A New Method for Estimating Permanent Magnet Synchronous Machine Parameters

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1 J. Bsic. Appl. Sci. Res., (9) , 01 01, TextRod Publiction ISSN Journl o Bsic nd Applied Scientiic Reserch A New Method or Estimting Permnent Mgnet Synchronous Mchine Prmeters Akbr Rezie Srdrbdi 1, Mohsen Hosseini, Mohmmd Ali Noroozi 3 1 Electricl Engineering Deprtment, Islmic Azd University o Dezul, Dezul, Irn Shhid Rjee Techer Trining University, Tehrn, Irn 3 Amirkbir University o Technology, Tehrn, Irn ABSTRACT This pper presents new method or estimting equivlent circuit prmeters o permnent mgnet synchronous mchine. Previous methods or inding equivlent circuit prmeters re bsed on mgnetosttic inite element nlysis. Mgnetosttic inite element nlysis doesn t consider opertion requency. At higher requencies mchine prmeters might vry due to skin eect contribution. The new method is bsed on trnsient inite element nlysis. Thereore it cn tke opertion requency into ccount. The new method needs our inite element trnsient nlysis; one no lod nlysis nd three loding nlysis. Test results re gthered in set o three non-liner equtions. By solving this set o three equtions, equivlent circuit prmeters o the permnent mgnet synchronous mchine will be ound. A typicl solid rotor permnent mgnet mchine is chosen or cse study. It is shown the proposed method is simple nd ccurte. KEYWORDS: Equivlent circuit prmeters, Finite element method, Permnent Mgnet Mchine, Trnsient. 1. INTRODUCTION Using permnent mgnet (PM) excittion in electric mchinery hs some dvntges over electricl excittion. Min dvntges re ugmenttion in eiciency nd reduction in mchine volume [1]-[4]. Thereore permnent mgnet synchronous mchines (PMSMs) re being populr nd widely used. For good exploittion o PMSM, it is necessry to know its equivlent circuit prmeters ccurtely. A ew works hve been done on obtining equivlent circuit prmeters o PMSMs [5]-[8]. All o tht works re reltively complicte, nd cn t opertion requency into ccount. Although inductnce/resistnce clcultion methods ignoring requency eects re vlid t low requencies, the requency enhncement leds to inductnce/resistnce increse which consequently leds to dierences between theoreticl nd experimentl results. Thereore it is crucil to hve relistic nd vlidted models tht could tke the requency into ccount. This pper presents new esy, but ccurte method or prmeters identiiction o PMSM. The new method uses trnsient inite element nlysis (FEA), so it cn consider eects o opertion requency in clcultion o equivlent circuit prmeters. The new method needs our trnsient FEA; one no lod nlysis nd three loding nlysis. Test results re gthered in set o three non-liner equtions. By solving this set o three equtions, equivlent circuit prmeters o the PMSM will be ound. In this pper irst, the bsis o the new method is described. Bsed on equivlent circuit o PMSM nd its phsor digrm, n eqution is derived. By using this eqution nd our trnsient FEA results, it is possible to ind PMSM equivlent circuit prmeters. FEA include one no-lod nlysis nd three lod nlysis. A typicl solid rotor PMSM is chosen or cse study. Perormnce chrcteristics o the mchine re computed by obtined equivlent circuit prmeters. The proposed method is esy to implement nd cn tke opertion requency into ccount, becuse it uses trnsient FEA results.. Equivlent Circuit o Three Phse PMSM Fig. 1 shows per phse equivlent circuit o three phse PMSM in genertor mode. Fig.1. Per phse equivlent circuit o PMSM in genertor mode. *Corresponding Author: Akbr Rezie Srdrbdi, Electricl Engineering Deprtment, Islmic Azd University o Dezul, Dezul, Irn. 9145

