Optimum Air-Gap Flux Distribution with Third Harmonic Rotor Flux Orientation Adjustment for Five-Phase Induction Motor

Transcription

1 J Elect Eng Technol.018; 13(1): ISSN(Pnt) ISSN(Onlne) Optmum A-Gap Flux Dstbuton wth Thd Hamonc Roto Flux Oentaton Adjustment fo Fve-Phase Inducton Moto Mn Kang*, Wenjuan Yu**, Zhengyu Wang***, Wubn Kong and Ye Xao*** Abstact Ths pape nvestgates optmum a-gap flux dstbuton wth thd hamonc oto flux oentaton adjustment fo fve-phase nducton moto. The technque of objectve s to geneate a nealy ectangula a-gap flux, and t mpoves on utlzaton unde vaaton loadng condtons. The popotonal elatons between thd hamonc and fundamental plane cuents s usually adopted n the conventonal method. Howeve, msalgnment between fundamental and thd hamonc component occus wth vaaton loadng. The on of stato teeth s satuated due to ths msalgnment. Ths poblem s solved by thd hamonc oto flux oentaton adjustment smultaneously, and decton and ampltude ae changed wth mechancal load vaaton. The poposed method ensues that the agap flux densty s nea ectangula fo a maxmum value fom no load to ated load. It s confmed that the poposed method guaantees complete both planes decouplng wth thd hamonc flux oentaton adjustment. The effectveness of the poposed technque s valdated expementally. Keywods: A-gap flux, Fve-phase nducton moto, Thd hamonc, Nealy ectangula, Oentaton adjustment 1. Intoducton In ecent yeas, hgh powe moto dves ae equed n some applcatons, such as locomotve tacton, electc shp populson and acaft dves. Multphase moto dves ae sutable fo hghe powe condton wth moe exta phase, and the cuent pe phase s educed fo a gven phase voltage and total powe atng [1-3]. Moeove, hgh pefomance multphase nducton moto (IM) dves have othe advantages, such as elablty, obustness and hgh toque densty [4-6]. In multphase dves, the fundamental and hamonc planes can be contolled ndependently, and ths popety allows educng the toque pulsaton. The elablty s a dstngushed met compaed to thee-phase dve, and fault-toleant contol stateges fo contnuous smooth and steady opeaton wthout moto halt [7-9]. The global faulttoleant contol technque s flexblty and smplcty n dealng wth all possble fault condtons [10]. Hgh toque densty multphase moto dve to mpove the delveed toque has been of nteest to eseaches [11-1]. The enhancement benefts fom the hamonc a-gap fluxes, whch effectvely ncease the magntude of fundamental flux densty wthout on satuaton [13-14]. DC-lnk voltage utlzaton s also mpoved by modulaton Coespondng Autho: State Key aboatoy of Advanced Electomagnetc Engneeng and Technology, Huazhong Unvesty of Scence and Technology, Chna. (wubnkong@16.com) * College of Automaton and Electcal Engneeng, Zhejang Unvesty of Scence and Technology, Chna. ** Cental Chna Banch of State Gd Copoaton of Chna, Chna. *** Hunan CRRC Tmes Electc Vehcle Co. TD., Chna. Receved: June 16, 017; Accepted: Octobe 0, 017 stateges fo the pulse wdth modulaton wth hamonc cuent njecton [15-18]. The moto dve s fed by quasectangula voltage, and the flatted a-gap flux densty wavefom s obtaned. The quas-tapezodal a-gap flux densty s essental fo toque densty mpovement [19-0]. Some moe studes have nvestgated the pefomance of optmum a-gap flux dstbuton moe deeply [1-4]. A novel contol method fo a sx-phase IM wth nealy squae a-gap flux densty s poposed wth no vecto tansfomaton, because the stato phase wndngs act as ethe o toque-poducng phases [5]. The study n [6] pesents steady-state analyss and pefomance of an eleven-phase IM when hamonc njecton up to nnth hamonc. Fo the same RMS fundamental cuent, the moto could be oveloaded by appoxmately 37.5%, and the coespondng ncease n the RMS phase cuent s 5%. In [7], the use of genetc algothm s poposed to detemne the optmum quas-squae wave flux densty dstbuton fo an