Max. torue 105 Output Power 15 kw Max. Current lmt 200 A rms Max. Base speed 2000 rpm MTPA Max. speed 6000 rpm Flux weakenng Fgure2: Varaton of lnkage flux accordng to armature reacton 4 Analyss model Analyss model s desgned for HEV tracton motor. The specfcaton of an analyss model s shown n Table1. The battery voltage s 155V DC and R.M.S. value of current lmt s 200A. The maxmum torue, 105Nm s produced by maxmum torue per ampere (MTPA) control at the low speed, from 0 to 1200rpm. Flux weakenng control s appled to mantan constant power 15kW untl 6000rpm. 5 Calculaton of lnkage flux from PM The constant value of no-load lnkage flux Ψ a s consdered n conventonal ECA. However, lnkage flux Ψ a generated by PM s vared because of magnetc saturaton whch s changed by lne current level and current angle. Therefore no-load lnkage flux Ψ a whch s consdered magnetc saturaton at load condton may nput ECA wth form of look up table as a functon of lne current and current angle as shown n Fgure3. The Ψ a of analyss model s calculated by fnte element analyss. 6 Improved ECA Overall process of characterstcs analyss s shown n Fgure4. In the conventonal ECA, the d- and -axs nductance profle s nput n the conventonal ECA to consder nonlnearty of magnetc crcut. On the other hand, analyss process of mproved ECA s smlar wth conventonal method except lnkage flux Ψ a. The d- and -axs nductance s calculated by euaton (5) [3]. Ψa Ψocosα Ψosnα Ld =, L = (5) d Improved ECA can consder the varaton of Lnkage flux Φ ' a [ Wb ] A rms 40A rms 60A rms 80A rms 100A rms 120A rms 140A rms 160A rms Lnkage flux not consderng load condtons Lnkage flux consderng load condtons Current angle [ o ] Fgure3: Varaton of lnkage flux accordng to armature reacton Ψ a accordng to current level and current angle. Two analyss stages are reured to analyze lnkage flux Ψ a. Frst, load analyss s performed usng by FEA wth nput current and current angle. Second, no- load analyss s performed wthout current source. In the analyss of stage two, magnetc saturaton nformaton calculated n frst analyss stage s consdered for calculaton of Ψ a. The value and angle of lnkage flux Ψ a has a dfference wth Ψ a as shown n Fgure5. Therefore torue euaton (3) can be modfed as follow euaton (6). ' T = P ψ cos χ + L L (6) { ( ) } n a o d od o S T A R T Current ; off PM; On No-Load analyss (Calculaton of Ψ a ) FEA Current ; On PM; On FEA Load analyss wth d, (Case of Lne current, current angle) Save the nformaton of magnetc saturaton each element Current ; off PM; On FEA Calculaton of Ψ a Calculaton of L d, L Ψa Ψocosα Ψ o snα Ld = L = Fgure4: Overall process of presented ECA d L d, L profle Lnkage flux Ψ a profle Calculaton of extra parameters R c (FEA),R a (Analytc) Characterstc analyss (Euvalent crcut analyss) E N D EVS24 Internatonal Battery Hybrd and Fuel Cell Electrc Vehcle Symposum 3

4 Page 0117 World Electrc Vehcle Journal Vol. 3 - ISSN AVERE -axs -axs Ψ 0 Ldd Ψ 0 Ldd Power analyzer α L d-axs Ψ a L d-axs χ Ψ a Ψ a Fgure5: Vector dagram of IPMSM consdered magnetc saturaton Control unt Test motor 7 Verfcaton of mproved ECA In order to verfy mproved ECA, current mappng s performed. The eupment of experment s shown as Fgure6. IPMSM produces not only magnetc torue but also reluctance torue. Therefore, IPMSM produces hgh torue better than surface mounted PM type motor wth same volume. In order to acheve maxmum torue from the IPMSM, current vector control s reured. Therefore, current mappng s necessary to fnd optmal current and current angle. Lne current whch s measured as shown n Fgure7 s measured by current mappng. The lne current calculated by presented method s compared wth measured value to verfy accuracy of presented analyss method. Fgure7 shows comparson