2 Srdrbdi et l., 01 In Fig. 1, X nd X re d- nd q-xis components o synchronous rectnce, respectively. I, V, R, nd X re the one phse current o the rmture winding, per phse put voltge o the mchine, lod resistnce connected to one phse o the rmture winding, nd lod rectnce connected to one phse o the rmture winding, respectively. The induced electromotive orce o the rmture winding due to the undmentl lux linkge o PMs in the ir-gp is depicted by E. The phsor digrm o Fig. 1 is shown in Fig.. I d nd I q re the projections o the rmture current I on the d- nd q- xes, respectively. Fig.. Phsor digrm o one phse o the PMSM in the genertor mode loded with R lod. The ssocited put voltge projections on the d- nd q-xes re [9]-[10] V sin I X R I nd V V V q cos E sin I cos I d q I R d I R I X q d where the lod ngle is the ngle between the put voltge V nd EMF E. Combining (1) nd (), the d- nd q-xes currents, independent o the lod ngle, re determined by E X X Id (3) R R X X X X I q X X d I q R R X X X X E R R The per phse put electricl power o the PMSM is P E I I I X X R I (5) q d q R The internl electromgnetic power o the PMSM, P elm, is sum o the sttor winding losses, deined by P sttor core losses, deined by PlFe, nd put power, 3 P. Pelm 3P Plw PlFe (6) 3[ E I I I X X ] P q d q lfe (1) () (4) lw 3RI Sttor core losses cn be clculted i the mplitude nd the requency o time vrying mgnetic lux in the sttor cores re known. Eiciency is deined s 3P (7) P P P where P rot nd P str re rottionl losses nd stry losses, respectively. Combing (3) nd (4) with considering ollowing reltion I I I (8) elm d rot q str, nd 9146

3 J. Bsic. Appl. Sci. Res., (9) , 01 gives I R R X X E X R R (9) For obtining (9) it is ssumed X =0. Using (9) nd our test results on the PMSM, equivlent circuit prmeters o the PMSM re determined. 3. Cse Study A typicl solid rotor PMSM is chosen or cse study. Fig. 3 shows D view o the solid rotor PMSM. Fig.3. D view o the solid rotor PMSM. The sttor core is bricted by lminted steel sheets. PMs re rre erth NdFeB mgnets, nd the directions o PMs re shown in Fig. 3. Armture winding is three phse, two pole winding. Here, the rotor is rotted with the ixed speed 3000 rpm. The rottion o the rotor cuses mgnetic luxes chnge in the sttor core nd voltge induction in the rmture windings. Induced voltges nd currents re oscillting with the time. The proposed method or identiiction o PMSM equivlent circuit prmeters needs our seprte D trnsient FEA. One D trnsient FEA with high impednce lod to determintion o E, nd three other D trnsient FEA with rbitrry inite impednce lods to determintion o the corresponding I. All trnsient (time-stepping) nlyses must be continued until the put voltges, V, nd lod currents, I, rech to their stedy stte vlues. Fig. 4 shows lux lines in no lod nlysis t t=0 second nd t=0.005 second. Fig. 5 shows lux lines with lod R =10Ω nd X =0Ω, t t=0 second nd t=0.005 second. Eect o lod current is shown in Fig. 5(b). Fig.4. Flux lines in no lod trnsient inite element nlysis t () t=0 second, nd (b) t=0.005 second. 9147

4 Srdrbdi et l., 01 Fig.5. Flux lines in lod nlysis with R =10Ω t () t=0 second, nd (b) t=0.005 second. Fig. 6 illustrtes wveorm o stedy stte E obtined by using D trnsient FEA. Fourier nlysis on Fig. 6 t stedy stte gives: pek o undmentl component =83.5 V, nd THD=9.5%. Stedy stte lod currents or R =5, 8 nd 10 ohm re shown in Fig. 7. Becuse o rectngulr shpe o PMs, put wveorms contin hrmonics. Fourier nlysis results on Fig. 7 wveorms re given in Tble I no lod EMF (V) Electricl Angle (degree) Fig.6. Wveorms o stedy stte E obtined by using D trnsient FEA ohm 8 ohm 10 ohm I (A) Electricl Angle (degree) Fig.7. Stedy stte lod current wveorms or three resistive lods obtined by using D trnsient FEA. 9148

