This is repository copy of Design Guidelines for Frctionl Slot Multi-Phse Modulr Permnent Mgnet Mchines. White Rose Reserch Online URL for this pper: http://eprints.whiterose.c.uk/110126/ Version: Accepted Version Article: Li, G. orcid.org/0000-0002-5956-4033, Ren, B. nd Zhu, Z.Q. (2017) Design Guidelines for Frctionl Slot Multi-Phse Modulr Permnent Mgnet Mchines. IET Electric Power Applictions. ISSN 1751-8660 https://doi.org/10.1049/iet-ep.2016.0616 Reuse Unless indicted otherwise, fulltext items re protected y copyright with ll rights reserved. The copyright exception in section 29 of the Copyright, Designs nd Ptents Act 1988 llows the mking of single copy solely for the purpose of non-commercil reserch or privte study within the limits of fir deling. The pulisher or other rights-holder my llow further reproduction nd re-use of this version - refer to the White Rose Reserch Online record for this item. Where records identify the pulisher s the copyright holder, users cn verify ny specific terms of use on the pulisher s wesite. Tkedown If you consider content in White Rose Reserch Online to e in rech of UK lw, plese notify us y emiling eprints@whiterose.c.uk including the URL of the record nd the reson for the withdrwl request. eprints@whiterose.c.uk https://eprints.whiterose.c.uk/
Design Guidelines for Frctionl Slot Multi-Phse Modulr Permnent Mgnet Mchines G. J. Li, B. Ren, nd Z. Q. Zhu, Fellow, IET Deprtment of Electronic nd Electricl Engineering, University of Sheffield, Sheffield, S10 2TN, U.K. g.li@sheffield.c.uk. Astrct: This pper presents the design considertions for frctionl slot multi-phse modulr permnent mgnet (PM) mchine with single-lyer concentrted windings. The winding fctors for vrious slot/pole numer comintions re clculted to identify the optiml slot/pole numer comintions for different phse numers. In ddition, the electromgnetic performnce influenced y flux gps (FGs), such s ir-gp MMF, ck-emf, cogging torque, on-lod torque nd torque ripple, etc., re comprehensively investigted y using the 2-D finite element (FE) method. Severl generl rules with respect to the influence of FGs on multi-phse modulr PM mchines performnce re estlished. The prototypes of modulr PM mchines re uilt nd the finite element results re vlidted with experiments. 1. Introduction PERMANENT mgnet (PM) mchines hve een incresingly pplied to mny pplictions such s electric nd hyrid vehicles, erospce ctution nd renewle energy, eg. wind power genertors, due to their inherent dvntges, including high torque density nd efficiency. [1]-[3]. However, for some sfety-criticl pplictions such s offshore wind power, the PM mchines re not only required to hve excellent performnce (high torque nd efficiency) ut lso good fult-tolernt cpility. To chieve such cpility, the single-lyer concentrted winding lyouts [4] re often employed, which cn reduce the short-circuit current nd limit the fult propgtion etween phses. In ddition, multiphse (>3) mchines cn lso e employed, which provide extr freedom when deling with the fults such s rmture phse open-circuit or short-circuit [5]. There re mny inherent dvntges offered y multi-phse mchines, eg. the improvement on reliility, the reduction in the phse current without the increse in phse voltge, nd the mitigtion of the torque ripple, etc. [6]. The influence of phse numer on the winding fctors, cogging torque frequency nd net rdil forces re comprehensively investigted in [7], which lso provides guidelines for selecting the optiml slot/pole numer comintions for multi-phse PM mchines. Five-phse [8]- [12], six-phse[13]-[15] nd dul three-phse [16]-[17] mchines (similr to six-phse mchines) re the most widely studied multi-phse mchines in the existing literture. In [17], novel dul three-phse, 78-slot/12-pole PM synchronous motor with symmetric sttor winding is proposed (phse shift ngle etween phses A nd B is 120.3 Elec. Deg. rther thn 120 Elec. Deg. in conventionl symmetricl mchines) in order to chieve good performnce nd lower MMF hrmonic contents. It is shown tht 1
