Simplified Thermal Model of a Radial Flux Motor for Electric Vehicle Application

Transcription

1 Journal of Asian Electric Vehicles, Volue 8, Nuber 2, Deceber 2010 Siplified Theral Model of a adial Flux Motor for Electric Vehicle Application Moez Ayadi 1, Hana Kebaili 2, Mohaed Aine Fakhfakh 3, and afik Neji 4 1 Departent of Electrical Engineering, University of Sfax, oez.ayadi@enis.rnu.tn 2 Departent of Electrical Engineering, University of Sfax, hana@alinto.co 3 Departent of Electrical Engineering, University of Sfax, fakhfakhaine@yahoo.fr 4 Departent of Electrical Engineering, University of Sfax, rafik.neji@enis.rnu.tn Abstract Heat transfer is the science that seeks to predict the energy transfer that takes place between aterial bodies as a result of a teperature difference. When designing an electric otor, the study of heat transfer is as iportant as electroagnetic and echanical design. However, due to its three diensional nature, it is generally considered to be ore difficult than the prediction of the electroagnetic behaviour. For this reason, and the fact that the ajority of designers have an electrical rather than echanical background, theral analysis is usually not given as uch ephasis as the electroagnetic design. This paper presents the theral odel siplified of Peranent Magnet Synchronous Motor (PMSM) with radial flux for electric vehicle (EV) application. The theral design technique used is the analytical luped circuit. The equivalent circuit of the otor is ipleented and siulated with MATLAB siulator. Siulations by Motor-AD software were ade in order to shows the accuracy of the proposed theral odel. Keywords theral analysis, otor-ad, PMSM, luped circuit, flux radial 1. INTODUTION Heat transfer is the science that seeks to predict the energy transfer that takes place between aterial bodies as a result of a teperature difference. The theral anageent of the otor in a hybrid electric vehicle is iportant because the electrical insulation has a teperature liit, and also because the teperature of the otor affects its efficiency. Indeed, the theral odeling reains a very coplex proble by the diversity of heat exchange which conditions the general behavior of the otor. An accurate siulationon of the theral behaviour of the otor within the power train is therefore an iportant aspect of designing an appropriate cooling syste and strategy. An approach consists in working out a theral odel of equivalent luped circuit on the basis of analogy between electric agnitude and theral agnitude: the power sources correspond to the heat sources, the currents with the heat flows and the potential differences to the differences in teperatures [haieb et al., 2010; Fakhfakh et al., 2008]. In this paper we prensent first the geoetry of Peranent Magnet Synchronous Motor studied. In the second part of the paper, an advanced theral odel siplified is proposed. This odel represented by an equivalent electrical circuit which sweet well with circuit siulators where electrical behavior are studied. In the third part of the paper, siulations by Motor- AD and by theral odel are perfored in order to validate the proposed advanced odel. The final section concerns the otor behavior in the case of pulsed losses. Discussion about the theral odel accuracy is presented. 2. Geoetry of the otor studied Figure 1 shows the geoetry of the PMSM design used in this study. The design is a peranent agnet, Magnet 1,24 c 4,2 c 23,5 8,4 12,25 c 14,6 c Stator yoke 1,7 c 0,002 c 16,3 c oil 19 c Fig. 1 Studied geoetry of PMSM arter 1433

