Speed Control of Matrix Converter-Fed Five-Phase Permanent Magnet Synchronous Motors under Unbalanced Voltages

Transcription

1 enegie Aticle Speed Contol of Matix Convete-Fed Five-Phae Pemanent Magnet Synchonou Moto unde Unbalanced Voltage Bozou Youefi 1 ID, Soodabeh Soleymani 1, *, Babak Mozafai 1 and Seid Agha Gholamian 2 1 Depatment of Electical and Compute Engineeing, Science and Reeach Banch, Ilamic Azad Univeity (IAU), Tehan , Ian; bozou.youefi@biau.ac.i (B.Y.); mozafai@biau.ac.i (B.M.) 2 Faculty of Electical and Compute Engineeing, Babol Nohivani Univeity of Technology, Babol , Ian; gholamian@nit.ac.i * Coepondence:.oleymani@biau.ac.i; Tel.: Academic Edito: Chunhua Liu Received: 2 Augut 2017; Accepted: 25 Septembe 2017; Publihed: 28 Septembe 2017 Abtact: Five-phae pemanent magnet ynchonou moto (PMSM) have pecial application in which highly accuate peed and toque contol of moto ae a tong equiement. Diect Toque Contol (DTC) i a uitable method fo dive tuctue of e moto. If in thi method, intead of uing a common five-phae ouce invete, a e-phae to five-phae matix convete i ued, low-fequency cuent hamonic and high toque ipple ae limited, and an impoved input powe facto i obtained. Becaue input of uch convete ae diectly upplied by input e-phae upply, an imbalance in will caue poblem uch a unbalanced tato cuent and electomagnetic toque fluctuation. In thi pape, a new method i intoduced to emove peed and toque ocillato facto. Fo thi pupoe, moto toque equation wee developed and ocillation component ceated by unbalanced ouce, detemined. Then, uing active and eactive powe efeence geneato, contolle powe efeence wa adjuted in uch a way that electomagnetic toque of moto did not change. By thi mean, a numbe of featue including peed, toque, and flux of moto wee impoved in tem of above-mentioned condition. Simulation wee analyzed uing Matlab/Simulink oftwae. Keywod: pemanent magnet ynchonou moto; matix convete; diect powe contol; unbalanced upply 1. Intoduction Pemanent magnet ynchonou moto (PMSM) ae imila to odinay ynchonou moto, with exception that i field winding ha been eplaced with a pemanent magnet. Among e moto, five-phae PMSM ha a numbe of featue uch a highe efficiency, eliability, and powe denity than o type of PMSM [1]. Thee moto ae commonly ued in pecial indutial cae uch a maine populion ytem, hybid vehicle, and aeopace induty. In mot cae, it i neceay to deign a pope dive with mall ize and high eliability [2,3]. One of common method to contol toque (and thu finally peed) of e moto i Diect Toque Contol (DTC). The block diagam of Switching Table baed Diect Toque Contol (ST-DTC) cheme i hown in Figue 1 [4]. Enegie 2017, 10, 1509; doi: /en

2 Enegie 2017, 10, of 21 Enegie 2017, 10, of 21 Enegie 2017, 10, of 21 Figue 1. A block diagam of Switching Table Baed Diect Toque Contol with cicula tato flux path. Figue1. 1. A block diagamof of Switching Table Baed Diect Toque Contol with cicula tato flux The path. cheme include two hyteei contolle. A tato flux contolle impoe time duation of active vecto, which move tato flux along efeence tajectoy, and toque The The cheme cheme contolle include include detemine two two hyteei hyteei time contolle. duation contolle. of A tato A zeo tato flux contolle flux vecto, contolle impoe which impoe keep time duation moto time duation of toque active in of defined-by-hyteei active vecto, which vecto, move toleance which move tato band. flux Finally, tato along flux fo along efeence evey ampling tajectoy, efeence time tajectoy, and toque and contolle vecto toque election detemine contolle block detemine chooe time duation time invete of duation zeo witching of zeo vecto, tate (SA, which vecto, SB, keep SC), which which moto keep toque educe moto in toque defined-by-hyteei intantaneou defined-by-hyteei and toque toleance eo. band. toleance Finally, fo band. evey Finally, ampling fo time evey ampling vecto time election block vecto chooe Figue election invete 2 how block witching chooe diagam tate of (SA, a invete five-phae SB, SC), witching which educe ouce tate (SA, invete intantaneou SB, which SC), which i and called toque educe claic eo. intantaneou method Figue of diect 2 how and toque contol diagam eo. in of thi a five-phae aticle. ouce invete which i called claic method Figue of diect 2 how toque contol diagam in of thi a five-phae aticle. ouce invete which i called claic method of diect toque contol in thi aticle. Figue 2. Diagam of five-phae ouce invete. Figue 2. Diagam of a five-phae ouce invete. Thee Thee ae ae two two majo majo Figue dawback dawback 2. Diagam to to applying applying of a five-phae invete: invete: low-fequency low-fequency ouce invete. hamonic hamonic and and high high toque toque ipple ipple [5 7]. [5 7]. To To eliminate eliminate e e poblem, poblem, diect toque diect contol toque method contol with method a e-phae with a to e-phae five-phae Thee ae to matix two five-phae majo convete dawback matix (Figue convete to applying 3) i (Figue intoduced invete: 3) i intoduced [8 10]. low-fequency Thi [8 10]. cicuit Thi i an cicuit hamonic AC to i AC an AC convete. and to high AC toque Compaed convete. ipple Compaed to [5 7]. VSI convete, To to eliminate VSI intemediate convete, e poblem, intemediate cicuit and DC cicuit diect link have and toque DC been contol link emoved have method been [11,12]. emoved with a e-phae [11,12]. to five-phae matix convete (Figue 3) i intoduced [8 10]. Thi cicuit i an AC to AC convete. Compaed to VSI convete, intemediate cicuit and DC link have been emoved [11,12].