eleven-phase IM, and the pape ndcates that the feld hamonc contbuton of ode geate than fve s neglgble. The study n [8] eveals that the hghode spatal hamoncs poduce hgh loss n the stato back on, and the stato back on s nceased by 0% wth thd hamonc njecton. The study n [9] extends the speed opeaton ange, and the ampltude of the feld hamoncs s pogessvely educed to ensue the wdest possble opeaton at hgh speeds. Howeve, lttle eseach has been pesented on loanng vaaton effect on a-gap flux densty dstbuton. An mpoved flux patten s poduced wth a synchonzaton block, whch s used to lock elatve poston Copyght c The Koean Insttute of Electcal Engnees Ths s an Open-Access atcle dstbuted unde the tems of the Ceatve Commons Attbuton Non-Commecal cense ( lcenses/by-nc/3.0/) whch pemts unestcted non-commecal use, dstbuton, and epoducton n any medum, povded the ognal wok s popely cted. 315

2 Optmum A-Gap Flux Dstbuton wth Thd Hamonc Roto Flux Oentaton Adjustment fo Fve-Phase Inducton Moto between fundamental and thd hamonc fluxes [30]. The shotage of ths method s that the gan n popotonal loop should be lmted to avod system nstablty. A pomoted contolle gves a nealy flat flux patten espectve of mechancal loadng, and t calculates the dect and quadatue cuent components of the thd hamonc plane as a nonlnea functon. Howeve, ths contolle neglects that the thd hamonc flux oentaton s changed n tme due to load vaaton, whch s not synchonzed wth fundamental flux oentaton. Moeove, the devaton of the electomagnetc toque calculaton n the thd hamonc plane s not coect. Concenng ths poblem, ths pape mpoves the analyss n [31] to oto flux angle adjustment between fundamental and thd hamonc plane. In ths pape, the poposed method s nvestgated fo optmum a-gap flux dstbuton wth thd hamonc oto flux oentaton adjustment fo fve-phase IM. The elatons between oto flux and a-gap flux ae llustated by vecto dagam n both planes. The thd hamonc oto flux oentaton acts as a eal-tme adjustment unde mechancal load vaaton. Then, the dect and quadatue cuent components n the thd hamonc ae deved as a nonlnea functon of the fundamental ones. The deved functon ensues that the optmum a-gap flux densty n vaous mechancal loads, and t makes coectons fo electomagnetc toque calculaton n [31] fo the thd hamonc plane. The pefomance of the poposed method s compaed wth the conventonal contolle that has a constant elaton between the command cuent n both planes. Fnally, a fve-phase IM dve s constucted, and expemental esults vefy the feasblty of the poposed method.. Vecto Contol n the Dual-Planes.1 Fve-phase IM model The topology fo fve-phase IM dve s shown n Fg.1, and the typcal solated neutal s adopted. Fve-phase nvete confguaton s used to dve a sta connected wth squel-cage IM. Ths pape adopts a fou-pole fve-phase nducton moto wth dentcal quas-concentated stato wndngs. The stato wndngs ae dstbuted wth 7 o spatal angle Fg.. Sketch of stato wndng dstbuton and each phase occu eght stato slots, as shown n Fg.. Each stato slot has 6 conductos and the squel cage oto has 6 bas. The man dmensons and ated paamete fo fve-phase IM s contaned n the Appendx. By vecto space decomposton, the fundamental and thd hamonc of the moto ae decoupled n the d 1 -q 1 and d 3 -q 3 synchonous efeence fame. Ths model s smla to that n [30], and othogonal matx ae used to tansfom stato quanttes between the a-b-c-d-e natual efeence fame and the d 1 -q 1 -d 3 -q 3 -n synchonous efeence fame. The dual-plane vecto contol s set n the synchonous efeence fame.. Dual-plane vecto contol Ths secton studes the dual-plane vecto contol wth thd hamonc njecton, and ndect feld oentaton contol (IFOC) s used fo decoupled flux and toque contol [0]. It s assumed that the fundamental and thd hamonc oto flux lnkages ae attached to d 1, d 3 axes, and no lnkages on the q 1, q 3 axes n IFOC ìy îy = y d1 1 = y d 3 3 In IFOC, the dect cuent epesents the magnetzng cuent, and the elatonshp between oto fluxes and dect cuents at steady state ae ì y sd1 = y sd 3 = î d1 d 3 (1) () U dc v a 0 v b v c vd v e c d b o e a To mantan a quas-tapezodal a-gap flux densty dstbuton, the optmum a-gap flux densty s descbed as B ( f ) = B (snf + k sn 3 f ) (3) m s s 3 s Fg. 1. Topology of fve-phase IM dve whee B s ampltude fo the fundamental component, 316 J Elect Eng Technol.018; 13(1):