2 M. Ayadi et al.: Siplified Theral Model of a adial Flux Motor for Electric Vehicle Application concentrated winding, opened ot, radial flux and sinusoidal wave-for [Tounsi et al., 2004; Neji et al., 2005]. This sinusoidal wave-for is characterized by pairs pole nuber (p = 5). The phase resistance is given by the forula: NsphLsph S c Different operating losses generated in various regions are calculated accordingly and for heat sources in the theral analysis. opper losses are a function of teperature as the winding resistance is teperature dependent [Tounsi et al., 2003]. The ot height is given by the forula: 2I pnsph g g hs 2N K A 2 2 t fu ws The weight of stator yoke W sy and teeth W t are given by respectively: A wt g g Wt Nt hs ld (3) g g Wsy hs tsy hs ld (4) 2 2 The weight of rotor yoke is obtained by forula: g g Wry t t try ld (5) 2 2 The weight of the copper is: g hs I p Wc 32l 4Aws Nsph dc (6) 2 The weight of the agnet is: theral circuit in the steady state consists of theral resistances and heat sources connected between otor coponent nodes [hin et al., 2003; Staton et al., 2003; Staton et al., 2001; André et al., 2007; Wen et al., 2007]. For transient analysis, the heat/theral capacitances are used additionally to take into account the change in internal energy of the body with tie. Theral resistances for conduction and convection can be obtained by forula [Boglietti et al., 2009]: condu conve l ( K / W ) (8) Ak 1 ( K / W ) (9) A h c The heat capacitance is defined as: V c ( Ws / K) (10) Figure 2 presents the scheatic diagra of a transient state theral network of a PMSM. As described earlier, the theral resistance values are autoatically calculated fro otor diensions and aterial data. The accuracy of the calculation is dependent on knowledge of the various theral contact resistances between coponents within the otor, e.g. ot-liner to laination and laination to housing interface. Figure 3 shows a siplified stator for the theral study. The theral resistances are calculated along the radial direction. The i radius are calculated fro diensions of otor. W g g W t l 2 p d (7) = 4 5 =6 ooling syste 3. Luped-circuit analysis The theral odel is based upon luped-circuit analysis. It represents the theral probles by using the theral networks, analogous to electrical circuits. The oil Isolating Stator yoke arter Fig. 3 Siplified stator for the theral study coil T iso iso-yo j yo-ca co T iso T yo ca T ca yo f ra ra P j co iso ca P f T ref Fig. 2 Theral odel siplified of the otor 1434

3 Journal of Asian Electric Vehicles, Volue 8, Nuber 2, Deceber 2010 With: 1 = 2 = 1 + hs 3 = = 3 (11) 5 = 4 + tsy 6 = 5 7 = The sources of heat in this odel correspond respectively to the copper losses (P j ) and iron losses (P f ) in the stator. The variables T i correspond to the teperatures in various points of the otor. The expressions of theral resistances result fro the resolution of the equation of heat at the borders of the fields. coil : represents the coil theral resistance (K/W). This resistance is given by following equation: coil ln 4lc (12) The isolating theral resistance ( iso ) is given by following equation (K/W): iso 3 ln 2 2l i (13) The theral resistance of contact between isolating and stator yoke ( iso-yo ) is given by (K/W): iso yo r1 2l 3 (14) j : Theral resistance of stator yoke (K/W), is given by forula: j 5 ln 4 2l yo (15) f : represents the isolating theral represent the theral resistance of conduction of heat in the iron yoke (K/W), is given by: f ln 4l yo (16) yo-ca : represents the theral resistance between stator yoke and the carter (K/W). This resistance is given by following equation: yoca r2 2l 5 (17) ca : represent the theral resistance of carter (K/W). This resistance is given by following equation: ca 7 ln 6 2l ca (18) The expressions of the heat capacities are given by: Heat capacity of coil (J.K co Wc pco (19) N Heat capacity of isolating (J.K iso iso Viso piso (20) 2N Heat capacity of stator yoke (J.K yo Wsy pf (21) 2N Heat carter capacity (J.K ca alal 2 l 7 6 (22) 2N ra and rd : theral resistance and capacity of the cooling syste respectively. 4. Machine Model in Motor-AD Motor-AD is a coercial software package dedicated to the optiization of otor cooling. Its solver is based on theral luped circuit analysis. This provides near instantaneous calculations speeds allowing what-if scenarios to be run in real tie. The user inputs geoetric data for the design they wish to siulate using the graphical radial and cross-section editors. The otor PMSM represented in Figure 1 is ipleented in the Motor-AD software [Motor-AD v3.1, 2006]. The cross-section and axial views in Motor-AD are shown in Figures 4 and 5. Fig. 4 ross-section showing fining fro Motor-AD 1435