the proposed dul 3-phse (multi-phse) PM mchine offers extremely low cogging torque nd torque ripple nd lso very low ck-emf totl hrmonic distortion. Furthermore, the torque density cn e slightly improved compred with tht of the dul 3-phse, 72-slot/12-pole PM mchines with symmetricl windings. Alterntively, modulr topologies with single lyer concentrted windings, such s those shown in Fig. 1, cn lso e employed to improve the fult-tolernt cpilities. Due to the fct tht the segments re seprted physiclly nd mgneticlly in modulr mchines, the fults would not propgte from one segment to nother. This cn reduce the short-circuit current nd weken the fult interction etween phses. Hence, the modulr mchines re excellent options for sfety-criticl pplictions s well. There re three dvntges to employing the modulr structures: 1) the mnufcturing process cn e gretly simplified especilly for the winding process [18]-[19]; 2) mintennce cn e simplified ecuse insted of hving to chnge the entire mchine, one cn simply replce the fulty segment; 3) the cooling cpility cn e improved ecuse the flux gps cn e used s wter ducts providing extr freedom for cooling [20]. Given the previously mentioned dvntges of modulr mchines over their conventionl nonmodulr counterprts, they re ttrcting growing ttention in recent yers. Spooner et l hve introduced new type of modulr mchine for wind turine pplictions in [21]. The proposed modulr mchine not only hs modulr sttor ut lso modulr rotor. This cn reduce the ctive mss of the mchines nd slightly increse their efficiency compred to their non-modulr counterprts with the sme mchine dimensions. Severl similr modulr structures with flux rriers in sttor teeth re reported in [22]. By doing so, the sttor core is segmented y the flux rriers nd forms modulr sttor structures. In [23], new sttor design y employing flux rriers in the sttor yoke to reduce or even cncel su-hrmonics in irgp flux density is proposed. It shows tht the new sttor design results in more thn 60% reduction in su-hrmonics, remrkle core loss reduction nd high flux-wekening cpility. A novel 3-phse modulr surfce mounted PM (SPM) mchine in which the flux-gps (FGs) re inserted into the lternte sttor teeth while the single lyer winding re wound on the sttor teeth without flux gps is proposed in [24]. This is shown in Fig. 1, where represents the tooth ody width. Similr novel modulr PM mchines with sttor tooth tips hve een presented in [25]. The electromgnetic performnce of the proposed modulr PM mchines such s ir-gp flux density, phse ck-emf, cogging torque, on-lod torque, copper nd iron losses, etc., ccounting for the influence of FGs, hve een comprehensively investigted nd some generl rules for modulr PM mchines with different slot/pole numer comintions hve een estlished. It ws found tht the FGs etween the sttor segments hve negtive effects on the modulr PM mchines with slot numer higher thn the pole numer, eg. the verge torque is reduced. On the contrry, when the slot numer is lower thn the 2
pole numer, the electromgnetic performnce cn e improved y choosing proper flux gp width, eg. the verge torque cn e incresed while cogging torque nd torque ripple cn e reduced, s re the mchine iron losses. c Fig. 1. Cross sections of modulr nd non-modulr PM mchines with open-circuit flux distriutions. 3-phse 12-slot/10-pole [24] 4-phse 16-slot/12-pole c 5-phse 20-slot/18-pole Nevertheless, the ville literture is only focused on 3-phse modulr PM mchines nd very few studies of multi-phse modulr PM mchines hve een crried out. Therefore, to fill in this gp, the multi-phse modulr PM mchines hving different slot/pole numer comintions nd single-lyer concentrted windings will e investigted, with prticulr focus on the electromgnetic performnce such s ir-gp rmture MMF, torque, etc. Consequently, some generl rules which cn cover the influence of FGs on the multi-phse modulr PM mchines will e estlished nd cn e used s design guideline for modulr mchines in prctice. 3