3 Mn Kang, Wenjuan Yu, Zhengyu Wang, Wubn Kong and Ye Xao and f s s electcal angle. k 3 s gan fo thd hamonc flux densty, and the value s 1/6 fo the optmum a-gap flux densty [0]. Substtutng (3) nto (), the elatonshp between the dect components ae k = (4) 3 sd 3 sd1 3 The elaton between the quadatue components can be deved fom the slp fequency Smlaly, the total quadatue cuent s sq k3 3 = sq1 1 + ( ) (11) k 3 1 Smlaly, the total quadatue cuent s I = + / (1) s sd sq ì w = w î = s1 sq1 t1y 1 s3 sq3 t3y 3 (5) 3. Optmum A-Gap Flux Densty Dstbuton wth Poposed Method 3.1 A-gap flux densty dstbuton whee m s magnetzng nductance. Substtutng (5) nto ws3 = 3w s1, the quadatue component elaton between fundamental and thd hamonc plane s t k = k = (6) sq3 3 sq1 sq1 t1 k3 1 whee k3 = R 3 / R1, and t s epesent the oto esstance ato between fundamental and thd hamonc plane [31]. k 3 s unty f the skewng effects ae neglected, and the Eq. (5) can be smplfed = k (7) sq3 3 sq1 Substtutng (), (4) and (7) nto toque expesson n IFOC, the toque enhancement can be expessed as a functon of the dect and quadatue cuent ì 5P T = y T T î e1 3 sq P k3 e3 = y 3 sq3 = e1 4 3 k3 The moto toque gan due to thd hamonc njecton s gven T Gan 3 3 (8) k = K(1 + ) (9) k whee K s the ncease n the fundamental flux due to hamonc njecton [], and the s equal to Toque/RMS s key chaactestc fo moto pefomance, and t s necessay to calculate the RMS phase cuent. The total dect axs cuent s sd k3 = Ksd1 1 + ( ) (10) 3 The dual contol fo fve-phase IM s based on IFOC, and the oto flux oentatons ae algned to y v 1 and y v 3. The a-gap flux densty dstbuton s elated to y v and y v dectly [31], and the vectos elaton between oto flux and a-gap flux s shown n Fg. 3. The angle between oto flux and a-gap flux depends on mechancal loadng, snce thee s no guaantees that agap flux space phaso dagam fo two planes ae algned. The msalgnment causes dstoton of the flux densty dstbuton, then the a-gap flux densty expesson n (3) should be modfed B ( f ) = B (snf + k sn(3 f - d )) (13) m s s 3 s 3 whee d3 s msalgnment angle between fundamental and thd hamonc component. The desed a-gap flux densty dstbuton s depcted n Fg. 4, whee both the fundamental and thd components ae algned. Meanwhle, the value of d 3 s equal to zeo. The deal dstbuton has two peaks at 60 o and 10 o. Howeve, the wavefom n Fg. 4 llustates the same case wth a 9 o msalgnment between two flux densty components due to a cetan mechancal loadng. It s shown that the fst peak at 60 o s enlaged, and the second peak s mnmzed. Accodngly, t esults n stato on satuaton. The tadtonal contol method wth constant gans neglects ths effect, snce t focuses on the I 1 E 1 = - jw e y 1 d d E - jw I I e s 1 1 y y s 1I1 1 = - jw y e I 3 E = - j 3 w y 3 e 3 d E y y s 3I3 d - j I I 3 e 3w e s 3 3 = - j3w y Fg. 3. Vectos elaton between the oto flux and a-gap flux 317

