[2006] IEEE. Reprinted, with permission, from [Youguang Guo1, Jianguo Zhu, Jiaxin Chen1 and Jianxun Jin, Performance Analysis of a PM Claw Pole SMC

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1 [26] IEEE. Reprinted, with perission, fro [Youguang Guo1, Jianguo Zhu, Jiaxin Chen1 and Jianxun Jin, Perforane Analysis of a P Claw Pole SC otor with Brushless DC Control Shee, Power Eletronis and otion Control Conferene, 26. IPEC 26. CES/IEEE 5th International (Volue:2 ) Aug. 26]. This aterial is posted here with perission of the IEEE. Suh perission of the IEEE does not in any way iply IEEE endorseent of any of the niversity of Tehnology, Sydney's produts or servies. Internal or personal use of this aterial is peritted. However, perission to reprint/repulish this aterial for advertising or prootional purposes or for reating new olletive works for resale or redistriution ust e otained fro the IEEE y writing to pusperissions@ieee.org. By hoosing to view this douent, you agree to all provisions of the opyright laws proteting it

2 Perforane Analysis of a P Claw Pole SC otor with Brushless DC Control Shee Youguang Guo 1, Jianguo Zhu 1, Jiaxin Chen 1,2, and Jianxun Jin 3 1 Faulty of Engineering, niversity of Tehnology, Sydney, P.O. Box 123, Broadway, NSW 27, Australia 2 College of Eletroehanial Engineering, Donghua niversity, Shanghai 251, China 3 Shool of Autoation Engineering,. of Eletroni Si. & Teh. of China, Chengdu, Sihuan 6154, China youguang@eng.uts.edu.au, joe@eng.uts.edu.au, hjiaxin@dhu.edu.n, jxjin@uest.edu.n Astrat Thanks to its unique properties, suh as isotropi agneti and theral properties and low eddy urrent loss, the soft agneti oposite (SC) aterial is suitale for appliation in eletrial ahines, espeially those with oplex strutures and three-diensional (3D) agneti fluxes. This paper presents the perforane analysis of a three-stak peranent agnet (P) law pole otor with an SC stator ore. 3D finite eleent agneti analysis and iproved forulations are applied to aurately opute the otor paraeters, suh as the ak eletrootive fore, inreental indutane, ogging torque, and ore loss. An equivalent eletrial iruit is derived to predit the otor s steady-state perforane under a rushless DC ontrol shee. Beause of the large winding indutane of this type of otors, the ontrol of the output torque and speed an e diffiult. To verify the otor ontrollaility, a atla/siulink-ased siulation odel is opiled to siulate the otor dynai and steady-state perforanes. Experients are onduted on the otor prototype, validating the theoretial oputations and analyses. Keywords-soft agneti oposite; law pole otor; rushless DC ontrol; finite eleent agneti field analysis; perforane siulation. I. INTRODCTION Copared to the lainated steels oonly used in eletrial ahines, the soft agneti oposite (SC) aterial possesses a nuer of advantages, suh as isotropi agneti and theral properties, low eddy urrent loss and relatively low total ore loss at ediu and higher frequenies, net-shape fariation proess with sooth surfae and good finish (without need of any further ahining), and prospet of very low ost ass prodution [1]. Therefore, SC aterials have a great potential for eletrial ahine appliations, espeially for those with oplex topologies and three-diensional (3D) agneti fluxes, suh as law pole and transverse flux otors [2]. Due to its powdered nature, SC is naturally agnetially isotropi, and this reates key design enefits [3]. The agneti iruits an now e designed with 3D flux paths, and different radial topologies an e exploited to ahieve high otor perforanes, for the reason that the agneti field does not have to e restrited in the two-diensional (2D) plane of lainated steels. To investigate the appliation potential of SC, a three-stak peranent agnet (P) law pole otor with an SC stator ore has een developed y taking advantage of the unique properties of the aterial, as shown in Fig. 1 [4]. In this otor, the fluxes generated y the rotor Ps and the stator windings are 3D. For exaple, the flux produed y the Ps passes the air gap and flows into the stator law poles via oth the fae and the side