3 Enegie 2017, 10, of 21 Enegie 2017, 10, of 21 V SA i A V SB SAa SAb SAc SAd SAe i B V SC R f C f SBa SBb SBc SBd SBe i C L f SCa ia v SCb an i b vbn SCc i c v cn SCd i d v SCe dn i e ven Figue 3. Diagam of e-phae to five-phae matix convete. Figue 3. Diagam of a e-phae to five-phae matix convete. Uing moe degee of of feedom in in thi convete, an an optimal witching table i i povided, along with elimination of of mentioned poblem, input input powe powe facto facto i i alo alo contolled. Becaue input of of matix convete ae diectly upplied by by input ouce, one of facto that make uch convete inefficient i i imbalance in in e-phae input upply [13]. In In a e-phae ytem, imbalance uually take place when magnitude o phae angle of line ae diffeent fom balanced condition. The The imbalance deceae moto pefomance. It It can alo caue cuent imbalance which i i moe intene than than imbalance. Unbalanced cuent lead to to toque pulation and inceae loe. Theefoe, powe quality and and enegy enegy efficiency will will be be educed educed [14]. [14]. Common caue of of imbalance ae faulty opeation of of powe facto facto coection equipment, unbalanced o untable utility upply, unevenly ditibuted ingle-phae load on on ame powe ytem, and and unidentified ingle-phae to to gound gound fault. fault. Becaue uch matix convete ae geneally applied whee accuate contol of of peed peed and and toque of of a moto i i conideed, developing a new new method to to eliminate imbalance impact on on poce poce pefomance i i neceay. Thi Thi pape pape popoe popoe a diect diect powe powe contol contol technique technique to to olve olve thi thi poblem. poblem. Fit, Fit, moto powe and toque equation ae ae developed and and ocillato phae which come come into into exitence exitence by by imbalance imbalance ae ae epaated. epaated. Then, uing an an active and and eactive eactive powe powe efeence geneato, geneato, contolle contolle powe powe efeence efeence i i changed changed o o that that machine machine electomagnetic toque toque emain emain contant. contant. It It mean mean that that active active and and eactive eactive powe powe poduced poduced by by geneato geneato hould hould popely popely follow follow active active and and eactive eactive powe powe efeence efeence which which i i favoable. favoable. In thi way, in in addition addition to to optimal optimal peed peed contol, contol, toque toque ocillato ocillato paamete paamete will will alo alo be be eliminated. eliminated. 2. Modeling of Five-Phae PMSM and Matix Convete The five-phae PMSM tato equation can be expeed a follow: d Λ, Λ = L I Λ V (1) = R I dλ, Λ = L I Λ m (1) whee R i tato eitance matix, i ai gap flux, L whee R i tato inductance matix i tato eitance matix, Λ i ai gap flux, L i tato inductance matix including elf-inductance and and mutual mutual inductance, and Λand m iλ m linkage i linkage flux matix flux which matix i geneated which i by geneated pemanent by pemanent magnet andmagnet can beand expeed can be a expeed follow: a follow: [ ] Λ Λ = λ in( θ )in( θ 2 π /5)in( θ 4 π /5)in( θ 4 π /5)in( θ 2 π /5) T m = λ m [in(θ m ) in(θ 2π/5) in(θ 4π/5) in(θ 4π/5) in(θ 2π/5)] T (2) (2) whee λ i value of pemanent magnet flux and θ i oto poition. whee λ m i value of pemanent magnet flux and θ i oto poition. Fo tanfe of component of a five-phae ytem fom (abcde) pace to pependicula ( α β ) and ( Z Z ) pace [15], namely ( α β Z Z ), following equation ae ued:

4 Enegie 2017, 10, of 21 Fo tanfe of component of a five-phae ytem fom (abcde) pace to pependicula (α β) and (Z 1 Z 2 ) pace [15], namely (α β Z 1 Z 2 ), following equation ae ued: f αβ = 2 5 ( f a a f b a 2 f c a 3 f d a 4 f e ) (3) f z 1 z 2 = 2 5 ( f a a 3 f b a f c a 4 f d a 2 f e ) (4) In above equation, a = exp(2π/5). Incopoating Equation (3) and (4) into Equation (1), tato can be expeed a follow: V q = i q ωλ d dλ q, V d = i d ωλ q dλ d, V z1 = i z1 dλ z1, V z2 = i z2 dλ z2 (5) whee v q, v d, v z1, and v z2 ae q, d, z 1, and z 2 axe of of tato, i q, i d, i z1, and i z2 ae q, d, z 1, and z 2 axe of cuent of tato, ω i angula velocity, and λ q, λ d, λ z1, and λ z2 ae q, d, z 1, and z 2 axe of flux linkage of tato. They can be expeed a follow: λ d = L d i d λ m, λ q = L q i q, λ z1 = L l i z1, λ z2 = L l i z2 (6) whee L q and L d ae inductance of q and d axe, epectively, and L l i leakage inductance of tato. The electomagnetic toque can be obtained a follow: T e = W co θ m (7) whee θ m i mechanical angle of oto and W co i co-enegy. Regadle of o fomula, final equation fo toque i obtained a follow: T e = p [λ mi q (L d L q )i d i q ] (8) In Equation (8), p i pole pai numbe. Accoding to above equation, in a five-phae pemanent magnet ynchonou moto, only baic component of (α β) ubpace influence poduction of electomagnetic toque. Thu, in dive ytem of thi moto, pace vecto of thi ubpace ae elected. It hould be noted that when a vecto of (α β) ubpace i choen, it coeponding vecto in (Z 1 Z 2 ) ubpace will be alo timulated imultaneouly. Having thi infomation, it i poible to eaily imulate a five-phae PMSM. In next tep, modeling of a five-phae matix convete will be dicued. The cicuit topology of a e-phae to five-phae matix convete i hown in Figue 3. A can be een, thi convete ha five bae; evey bae ha e two-way witche. Each witching function i defined a follow: { 0 witch, S S jk (t) = jk i open j = { A, B, C}, k = { a, b, c, d, e} (9) 1 witch, S jk i cloed whee J and k ae input and output phae, epectively. The convete output vecto in (α β) and (Z 1 Z 2 ) ubpace can be obtained by: { V αβ o = 2 5 (V a V b e j 2π 5 V c e j 4π 5 V d e j 4π 5 V e e j 2π 5 ) = V o e jα o V Z 1Z 2 o = 2 5 (V a V b e j 4π 5 V c e j 2π 5 V d e j 2π 5 V e e j 4π 5 ) = V o e jα o whee v o i ize of output vecto and α o i phae angle. Geneally, e ae 3 5 = 243 witching tate in matix convete; howeve, only 93 vecto coniting of e zeo vecto and 90 active vecto which have contant diection can be ued. Like five-phae ouce invete (VSI), e 90 vecto fom ten concentic egula polygon which ae divided (10)