2. Winding Arrngements of Multi-phse Modulr PM Mchines In this section, the optiml slot/pole numer comintions for ech modulr PM mchine with different phse numer will e identified first so s to chieve the highest winding fctor which is clculted sed on its non-modulr counterprt. Then, the influence of FGs on the winding fctors of multi-phse modulr PM mchines hving different slot/pole numer comintions will e investigted. 2.1. Winding Fctors of Non-modulr PM Mchines For clssic non-modulr nd equl teeth PM mchines, without considering the higher order hrmonics, the distriution fctor ( ), the pitch fctor ( ), nd hence the winding fctor ( ) cn e clculted y: sin sin (1) sin sin (2) (3) where is the numer of coil per phse, is the ngulr phse ngle etween djcent EMF vectors of one phse (in Elec. Deg.), which equls to pole pitch nd the slot pitch. Additionlly, is the slot numer while is the rotor pole pir numer. As it is well estlished tht depends on the slot/pole numer comintion rther thn on the phse numer. Therefore, the clcultion of winding fctor is focused on the clcultions of distriution fctors for frctionl slot PM mchines with different phse numers. Since the multi-phse PM mchines studied here hve single-lyer concentrted windings, the theory developed in [26] for doule-lyer concentrted winding structure is no longer pplicle, therefore certin modifictions hve to e tken into ccount. The improved method is detiled s follows: When phse numer is odd (1, 3, 5, 7, ) with sin sin sin sin (4) (5) (6) 4
When phse numer is even (2, 4, 6, ) sin sin where is the phse numer, is the gretest common divisor etween the slot numer divided y 2 (single lyer winding) nd the pole pir numer. This mens tht the mchine is composed y elementry mchines with slot numer of (7) nd pole pir numer of. is the numer of slot vectors which form one phse of the elementry mchine while is the electricl ngle etween two djcent ck-emf vectors. By using the ove method, the winding fctors for frctionl slot single-lyer concentrted winding modulr mchines with different phse numers hve een clculted, nd hence, the optiml slot/pole numer comintions for ech phse numer cn e determined ccordingly. The results re shown in Tle 1, in which only the results for ech phse numer with its relevnt minimum chievle slot numer hve een given. Tle 1 Winding fctors of single lyer concentrted winding N-phse mchines with non-modulr sttors 1-phse 2-phse 3-phse 4-phse 5-phse 6-phse 2p\N s 4 8 12 16 20 24 2 0.707 0.271 0.259 0.180 0.156 0.126 4 1 0.707 0.500 0.383 0.309 0.259 6 0.707 0.653-0.513 0.454-8 0-0.866-0.5878-10 -0.707 0.653 0.966 0.768-0.588 12-1 0.707-0.924 0.809-14 -0.707 0.271 0.966 0.906 0.891 0.766 16 0-0.866-0.951-18 0.707-0.271-0.906 0.988-20 1-0.707 0.500 0.924-0.966 22 0.707-0.653 0.259 0.768 0.988 0.958 24 0 - - - 0.951-26 -0.707-0.653-0.259 0.513 0.891 0.958 28-1 -0.707-0.500 0.383 0.809 0.966 Bsed on the previous results, it cn e concluded tht in order to chieve the mximum winding fctors for frctionl slot modulr PM mchines with different phse numers nd different slot/pole numer comintions, the following rules should e stisfied: (8) (9) (10) 5