of lne current among the results from conventonal ECA, mproved ECA and measured value at the speed 1000, 3000, 6000rpm and each pont of torue. The three results are almost same at the relatvely low speed 1000rpm. However, results of mproved ECA have good accuracy at the hgh speed 6000rpm batter than result from conventonal ECA. These results show that mproved ECA can be used to predct lne current more exactly batter than conventonal ECA durng flux weakenng control. Concluson Many of analytc technue are reured for characterstc analyss of IPMSM because of nonlnear characterstc. ECA whch s one of generally used n desgn of IPMSM s not consderng nonlnearty of IPMSM perfectly. In ths paper, mproved ECA s presented by consderng lnkage flux profle Ψ a. Presented method s helpful to predct relable T-N-I curve of IPMSM. The next job s calculaton of mproved d- and - axs nductance consderng Ψ a. It wll be also mprovng accuracy of ECA. Lne current [ A rms ] Fgure6: Eupment for experment Torue [ Nm ] Fgure7: Comparson between expermental and analyss results References Exp._1000rpm Exp._3000rpm Exp._6000rpm Pren.ECA_1000rpm Pren.ECA_3000rpm Pren.ECA_6000rpm Conv.ECA_1000rpm Conv.ECA_3000rpm Conv.ECA_6000rpm [1] F. B. Fdel, G. C. Aurelo, and F. Roberto, "Determnaton of parameters n nteror permanent-magnet synchronous motors wth ron losses wthout torue measurement," IEEE Trans. Ind. Appl., vol. 37, no. 5, pp , Sep./Oct [2] K. Yamazak, "Torue and effcency calculaton of an nteror permanent magnet motor consderng harmonc ron losses of both the stator and rotor," IEEE Trans. Magn., vol. 39, no. 3, pp , May [3] J. Y. Lee, S. H. Lee, G. H. Lee, J. P. Hong, and J. Hur, "Determnaton of parameters consderng magnetc nonlnearty n an nteror permanent manet synchronous motor," IEEE Trans. Magn., vol. 42, no. 4, pp , Apr [4] T. Sebastan, G. R. Slemon, and M. A. Rahman, "Modelng of permanent magnet synchronous motors," IEEE Trans. Magn., vol. 22, no. 5, pp , Sep EVS24 Internatonal Battery Hybrd and Fuel Cell Electrc Vehcle Symposum 4

5 Page 0118 World Electrc Vehcle Journal Vol. 3 - ISSN AVERE Authors Jae-Woo Jung receved M.S. degree n electrcal engneerng from the Changwon Natonal Unversty, Korea, n Currently he s pursung the Ph.D. degree n automotve engneerng from Hanyang Unversty, Korea. Hs man felds of nterests are optmzaton, analyss and desgn of electromagnetc machne. Jeong-Jong Lee receved M.S. degree n electrcal engneerng from the Changwon Natonal Unversty, Korea, n Currently he s pursung the Ph.D. degree n automotve engneerng from Hanyang Unversty, Korea. Hs research nterests are the desgn of automotve electrc machnes, and numercal analyss of electromagnetc. Soon-O Kwon receved M.S. degree n electrcal engneerng from the Changwon Natonal Unversty, Korea, n Currently he s pursung the Ph.D. degree n automotve engneerng from Hanyang Unversty, Korea. Hs research nterests are electromagnetc feld analyss and electrcal motor desgn related to the nteror permanent magnet synchronous motor for electrcal power steerng and tracton. Jung-Pyo Hong receved Ph.D. degree n electrcal engneerng from the Hanyang Unversty, Korea, n From 1996 to 2006, he was professor wth Changwon Natonal Unversty, Changwon, Korea. Snce 2006 he has been workng as a professor n the Hanyang Unversty, Korea. Hs research nterests are the desgn of electrc machnes, optmzaton and numercal analyss of electromagnetcs. K-Nam Km receved Ph.D. degree n electrcal engneerng from the Hanyang Unversty, Korea, n He joned Mando n He has been joned Hyunda Motor Company as a chef of HEV motor desgn group Snce Hs man felds of nterest are analyss and desgn of nteror permanent magnet motor. EVS24 Internatonal Battery Hybrd and Fuel Cell Electrc Vehcle Symposum 5