5 Enegie 2017, 10, of 21 Enegie e zeo 2017, 10, vecto 1509 and 90 active vecto which have contant diection can be ued. Like 5 of 21 five-phae ouce invete (VSI), e 90 vecto fom ten concentic egula polygon which into ae divided lage, medium, into lage, and medium, mall ize. and Figue mall 4 ize. how Figue 4 how vecto in vecto (α β) in and (Z ( 1 α Z 2 β ) ubpace. and ( Z Z The ) numbe ubpace. hown The numbe in thi figue hown coepond in thi figue to coepond witching to tatu. witching tatu. 1 2 V 4 V 3 V 5 V 2 V 6 V 1 V 7 V 10 V 8 V 9 (a) (b) Figue 4. Phae-to-gound output vecto in ubpace (a) ( α β ) (b) ( Z Figue 4. Phae-to-gound output vecto in ubpace (a) (α β) (b) (Z 1 1 Z 2 ). 2) DTC DTC Method Method Uing Uing a Matix Matix Convete Convete The The pinciple pinciple of of diect diect toque toque contol contol method method uing uing a matix matix convete convete i i imila imila to to claic claic method method of of diect diect toque toque contol contol (uing (uing ouce ouce invete). invete). Fit, Fit, claic claic diect diect toque toque contol contol i i done done and and invete invete output output vecto vecto ae ae detemined. detemined. Thee vecto ae ae called called vitual vitual vecto vecto (vecto (vecto v though 1 though v 1 10 inide inide mall mall cicle ae hown in in Figue Then, it it mut be be detemined which which vecto of of matix matix convete can can be eplaced be eplaced by by invete invete vitual vitual vecto. vecto. In geneal, In geneal, e e ae ix ae matix ix matix convete convete vecto vecto fo each fo each vitual vitual vecto. vecto. Fo Fo example, example, vecto vecto v 1 mean v mean vecto vecto 3, 5, 13, 5, 15, 13, 23, 15, and 23, and 25 fom 25 fom 1 witching witching tatu. tatu. The The next next tep tep i to i tudy to tudy whee whee phae-to-gound vecto vecto ae ae located, located, in which in which ecto ecto of of ix ix vecto vecto pace. pace. Figue Figue 5 how 5 how path path of of input input of a of e-phae a e-phae to a to five-phae a five-phae convete. convete. Knowing Knowing input input vecto vecto ection, ection, and accoding and accoding to Figue to Figue 5, 5, path i path divided i divided into ix into ecto, ix ecto, fit of fit which of which tat tat fom 0ad. fom 0ad. V AB V AC V BC V BA V CA V CB Small Vecto Lage Vecto Sec 6 Sec 1 Sec 2 Sec 3 Sec 4 Sec 5 π /3 0 π /3 2 π /3 π 2 π /3 π /3 Figue 5. Input vecto diection tating fom 0ad. Figue 5. Input vecto diection tating fom 0 ad. In thi cae, e will be ix vecto in evey ecto which do not change i ign in ecto, In thi and cae, thu e can will be ued be ix in diect vecto toque in contol evey method. ecto which Fom do among not change ix i vecto, ign fou in vecto ecto, ae and mall thu and can two be vecto ued in ae lage. diect Thee toque contol vecto method. (two Fom mall among vecto and ix one vecto, lage fou vecto ae mall and two vecto ae lage. Thee vecto (two mall vecto and