where is n integer nd equl to. By wy of exmple, for 3-phse mchines with 12-slot, the pole numers enling the mchines to hve their mximum winding fctor re 10-pole nd 14-pole; for 4-phse mchines with 16-slot, the pole numers re 12-pole nd 20-pole; for 5-phse mchines with 20-slot, the pole numers re 18-pole nd 22-pole. Therefore, the slot/pole numer comintions mentioned ove re chosen for modulr PM mchines with different phse numers in order to nlyse the influence of FGs on the mchine s electromgnetic performnce. 2.2. Winding Fctors for Modulr PM Mchines The winding fctors for modulr mchines cn e clculted using similr methods s those for clssic non-modulr mchines. However, when the FGs re inserted into the lternte sttor teeth, the coil pitch nd hence the fundmentl pitch fctors ( need to e modified with the vrition of the flux gp widths (. According to [24], the pitch fctor ccounting for the influence of FGs cn e clculted y: sin (11) sin (12) where R i, nd re sttor inner rdius, coil pitch nd pole pitch, respectively. The flux gps will reduce the coil pitch ut they do not influence the pole pitch. Therefore, they will increse the pitch fctor for mchines with, while reducing it for mchines with. Since the distriution fctors re unchnged due to the fixed ck-emf nd slot vectors distriutions for given slot/pole numer comintion, the resultnt winding fctors of modulr PM mchines with different phse numers re only ffected y the pitch fctors, s shown in Fig. 2. Fig. 2. Winding fctors versus flux gp width of 3-phse, 4-phse nd 5-phse modulr PM mchines with different slot/pole numer comintions. It is evident from Fig. 2 tht for multi-phse modulr PM mchines hving, the winding fctors decrese with the increse in FG width. Wheres, when multi-phse modulr PM mchines hving, their winding fctors increse with the incresing FG width until they rech prity nd 6
susequently decrese. The winding fctor lrgely determines the electromgnetic performnce. Therefore, the influence of FGs will lso e reflected on the mchine s performnce, nd will e investigted in the following sections. 3. Design of Modulr PM Mchines The cross sections of modulr PM mchines with different phse numers re depicted in Fig. 1. The rotors for ll mchines hve surfce-mounted, full rc permnent mgnets lthough other rotor topologies cn e employed such s interior or inset permnent mgnets. Furthermore, it is worth mentioning tht the totl ctive tooth ody width for the sttor teeth with or without FGs is unchnged for different FG widths, s shown in Fig. 1. This is to void hevy locl mgnetic sturtion occurring in the tooth odies when lrge FGs re employed. Some of the generl design prmeters re exctly the sme for the modulr PM mchines hving different slot/pole numer comintions nd phse numers, s shown in Tle 2. Some other design prmeters re optimized individully in certin sequence, eg. split-rtio (rtio of sttor inner dimeter to sttor outer dimeter) tooth ody width ( ) sttor yoke height (. The optimized design prmeters for ech modulr PM mchine with different phse numer re given in Tle 3. It is worth mentioning tht the sttor outer dimeter nd ctive length of the 3, 4 nd 5-phse modulr PM mchines re lwys the sme during the optimiztion process. Tle 2 Generl design prmeters of modulr PM mchines Phse voltge (V) 36 Stck length (mm) 50 Rted torque (Nm) 5.5 Air-gp length (mm) 1 Rted speed (rpm) 400 Mgnet thickness (mm) 3 Sttor outer rdius (mm) 50 Mgnet remnence (T) 1.2 Filling fctor 0.37 Numer of turns per phse 132 Tle 3 Optimized design prmeters of modulr PM mchines for chieving similr output torque Modulr PM mchines (mm) (mm) (A) 3-phse 0.57 7.1 3.7 7.35 4-phse 0.61 5.9 2.7 4.83 5-phse 0.64 4.7 1.9 3.41 4. Electromgnetic Performnce of Modulr PM Mchines 4.1. Armture Mgneto-Motive Force (MMF) Although the frctionl slot single-lyer concentrted winding hs dvntges s mentioned ove, the inherent drwcks of such winding lyout cnnot e overlooked. By wy of exmple, the rich su-hrmonics in the rmture MMF in the ir-gp will result in mny undesirle effects on the performnce of PM mchines, such s incresing PM eddy current loss nd core losses, hevy locl sturtion, coustic noise nd virtions, etc. Fortuntely, the modulr structure cn help to effectively mitigte those MMF su-hrmonics s will e demonstrted in this section. 7
