Performance Analysis of a Claw Pole PM Motor Using Improved FEA-Based Phase Variable Model

Transcription

1 Pefomne Anlysis of Clw Pole PM Moto sing Impoed FEA-Bsed Phse Vible Model Yougung Guo 1, Jinguo Zhu 1, Jixin Chen 2, Steen Su 1, Hiyn u 1, nd Jinxun Jin 3 1 Fulty of Engineeing nd Infomtion Tehnology, niesity of Tehnology, Sydney, SW 2007, Austli 2 College of Eletomehnil Engineeing, Donghu niesity, Shnghi, , Chin 3 Cente of Applied Supeondutiity, niesity of Eletoni Siene nd Tehnology of Chin, Chengdu, , Chin Abstt- This ppe pesents the pefomne nlysis of thee-phse thee-stk pemnent mgnet (PM) lw pole moto by using n impoed phse ible model, whih hs been deeloped fo ute nd effiient pefomne simultion of PM bushless d motos. The impoed model n tke into ount the effet of mgneti stution nd oto position dependene of key pmetes inluding bk eletomgneti foe, winding indutne, ogging toque nd oe loss, whih e obtined fom time-stepping nonline mgneti field finite element nlysis (FEA). The pesented model hs been implemented in Simulink enionment nd employed to simulte the dynmi nd stedy-stte pefomne of the thee-phse thee-stk PM lw pole moto with soft mgneti omposite stto. Pmete omputtion nd pefomne simultion e lied by expeiments on the moto pototype. I. ITRODCTIO Thnks to thei mny dntges suh s high powe density, high effiieny nd high die pefomne, pemnent mgnet (PM) synhonous motos with bushless d (BDC) ontol shemes he been widely pplied in industil nd domesti pplines. In the design of high pefomne BDC die, n ute nd fst model fo pediting, eluting nd optimizing the die system pefomne is lwys desible. Muh wok hs been onduted on the simultion models nd pefomne pedition of BDC motos by ious esehes. Howee, these nlyses e genelly bsed on mny ssumptions nd simplifitions suh s tpezoidl bk eletomotie foe (EMF), onstnt winding indutne, onstnt oe loss, nd negligible ogging toque. To utely pedit the pefomne of the BDC moto, the el wefoms of these pmetes ginst oto position should be onsideed [1-3]. Fo omputtion of moto pmetes nd pefomnes, omping to the equilent iuit method, mgneti field finite element nlysis (FEA) poides moe ute esults but n be time onsuming. A phse ible model ws deeloped in [3], whih n pefom muh fste thn FEA but with the sme leel of omputtionl uy. The oto dependenes of the pmetes e peiously obtined by seies of FEAs nd stoed in lookup tbles. In BDC opetion, thee lwys exists phse winding whih is nonenegized nd the oltge of the phse is immesuble, so the eqution-bsed model nnot be pplied to the BDC moto dietly. An ltentie model, onsisting of seel iuit omponents, hs to be used [3]. To oeome the boe shotoming, n impoed phse ible model hs been intodued, whih employs pue mthemtil ppoh to ompute the oltge of the entl point of st-onneted 3-phse windings so tht the oltge of eh phse n be obtined nd the eqution-bsed model n be dietly pplied to the BDC moto [4-5]. The model hs been pplied to simulte the stedy-stte nd dynmi pefomne of 3-phse 3-stk PM lw pole moto with soft mgneti omposite (SMC) stto unde sensoless BDC sheme [6-7], in whih the ition of bk EMF, winding indutne nd ogging toque e onsideed. This ppe pesents the pefomne nlysis of the lw pole SMC moto by futhe inluding the effet of tnsient oe loss, whih usully tkes signifint pt in the oe loss of SMC mhines [8]. Both pmete omputtions nd pefomne simultions e eified by expeimentl esults. II. PHASE VARIABE MODE The phse ible model is omposed of seel eletil nd mehnil equtions. The oltge eqution of phse winding (=, b, ) is gien s i d / e (1) whee,, i, nd e e the phse oltge, esistne, uent, flux linkge nd bk EMF, espetiely. The flux linkge n be witten in tems of ppent indutne s k i (2) k k Sine the flux linkge is funtion of stto uents nd oto position, the seond tem of (1) n be expnded s d di k d d k ( k ik ) (3) i d k k k whee k nd k e the ppent nd inementl indutnes, espetiely, is the oto mehnil ngle, nd is the oto ngul speed Austlsin niesities Powe Engineeing Confeene (APEC'08) Ppe P-078 pge 1