4 M. Ayadi et al.: Siplified Theral Model of a adial Flux Motor for Electric Vehicle Application oil teperature (T co ) Stator yoke teperature (Tyo) Fig. 5 Axial section 5. esults and discussion The theral odel shown in Figure 2 is ipleented in MATLAB siulator [MATLAB, 2002] in order to estiate the different teperatures at any part of the otor. In order to shows the good accuracy of the proposed odel, siulations by Motor-AD software are perfored in static and dynaic conditions. 5.1 Static behaviour of the proposed theral odel Figure 6 show the evolution of the coil teperature and stator yoke teperature in the otor as a function of the copper losses and the iron losses injected in the otor. The abient teperature is fixed at 40 degrees elsius. These results are obtained by the otor-ad and by the proposed odel. Fig. 7 Evolution of the coil teperature and stator yoke teperature in the otor as a function of ra (abient air = 40, P j = 200 W and P f = 60W) (: obtained by theral odel and : obtained by otor- AD) 5.2 Transient analysis To verify the accuracy of the theral odel in the transient state, copper losses and the iron losses injected in the otor Figure 8 shows the transient theral responses at the coil teperature and stator yoke teperature in the otor when copper losses and the iron losses is equal to 200 W and 60 W respectively. These results are obtained by the theral odel proposed and the otor- AD software considered as a reference. ra ( /W) oil teperature (T co ) P j /P f = 3,33 oil teperature (T co ) Stator yoke teperature (T yo ) Stator yoke teperature (Tyo) opper losses P j (W) Fig. 6 Evolution of the coil teperature and stator yoke teperature in the otor as a function of copper losses injected in the otor (abient air = 40 ) (: obtained by theral odel and : obtained by otor- AD) Figure 7 shows the evolution of the coil teperature and stator yoke teperature in the otor as a function of the conditions cooling syste ( rd ). A good accuracy is noted between the different results, this iplies that the theral odel is an accurate odel for static theral analysis. Fig. 8 Evolutions of the coil teperature and stator yoke teperature (: obtained by theral odel and : obtained by otor- AD) (P j = 200 W, P f = 60 W and ra = K/W) Figure 9 shows the transient theral responses at the coil teperature, stator yoke teperature and carter teperature in the otor when copper losses and the iron losses is equal to 500 W and 100 W respectively. These results are obtained by the theral odel proposed and the otor-ad software considered as a reference. A good accuracy is noticed between the theral odel and the results obtained by otor-ad software. 1436

5 Journal of Asian Electric Vehicles, Volue 8, Nuber 2, Deceber 2010 oil teperature (T co ) Stator yoke teperature (Tyo) Fig. 9 Evolutions of the coil teperature and stator yoke teperature (: obtained by theral odel and : obtained by otor- AD) (P j = 500 W, P f = 100 W and ra = 0.04 K/W) So, transient theral behavior of the proposed odel is correct and the introduced error is not iportant. We notice that the siulation cost of the proposed theral odel is very sall copared to the siulation cost of the otor-ad. A PU-cost ratio of (10 4 ) is registered between the two siulations when they are perfored with a Pentiu processor. 5.3 Theral behavior of the otor in the case of pulsed losses Soe recent technological approaches in traction application are of interest. With a growing awareness of electronic and acoustic noise in the consuer environent, anufacturers are beginning to raise the operating frequency of devices fro a few KHz to above 10 KHz. The duty factor is a fraction of the cycle period spent t on at peak power, T and the frequency as the inverse the cycle period tie f 1. To predict the pulse T operation characteristics, these definition are used as shown in Figure 10. Fig. 11 Transient theral coil (T co ) teperature evolution (: obtained by theral odel and : obtained by otor- AD) (P jax = 600 W, P fax =180 W, a = 0,5 and ra = 0.04 K/W) applying the pulse train sketched in Figure 10. A good accuracy is noticed between the theral odel and the Motor-AD siulations. So, transient theral behavior of the proposed odel is correct and the introduced error is not iportant. We notice that the siulation cost of the proposed theral odel is very sall copared to the siulation cost of the otor- AD. A PU-cost ratio of (10 4 ) is registered between the two siulations when they are perfored with a Pentiu processor. The otor is running at a repeated operation periods. Each period consist of one part with constant power. The operation period is uch shorter that the theral equilibriu is not reached. The copper losses and the iron losses are injected into the theral odel is show in Figure 12. Figure 13 shows the transient theral coil (T co ) teperature evolution and the transient theral stator yoke (T yo ) teperature evolution obtained by the advanced odel. Losses (W) P j ax P j P f Power (in W) P f ax t ON T Fig. 10 The wavefor sketch of pulsed power losses injected in the otor Figure 11 shows the transient theral coil (T co ) teperature evolution obtained by the advanced odel and by the Motor-AD. These results are obtained by Fig. 12 opper losses and iron losses injected into the theral odel 5.4 Theral behavior of the otor in the case of ission circulation For interittent operation a ission of circulation is 1437