6 Enegie 2017, 10, of 21 Enegie 2017, 10, of 21 one vecto) lage can vecto) be ued canin beach uedecto in each a hown ecto a in hown Figue in 5. Figue It can be 5. concluded It can be concluded that compaed that compaed to claical to claical diect toque diectcontol toquein contol which inonly which one only one vecto i vecto poduced i poduced in each ampling each ampling cycle, cycle, matix matix convete convete can delive can delive e e vecto. vecto. Thee Thee vecto vecto have have ame ameffect on oninceaing o deceaing flux and toque. Theefoe, matix matix convete ha ha two two moe moe degee degee of feedom of feedom than than ouce ouce invete, invete, which which i uedi toued contol to contol o paamete o paamete of machine of machine uch auch powe a facto powe and facto lineand cuent line THD, cuent efoe, THD, efoe, educing educing high fluxhigh and toque flux and ipple. toque Accoding ipple. Accoding to above to tatement, above atatement, witchinga table witching i povided table fo i povided diectfo toque diect contoltoque of five-phae contol of PMSM, five-phae which can PMSM, be een which a can a pat be of een a block a pat diagam of block of diagam DTC method of DTC uingmethod a matix uing convete, a matix aconvete, hown in Figue a hown 6 [16]. in Figue 6 [16]. Figue 6. A block diagam of diect toque contol method uing a matix convete. 4. Five-Phae PMSM Contol in Tem of of Unbalanced Supply Voltage 4.1. Diect Powe Contol of a Five-Phae PMSM In oto efeence fame of PMSM, of tato equation can be expeed a follow [17]: V = R I d dϕ ϕ jω ϕ (11) V = R I jωϕ (11) whee V, R, and ϕ epeent tato, eitance, and flux, epectively. whee The V tato, R, flux and linkage ϕ epeent vecto in tato oto, efeence eitance, fame and expeed flux, epectively. a follow: The tato flux linkage vecto in oto efeence fame i expeed a follow: ϕ = L I ϕ (12) ϕ = LI ϕ (12) whee L i elf-inductance of tato. whee The L elationhip i elf-inductance of tato. between oto flux and tato flux in tationay efeence ytem (α β) and The oto elationhip efeence between ytem (α oto β ) flux i hown and tato in Figue flux in 7. tationay efeence ytem ( α β) and oto efeence ytem ( α β ) i hown in Figue 7.

7 Enegie 2017, 10, of 21 Enegie 2017, 10, of 21 β β φ inθ θ φ φ coθ φ α α Figue 7. Flux of oto and tato flux vecto in oto and tationay efeence fame. The tato flux in ( α The tato flux in (α efeence fame i expeed a follow: β ) efeence fame i expeed a follow: j ϕ ϕ e θ (13) ϕ = ϕ e jθ (13) whee θ i angle of tato flux in oto efeence fame, a well a angle between whee θ i angle of tato flux in oto efeence fame, a well a angle between tato flux and oto flux. tato flux and oto flux. The tato active powe Equation i a follow [18]: The tato active powe Equation i a follow [18]: 5 P = V i (14) P = V i (14) Subtituting Equation (11) in Equation (14), and egadle of tato eitance, P can be Subtituting Equation (11) in Equation (14), and egadle of tato eitance, P expeed a follow: can be expeed a follow: ) P P= 5 jωϕ I 2 ( dϕ ϕ ) I (15) whee ω whee ω i angula fequency of oto. i angula fequency of oto. By deiving Equation (13), Equation (16) can be obtained: By deiving Equation (13), Equation (16) can be obtained: dϕ d ϕ = d ϕ d ϕ e jθ dθ jθ = jθ dθ je jejθ ϕ ϕ (16) (16) Refeing Refeing to to Figue Figue 7, 7, following following Equation Equation i i obtained: obtained: dθd θ 2 = ω 1 ω 2 (17) whee ω 1 i i tato angula fequency. Subtituting Equation (17) in Equation (16): dϕ d d ϕ d ϕ ϕ jθ jθ jθ = d ϕ = e jθ e j(ω j( ω ) e ϕ e j( ω ω ) ϕ (18) ω )e jθ ϕ = d ϕ e jθ j(ω 1 ω )ϕ (18) On ohand, hand, tato tato cuent cuent in inoto fame oto can fame be calculated can be calculated uing uing following Equation: following Equation: I = ϕ ϕ ϕ ϕ (19) I = L (19) L Uing equation obtained above, active powe Equation can be witten a follow: Uing equation obtained above, active powe Equation can be witten a follow: P = 51 P = 5 1 in 2 L ωϕ ω ϕ 2 L ϕ ϕ in θ θ (20) (20) By deiving Equation (19), active powe change ae obtained a follow:

8 Enegie 2017, 10, of 21 Enegie 2017, 10, of 21 By deiving Equation (19), active powe change ae obtained a follow: dp d( ϕ inθ ) =kω ϕ (21) t dp = k t ω ϕ d( ϕ in θ) (21) Similaly, eactive powe i obtained fom following Equation [19]: Similaly, eactive powe i obtained fom 5 following Equation [19]: Q = V i (22) 2 Q = 5 2 V i (22) Incopoating equation, Equation (23) i expeed a follow: Incopoating equation, Equation (23) i 5 expeed d ϕ a follow: ( ) Q = jωϕ I 2 (23) Q = 5 2 ( dϕ A a eult, eactive powe Equation can jω ϕ be witten ) a Ifollow: (23) A a eult, eactive powe Equation 5 ω can be L m = ( witten co afollow: Q ) ϕ ϕ θ ϕ 2 σ L L (24) ω Q = 5 ϕ 2 σl ( L m and imila to Equation (21), eactive powe ϕ change L co θ ϕ ) (24) ae obtained a follow: and imila to Equation (21), eactive dq powe change d ( ϕ co ae obtained θ) = k ω ϕ a follow: (25) t dq = k t ω ϕ d( ϕ co θ) Accoding to Equation (21) and (25), apid change (25) of active and eactive powe can be made by change in ϕ inθ and ϕ coθ epectively. It can be een fom Figue 7 that ϕ inθ and Accoding to Equation (21) and (25), apid change of active and eactive powe can be made by change ϕ coθ in ae ϕ in θcomponent and ϕ coof θ epectively. tato flux It canϕ be een fom Figue 7 that ϕ in θ and ϕ, pependicula to oto flux, and in co θ ae diection component of oto oflux, epectively. tato flux ϕ, Thi pependicula how that, to if tato oto flux, vaiation and in i diection in diection of oto flux, epectively. Thi of oto flux, namely ϕ how coθ, that, eactive if powe tatoq fluxchange. vaiationsimilaly, i in diection if tato of flux oto vaiation flux, namely ϕ co θ, eactive powe Q change. Similaly, if tato flux vaiation i pependicula to oto flux, namely ϕ i pependicula to oto flux, namely ϕ inθ, active powe P change. in θ, active powe P change Invetigating Effect of Two-Level Invete Voltage Vecto on Active and Reactive Powe Change To tudy effect of of vecto, vecto, vecto vecto pace pace of of of a two-level of a two-level invete invete i dividedi into divided ix ecto, into ix each ecto, ecto each cove ecto 60cove degee 60 [20]. degee Thi[20]. illutated Thi i illutated in Figuein 8. Figue 8. V 3 V 2 V 4 V 1 V 5 V 6 Figue 8. Six vecto ecto of a e-phae ouce invete. In efeence [21], effect of vecto on active and eactive powe change wa In efeence [21], effect of vecto on active and eactive powe change invetigated. wa invetigated. Accoding to Figue 9, uppoe that tato flux vecto in efeence fame of oto ( ϕ ) 1 i located in econd ection of vecto pace. A hown in thi figue, thi vecto lead oto flux vecto by θ degee. Now, if vecto V i applied to convete, poition of 1 1