5 J. Bsic. Appl. Sci. Res., (9) , 01 TABE I Fourier Anlysis Results on od Current Wveorms R (Ω) Fundmentl o I (A) THD (%) Now, identiiction o the equivlent circuit prmeters o the TFPMDG with the id o D trnsient FEA results is explined. Putting results o Tble I into (9), it leds to the ollowing non-liner systems o three equtions in the three unknowns R, X nd X R X X X 5 R R X X X 8 R R X X X 10 R (10) Solving (10) is done by using computer progrm bsed on Guss-Newton method [11]. Results o proposed method or genertor equivlent circuit prmeters identiiction re given in Tble II. Note tht in (10) R is ssumed unknown, becuse o skin eect due to AC current should be considered. TABE II Equivlent Circuit Prmeters o The Solid Rotor PMSM Obtined by Using The New Method E (V) X (Ω) X (Ω) R (Ω) By using Tble II results nd presented reltions in section II, it is possible to clculte mchine chrcteristics. Fig. 8 shows the vrition o put voltge versus lod current. Fig. 9 illustrtes the put power versus lod current. In Fig. 10, the vrition o eiciency versus lod current is depicted. Becuse the proposed method uses trnsient FEA results, so the proposed method cn consider requency eects in estimtion o PMSM prmeters. In previous works eects o requency just considered in rmture resistnce by using n pproximte coeicient [5]-[8]. Fig.8. Vrition o put voltge versus lod current. 9149

6 Srdrbdi et l., 01 Fig.9. Vrition o three phse put power versus lod current. Fig.10. Vrition o eiciency versus lod current. 4. Conclusion This pper presented new method in modeling PMSM with high precision. The new method needs our simple tests in genertor mode. A typicl solid rotor PMSM is chosen s cse study. Four tests were done by D trnsient FEA, nd equivlent circuit prmeters o the solid rotor PMSM were ound. One beneit o the new method is its cpbility or modeling o PMSM in ny rbitrry requency. Note tht previous methods or modeling o PMSM don t consider eects o requency in PMSM modeling. The new method cn be used or equivlent circuit prmeters identiiction or ny type o synchronous mchines by tking opertion requency into ccount. REFERENCES [1] A. Mhmoudi, N. A. Rhim, W. P. Hew, Anlyticl Method or Determining Axil-Flux Permnent-Mgnet Mchines Sensitivity to Design Vribles, Interntionl Review o Electricl Engineering (IREE), vol. 5, n. 5, October 010, pp [] J. A. Kinnunen, J. Pyrhönen, M. Niemelä, O. iukkonen, P. Kurronen, Design o Dmper Winding or Permnent Mgnet Synchronous Mchines, Interntionl Review o Electricl Engineering (IREE), vol., n., April 007, pp [3] N. Adbelkrim, J. Azzouzi, G. Brkt, Winding Functions Theory nd Mxwell's Equtions Coupled Anlyticl Modeling o n Axil Flux PM Synchronous Mchine, Interntionl Review o Electricl Engineering (IREE), vol.0, n. 0, Februry 006, pp. 14. [4] S. Asghr Gholmin, M. Ardebili, K. Abbszdeh, Selecting nd Construction o High Power Density Double-Sided Axil Flux Slotted Permnent Mgnet Motors or Electric Vehicles, Interntionl Review o Electricl Engineering (IREE), vol.4, n. 3, June 009, pp [5] J. F. Giers, E. Sntini, nd M. Wing, Clcultion o Synchronous Rectnces o Smll Permnent-Mgnet Alternting- Current Motors: Comprison o Anlyticl Approch nd Finite Element Method with Mesurements, IEEE Trnsction on Mgnetics, vol. 34, No. 5, pp , September [6] S. Ymmoto, T. Kno, Y. Ymguchi, nd T. Ar, A Method to Determine Direct- nd Qudrture-Axis Inductnces o Permnent Mgnet Synchronous Motors, Electricl Engineering in Jpn, vol. 171, No. 3, pp , July

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