High speed mchines using dvnced mgnetic mterils nlyzed y pproprite finite element models G. D. KALOKIRIS, A. G. KLADAS Lortory of Electricl Mchines nd Power Electronics, Electric Power Division Fculty of Electricl nd Computer Engineering Ntionl Technicl University of Athens 9, Heroon Polytechneiou Street, Athens 15780 GREECE Astrct: - The pper presents methodology for electricl mchine modeling enling to exploit new mgnetic mteril chrcteristics. The proposed models enle nlysis of high speed electricl mchines, fvored in recent mrine pplictions. The mterils considered re thin mgnetic lmintions, morphous lloy rions s well s Neodymium lloy permnent mgnets involving very low eddy current losses. 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 instlltion. Key-Words: - Advnced mgnetic mterils, finite element method, induction motor, iron losses. 1 Introduction Recent technologicl trends fvor All Electric ship strtegy development in mrine engineering pplictions. This strtegy, envisges the use of long life, fuel efficient, dvnced cycle mrine gs turine lterntor sets in n integrted electric popultion system driving pproprite genertors, [1],[2]. In this pper, 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 [3],[4]. In second the designed mchine chrcteristics re checked y mens of detiled field clcultion through finite element modeling ssocited to sensitivity nlysis techniques [5]. In third step prototype is constructed in order to vlidte the mchine performnce [6],[7]. Low losses nd high volumic power ssocited with high speed nd converter mchine opertion re the min dvntges of such pplictions [8],[9]. 2 Finite Element Modeling 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. 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: ( 2A ) Φ = B ds = A dl l (1) m S 1 C 1 where l 0 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 flow in m 2 nd C 1 is gp 0 1
the contour surrounding the surfce S 1 in m. The electromotive force t no lod cn e clculted s follows: dφm E = - (2) dt c Fig. 1 One pole prt of the permnent mgnet mchine constructed (unskewed rotor) : Employed tringulr mesh : Field distriution t no lod c: Mgnetic field distriution t full lod l R = ρ (4) The vlue of voltge t full lod cn e clculted S y reltion (3): V = E - RI - jlσω 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). Furthermore, the totl resistnce of sttor winding cn e clculted y the following reltions: where ρ is the electric resistivity of copper, l the winding totl length nd s the conductor cross section. The winding length l cn e estimted from reltion (5): l=2*(l x +l p )* N w *P (5) where: l x : mchine's xil length (m) l p : polr step length (m) N w : totl numer of series connected turns irgp flux density distriution t the middle of the mchine 0,8 2D FEM model 0,7 0,6 Flux Density in Tesl 0,5 0,4 0,3 0,2 0,1 3D FEM model unskewed rotor 3D FEM model skewed rotor 0 0 20 40 60 80 100 120 140 160 180 Electricl Degrees 2
Fig. 2 Flux density distriution in the ir gp in the middle of the rotor (3D & 2D fem simultion) Finlly, we clculte the iron losses for this mchine t the low nd high frequency opertion y the eqution: P iron=ptotl-pcu (6) where P Cu=P Cu rotor+pcu sttor 3 Results nd Discussion The permnent mgnet mchine nlysis procedure descried previously hs een pplied to construct 2.5 kw, 26 rd/sec genertor to e connected to six pulse diode rectifier ridge. The ir-gp width hs een chosen 1 mm while multipole peripherl mchine structure hs een dopted (Fig. 1). The geometry of the permnent mgnet mchine is shown in Fig. 1 giving lso the mesh employed for the two dimensionl finite element progrm of the mchine involving pproximtely 2100 nodes 4000 tringulr elements. The corresponding mgnetic field distriution t no lod is shown in Fig. 1. The field distriution t full lod is given in Fig. 1c. In these figures the disymmetry cused in the field distriution y the loding current cn e oserved. Figure 2 gives comprison of the simulted flux density distriution in the middle of the ir-gp with nd without rotor skew y 3D FEM simultion nd the sme distriution otined y 2D simultion. From the results, it comes up tht the mgnitude of mgnetic flux density is less with rotor skew. In fig. 3 is presented the mgnitude of mgnetic flux density in the ir gp of the mchine without rotor skew y using 3D