9 Enegie 2017, 10, of 21 Accoding to Figue 9, uppoe that tato flux vecto in efeence fame of oto (ϕ 1 ) i Enegie located 2017, in10, 1509 econd ection of vecto pace. A hown in thi figue, thi vecto lead oto 9 of 21 flux vecto by θ 1 degee. Now, if vecto V 1 i applied to convete, poition of tato flux vecto i changed and moved to ϕ 2. It tato flux vecto i changed and moved to ϕ can. It can be een be een that that by applying by applying vecto vecto V 2 1 to convete, value of ϕ V to convete, value of inϕ θ in deceae θ and value of ϕ co θ inceae. A a eult, with 1 deceae and value of ϕ coθ inceae. A a eult, epect with epect to to Equation Equation (21) and (21) (25), and (25), active active and eactive and eactive powe powe inceae. inceae. β β II III 1 1 φ inθ 2 2 φ inθ φ 1 θ 1 θ 2 V φ coθ φ φ coθ 2 2 φ 2 α α IV VI I V Figue 9. Effect of vecto V 1 on on active active and and eactive eactive powe powe change. change. In ame way, knowing poition of of tato flux flux in in oto oto efeence fame, fame, effect effect of all of all vecto vecto on on active active and and eactive powe change can can be be tudied. Accoding to example, a witching table can be pepaed and ued fo diffeent mode Vecto Space unde Imbalance Condition In In thi ection, an an imbalance caued by by an an unbalanced load i i tudied. An aymmetic five-phae ytem can can be be decompoed into five ymmetical ytem of of five five phae. Thee five ytem ae called equence equence of of zeo, zeo, poitive poitive equence equence (α ( β) α ubpace, β) ubpace, negative negative equence equence (α β) ( ubpace, α β) ubpace, poitive equence (Z poitive equence 1 Z 2 ) ubpace, and negative equence (Z ( Z Z ) ubpace, and negative equence 1 Z 2 ) ubpace. They can be obtained by, ( Z Z ) ubpace. They can be obtained by, x a [ ] xa x 0 x αβ x αβ x z 1 z 2 x T 1 1 a a 2 a 3 a 4 x b z 1 z 2 = a a a a x b T a 3 a 2 a x 1 a x x x x x = 3 a a 4 a αβ αβ z1z2 z1z2 1 a a a 2 c (26) x x d c (26) 5 1 a 2 a 4 a 1 a 3 a a 4 a 2 a 3 x e xd whee a = e j(2π/5). Paamete x 1 a a a a x a, x b, x c, x d, and x e epeent unbalanced e ytem. Paamete x 0, x, and x epeent zeo, poitive, and negative equence component, epectively. It i aumed (2 /5) whee a= e j π 0 that five-phae. Paamete ytem being xa, tudied xb, xc, xd, iand a five-wie x e epeent five-phae unbalanced ytem. Thiytem. mean Paamete that ytem x, doe x, and not have x epeent a neutalzeo, wie. poitive, In thi cae, and negative um of equence five-phae component, cuent epectively. i alway equal It i aumed to zeo (i that a i b five-phae i c i d i e ytem = 0). A being a eult, tudied i zeo a five-wie equence five-phae cuent component ytem. Thi would mean bethat equal to ytem zeo. Conequently, doe not have a neutal component wie. In ofthi cae, zeo equence um of five-phae ae zeo (v cuent a v b i valway c v d equal v e = to 0). zeo ( i Theefoe, i i i to itake = 0) into. A account a eult, poitive zeo equence and negative cuent equence, component would and be cuent equal vecto zeo. a b c d e can Conequently, be expeed acomponent follow: of zeo equence ae zeo ( v v v v v = 0). a b c d e Theefoe, to take into account poitive and negative equence, and cuent vecto v = can ( v v be ) = v expeed α jv β = (v a follow: α v α ) j(v β v β ), v = ( v v ) = v z1 jv z2 = (v z1 v z1 ) j(v z2 v z2 ) i = ( i i ) = i α ji β = (i α iα ) j(i β i β ), i = ( i (27) i ) = i z1 ji z2 = (i z1 i z1 ) j(i z2 i z2 ) v= ( v v) = v jv = ( v v) jv ( v), v= ( v v) = v jv = ( v v ) jv ( v ) α β α α β β z1 z2 z1 z1 z2 z2 (27) i = ( i i ) = i ji ( i i ) ji ( i ), i ( i i ) i ji ( i i ) ji ( i ) α β = α α β β = = z1 z2 = z1 z1 z2 z2 Thu, two pace vecto of five-phae ytem can be expeed a follow:

10 Enegie 2017, 10, of 21 Enegie 2017, 10, of 21 Thu, two pace vecto of five-phae ytem can be expeed a follow: x = x jx = ( x ax ax ax ax ), x = x jx = ( x ax ax ax ax ) α β x αβ = x α jx β = 2 α β a b c d e z1 z2 z1 z2 5 (x a ax b a 2 x c a 3 x d a 4 x e ), x z1z2 = x z1 jx z2 = 2 a b c d e (28) 5 5 (x 5 a a 3 x b ax c a 4 x d a 2 x e ) (28) A five-phae unbalanced ytem can be demontated a um of poitive and negative equence A five-phae a follow: unbalanced ytem can be demontated a um of poitive and negative equence An a unbalanced follow: five-phae ytem can be epeented a um of two poitive and negative equence An unbalanced vecto that five-phae otate in ytem oppoite can be diection epeented with a ame um fequency of two poitive a follow: and negative equence vecto that otate in oppoite diection with ame fequency a follow: j( ωt θ ) j( ωt θ ) x = x x = x x x = x e x e = x e j(ωtθ) (29) x e j(ωtθ ) (29) 4.4. Diect Powe Contol 4.4. Diect Powe Contol Figue 10 how a block diagam of diect powe contol method of a five-phae PMSM. Figue 10 how a block diagam of diect powe contol method of a five-phae PMSM. 5 Figue Figue A block A block diagam diagam of diect of diect powe powe contol. contol. It can It can be be een een fom fom figue figue that that and and cuent cuent ae ae ampled ampled fom fom tato tato and and tanmitted to to tationay tationay efeence efeence fame. fame. Then, Then, uing uing e e and and cuent, cuent, active active and and eactive eactive powe powe can can be calculated. be calculated. Moeove, Moeove, ize ofize of tato flux tato andflux it angle and it aeangle obtained ae obtained uing uing following following Equation Equation [22]: [22]: β ϕ = ( V R I ), ϕ tg ( ) ϕ = (V R I ), ϕ = tg 1 ( ϕ β (30) ϕ ) (30) αϕ α The tato flux obtained fom ynchonou efeence fame i tanmitted to oto The tato flux obtained fom ynchonou efeence fame i tanmitted to oto efeence fame efeence and ϕ fame and ϕ i calculated. Then, accoding to angle of flux, egion whee i calculated. Then, accoding to angle of flux, egion whee flux vecto i located flux vecto i obtained i located (withi Nobtained a hown(with in Figue N a 10). hown In geneal, in Figue 10). pupoe In geneal, of diect pupoe powe of contol diect method powe icontol that method active i and that eactive active powe and of eactive moto powe popely of moto followpopely favoable follow active favoable and eactive powe and eactive efeence. powe In ode efeence. to achieve In ode thi, to achieve etimated thi, powe value etimated ae compaed powe value withae compaed with efeence value, and i diffeence ae tanmitted to two e-level hyteei compaato, which ae decibed below. 3

11 Enegie 2017, 10, of 21 efeence value, and i diffeence ae tanmitted to two e-level hyteei compaato, Enegie which2017, ae decibed 10, 1509 below. 11 of Thee-Level Hyteei Compaato To To detemine tatu tatuof ofactive activeand andeactive eactivepowe, e-level hyteei compaato ae ae ued ueda ahown hownin infigue (a) (b) Figue Figue Thee-level Thee-level hyteei hyteei compaato: compaato: (a) (a) active active powe; powe; (b) (b) eactive eactive powe. powe. The diffeence between actual value of powe and efeence value i expeed by: P = P P, Q = Q Q, (31) * * P eo eo = P P, Q eo = Q Q, (31) * In thi equation, efeence value of active and eactive powe ae hown by P and * In thi equation, efeence value of active and eactive powe ae hown by P and epectively. Q, epectively. Thee eo value ae ent to compaato and, accoding to allowable band of eo, Thee eo value ae ent to compaato and, accoding to allowable band of eo, y y poduce uitable active and eactive powe hown a S p and S q, epectively. poduce uitable active and eactive powe hown a S p and S q, epectively. If Ifthi diffeencei i geate geate than than pemitted pemitted eo eo value value that i that intepeted i intepeted a a allowed allowed band, band, compaato compaato output output end end digital digital numbe numbe (1), and (1), and if if eo eo i i in init it allowed band, compaato output end digital numbe (0). Alo, if if eo eo i le i le than than allowed allowed band, band, compaato compaato output output end end digital numbe digital (1). numbe (1) Analyiof of Five-Phae PMSM unde Imbalance Condition The five-phae PMSM PMSM tato tato equation equation wa given wa in Equation given in (1). Equation Fom Equation (1). (1) Fom and (8), Equation toque (1) and equation (8), can toque alo be equation expeed cana alo follow: be expeed a follow: * p 5 T λ. [ λ i λ. i ] α β β α (32) e = 5 { λ 2 ρim. } i = p [λ αi β λ β.i α ] (32) whee i deivative opeato and * ign epeent conjugate of each complex vecto. whee ρ i deivative opeato and * ign epeent conjugate of each complex vecto. When When tato tato i unbalanced, i unbalanced, all vecto all vecto in Equation in Equation (1) have (1) a have poitive a poitive and negative and negative equence. equence. Fitly, Fitly, effect of unbalanced effect of unbalanced on tato on flux tato i tudied. flux i Fom tudied. Equation Fom Equation (1) and (27), (1) and elationhip (27), elationhip between between tato flux tato and flux and can be expeed can be expeed a follow: a follow: V = i jωλ, V = i jωλ (33) V = i jωλ, V = i jωλ (33) A can be een fom Figue 12, tato flux include two et of poitive and negative component A canthat be een otate fom in oppoite Figue diection. 12, tato flux include two et of poitive and negative component that otate in oppoite diection.