4 Optmum A-Gap Flux Dstbuton wth Thd Hamonc Roto Flux Oentaton Adjustment fo Fve-Phase Inducton Moto B B m B 3. The Poposed Method wth Thd Hamonc Roto Flux Oentaton Adjustment The phase angle expesson fo fundamental and thd hamonc plane n (14) should satsfy Eq. (15) -1 s 33-1 s 11 sn ( ) = 3sn ( ) (16) y y To obtan a nea quas-squae a-gap flux dstbuton, the ampltude elaton between y and y s B B m B whee y k = y (17) 3 3 oto flux lnkage athe than a-gap flux lnkage. The a-gap flux oentaton contol s sutable fo agap flux densty optmzaton, but the contol stategy s athe complcated wthout decouplng contol. Hence, the pomoted contol n the dual-plane should be nvestgated. The vectos elaton between oto flux and a-gap flux s demonstated n Fg. 3. d s the phase angle between oto flux and a-gap flux fo the fundamental plane, and d s the phase angle fo the thd hamonc plane. The expessons of d and d ae ì -1 s 11 d = sn ( ) y s 3 d = sn ( ) î y (14) The space phase of the a-gap flux ( y and y ) should be algned to obtan a nealy ectangula flux dstbuton. The condton s acheved by d Fg. 4. Wavefoms of flux densty dstbuton = 3d (15) The devaton s ncluded n [31] ndcates that the dect and quadatue cuent components ae calculated as a nonlnea functon to satsfy the Eq. (15). Howeve, the pomoted contolle n [31] has neglected that the thd hamonc flux oentaton s changed n tme due to load vaaton, whch s not synchonzed wth fundamental flux oentaton. Concenng ths poblem, the poposed method wth thd hamonc oto flux oentaton adjustment s elaboated n secton B. ì y = y + y î y y y md1 mq1 = md 3 + mq3 (18) In IFOC contol stategy, the quadatue cuent elaton n the stato and oto s ì = = î q1 sq1 1 q3 sq3 3 (19) Substtutng (17) and (19) nto (16), the q-axs cuent elaton s k y s 1 sq1 sq3 = sn(3sn ( )) (0) 3 s 3 1y Then, the dect cuent fo thd hamonc plane can be deved by vectos elaton -1 s 1 sq1 sd 3 = cos(3sn ( )) (1) 1y y The dect and quadatue cuent devaton n (0) and (1) can meet the a-gap flux densty dstbuton, but the method can t satsfy the slp fequency equaton n (5). Thee s a contadcton fo meetng Eqs. (5), (15) and (17) smultaneously. The dect and quadatue cuent vaaton n the thd hamonc plane can satsfy only two equatons. Hence, anothe contol feedom should be added. In fact, the oto flux oentatons ae not equed to set at the same decton. Futhemoe, the specfc flux oentaton vaaton can be used fo anothe contol feedom, and the contadcton mentoned above can be solved. The thd hamonc oto flux oentaton can be utlzed fo anothe contol degee, and the angle elatonshp n Eq. 318 J Elect Eng Technol.018; 13(1):

5 Mn Kang, Wenjuan Yu, Zhengyu Wang, Wubn Kong and Ye Xao (15) s also changed. The dffeental angle Vd m between two fluxes s shown n Fg. 5. Assumng the popotonal gan between dect and quadatue k = / () p sq1 sd1 Substtutng () nto slp fequency Eq (5), the quadatue n the thd hamonc plane s 3t = k (3) 3 sq3 p sd 3 t1 Substtutng (19) and () nto (17) and (18), the dect cuent n the thd hamonc plane s deved q 3 Vd m q 1 ( s 1k p 1 ) / = / ( ) sd 3 sd1 ( s 3k pt 3 t1 3 ) The quadatue cuent n the thd hamonc plane s ( s k p ) 33t / 1 = k 18t 1+ 3 t / ( t ) sq3 p sd1 ( s k p ) (4) (5) Hence, the dect and quadatue cuents n (0) and (1) ae coected fo (4) and (5). The d and d can be deved by as follow ì d = ac tan d ac tan î = s 1 sq1 1 sd1 s 3 sq3 3 sd 3 (6) Fom expesson (4), the phase angle elaton n (15) s satsfed when the load s set to zeo. Howeve, the thd hamonc oto flux oentaton should be eal-tme adjusted when the mechancal s changed. The expesson fo V d s m Vd m Fg. 5. Roto flux oentaton fo fundamental and thd hamonc plane V d = 3d -d (7) m d 3 d 1 y d Vd m y 3 I s 3 3 y d s 1I 1 y 1 Fg. 6. A-gap flux dstbuton wth dffeent oto flux oentaton é 1 cos( a) cos( a) cos(3 a) cos(4 a) ù ê 0 sn( a) sn( a) sn(3 a) sn(4 a) ú ê ú Ts = ê cos( Vd m ) cos(3 a + Vd m ) cos(6 a + Vd m ) cos(9 a + Vd m ) cos(1 a + Vd m ) ú 5 ê ú ê sn( Vd m ) sn(3 a + Vd m ) sn(6 a + Vd m ) sn(9 a + Vd m ) sn(1 a + Vd m ) ú ê ë 1/ 1/ 1/ 1/ 1/ ú û a = p / 5 (8) Accodngly, the othogonal matx s modfed fo Eq (8), whch has dffeental angle n thd hamonc plane. The vectos elaton between fundamental and thd hamonc plane s shown n Fg. 6. The thd hamonc flux oentaton s changed n tme due to load vaaton, whch s not synchonzed wth fundamental flux oentaton. 