nlysis while in fig. 3 is presented the sme nlysis with rotor skew. The sme remrk tht the mgnitude of mgnetic flux density is less with rotor skew cn eqully e oserved. Fig. 3 No lod distriution of ir-gp rdil mgnetic flux density (3D fem simultion) : without rotor skew : with rotor skew 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 400 Hz, t voltge of 208 V while the nominl, speed is 10.800 rpm. The motor ws tested under no lod nd low lod operting conditions, for vrious frequencies. The test results re presented in tle 1. Figure 4 shows the field distriution in the mchine supplied t fundmentl frequency of 300 Hz, while Fig. 4 gives the field distriution t the switching frequency of 11 khz. Figure 5 presents the respective mesured phse voltge nd current time vritions. In tle 2 re given the simulted results for motor torque, which re in good greement with the experimentl ones. The experimentl nd simulted results for the resistnce of the sttor windings re presented in tle 3. Moreover, the iron losses hve een clculted nd the results of this investigtion re tulted in tle 4. From figure 6, showing the respective mesured voltge nd current spectr, the totl power nd the iron losses t the switching frequency cn e determined. 3
Fig. 4: Simulted field distriution in the mchine : fundmentl supply frequency of 300Hz, t low-lod : switching frequency of 11 khz, t low-lod Fig. 5: Mesured supply quntities in the mchine for supply frequency of 300Hz, semi-lod condition : phse voltge time vrition : phse current time vrition Tle 1: Test results for the 4-pole synchronous motor Tle 2: Test nd simulted results for the motor torque Tle 3: Test nd simulted results of the resistnce of sttor winding Fig. 6 Mesured frequency spectr of the supply t fundmentl frequency of 300 Hz nd switching frequency of 11 khz under low-lod conditions : Frequency spectrum of voltge : Frequency spectrum of current 4
f (Hz) P Cu rotor P Cu sttor P totl P iron 300 109 39 405 257 semilod 250 77 32 279 147 50 5 11 15 170 300 53 19 219 75 no 250 37 15 127 lod 50 2 4 2 Tle 4: Results of iron losses of the motor 4 Conclusion The pper proposes models for high speed electricl mchine nlysis, fvored in recent mrine engineering pplictions. 2D nd 3D finite element models hve een used nd the results presented sufficient ccurcy with the mesured ones, in permnent mgnet synchronous genertor prototype. The simultions performed hve shown tht the skew of permnent mgnets in the rotor results in reduction of the fundmentl component of the electromotive force induced ecuse of the reduction in the flux density in the ir-gp. So, the sttor current hrmonics nd torque ripple re estimted to e susequently reduced in the cse with rotor skew. Moreover, the method of finite elements cn efficiently simulte the operting chrcteristics ssocited with the fundmentl frequency of three phse synchronous high speed mchine, ut the switching frequency losses need further investigtion. Permnent Mgnet Genertors", IEEE Trns. on Mgnetics, Vol. 37, no 5/1, 2001, pp. 3618-3621. [6] 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 Trnsctions on Energy Conversion, Vol. 9, no 1, 1994, pp. 1-35. [7] 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, 1994, pp. 53-56. [8] T. Nkt, N. Tkhshi nd K. Yoned, "Numericl Anlysis of flux distriution in permnent-mgnet stepping motors", IEEE Trnsctions on Mgnetics, Vol. 14, no 5, pp. 548-550, 1978. [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, no 3, pp. 1784-1792, 2003. References: [1] S. Nishikt, A. Odk, Y. Koishikw, nd T. Ktok, "Performnce Anlysis of Shft Genertor Systems", Electricl Engineering in Jpn, Vol. 131, No. 3, 2000, pp. 1209-1216. [2] B. Wttier nd N. M. Morrish, "The development of 1-2 MW Advnce Cycle Gs Turine Alterntor for nvl use", Imrest 2003. [3] T. Higuchi, J. Oym, E. Ymd, E. Chiricozzi, F. Prsiliti nd M. Villni, Optimiztion procedure of surfce permnent mgnet synchronous motors, IEEE Trnsctions on Mgnetics, Vol. 33, no 2, 1997, pp. 1943-6. [4] A. To, T. Lipo, "Generic torque mximizing design methodology of surfce permnent mgnet Vernier mchine", IEEE Trns. on Industry Applictions, Vol. 36, no 6, 2000, pp. 1539-1546. [5] G. Tsekours, S. Kirtzis, A. Klds, J. Tegopoulos, "Neurl Network Approch compred to Sensitivity Anlysis sed on Finite Element Technique for Optimiztion of 5