The hrmonics of rmture MMF for modulr PM mchines hving different slot/pole numer comintions nd different phse numers hve een clculted. The results of the 3-phse, 4-phse nd 5-phse mchines re shown in Fig. 3. It hs een estlished tht the working (or fundmentl) hrmonics re 5 th or 7 th order hrmonics depending on slot/pole numer comintion for 3-phse, 6 th or 10 th for 4-phse, nd 9 th or 11 th for 5-phse mchines. As shown in Fig. 3, when the flux gp width chnges, the vritions of the working hrmonics, which produce the electromgnetic torque, re similr to those of the winding fctors. This is minly due to the fct tht the working ir-gp MMF is lrgely determined y the winding fctor. c Fig. 3. Spectr of rmture MMF of modulr SPM mchines. 3-phse modulr PM mchines 4-phse modulr PM mchines c 5-phse modulr PM mchines However, for 3-phse nd 5-phse modulr PM mchines, the su-hrmonics re minly contriuted y the 1 st order hrmonic, while for 4-phse modulr PM mchines the 2 nd order hrmonic is the min su-hrmonic. It is evident tht for ll modulr mchines, regrdless of slot/pole numer comintion nd phse numer, the min su-hrmonics re significntly reduced when the FGs re introduced into the lternte sttor teeth. In order to understnd the influence of FGs on the rmture MMF in ir-gp of modulr PM mchines, it is necessry to seprte the influence of FGs from tht of slot openings (SOs). This is ecuse for the modulr PM mchines, the primry two fctors tht influence the rmture MMF in ir-gp re the SOs nd FGs, s cn e descried y (13). Here, the corresponding non-modulr PM mchines with unequl teeth (UNET) re introduced, which cn e 8
simply otined y replcing the FGs (ir) y iron. This gives n rmture MMF component due to SOs only ( ). As result, the MMF due to FGs only cn e otined y using the resultnt MMF nd sutrcting the. This is possile ecuse, to clculte the rmture MMF in the ir-gp, the PMs re removed nd the mgnetic sturtion cn e neglected due to the lrge ir-gp length of the surfce mounted permnent mgnet mchine. (13) Fig. 4 depicts the MMF components (due to SOs, FGs nd resultnt MMF) of non-modulr nd modulr PM mchines. For the ltter, 3-phse mchine with 12-slot/10-pole nd FG=2mm is shown s n exmple. It is evident tht the FGs significntly reduce the suhrmonics while incresing the working hrmonics when the slot/pole numer comintion is properly selected. This is ecuse the suhrmonic component cused y FGs is lwys negtive while for certin working hrmonics, eg. the 7 th order, the component due to FGs cn e positive. Fig. 4. Influence of FGs on the ir-gp MMF of 3-phse modulr PM mchines. Wveforms Spectr In order to further investigte the influence of FGs on the min ir-gp MMF su-hrmonics, the flux distriution due to rmture currents for 3-phse, 4-phse non-modulr nd modulr PM mchines re shown in Fig. 5. The 5-phse mchines re not shown ecuse its min suhrmonic is similr to tht of 3-phse mchines. As expected, the min rmture MMF suhrmonic for the 3-phse mchine is 2 poles, while for the 4-phse mchines it is 4-poles regrdless of whether the mchines re modulr or not. However, when the modulr structure is employed s shown in Fig. 5 (c) nd (d), the FGs in the sttor teeth dd extr equivlent ir-gp length to the flux pth of the min rmture suhrmonic MMF compred to its non-modulr counterprts [Fig. 5 () nd ()]. As result, the min su-hrmonics of ir-gp MMF for modulr PM mchines with different phse numers cn e significntly reduced, s shown in Fig. 3 9