4. Smulaton Results wth Poposed Method A contol scheme obtaned n Secton III has been developed, and ts block dagam s shown n Fg. 7, whch can be deally dvded nto two components wth dffeent ams. The fst components concens the cuent contol loop, the second one s the tackng of speed efeence. In Fg. 7, the contolled vaables ae expessed n two efeence fames d 1 q 1 and d 3 q 3, whch ae synchonzed and algned wth the coespondng oto flux oentatons. The poposed method s test fo no-load and ated load, and the speed efeence s set at 600 /mn. The moto s mechancally load wth a step toque of ated value at.0 s. The dect and quadatue cuent components fo both planes ae shown n Fg. 8. Fg. 8(c) and Fg. 8(d) show w * * sd1 sd1 * sq1 sq1 * sd 3 sd 3 * sd1 * sd1 * sq3 sq1 sq 1 sq3 w * sd1 w s * 1 sq1 P ò w sd 3 sq3 q 1 sq1 sd1 sd 3 sq3 q 1 * M1T1 u a1b s ab 1 1 M T a b 3 3 * a1b1 us ab 3 a3b3 d1q1 d q a 1b1 s ab 1 a3b3 s ab 3 a1b1 a b 3 3 ab cde ab cde sa sb sc sd se Fg. 7. Block dagam of vecto contol fo fve-phase nducton moto wth thd hamonc oto flux oentaton adjustment 319

6 Optmum A-Gap Flux Dstbuton wth Thd Hamonc Roto Flux Oentaton Adjustment fo Fve-Phase Inducton Moto 0.06 E 0.04 E m E x 10 4 E 0.06 E m E (c) Fg. 9. Smulaton esults fo EMF dstbuton unde loadng opeaton: the conventonal method; the poposal method esults fo the conventonal and poposed methods. The agap flux dstbuton wth the conventonal method s dstoted afte mechancal loadng. One peak nceases and the othe deceases compaed wth no-load case. Howeve, the flux dstbuton wth the poposed method s appoxmately the same as no-load case, and the ampltude s nceased slghtly. The poposed method valdates the contol objectve, and a-gap flux densty dstbuton sn t affected by mechancal loadng. x Expemental Results and Dscusson 5.1 System mplementaton (d) Fg. 8. Smulaton esults fo the poposal method unde loadng opeaton: d1 cuent; q1 cuent; (c) d3 cuent; (d) q3 cuent the vaaton of the dect and quadatue cuents fo the poposed method. The quadatue cuent s lnealy popotonal to the mechancal loadng, whle the dect cuent sd3 deceases wth mechancal loadng. The ato between the cuent components ( sd1, sd3 ) and ( sq1, sq3 ) ae not constant compaed wth the tadtonal method. Fg. 9 demonstates the EMF dstbuton smulaton The basc confguaton of expemental system s pesented n Fg. 10. It conssts of fve-phase IM ntefaced wth a dgtal contol boad based on a TMS30F8335. Coupled wth a Votex loade, multphase moto s dven by a fve-phase voltage-souce nvete, whch opeates at 10 khz swtchng fequency. The a-gap flux dstbuton can be obtaned by measung the EMF wth seach col wthn one stato phase, whch s occuped n the same slots. 5. A-gap flux dstbuton wth conventonal method The conventonal method expemental esults fo dual- 30 J Elect Eng Technol.018; 13(1):

7 Mn Kang, Wenjuan Yu, Zhengyu Wang, Wubn Kong and Ye Xao Fg. 10. The platfom fo the moto testng sd1 sq1 sd 3 sq3 Fg. 1. Expemental esults fo the conventonal method unde no-load: stato cuent; EMF dstbuton Fg. 11. Expemental esults of load opeaton fo conventonal method: stato cuent locus on the d-q fame; speed and toque plane vecto contol unde mechancal load vaaton ae shown n Fg. 11. The speed command s 600 /mn, and speed and toque values ae measued by JN 380 tansduce. The quadatue cuents sq1 and sq3 ae appoxmately popotonal to mechancal load, whle the dect cuents sd1 and sd3 ae constant. It should be noted that thee s noload toque wth Votex loade otaton, and the value s about 5.0 N.m at 600/mn. Fg. 1 demonstates the conventonal method esults of stato cuent and EMF, and the Votex loade s emoved. The stato cuent s magnetzed component wthout any toque component, and the EMF dstbuton s pesented n Fg. 1. The desed a-gap flux densty dstbuton s acheved wthout load fo the conventonal method. Fg. 13 shows the expemental esults fo the conventonal method unde ated load condton. The EMF wavefom n Fg.13 has an obvous dstoton, and the Fg. 13. Expemental esults fo the conventonal method unde ated load: stato cuent; EMF dstbuton dstoton degee s detemned by mechancal load. The fst peak s enlaged, and the second peak s mnmzed. The ampltude dstoton degee s about 5.%. 31