2 Substituting (3) into (1), the oltge eqution of the -th phse winding beomes di d k k i ( k ik ) e k d The eletomgneti toque nd motion eqution e (4) Tem ( ei )/ T (5) og Jd / T P / T, d / (6) em fe whee T og is the ogging toque, J the totl ineti of otting pts, P fe the oe loss, T the lod toque, nd the fition oeffiient. Fo the symmetil 3 phse windings, whih e stonneted without entl line, we he k, k k, i 0 (, k=, b, ) (7) The boe equtions onstitute the so-lled phse ible model. The pofiles of the bk EMF, ppent indutne, inementl indutne, ogging toque nd oe loss e obtined in dne bsed on non-line time-stepping mgneti field FEAs, in whih mgneti stution nd oto position dependene e onsideed. All these pmetes e stoed s lookup tbles nd will be etieed duing the pefomne simultion oding to oto position o time. III. COMPTATIO OF CETRA POIT VOTAGE Suppose the eletil potentils (oltges) of thee phse winding teminls nd entl point e, b, nd, espetiely, we he, (=, b, ) (8) ( ) / 3 (9) Substituting (4) into (9) with the onsidetion of (7), one n obtin: 1 di d k k k ik e (10) 3 k d The lues of, b nd e deided by the swithing sttes of inete with the 3 phse windings, PWM stte, nd phse uents. nde the BDC mode, thee e only two phse windings tht e exited t eh moment, e.g. the uent flows into phse b nd then out of phse i the entl point, nd phse is non-enegized. Consideing (7), nd n be deided by 1 di d i e 2 b d (11) di dk e k ik kb d (12) When the phse uent is not equl to zeo nd PWM is unde the duty-off stte, is deided by if I 0, 0 if I 0 (13) bus whee bus is the potentil of the powe bus line. sing (11)-(13), one n wok out the potentils of the input pots nd the entl point of the thee phse windings, nd hene the thee phse oltges. By defining tht m kb k k nd efeing to (7), one n obtin dk ik d (14) di ( i ) m e (15) di m ( i ) e (16) Similly, bm, b, m nd n be defined. IV. AAYSIS OF A PM CAW POE SMC MOTOR DER BDC SCHEME BY THE IMPROVED PHASE VARIABE MODE A. Implementtion of the Impoed Phse Vible Model Bsed on (1)-(13), omplete simultion model of BDC is built in Mtlb/Simulink enionment, s shown in Fig. 1, whee m, nd (=, b, ) e obtined fom Mtlb funtion oding to (14-16). The est of wok is simil to the modeling of onentionl d moto, so the deeloped model n be esily elized in Simulink. By using the model, ompehensie pefomne of the BDC moto n be simulted. As n exmple, the model hs been pplied to nlyze the stedy-stte nd dynmi pefomne of 3-phse 3-stk PM lw pole SMC moto, e.g. whethe o not the moto n eh the desied speed with the ted lod nd the ted inete oltge. B. Moto Pototype The PM lw pole SMC moto onsists of n intenl SMC stto (thee phses e xilly stked with n ngul shift of 120 o eletil) nd n extenl mild steel oto with thee 2008 Austlsin niesities Powe Engineeing Confeene (APEC'08) Ppe P-078 pge 2

