IRON LOSSES EVALUATION IN HIGH SPEED DRIVES. G. D. Kalokiris 1, P. S. Georgilakis 2 and A. G. Kladas 1. (

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1 IRON LOSSES EVALUATION IN HIGH SPEED DRIVES G. D. Klokiris 1, P. S. Georgilkis 2 nd A. G. Klds 1 1 Ntionl Technicl University of Athens, GR-1578, Greece (e-mil: kldsel@centrl.ntu.gr) 2 Technicl University of Crete, GR-731, Chni, Greece (e-mil: pgeorg@dpem.tuc.gr) ABSTRACT The pper presents electricl mchine design considertions introduced y exploiting new mgnetic mteril chrcteristics. The mterils considered re morphous lloy rions s well s Neodymium lloy permnent mgnets involving very low eddy current losses. Such dvnce mterils enle electric mchine opertion t higher frequencies compred with the stndrd iron lmintions used in the trditionl mgnetic circuit construction nd provide etter efficiently. Keywords: Finite element method, permnent mgnets, rotor skew, design methodology. 1. INTRODUCTION A methodology for electricl mchine modeling enling to exploit new mgnetic mteril chrcteristics re presented y the uthors. The mterils considered re thin mgnetic lmintions, morphous lloy rions s well s Neodymium lloy permnent mgnets involving very low eddy current losses s mentioned in (1)-(3). Such mterils enle electric mchine opertion t high frequencies compred with the stndrd iron lmintions used in the trditionl mgnetic circuit construction. Moreover, simpler winding configurtions re dopted, tking into considertion tht there will e power electronics converter ensuring the connection of the mchine to the electric grid (4)-(6). The study of synchronous nd permnent mgnet mchines sed on such mterils is undertken in three steps. In first step the typicl design procedure is conveniently dpted in order to include the new mgnetic mteril properties. In second the designed mchine chrcteristics re checked y mens of detiled field clcultion through finite element modeling ssocited to sensitivity nlysis techniques. In third step prototype is constructed in order to vlidte the mchine performnce. Low losses nd high volumic power ssocited with high speed nd converter mchine opertion re the min dvntges of such pplictions (7)-(1). 2. CALCULATION METHODOLOGY The proposed mchine design procedure involves two steps. In first step stndrd design methodology is used for preliminry design. In second step the method of finite elements is implemented to clculte the mchine efficiency nd performnce. Finlly, prototypes re constructed in order to vlidte nd compre the simulted mchine chrcteristics to the corresponding experimentl results (11)-(12). In cse of vrile reluctnce mchines, the electromechnicl conversion is sed on the mgnetic energy exchnges in the mgnetic circuit with the vrition of reluctnce with rotor position nd of excittion. In generl, the stored energy in the mgnetic circuit is mximized when the reluctnce is minimum (conjunction) nd is minimized when the reluctnce is mximum (opposition), while the pproprite current vrition ensures pproprite torque. The studied structure of mchines is multidiscoidl (Fig. 1) with discs composed from non-mgnetic resins where convenient ferromgnetic prts re emedded (1). The method of finite elements, is sed on discretistion of the solution domin into smll regions. In mgnetosttic prolems the unknown quntity is usully the mgnetic vector potentil A, nd is pproximted y mens of polynomil shpe functions. In two dimensionl cses tringulr elements cn esily e dpted to complex configurtions nd first order elements exhiit dvntges in iron sturtion representtion (13). The size of elements must e smll enough to provide sufficient ccurcy. In this wy the differentil equtions of the continuous prolem cn e trnsformed into system of lgeric equtions for the discrete prolem. The prcticl prolems necessitte usully severl tenths of thousnds of unknowns. However, pproprite numericl techniques hve een developed, enling to otin the solution of such systems within resonle time, even when personl computers re used. It should e mentioned tht the 3D prolems require considerly higher computtionl resources thn the 2D ones. In the present pper the 2D finite element model dopted, involves vector potentil formultion, while the mgnetic flux Φ m per pole cn e clculted s follows:

2 Figure 1. Multidiscoidl Vrile Reluctnce Mchine structure studied. : sttor prt : rotor prt ( 2 A ) Φ = B ds = A dl L (1) m S 1 C 1 where L is the length of the mgnetic circuit in m, A is the mgnetic vector potentil, A gp is the vector potentil vlue in the middle of the ir-gp, B is the flux density in Tesl, S 1 is the cross-sectionl re norml to the direction of flux in m 2 nd C 1 is the contour surrounding the surfce S 1 in m. The electromotive force t no lod cn e clculted s follows: d Φ m E = - (2) dt The vlue of the voltge of the mchine operted s genertor under lod conditions cn e clculted y reltion (3): V = E - RI - jl ω Ι (3) where V is the voltge on sttor windings in V, E is the electromotive force t no lod in V, R is the sttor resistnce in Ω, L σ is the sttor lekge inductnce in H, ω is the rotor ngulr velocity in rd/sec nd I is the sttor current in A. Then the mgnetic flux nd electromotive forces cn e derived y using equtions (1) nd (2). Finlly, we clculte the iron losses for this mchine t the low nd high frequency opertion y the eqution: σ gp c Figure 2. Flux distriution in the two dimensionl vrile reluctnce mchine configurtion for low excittion. : Conjunction : Intermedite position c: Opposition P =P -P iron totl Cu where P =P +P Cu Cu rotor Cu sttor 3. RESULTS AND DISCUSSION A. Vrile Reluctnce Mchines (4) The vrile reluctnce mchine considered is three phse comprising three sttor discs nd two rotor discs for ech phse mounted on the sme trnsxle, s shown in Fig. 1. Ech disc comprises 24 ferromgnetic teeth while ech phse hs pproprite flux return core prts. The mgnetic field nlysis hs een performed in two dimensionl Crtesin pproximtion y considering peripherl cutwy of the ctive prt of the mchine s shown in Fig.2. This figure shows the mgnetic field density distriution for different rotor

3 conjunction opposition Figure 4. Reduced torque per excittion in the vrile reluctnce mchine with rotor position. c Figure 3. Flux distriution in the two dimensionl vrile reluctnce mchine configurtion for high excittion. : Conjunction : Intermedite position c: Opposition positions in cse of low excittion current. The mgnetic circuit in this cse is unsturted. The sme results for high excittion current re shown in Fig. 3. It my e noted tht the teeth re highly sturted in this cse, especilly in the corners for intermedite positions (Fig. 3). The reduced torque per excittion cn e clculted y convenient rdil extrpoltion of the two dimensionl results nd the otined results re shown in Fig. 4. This figure compres the numericl (continuous line) results with the mesured ones (dshed line). The two curves vritions with rotor position re similr ut the mesured results re somewht smller due to the fct the return flux circuits (3D feture) hs een neglected in the two dimensionl representtion. An importnt prt of losses in vrile reluctnce mchines is due to hysterisis effect nd in order to ccount for this n pproprite Preisch-Neel model hs een developed for the iron lmintions used (14). In order to ssocite pproprite weights to this model the experimentl hysterisis curves otined for the iron lmintions used hve een considered, shown in Fig. 5. In vrious points of the ferromgnetic teeth of the vrile reluctnce mchine different hysterisis curves re otined, which vry lso with the excittion imposed. One chrcteristic of the mchine tested, involving unidirectionl excittion, is tht minor hysterisis curves re otined s shown in Figs. 6 nd 7. The clculted curves in these figures hve een otined y mking two importnt ssumptions: the field density vlues re computed through the two dimensionl nlysis presented (end mgnetic circuit effects s well s return flux pths re neglected) while eddy currents in iron lmintions ws supposed to hve negligile effects on locl field vlue vritions (sttic field nlysis). Moreover, the Preisch-Neel model dopted ignores frequency vrition effects nd ssumes unidirectionl flux density vritions (rottionl field effects re not ccounted). Figure 5. Experimentl hysterisis curves otined with direct current excittion for the.35 mm width iron lmintions used.