8 Optmum A-Gap Flux Dstbuton wth Thd Hamonc Roto Flux Oentaton Adjustment fo Fve-Phase Inducton Moto sd1 sq1 sd 3 sq3 d Fg. 15. Expemental esults fo the poposed method unde no-load: stato cuent; EMF dstbuton. d Dd m (c) Fg. 14. Expemental esults of d-q cuent fo the poposed method: d 1 -q 1 cuent; d 3 -q 3 cuent; (c) oto flux angle 5.3 A-gap flux dstbuton wth poposed method Fg. 14 demonstates the pefomance of the dect and quadatue cuents fo the poposed method. The dect cuent sd1 s constant, and the quadatue cuent s popotonal to loadng vaaton. Howeve, the dect and quadatue cuent fo the thd hamonc plane as nonlnea functon elaton, and t depends on mechancal loadng. The dect cuent s deceased by 8.1% at ated load, and the quadatue cuent s nceased by 5.4% compaed wth conventonal method. The oto flux oentaton angle s depcted n Fg. 14(c), and d s not thee tmes as lage as d. The dffeental angle V d m has nonlnea functon elatonshp wth mechancal loadng, and angle value becomes lage fom no-load to ated-load condtons. Fg. 16. Expemental esults fo the poposed method unde ated load: stato cuent; EMF dstbuton 3 J Elect Eng Technol.018; 13(1):

9 Mn Kang, Wenjuan Yu, Zhengyu Wang, Wubn Kong and Ye Xao Fg. 15 shows the expemental esults fo the poposed method wth no-load, and wavefoms ae dentcal wth ones n Fg. 1. The a-gap flux densty s affected by the leakage oto flux n the q-axs, and the quadatue cuent s zeo wthout mechancal loadng. Hence, the a-gap flux densty dstbuton ae the same fo both methods. The a-gap flux densty dstbuton wth poposed method s depcted n Fg. 16, when the mechancal load s nceased to ated value. The a-gap flux densty dstbuton s optmzed, whle the esult n Fg. 13 s dstoted wth the conventonal method. Fo the poposed method, the desed a-gap flux densty dstbuton can be obtaned unde vaous mechancal loadng condtons, and the ampltude of flux densty nceases wth loadng ncement. The EMF value s nceased by 18.5% compaed wth pefomance unde no-load condton. The eason s that the dect a-gap flux mantan constantly n the IFOC, and the quadatue one nceases wth load ncement. 6. Concluson Ths pape nvestgates optmum a-gap flux dstbuton wth thd hamonc oto flux oentaton adjustment fo fve-phase nducton moto. The poposed method s compaed wth the conventonal method, whch has constant cuent gans between the fundamental and thd hamonc planes. The poposed method s desgned to acheve the desed a-gap flux densty dstbuton wth vaous mechancal loadng, whch ovecomes the flux dstoton poblem n the conventonal method. The nonlnea cuent functons between fundamental and thd hamonc planes ae deved, and the thd hamonc flux oentaton s eal-tme adjusted wth loadng vaaton. It s confmed that the poposed method guaantees complete both planes decouplng, snce the thd hamonc oto flux oentaton s utlzed as anothe contol feedom. Nealy ectangula a-gap flux s obtaned wth the poposed method, and on utlzaton s mpoved. The poposed method s valdated by tansent and steady-state expementaton. Acknowledgements Ths wok was suppoted by the Natonal Natual Scence Foundaton of Chna unde Poject , It was also suppoted by Natonal Key Reseach and Development Plan unde Gant 017YFB Appendx The man dmensons and ated paametes fo fvephase IM ae demonstated n Table 1 and Table, espectvely. Table 1. Man dmensons of fve-phase IM - Value Paamete Value Oute damete (mm) 165 Teeth