surfaes. The three phases of the otor are staked axially with an angular shift of 12 o eletrial fro eah other. Eah stator phase has a single oil (not shown in the figure for larity) around an SC ore, whih is olded in two halves. The outer rotor oprises a tue of ild steel with an array of agnets for eah phase ounted on the inner surfae. ild steel is used for the rotor eause the flux density in the yoke is alost onstant. The ajor diensions inlude: 94 for the outside diaeter, 93 for the ative axial length, 1. for the ain air gap, and 4.5 for the average diaeter of the airgap, et. The otor is designed to operate under a rushless DC ontrol shee, delivering a torque of 2.65 N at 18 rp. Figure 1. agnetially relevant parts of the law pole SC otor

3 Due to the opliated struture, 3D nuerial field analysis is required for aurate oputation of the otor paraeters. In this paper, the 3D agneti field finite eleent analysis (FEA) is perfored to alulate the key paraeters, suh as the winding flux, ak eletrootive fore (ef), indutane and ore losses. To predit the otor harateristis, an equivalent eletrial iruit is derived under the optial rushless DC ontrol ondition, i.e. the ak ef is in phase with the stator urrent. Generally, the law pole ahine has a large winding indutane, whih ay ause diffiulty in the ontrol of the output torque and speed. To verify the ontrollaility of the otor, espeially at high speed operation, a atla/siulink-ased odel is oplied to siulate the dynai and steady-state perforanes. The experiental results on the otor prototype validate the theoretial analyses. II. PARAETER CALCLATION BY 3D FEA A. 3D agneti Field FEA By onsidering the detailed struture and diensions of the otor and the non-linearity of ferroagneti aterials, the agneti field FEA an aurately deterine the agneti field distriution and hene the paraeters. Due to the alost agneti independene and strutural syetry etween staks, only one pole region of one stak is needed for FEA, as illustrated in Fig. 2. On the two radial oundary surfaes, the agneti salar potentials oey the half-periodial onditions as ( r, θ / 2, z) ϕ ( r, θ / 2, z) ϕ (1) where θ 18 o is the angle of one pole pith. Fig. 3 illustrates the no-load agneti flux density vetors produed y the rotor Ps. It an e seen that the ajor path of the P flux is along one of the Ps the ain air gap half of the SC law pole stator ore disk the stator yoke another half of SC law pole stator ore disk ain air gap another P and then the ild steel rotor yoke to for a losed loop. The agneti field in the arature is really oplex and SC is an ideal andidate as the ore aterial. B. Bak ef The P flux, defined as the flux linking a stator phase winding produed y the rotor Ps, an e otained fro the no-load agneti field distriution (Fig. 3). The flux wavefor is alulated y rotating the rotor agnets for one pole pith in 12 steps. As plotted in Fig. 4, this flux wavefor is alost perfetly sinusoidal versus the rotor position. When the rotor rotates, the P flux varies and an ef is indued in the stator winding. The ef frequeny depends on the rotor speed, while its wavefor is deterined y the profile of the flux versus the rotor position. The ef onstant is.2594 Vs/rad, y p φ1 K E N (2) where p2 is the nuer of poles, N 1 75 is the nuer of turns of a phase winding, and φ 1 the agnitude of the sinusoidal flux wavefor. C. Winding Indutanes The ehavior of an eletrial iruit is governed y the inreental indutane rather than the seant indutane [5]. In this paper, the phase winding inreental indutane of the law pole otor is alulated y a odified inreental energy ethod [6], whih inludes the following steps: (1) For a given rotor position θ, ondut a non-linear field analysis onsidering the saturation due to the Ps to find out the operating point of the otor, and save the inreental pereaility in eah eleent; (2) Set the reanene of Ps to zero, and ondut a linear field analysis with the saved pereailities under a pertured stator urrent exitation, Δi; (3) Find out the o-energy; and (4) Calulate the self inreental indutane y 2W ( ) (, i θ ) 11 ( i) 2 L θ (3) The utual indutane etween phase windings an e onsidered as zero due to the independent agneti iruit of eah stak. Fig. 5 shows the oputed self inreental indutane (L in ) of one phase winding at different rotor positions. For oparison, the oputed seant indutane (L se ) and the easured indutane (L ea ) y the AC voltage-urrent ethod, are also plotted in the figure. Figure 2. Region for agneti field FEA Figure 3. Plots of agneti flux density vetors at no-load Figure 4. Per turn no-load flux of a phase winding