4 Figure 8. No lod voltge wveform of permnent mgnet mchine (simultion) Figure 6. Unidirectionl excittion of the vrile reluctnce mchine nd minor hysterisis curves clculted. Figure 9. No lod voltge wveform of permnent mgnet mchine (mesurement) 3 2 Figure 7. Minor hysterisis curves clculted in vrious points of the teeth of the vrile reluctnce mchine. Phse Voltge (V) B. Permnent Mgnet Mchines The cse of permnent mgnet mchine hs een considered. The mchine designed hs een checked through 2.5 kw prototype which hs een connected to n pproprite power electronics converter. The irgp width hs een chosen 1 mm while multipole peri-pherl mchine structure hs een dopted. The geometry of the permnent mgnet mchine is given in (6) providing lso the mesh employed for the two dimensionl finite element progrm of the mchine involving, pproximtely 21 nodes 4 tringulr elements. In first step the no lod operting conditions hve een exmined. The corresponding simulted voltge wveform is shown in Fig. 8 while the mesured one is given in Fig. 9, respectively. In these figures good greement etween the simulted nd mesured results cn e oserved. The simultion results concerning full lod voltge of synchronous genertor re presented in Fig Angle (degrees) Figure 1. Full lod voltge wveform of permnent mgnet mchine (simultion) Figure 11. Full lod voltge wveform of permnent mgnet mchine (mesurement) Figure 11 gives the mesured results under the sme operting conditions. A good greement cn e oserved in these figures etween the simulted nd mesured results lso in the cse of full lod.

5 C. Asynchronous Mchines where F t is the totl circumferentil tngentil force in Newton nd r g is the middle ir-gp rdius in meters. The Mxwell s stress tensor is clculted y reltion (6): Moreover, mesurements were relized for n synchronous motor, which ws supplied y n inverter with vrile frequency. The motor is three phse, 4-pole, mchine supplied t frequency of 4 Hz, t voltge of 28 V while the nominl, speed is 1.8 rpm. The motor ws tested under no lod nd low lod operting conditions, for vrious frequencies. Fig. 12 shows the field distriution in the mchine supplied t fundmentl frequency of 3 Hz, while Fig. 12 gives the field distriution t the switching frequency of 1 khz. 1 Ft = B n Β t dl L µ C where B n nd B t re the norml nd tngentil mgnetic flux density components, respectively, to the integrtion surfce of ir-gp C in Tesl, µ is the permeility of ir nd L is the ctive prt of the mchine. 4 voltge (V) f = 3 Hz (6) 2 15 f=3 Hz current (A) Figure 12. Simulted field distriution in the mchine under low lod conditions : fundmentl supply frequency of 3Hz : switching frequency of 1 khz Fig. 13 presents the respective mesured phse voltge nd current time vritions. Fig. 14 shows the field distriution in the mchine supplied t fundmentl frequency of 1 Hz, while Fig. 15 presents the respective mesured phse voltge nd current time vritions t the switching frequency of 1 khz. Tle I presents the mesured nd simultion results under no lod conditions with switching frequency of 1 khz. Tle II presents the sme results under low lod conditions. Tle III presents the results relted to switching frequency of 1 khz. The simulted torque T s is clculted y the reltion: T = F r (5) s t g Figure 13. Mesured supply quntities in the mchine for supply frequency of 3 Hz, under low lod conditions : phse voltge time vrition : phse current time vrition Figure 14. Simulted field distriution in the mchine, fundmentl supply frequency of 1 Hz under low-lod conditions