6 M. Ayadi et al.: Siplified Theral Model of a adial Flux Motor for Electric Vehicle Application (T co ) (T co ) (T yo ) (T yo ) used. The Figures 14 and 15 illustrate the losses in the channel of traction on a ission of circulation. The copper losses and the irons losses are injected into the theral odel. Figure 16 shows the results siulated during repeating operation periods. Power (in W) Power (in W) Fig. 13 Transient theral coil (T co ) and theral stator yoke (T yo ) teperature evolution ( ra = 1K/W) Fig. 14 opper losses injected in the theral odel Fig. 15 Irons losses injected in the theral odel 6. onclusion The theral analysis of peranent agnet synchronous otor is presented. The luped circuit approach Fig. 16 Transient theral coil (T co ) and theral stator yoke (T yo ) teperature evolution ( ra = 1 K/W) is eployed in this investigation. The proposed odel is copatible with circuit siulators. Siulations by Motor-AD software perfored in order to study the variations of the teperature at any part of the otor, according to the copper losses and the iron losses injected in the otor and the boundary conditions at the cooling systes. We not, that this ethod can be applied to all other type of otor. We notice that the siulation cost of the proposed theral odel is very sall copared to the siulation cost of the otor-ad. A PU-cost ratio of (10 4 ) is registered between the two siulations when they are perfored with a Pentiu processor. eferences André, M. S., X. M. López-Fernández, and A. J. Marques ardoso, Theral behavior of a threephase induction otor fed by a fault-tolerant voltage source inverter, IEEE Transaction on Industry Applications, Vol. 43, No. 3, , Boglietti, A., A. avagnino, and. Mejuto, Evolution and odern approaches for theral analysis of electrical achines, IEEE Transactions on Industrial Electronics, Vol. 56, No. 3, , hin, Y. K., E. Nordlund, and E. A Staton, Theral analysis: Luped circuit odel and finite eleent analysis, Proceesings of Sixth International Power Engineering onference, 952, haieb, M., N. B. Hadj, J. K. Kaoun, and. Neji, A coparative study of tow peranent agnet otor structures with interior and exterior rotor, Journal of Asian Electric Vehicles, Vol. 8, No. 1, , Fakhfakh, M. A., M. H. Kase, S. Tounsi, and. Neji, Theral analysis of a peranent agnet synchronous otor for electric vehicles, Journal of Asian Electric Vehicles, Vol. 6, No. 2, ,

7 Journal of Asian Electric Vehicles, Volue 8, Nuber 2, Deceber 2010 Motor-AD v3.1, software anual, MATLAB, MATLAB 6p5 Siulator Data Book, Neji,., S. Tounsi, and F. Sellai, Optiization and design for a radial flux peranent agnet otor for electric vehicle, Journal of Electrical Systes, Vol. 1, No. 4, 47-68, Staton, D. A., A. Boglietti, and A. avagnino, Solving the ore difficult aspects of electric otor theral analysis, Proceesings of IEEE IEMD, 47-55, Staton, D. A., Theral coputer aided design: Advancing the revolution in copact otors, Proceedings of IEEE IEMD, 858, Tounsi, S.,. Neji, and F. Sellai, Modélisation des pertes dans la chaîne de traction du véhicule electrique, Proceedings of TGE, , Tounsi, S.,. Neji, F. Sellai, Design of a radial flux peranent agnet otor for electric vehicle, Proceeding of EPE, D-o, Wen, X., W. Hu1, T. Fan, and J. Liu, Lifetie odel research of otor drive syste for electric vehicles, Proceedings of International onference on Electrical Machines and Systes, , (eceived October 8, 2010; accepted Deceber 18, 2010) Appendix Noenclature: r: Density N sph : Nuber of spire per phase L sph : Length of spire per phase S c : opper area I p : Pick current feeding the otor K fu : oefficient of filling ot D c : Density of the copper N t : Nuber of teeth d: urrent density A ws : Slot angular width : Bore radius g: Air-gap thickness A wt : Tooth angular width l : Motor length d: Density of the etal sheet T sy : Stator yoke height t : Magnet height t ry : otor yoke height d : Density of agnet l c : opper theral conductivity l t : Isolation theral conductivity r 1 : Theral resistance of surface contact between isolating aterial and stator yoke l yo : Iron theral conductivity r 2 : Theral resistance of surface contact between stator yoke and carter l ca : arter theral conductivity pco : opper assive heat capacity N : Nuber total of spire r iso : Isolating density V iso : Isolating volue piso : Isolating assive heat capacity pf : Iron assive heat capacity r al : Aluinu density a : Aluinu assive heat capacity l: Distance between the point asses A: Interface area k: Heat conductivity A c : ooling cross section h: onvection coefficient V: Material volue c: Heat capacity of the aterial 1439