4 D. Core Losses Figure 5. Coputed and easured indutanes The ore loss is aused not only y alternating ut also y rotational agneti fields, and should e properly onsidered in the otor design and perforane analysis [7]. In this paper, an iproved ethod is applied to predit the ore losses in the 3D flux SC otor [8]. Different forulations are used for ore loss predition with purely alternating, purely irular rotating, and elliptially rotating flux density vetors, respetively. A series of 3D FEAs are onduted to deterine the flux density lous in eah eleent when the rotor rotates. It is found that the ore loss inreases alost linearly with respet to the rotor speed, due to the doinant hysteresis loss oponent in SC. At the rated speed of 18 rp, the ore loss is alulated as 58 W at no-load, and will inrease y aout 2% at the rated load due to the effet of arature urrent. III. STEADY-STATE PERFORANCE CALCLATION BY EQIVALENT ELECTRIC CIRCIT When running in synhronous ode, the otor s steady-state perforane an e predited y the equivalent iruit odel as shown in Fig. 6, where E 1 is the indued stator ef, R 1 the stator winding resistane, ω 1 the angular frequeny, and L 1 the synhronous indutane of the phase winding. The otor is assued to operate in the optiu rushless DC ode, i.e. I 1 in phase with E 1, so that the eletroagneti power and torque an e otained y P e E 1 I 1 (4) T Pe K (5) ω e r T I 1 where ω r is the rotor speed in rad/s, K T K E is the torque onstant, and 3 is the nuer of phases. The rs value of the ak ef is deterined y E 1 K E ω r. j ω 1L 1 R1 I1 E 1 V1 Figure 6. Per-phase equivalent eletrial iruit For a given terinal voltage, V 1, the relationship etween the rotor speed and eletroagneti torque is deterined y ωr R T 1 e 2 pωrlt 1 e ) 2 2 ( + ) + ( V (6) 1 KE KT 2KT The output power, output torque, input power, and effiieny are alulated y Pout Pe PFe Pe (7) Tout P out / ωr (8) P in Pe + Pu (9) 2 P u 3I1 R1 (1) η P out / P in (11) where P Fe is the ore loss, P e the ehanial loss inluding windage and frition, and P u the opper loss. IV. PERFORANCE ANALYSIS BY A ATLAB/SILINK-BASED SILATION ODEL The large winding indutane of law pole otors has effet on the rise rate of the stator urrent, whih ay ause diffiulties in otor ontrol and liit the otor output toqrue, espeially when the otor operates at high speeds. In this paper, the output apaity, suh as the axiu steady-state speed that the otor an reah for a given load torque and inverter voltage, is investigated y a atla/siulink-ased siulation odel. The presented odel an also e eployed to siulate the dynai harateristis, suh as the urves of speed, urrent and torque during the start-up or transients when the load or power supply varies. A. odeling of Brushless DC otor with Sinusoidal Wavefor Bak ef For siplifiation, the phase winding indutane an e onsidered as a onstant, e.g. the average value over a variation yle. Fro Fig. 5, the average self-indutane of a phase winding is L4.9 H. The utual indutane etween two phase windings is negligile, i.e.. The voltage equations of the three phase windings an e written as V a R1 V V R 1 ia L + i R i 1 L L d dt ia Ea + i E i E (12) where V a, V, and V are the voltages of three phase windings, i a, i, and i the three phase urrents, and E a, E, and E the three phase ak efs. For the syetrially distriuted three phase windings with star onnetion, the three phase urrents oey i i + i (13) a + The three phase ak efs are:

5 E a E E E E E sin( ωt) o sin( ωt 12) o sin( ωt 24) (14) where E 2 ω is the agnitude of the sinusoidal K E r ak ef, ω the angular frequeny, and ω(p/2)ω r. The eletroagneti torque is alulated y T E i + E i + E i a a e (15) ωr The otion equation is dωr Te TL δ ωr (16) dt J where T L is the load torque, δ the frition oeffiient, and J the total inertia of the rotating parts. B. Power Eletroni Drive Ciruit Fig. 7 illustrates the sheati diagra of the typial drive iruit of rushless DC otors, fro whih one an work out the relationship etween the phase voltages and terinal potentials (voltages) as Va a N V (17) N V N where a,,, and N are the eletrial potentials (voltages) of terinals a,, and N (the neutral point), respetively, and d is the DC link voltage of the inverter. Figure 7. A typial drive iruit for rushless DC otor Assuing that the hard swithing is applied, at the oent when phase a is positively exited and phase is negatively exited, the following equations an e otained: ( k Ek ) k a i (18) 3 N ( k Ek ) k a i 2 C. Perforane Siulation Aording to (12)-(18), a atla/siulink-ased siulation odel is uilt as shown in Fig 8. The asi design requireent for the otor drive syste is that for an output torque of 2.65 N, the steady-state speed an reah 18 rp when the applied voltage is V d 165 VDC. By using the proposed odel, the otor drive syste is siulated under these onditions and soe results are plotted in Figs. 9-11, showing that the otor an eet the design requireents. Figure 8. atla/siulink-ased siulation odel of the rushless DC otor with sinusoidal ak ef

6 Figure 9. Speed urve during the start-up with a load of 2.65 N when the inverter voltage Vd165 V VI. CONCLSION SC aterials have a great appliation potential in eletrial ahines, partiularly those with oplex topologies and 3D fluxes. This paper presents the perforane analysis of a three-stak P law pole otor with an SC stator ore y an equivalent eletrial iruit and a atla/siulink-ased siulation odel. For aurate oputation of the otor paraeters, the 3D finite eleent agneti field analysis is onduted. By the nuerial analysis, the rotor position dependene of the ak ef and indutane has een deterined and an e onsidered in the siulation odel for ore aurate analysis. The alulations and siulations have een validated y the experiental results on the law pole SC otor prototype. REFERENCES Figure 1. Steady-state eletroagneti torque when Vd165 V Figure 11. Voltage, ak ef and urrent of a phase winding V. EXPERIENTAL VALIDATION The otor prototype has suessfully operated with a sensorless rushless DC shee, delivering a toque of 2.65 N at 18 rp when the inverter DC link voltage is 165 V. Fig. 12 plots the easured torque/speed urves with different inverter voltages. It an e seen that the theoretial analysis agrees well with the experients Speed (rev/in) 165V 15V 13V 11V 9V 7V 5V Torque (N) [1] The latest developent in soft agneti oposite tehnology, SC pdate, Reports of Höganäs AB, Sweden, [2] Y. G. Guo, J. G. Zhu, P. A. Watterson, W. Wu, Coparative study of 3-D flux eletrial ahines with soft agneti oposite ore, IEEE Trans. on Industry Appliations, Vol. 39, No. 6, pp , Nov. 23. [3] A. G. Jak, Experiene with the use of soft agneti oposites in eletrial ahines, in Pro. Int. Conf. on Eletrial ahines, Istanul, Turkey, Sept. 1998, pp [4] Y. G. Guo, J. G. Zhu, P. A. Watterson, and W. Wu, Developent of a law pole peranent agnet otor with soft agneti oposite stator, Australian J. Eletrial & Eletroni Engineering, Vol. 2, No. 1, pp. 21-3, 25. [5]. Gyiesi and D. Ostergaard, Indutane oputation y inreental finite eleent analysis, IEEE Trans. agn., Vol. 35, pp , [6] Y. G. Guo, J. G. Zhu, H. W. Lu, R. Chandru, S. H. Wang, and J. X. Jin, Deterination of winding indutane in a law pole peranent agnet otor with soft agneti oposite ore, in Pro. Australasian niv. Power Eng. Conf., Hoart, Australia, Sept. 25, pp [7] Y. G. Guo, J. G. Zhu, J. J. Zhong, and W. Wu, Core losses in law pole peranent agnet ahines with soft agneti oposite stators, IEEE Trans. agn., Vol. 39, No. 5, pp , Sept. 23. [8] Y. G. Guo, J. G. Zhu, J. J. Zhong, P. A. Watterson, and W. Wu, An iproved ethod for prediting agneti power losses in SC eletrial ahines, Int. J. Applied Eletroagnetis and ehanis, Vol. 19, pp , 24. Figure 12. easured ehanial harateristis