6 In Tles I, II nd III good greement etween the mesured nd simulted results for oth voltge nd torque vlues cn e oserved. voltge (V) (A) current Tle I. Mesured nd simultion results under no lod conditions nd f s = 1 khz f = 1 Hz f = 1 Hz Figure 15. Mesured supply quntities in the mchine for supply frequency of 1 Hz under low lod conditions : phse voltge time vrition : phse current time vrition Tle II. Mesured nd simultion results under low lod conditions nd f s = 1 khz Tle III. Mesured nd simultion results under low lod conditions nd f s = 1 khz 1 4. CONCLUSIONS In this pper, methodologies re proposed in order to evlute the iron losses in vrious types of electricl mchines fvored for high speed drive pplictions. Electricl mchine opertion hs een investigted y using the finite element method for the mchine nlysis nd verified y mesurements. Moreover, the low cost involved mkes such drives ttrctive rivls of the conventionl ones. 5. REFERENCES 1. A. Klds, Etude du couple et des pertes fer d une mchine reluctnce vrile, report DEA, Universites Pris VI nd Pris XI, C. Mrchnd, Z. Ren, Z. nd A. Rzek, Torque optimiztion of uried permnent mgnet synchronous mchine y geometric modifiction using FEM, in Proceedings EMF 94, Leuven, pp , A. To, T. Lipo, "Generic torque mximizing design methodology of surfce permnent mgnet Vernier mchine", IEEE Trns. on Ind. Appl., Vol. 36, no 6, pp , G. Tsekours, S. Kirtzis, A. Klds, J. Tegopoulos, "Neurl Network Approch compred to Sensitivity Anlysis sed on Finite Element Technique for Optimiztion of Permnent Mgnet Genertors", IEEE Trns. Mgn., Vol. 37, no 5/1, pp , M. A. Alhmdi, N. Demerdsh "Modeling nd experimentl verifiction of the performnce of skew mounted permnent mgnet rushless dc motor drive with prmeters computed from 3D FE mgnetic field solutions", IEEE Trns. on Energy Conversion, Vol. 9, no 1, pp. 1-35, G. D. Klokiris, A. G. Klds: "New mgnetic mteril impct in electric mchine design: high speed opertion nd reduction of losses", Journl of Sensors nd Actutors A: Physicl (Elsevier), vol.16, no 1/3, pp G. D. Klokiris, A. G. Klds, J. A. Tegopoulos: "Permnent Mgnet Mchine Optimiztion y using FEM nd Sensitivity Anlysis Techniques", Optimistion nd Inverse Prolems in Electromgnetism, Kluwer Acdemic Pulishers, pp , ISBN G. D. Klokiris, A. G. Klds, J. A. Tegopoulos: 2D nd 3D finite element design of skewed mounted permnent mgnet synchronous genertors, Proceedings of the 3 rd Jpnese-Mediterrnen Workshop on Applied Electromgnetic Engineering for Mgnetic nd Superconducting Mterils, ccepted for puliction in the Journl of Mteril Processing Technology, Elsevier. 9. M.R. Duois, H. Polinder, nd J.A. Ferreir, "Contriution of Permnent-Mgnet Volume Elements to No-Lod Voltge in Mchines", IEEE Trnsctions on Mgnetics, vol. 39/3, 23, pp P. Dziwniel, B. Boulem, F. Piriou, J.P. Ducreux, nd P. Thoms "Comprison etween two Approches to Model Induction Mchines with Skewed Slots", IEEE Trnsctions on Mgnetics, vol. 36/4, 2, pp G. D. Klokiris, Th. Kefls, A. G. Klds: Specil ir-gp element for 2D FEM nlysis of electricl mchines ccounting for rotor skew, Eleventh Biennil IEEE Conference on Electromgnetic Field Computtion (CEFC 24), Seoul, Kore, June 6-9, 24, pp G.D. Klokiris, A.G. Klds: High speed mchines using dvnced mgnetic mterils nlyzed y pproprite finite element models, IASME Trnsctions, Vol. 1, no 2, April 24, pp H. De Gersem, K. Hmeyer, T. Weilnd, "Skew interfce conditions in 2-D finite-element mchine models", IEEE Trnsctions on Mgnetics, vol.39/3, 23, pp G. Friedmn, I.D. Myergoyz, Hysteretic energy losses in medi descried y vector Preisch model, IEEE Trnsctions on Mgnetics, Vol. 34, no 4, pp , July 1998.