3 ys of PMs mounted on the inne sufe of the oto yoke [6-7]. The mo dimensions inlude stto oute dimete of 80 mm, effetie xil length of 93 mm, 1 mm min igp length, nd 20 poles. The moto is designed to opete with sensoless BDC sheme, delieing toque of 2.65 m t 1800 pm. Figue 2. Pe-tun flux of one phse winding unde no-lod Figue 1. Simulink implementtion of the impoed BDC model C. Pofiles of Key Moto Pmetes Detemined by FEA In the deeloped phse ible BDC model, the pofiles of key moto pmetes e peiously obtined though nonline time-stepping FEA solutions. Fo exmple, bsed on the no-lod mgneti field distibution, the wefom of PM flux (defined s the flux of one phse winding podued by oto PMs) is quied s in Fig. 2, whee the oto ngle is in eletil degees, =p, p is the numbe of pole-pis. It n be seen tht the flux wefom is quite sinusoidl. The bk EMF n then be infeed by diffeentiting the PM flux linkge with espet to time (oto ngle). Consideing tht the PM flux domintes in the totl flux of PM moto, the stution used by winding uents is ignoed hee. Also fom the no-lod field solutions, the ogging toque n be obtined by the itul wok o the Mxwell stess tenso methods, s shown in Fig. 3. It n be seen tht wefom of the ogging toque is lose to sinusoid with fequeny of 6 times tht of the PM flux o bk EMF. Figue 3. Computed ogging toque of the 3-stk moto The winding indutnes e omputed by modified inementl enegy method [9], in whih two steps of nlyses e onduted. Fistly, nonline nlysis with the exittion of oto PMs is ied out, nd both the ppent nd inementl pemebilities in eh element e stoed, whih oespond to B (flux density)/h (field stength) nd B/H t the opeting point (B, H) on the mgnetiztion ue, espetiely. Seondly, the emnene of PM is set s zeo nd line nlysis is onduted with the sed pemebilities nd uent i in the phse winding to ompute the mgneti o-enegy W f. It should be noted tht the stoed ppent pemebility should be used fo ppent indutne omputtion nd the inementl pemebility fo inementl indutne. Then, the winding indutne n be omputed by 2 2W f / i (17) Fig. 4 shows the omputed ppent nd inementl indutnes of one phse winding, s well s the expeimentl esults, whih e obtined using the ommon V-I method by pplying smll uent (0.2 A, 500 Hz). In onentionl eletil mhine, oppe loss is the dominnt pt of totl powe loss nd hene the effet of oe loss is not signifint nd is often onsideed s onstnt. Howee, in SMC mhines, the oe loss is ompble to oppe loss, so it should be utely omputed nd inluded in the model. The tnsient oe loss of this lw pole moto is omputed by the following FEA-bsed fomultions [10]: 2008 Austlsin niesities Powe Engineeing Confeene (APEC'08) Ppe P-078 pge 3

4 db db db Pfe { H } ( ) { ( ) } C z 2 z z 3 k 2 2 ke x 2 x e x (18) whee the oeffiients, k, k e nd C e e obtined by ue fitting bsed on the mesuements on ubi SMC smple by using 3-D mgneti popety testing system [11]. The lultion is bsed on eh element, in whih the flux density nd field stength e obtined by time-stepping FEA. Fig. 5 shows the ue of oe loss ginst oto position when the moto uns t 1800 pm t no-lod. The ege oe loss is bout 58 W, whih is lose to the mesuement (61 W) by using the dummy oto method [6]. model, e.g. the wefoms of oltge, bk EMF nd uent of phse winding s shown in Fig. 7. The simultions he been lied by the expeimentl esults on the moto pototype [6]. As n exmple, Fig. 8 plots the mesued stedy mehnil hteistis. The moto n delie toque of 2.65 m t 1800 pm when the inete d oltge is 165 V. Figue 4. Computed nd mesued indutne of one phse winding Figue 6. Simulted speed, eletomgneti toque nd powe duing stt-up Figue 5. Coe loss ginst oto ngle t 1800 pm t no-lod D. Pefomne