wdth(mm) 4.8 Inne damete (mm) 104 Stato slots 40 A-gap length (mm) 0.4 Roto slots 6 Yoke length (mm) 14 Connecton sta Table. Paametes of fve-phase IM Paamete Value Paamete Value Rated Powe (kw) 5.0 Rated toque (N.m) 5.0 Rated voltage (V) 19.0 Rs (mω) 11.0 Rated cuent (A) 73.0 R 1 (mω) 8.1 Numbe of poles R 3 (mω) 7.8 Rated speed (pm) 1940 (mh) 1.63 Rated fequency (Hz) 66.7 (mh) 0.15 Refeences [1] E. ev, Multphase electc machnes fo vaablespeed applcaton, IEEE Tans. Ind. Electon., vol. 55, no. 5, pp , May 008. [] E. ev, R. Bojo, F. Pofumo, H. A. Tolyat, and S. Wllamson, Multphase IM dves A technology status evew, IET Elect. Powe Appl., vol. 1, no. 4, pp , Jul [3] R. Bojo, F. Pofumo, and A. Tencon, Dual-thee phase IM dves-a technology status evew, IET Elect. Powe Appl., vol. 16, no. 4, pp , 006. [4] H. A. Tolyat,. Y. Xu, and T. A. po, A fve-phase eluctance moto wth hgh specfc toque, IEEE Tans. Ind. Appl., vol. 8, no. 3, pp , May/ Jun [5] H. A. Tolyat, T. A. po, and J. Whte, Analyss of a concentated wndng nducton machne fo adjustable speed dve applcatons. II. Moto desgn and pefomance, IEEE Tans. Enegy Conves., vol. 6, no. 4, pp , Dec [6] D. Suman and. Pase, Fault-toleant contol of fvephase pemanent-magnet motos wth tapezodal back EMF, IEEE Tans. Ind. Electon., vol. 58, no., pp , Feb [7] A. Mohammadpou, S. Sadegh, and. Pasa, A genealzed fault-toleant contol stategy fo fvephase PM moto dves consdeng sta, pentagon, pentacle connectons of stato wndngs, IEEE Tans. Ind. Electon., vol. 61, no. 1, pp , Jan [8] H. Guzman, M. J. Duan, F. Baeo, B. Bogado, and S. Toal, Speed contol of fve-phase IMs wth ntegated open-phase fault opeaton usng modelbased pedctve cuent contol technques, IEEE Tans. Ind. Electon., vol. 61, no. 9, pp , Aug.013. [9] H. Guzman, F. Baeo, and M. J. Duan, IGBTgatng falue effect on a fault-toleant pedctve cuent-contolled fve-phase nducton moto dve, IEEE Tans. Ind. Electon., vol. 6, no. 1, pp. 15-0, 33

10 Optmum A-Gap Flux Dstbuton wth Thd Hamonc Roto Flux Oentaton Adjustment fo Fve-Phase Inducton Moto Jan [10] A. Mohammadpou and. Pase, Global faulttoleant contol technque fo multphase pemanentmagnet machnes, IEEE Tans. Ind. Electon., vol. 51, no. 1, pp , Jan./ Feb [11] H. S. Che, E. ev, M. Jones, W. Hew, and N. Abd. Rahm, Cuent contol methods fo an asymmetcal sx-phase IM dve, IEEE Tans. Ind. Electon., vol. 9, no. 1, pp , Jan.014. [1] A. G. Yepes, J. Malva, A. Vdal, O. ópez, and J. Doval-Gandoy, Cuent hamoncs compensaton based on multesonant contol n synchonous fames fo symmetcal n-phase machnes, IEEE Tans. Ind. Electon., vol. 6, no. 5, pp , May [13]. Pasa, and H. A. Tolyat, Fve-phase pemanentmagnet moto dves, IEEE Tans. Ind. Appl., vol. 41, no. 1, pp , Jan./Feb [14] H. Xu, H. A. Tolyat, and. J. Petesen, Fve-phase IM dves wth DSP-based contol system, IEEE Tans. Powe Electon., vol. 17, no. 4, pp , Jul. 00. [15] O. Dodevc, M. Jones, and E. ev Analytcal fomulas fo phase voltage RMS squae and THD n PWM multphase system, IEEE Tans. Ind. Electon., vol. 30, no. 8, pp , Mach [16] N. Bode, M. Jones, and E. ev, A space vecto PWM wth common-mode voltage elmnaton fo open-end wndng fve-phase dves wth a sngle DC supply, IEEE Tans. Ind. Electon., vol. 61, no. 5, pp , May [17] N. Bodo, E. ev, and M. Jones, Investgaton of cae-based PWM technques fo a fve-phase openend wndng dve topology, IEEE Tans. Ind. Electon., vol. 60, no. 5, pp , May [18] G. Caasco and C. A. Slva, Space vecto PWM method fo fve-phase two-level VSI wth mnmum hamonc njecton n the ove-modulaton egon, IEEE Tans. Ind. Electon., vol. 60, no. 5, pp , May [19] J. Wang, R. Qu, and. Zhou, Dual-oto multphase pemanent magnet machne wth hamonc njecton to enhance toque densty, IEEE Tans. Appl. Supecond., vol., no. 3, pp. 5004, Jun. 01. [0] H. Xu, H. A.Tolyat, and. J. Petesen, Roto feld oented contol of