c Fig. 5. Flux distriution due to rmture winding only (3-phse nd 4-phse). - Non-modulr PM mchines c-d Modulr PM mchines d 4.2. Phse Bck-EMF The phse ck-emf wveforms nd their spectr for modulr PM mchines with different phse numers (5-phse is not shown here due to the limited spce) nd FG widths re shown in Fig. 6. Only the results of phse A re presented. It is found tht for multi-phse modulr PM mchines hving, the fundmentl phse ck-emfs lwys decrese with the increse in FG width. When, the fundmentl phse ck-emf hrmonics cn e improved y ppropritely selecting the FG width. Such fetures re similr to the ir-gp MMF performnce s discussed in section 4.1, nd re minly due to the influence of FGs on winding fctors. 10
Fig. 6. Bck-EMF wveforms nd spectr. - 3-phse modulr PM mchines c-d 4-phse modulr PM mchines c d 4.3. Cogging Torque It hs een estlished in [27] tht, the periodicity nd the mplitude of cogging torque for nonmodulr PM mchines minly depend on the vlue of, which is the lest common multiple (LCM) etween the nd the. The higher the N c is, the lower the cogging torque will e. However, when the modulr structure is employed, the vlue of ecomes due to the chnge in sttor core symmetry. cn e otined y clculting the LCM etween nd the numer of FGs [28]. By wy of exmple, the optiml slot/pole numer comintions to chieve the highest winding fctor for 4-phse modulr PM mchines re 16-slot/12-pole nd 16-slot/20-pole nd the numer of FGs is 8. Hence, the vlues of re 48 nd 40, respectively. However, for 5-phse modulr PM mchines, the optiml slot/pole numer comintions re 20-slot/18-pole nd 20-slot/22-pole nd the FG numer is 10, leding to of 90 nd 110, respectively. As result, the pek-to-pek cogging torques of 4- phse modulr PM mchines re lwys higher thn those of 5-phse modulr PM mchines, s shown in Fig. 7. Moreover, for different multi-phse mchines, if the slot/pole numer comintion nd FG width re properly selected, the pek-to-pek cogging torque cn e significntly reduced. This will hve profound impct on the torque ripple s will e investigted in the following section. Fig. 7. Pek-to-pek cogging torque of modulr PM mchines with different phse numers. 4.4. On-lod Torque nd Torque Ripple 11
The results of verge torque nd torque ripple of modulr PM mchines with different phse numers nd supplied y sinusoidl wveform currents (the phse RMS currents re given in Tle 3) re shown in Fig. 9. It cn e found tht the verge torques of the modulr PM mchines hving, decrese with the incresing flux gp width regrdless of phse numer. However, for the modulr PM mchines hving, the verge torques cn e mximized y selecting pproprite FG widths. This is minly due to the impcts of FGs on the rmture MMF working hrmonics nd the fundmentl hrmonics of phse ck-emfs, s detiled previously. c Fig. 8. Averge torque nd torque ripple versus flux gp width of modulr PM mchines with different phse numers. - c-d d The torque ripples (pek-to-pek torques) follow similr trend s the pek-to-pek cogging torque. This is minly due to the fct tht higher order hrmonics, prticulrly the 5 th nd 7 th, re quite low in the phse ck-emfs of modulr mchines nd hence the torque ripples due to EMF hrmonics re much less dominnt thn those due to cogging torques. 5. Experimentl Vlidtion In order to vlidte the predictions crried out previously, the 3-phse 12-slot/10-pole nd 12- slot/14-pole prototype modulr PM mchines without tooth tips hve een uilt, which re referred to in [24]. The design prmeters re given in Tle 2 nd Tle 3. 5.1. Phse Bck-EMF 12