Simultion Fig. 6 illusttes the simulted ues of speed, eletomgneti toque nd powe duing the stt-up with the ted lod of 2.65 m when the ted inete d oltge of 165 V is pplied. It n be seen tht the moto n elete to the ted speed (1800 pm). As the itions of ll mo pmetes e onsideed, the simulted speed nd toque he moe ipples thn those esults fom [6], in whih the effet of tnsient oe loss toque ws ignoed. Moe dynmi nd stedy stte pefomnes n be obtined by the pesented Simulink-bsed phse ible Figue 7. Wefoms of oltge, bk EMF nd uent of phse winding t stedy stte 2008 Austlsin niesities Powe Engineeing Confeene (APEC'08) Ppe P-078 pge 4

5 Speed (e/min) 165V 150V 130V 110V 90V 70V 50V Toque (m) Figue 8. Mesued mehnil hteistis V. COCSIO This ppe pesents the pefomne nlysis of PM lw pole SMC moto unde sensoless BDC ontol sheme by using n impoed phse ible model, in whih mthemtil ppoh is pplied to obtin the oltges of both enegized nd non-enegized phses. The effets of itions of ll mo pmetes inluding bk EMF, winding indutne, ogging toque nd oe loss e onsideed in the simultion. The lultion of mo moto pmetes by FEA nd the pefomne simultions e epoted nd eified by expeimentl esults. REFERECES [1] S.. Ho, W.. Fu, H.. i, H. C. Wong, nd H. Tn, Pefomne nlysis of bushless DC motos inluding fetues of the ontol loop in the finite element modeling, IEEE Tns. Mgn., ol. 37, no. 5, pp , Sep [2] Y. S. Jeon, H. S. Mok, G. H. Choe, D. K. Kim, nd J. S. Ryu, A new simultion model of BDC moto with el bk EMF wefom, in Po. 7th Wokshop on Computes in Powe Eletonis, Blksbug, VA, SA, July 2000, pp [3] O. A. Mohmmed, S. iu, nd Z. iu, A phse ible model of bushless DC motos bsed on finite element nlysis nd its oupling with extenl iuits, IEEE Tns. Mgn., ol. 41, no. 5, pp , My [4] J. X. Chen, Y. G. Guo, nd J. G. Zhu, An impoed phse ible model bsed on eleto-mgneti field oupled with its extenl iuits fo pefomne elution of pemnent mgnet bushless d motos, in Po. Int. Conf. on Industil Eletonis nd Applitions, Hbin, Chin, My 2007, pp [5] J. X. Chen, Y. G. Guo, J. G. Zhu, nd J. X. Jin, Pefomne nlysis of sufe mounted pemnent mgnet bushless d moto using n impoed phse ible model, in Po. 42 nd IEEE Industy Applitions Soiety Annul Confeene, ew Olens, SA, Sept. 2007, pp [6] Y. G. Guo, J. X. Chen, J. G. Zhu, H. W. u, H. Y. u, nd J. X. Jin, An impoed phse ible model fo dynmi pefomne nlysis of PM lw pole SMC moto with bushless d ontol, in Po. Austlsin niesities Powe Engineeing Confeene, Melboune, Austli, De. 2006, ppe TS1-02. [7] Y. G. Guo, J. G. Zhu, Z. W. in, H. Y. u, X.. Wng, nd J. X. Chen, Influene of indutne ition on the pefomne of PM lw pole SMC moto, Jounl of Applied Physis, ol. 103, no. 7, pp. 07F , 1 Ap [8] Y. G. Guo nd J. G. Zhu, Applition of soft mgneti omposite mteils in eletil mhines, eiew, Austlin Jounl of Eletil & Eletonis Engineeing, ol. 3, no. 1, pp , [9] Y. G. Guo, J. G. Zhu, nd H. Y. u, Aute detemintion of pmetes of lw pole moto with SMC stto oe by finite element mgneti field nlysis, IEE Po. Eleti. Powe Appl., ol. 153, no. 4, pp , July [10] D. in, P. Zhou, W.. Fu, Z. Bdis, nd Z. J. Cendes, A dynmi oe loss model fo soft feomgneti nd powe feite mteils in tnsient finite element nlysis, IEEE Tns. Mgn., ol. 40, no. 2, pp , M [11] Y. G. Guo, J. G. Zhu, Z. W. in, nd J. J. Zhong, Mesuement nd modeling of oe losses of soft mgneti omposites unde 3D mgneti exittions in otting motos, IEEE Tns. Mgn., ol. 41, no. 10, pp , Ot Austlsin niesities Powe Engineeing Confeene (APEC'08) Ppe P-078 pge 5