fve-phase IM wth the combned fundamental and thd hamonc cuents, n Poc. IEEE APEC, Anahem, CA, 001, pp [1] M. J. Duan, F. Salas, and M. R. Aahal, Bfucaton analyss of fve-phase IM dves wth thd hamonc njecton, IEEE Tans. Ind. Electon., vol. 55, no. 5, pp , May [] C. C. Schalau,. F. A. Peea,. A. Peea, and S. Haffne, Pefomance of a fve-phase nducton machne wth optmzed a gap feld unde open loop V/f contol, IEEE Tans. Enegy Conves., vol. 3, no. 4, pp , Dec [3]. A. Peea, C. C. Schalau,. F. Peea, and J. F. Haffne, Geneal model of a fve-phase nducton machne allowng fo hamoncs n the a gap feld, IEEE Tans. Enegy Conves., vol. 1, no. 4, pp , Dec [4] R. O. C. ya, and T. A. po, Toque densty mpovement n a sx-phase IM wth thd hamonc cuent njecton, IEEE Tans. Ind. Appl., vol. 38, no. 5, pp , Sep./ Oct. 00. [5] A. Yong-e, M. J. Kampe, and A. D. Roux, Novel dect flux and dect toque contol of sx-phase nducton machne wth nealy squae a-gap flux densty, IEEE Tans. Ind. Appl., vol. 43, no. 6, pp , Nov./ Dec [6] A. Abdel-Khalk, M. Masoud, and W. Bay, Elevenphase nducton machne: Steady-state analyss and pefomance evaluaton wth hamonc njecton, IET Elect. Powe Appl., vol. 4, no. 8, pp , Sep [7] A. S. Abdel-Khalk, M. I. Masoud, and B. W. Wllams, Optmum flux dstbuton wth hamonc njecton fo a multphase nducton machne usng genetc algothms, IEEE Tans. Enegy Conves., vol. 6, no., pp , Jun [8] A. S. Abdel-Khalk, M. I. Masoud, S. Ahmed, and A. M. Massoud, Effect of cuent hamonc njecton on constant oto volume multphase nducton machne statos: A compaatve study, IEEE Tans. Ind. Appl., vol. 48, no. 6, pp , Nov./Dec. 01. [9] M. Mengon,. Za, A. Tan,. Pasa, G. Sea, and D. Casade, Hgh-toque-densty contol of multphase nducton moto dves opeatng ove a wde speed ange, IEEE Tans. Ind. Electon., vol. 6, no., pp , Feb [30]. Zheng, J. E. Fletche, B. W. Wllams, and X. He, Dual-plane vecto contol of a fve-phase nducton machne fo an mpoved flux patten, IEEE Tans. Ind. Electon., vol. 55, no. 5, pp , May [31] A. S. Abdel-Khalk, M. I. Masoud, and B. W. Wllams, Impoved flux patten wth hamonc njecton fo multphase nducton machnes, IEEE Tans. Ind. Electon., vol. 7, no. 3, pp , Ma. 01. Mn Kang eceved the B.S. and Ph.D. degees fom the College of Electcal Engneeng, Zhejang Unvesty, Hangzhou, Chna, n 003 and 008, espectvely. Fom 008 to 011, he was a ectue n the College of Electcal Engneeng, Zhejang Unvesty of Scence and Technology, Chna. He s cuently assocate Pofesso of Zhejang of Scence and Technology. Hs eseach nteests ae n multphase beangless machnes and AC dves. 34 J Elect Eng Technol.018; 13(1):

11 Mn Kang, Wenjuan Yu, Zhengyu Wang, Wubn Kong and Ye Xao Wenjuan Yu was bon n shandong, Chna, n She eceved the B.S. degee fom Huazhong Unvesty of Scence &Technology, Wuhan, n 008. She eceved the M.S. degee fom Zhejang Unvesty, Hangzhou, n 011. He eseach nteests ae hgh-powe multphase moto dves. Zhengyu Wang was bon n Hunan, Chna, n He eceved the Bachelo of Engneeng degee fom Xan Jaotong Unvesty n 00, and the Maste of Engneeng degee fom Southwest Jaotong Unvesty n 014, espectvely. He had been wokng at CRRC Zhuzhou Insttute and engaged n the feld of electc machne contol desgn fom Aug 00 to Jan 007,afte that he has been wokng at Hunan CRRC Tmes Electc Vehcle and engaged n the feld of moto dve contol system desgn untl now. Wubn Kong (M 15) was bon n Zhejang, Chna, n He eceved the B.S. and Ph.D. degee fom Zhejang Unvesty, Hangzhou, Chna n 009 and 014, espectvely. Hs eseach nteests ae hgh-powe multphase moto dves and fault toleant contol moto dve appled n EV. Fom 015, he has been a lectue wth Huazhong Unvesty of Scence &Technology, Wuhan, Chna. Ye Xao was bon n Hunan, Chna, n He eceved a bachelo's degee fom Bejng Unvesty of natonnaltes, Bejng, Chna n 005. Hs man eseach decton s the moto contol of new enegy vehcles. 35