The phse ck-emfs of the prototypes re mesured nd compred with the corresponding predicted results, s shown in Fig. 9. A good mtch cn e otined etween the predicted nd mesured results. Fig. 9. Predicted nd mesured phse ck-emfs. 12-slot/10-pole 12-slot/14-pole c Spectr of phse A s n exmple c 5.2. Sttic Torque The sttic torque ginst the rotor position cn e mesured y employing the method presented in [29] nd the test rig is shown in Fig. 10 (). The supply currents to phses A (, B ( nd C ( re set s, where is DC nd cn e chnged to represent different lod conditions. It is evident from Fig. 10 () tht the predicted nd mesured results re in good greement for ll prototype mchines. Fig. 10. Sttic torque mesurement (I=5A). The prototype mchines nd the test rig Sttic torque versus rotor position 13
6. Conclusion Multi-phse modulr PM mchines with single-lyer concentrted windings were investigted in this pper. The optiml slot/pole numer comintions for modulr PM mchines with different phse numers were identified. The electromgnetic performnce such s winding fctors, ir-gp MMF, ck-emf, cogging torque, verge torque nd torque ripple hve een investigted, it demonstrted tht: The min su-hrmonics of ir-gp MMF re significntly reduced y employing the modulr topologies for multi-phse PM mchines. This cn lrgely mitigte the negtive effects on the electromgnetic performnce due to such su-hrmonics. For multi-phse modulr PM mchines hving, the FGs hve negtive effects on the electromgnetic performnce such s decresing the winding fctors, MMF working hrmonics nd verge torques, etc. For the multi-phse modulr PM mchines hving, if the flux gp width is properly selected, the FGs cn improve the electromgnetic performnce, such s incresing verge torques nd reducing the torque ripples. The predictions otined y FE hve een vlidted y the experiments. The generl rules estlished in this pper summrized the influence of FGs on the electromgnetic performnce of multiphse modulr PM mchines. Although only three, four nd five-phse cses re discussed, the conclusions chieved in this pper cn e extended to modulr PM mchines with ll other phse numers nd cn e used s design guidelines for multi-phse modulr PM mchines in prcticl pplictions. Further, lthough only smll size mchines hve een investigted in this pper for the experimentl vlidtion purpose, the estlished generl rules cn e extended to the design nd nlysis of lrge PM mchines, eg. offshore wind genertors. 7. Reference [1] Wng, J., Ptel, V. I., nd Wng, W., 'Frctionl-slot permnent mgnet rushless mchines with low spce hrmonic contents', IEEE Trns. Mgn., 2014, 50, (1), pp. 1-9. [2] Zhu, Z. Q. nd Howe, D., 'Electricl mchines nd drives for electric, hyrid, nd fuel cell vehicles', Proc. IEEE, Apr. 2007, 95, (4), pp. 746-765. [3] Bekk, N., Zim, M. E., Bernrd, N., et l., 'Optimiztion of the MMF function of frctionl slot concentrted windings', Proc. 2014 Int. Conf. Electr. Mch. (ICEM), Berlin, Germny, Sep. 2014, pp. 616-622. [4] Binchi, N. nd Pre, M. D., 'Use of the str of slots in designing frctionl-slot single-lyer synchronous motors', IEE Proc. Elec. Power Appl., My. 2006, 153, (3), pp. 459-466. [5] Apsley, J. M., Willimson, S., Smith, A. C., et l., 'Induction motor performnce s function of phse numer', IEE Proc. Elec. Power Appl., Nov. 2006, 153, (6), p. 1. [6] Klingshirn, E. A., 'High phse order induction motors-prt I-Description nd theoreticl considertions', IEEE Trns. Power Apprtus Syst., 1983, PAS-102, (1), pp. 47-53. [7] Refie, A. M. E.-., Shh, M. R., Qu, R., et l., 'Effect of numer of phses on losses in conducting sleeves of surfce PM mchine rotors equipped with frctionl-slot concentrted windings', IEEE Trns. Ind. Appl., 2008, 44, (5), pp. 1522-1532. [8] Prs, L. nd Toliyt, H. A., 'Multi-phse permnent mgnet motor drives', Proc. 38th Ind. Appl. Conf. (IAS) Annu. Meeting, Oct., 2003, 1, pp. 401-408. [9] Prs, L., Toliyt, H. A., nd Goodrzi, A., 'Five-phse interior permnent-mgnet motors with low torque pulstion', IEEE Trns. Ind. Appl., 2007, 43, (1), pp. 40-46. 14
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