12 Enegie 2017, 10, of 21 Enegie 2017, 10, of 21 Figue Figue Relationhip Relationhipbetween betweenfluxe,,, and andcuent cuentvecto vectoof of tato. Subtituting component of poitive and negative equence of tato flux and cuent in Equation (32), following equation i obtained: 5 T ρim{ λ } *. i *. λ *. i λ * =. i e T (34) e = 5 { 2 ρim 2 λ. i λ. i λ. i λ }. i (34) It can be een that electomagnetic toque conit of two contant phae (phae that ae It can be een that electomagnetic toque conit of two contant phae (phae that ae poduct of identical equence) and two phae at 2ω peed (phae that ae poduct of poduct of identical equence) and two phae at 2ω peed (phae that ae poduct of diffeent equence). diffeent equence). Thu, ubtituting Equation (33) in Equation (34), following Equation i obtained: Thu, ubtituting Equation (33) in Equation (34), following Equation i obtained: Re * * * * T ρ e { v. i v. i v. i v. i R ( = { i i ) 2 ω } (35) T e = 5 2 ρ 1 ω Re v. i v. i v. i v. i R ( i 2 } i 2 ) (35) Equation (35) can be expeed a follow: Equation (35) can be expeed a follow: p T = ( A B C D E ) e ST ST ST ST ST (36) ω T which A S T, B S T, C S T, D e = p S Tω, and (A ST B E ST C S T ae: ST D ST E ST ) (36) which A ST, B ST 5, C * 5 5 * 5 A = Re { ST V. i, D } ST = ( v, and E i v ST ae: i ), B = Re { V. i = ( v i v i ) ST ST 2 α α β β 2 2 α α β β { 2 A ST = 5 5 * 5 5 * 5 2 C = Re. = ( ), = Re. = ( 2 (37) 2 Re V } {. i = 2 5 (v α i α v β i β ), B ST = 2 5Re V }. i = 5 2 (v α iα v β i β ST V i v i v i DS T V i v i v ) { 2 α α β β 2 2 i ), E = R ( i i ) α α β β T C ST = 2 5Re V } {. i = 5 2 (v α iα v β i β ), D ST = 2 5Re V }. i = 5 2 (v α i α v β i β ), E T = R ( i 2 i 2 (37) ) The The elationhip elationhip between between active active and and eactive eactive powe can be expanded a follow: 5 * * * * () () () ( powe can = =. be expanded. a follow:. S t P t jq t v i v i v i v. i ) 2 (38) S (t) = P (t) j Q (t) = 5 2 ( v. i v. i v. i v. i ) (38) The active powe equation extacted fom Equation (38) can be expeed a follow: The active powe equation extacted fom Equation (38) can be expeed a follow: P= ( A B C D ) p p p p (39) P = (A p B p C p D p ) (39) which A S p, B S p, C S p, and D S p ae: which A Sp, B Sp, C Sp, and 5 D Sp ae: * 5 5 * 5 A = Re V. i = ( v i v i ), B = Re { V. i } = ( v i v i ) SP { α α β β SP α α β β A SP = 5 2 Re V } {. i = 5 2 (v α i α v β i β ), B SP = 5 2 Re V }. i = 5 2 * 5 5 (v α iα v β i β ) { * 5 C. ( ), = Re. = ( SP i v i i α SP V i v i v i α β 2 2 ) (40) C SP = 5 2 Re V } {. i = 2 5 (v α iα v β i β ), D SP = 5 2 Re V } (40). i = (v α i α v β i β ) Similaly, eactive powe Equation can be expeed a follow:

13 Enegie 2017, 10, of 21 Enegie Similaly, 2017, 10, 1509 eactive powe Equation can be expeed a follow: 13 of 21 Q = (AQ SQ = ( A B SQ C C SQ D ) D SQ ) (41) (41) which A SQ SQ SQ SQ ae: S Q, B S Q, C S Q, and D S Q ae: { A SQ = 2 5Im V } {. i (v i v α i β ), B SQ = 5 2 Im V } A * *. i = 5 2 (v β i α v α i β ) S Q Im { { V. i } ( v i v i ), BS Q Im { V. i C SQ = 2 5Im V } { } ( v i v i = = β α α β = = β α α β ) i (v i v i β ), D SQ = 5 2 Im V } (42) 5 * 5 5 *. i 5 C Im = 52 (vβ iα v α i {. } ( ), Im {. } ( ) β ) (42) S Q= V i = v β i α v α i β DS Q= V i = v β i α v α i β A can be een fom Equation (37), C ST ST S and D S ae ocillating facto in electomagnetic toque, toque, ince ince y y include include and and cuent component with two two diffeent equence. equence. Similaly, accoding accoding to to Equation Equation (40) (40) and and (41), C(41), SP, DC SP C SQ and D SQ caue fluctuation S P, D S P, C S Q and DS Q caue in active and eactive powe, epectively. fluctuation in active and eactive powe, epectively. Meanwhile, accoding to Equation (37) and (40), it can be een that C T = C SP and Meanwhile, D T = accoding to Equation (37) and (40), it can be een that C = C D SP. T SP and D = D T SP. A a eult, ocillating facto of of active powe and and electomagnetic toque ae aeimila. In In following, it it i i fit tudied whe electomagnetic toque fluctuation will be eliminated by eliminating active and and eactive powe powe ocillato. Owie, becaue becaue pioity pioity i i to to eliminate eliminate electomagnetic toque toque fluctuation, condition to to eliminate ocillato of electomagnetic toque ae applied and unde e condition, new efeence fo active and eactive powe will be obtained Remove Powe Ocillato Facto SQ SQ SQ SQ Accoding to Figue 13, and a peviouly mentioned, a efeence value i conideed to contol powe. The contolle mut act o that tato powe popely follow efeence powe. Becaue e i an imbalance in ouce, contolle mut adjut ouce efeence o that it ceate a new efeence powe. In Figue 13, pimay efeence powe (befoe an imbalance) i hown a ((PP equied ) and ) and new new efeence powe powe (afte (afte an imbalance) an i hown i hown a a ( P (P) e. f ). ef Figue Figue Poduction Poduction of of new new powe powe ouce ouce in in an an imbalance imbalance condition. condition. It can be een fom Equation (39) that fo poduction of contant active powe, um of It can be een fom Equation (39) that fo poduction of contant active powe, um of two two ocillato facto ( C, D ) mut be zeo a follow: p p ocillato facto (C p, D p ) mut be zeo a follow: C D = 0 p p (43) C p D p = 0 (43) Alo baed on Equation (41), fo poduction of contant eactive powe, um of two ocillato Alo facto baed ( on C Equation, D ) mut (41), be fo zeo a poduction follow: of contant eactive powe, um of two Q Q ocillato facto (C Q, D Q ) mut be zeo a follow: C D = 0 Q Q (44) C Q D Q = 0 (44) Since each of value C p, D p, C Q, and D Q i dependent on poitive and negative equence component, none of m can be zeo by itelf. In that cae, tato cuent hould be zeo, which i not deiable. Theefoe, only i um can be zeo. ( C D = 0 and p p C D = 0 Q Q ). In thi condition efeence powe befoe and afte an imbalance will alo be equal a follow:

14 Enegie 2017, 10, of 21 Since each of value C p, D p, C Q, and D Q i dependent on poitive and negative equence component, none of m can be zeo by itelf. In that cae, tato cuent hould be zeo, which i not deiable. Theefoe, only i um can be zeo. (C p D p = 0 and C Q D Q = 0). In thi condition efeence powe befoe and afte an imbalance will alo be equal a follow: P equied = P e f = A p B p (45) The toque equation can alo be obtained a follow: Q equied = Q e f = A Q B Q (46) T e = p ω (A ST B ST 2C SP E ST ) = p ω (A ST B ST 2D SP E ST ) (47) A can be een fom Equation (45), toque ocillato facto ae till peent, which i not deiable. It hould be noted that main goal i to obtain a contant toque in imbalance condition, not contant powe Remove Toque Ocillato Facto Accoding to Equation (36), only way to eliminate toque ocillato facto i obtained unde following condition: C ST D ST = 0 (48) A a eult, electomagnetic toque value can be obtained a follow: T e = p ω (A ST B ST E ST ) (49) In thi condition, elationhip between efeence powe befoe and afte an imbalance condition i a follow: P e f = P equied 2 C SP = P equied 2 D SP (50) Q equied = Q e f = A Q B Q (51) Baed on Equation (50) and (51), contolle hould opeate o that moto powe popely follow new efeence powe and moto i ued in contant toque and conequently in contant peed. 5. Simulation Reult In thi ection, peed contol of a matix convete-fed five-phae PMSM unde an unbalanced input, which i impoved with popoed method in thi pape, i imulated uing Matlab/Simulink oftwae. The teady-tate and dynamic pefomance of moto i tudied. The eult ae compaed with thoe of a e-phae upply input unbalanced netwok without coection. The moto paamete i hown in Table 1.

15 Enegie 2017, 10, of 21 Table 1. Chaacteitic of five-phae pemanent magnet moto. Paamete Symbol Value Pole P 2 Refeence peed N 600 R.P.M D-axi inductance L d 18 mh q-axi inductance L q 42 mh Stato eitance 0.7 Ω Inetia J 0.01 Coefficient of fiction B Moto pemanent magnet flux ϕ f 0.5 wb Load toque T L 10 N.m Enegie 2017, 10, of 21 An unbalanced e-phae ouce ouce can can be be ceated ceated in in diffeent diffeent tate, tate, uch uch a a diffeence diffeence in in amplitude, amplitude, phae, phae, fequency, fequency, and/o and/o all all of of m. m. Figue illutate illutate an an unbalanced unbalanced e-phae e-phae ouce ouce whoe whoe amplitude amplitude of phae of A phae i diffeent A i diffeent fom o fom phae. o phae. Figue Figue Unbalanced Unbalanced e-phae e-phae ouce. ouce. O chaacteitic of ouce (phae and fequency) ae ame a a nomal e-phae powe upply. Thi happen when phae aea i loaded by epaate ingle phaed appliance connected to a typical e-phae input. Alo a hot pat of time (0.04 ) i elected. Figue 15 illutate imulation eult with popoed method unde above-mentioned condition. (a) (b)

16 O chaacteitic of ouce (phae and fequency) ae ame a a nomal e-phae powe upply. Thi happen when phae aea i loaded by epaate ingle phaed appliance connected to a typical e-phae input. Alo a hot pat of time (0.04 ) i elected. Figue 15 illutate imulation eult with popoed method unde above-mentioned condition. Enegie 2017, 10, of 21 (a) (b) (c) Figue Figue Chaacteiticof of moto motocompaed compaedwith with efeence. (a) (a) Speed Speed of of moto; moto; (b) (b) Electomagnetic Electomagnetic toque; toque; (c) (c) tato tato flux flux in in αaxi axiof of tationayfame. A hown in Figue 15a, moto peed will follow it efeence value popely. The efeence peed value i 600 R.P.M. and eult ae hown in in Table Table 2. Chaacteitic of moto peed cuve. Paamete Value Rie Time Settling Time Settling Min 540 Settling Max Ovehoot Undehoot Peak Peak Time Figue 15b how load toque in compaion with electomagnetic toque. The load toque value i 10 N.M. The infomation obtained fom imulation i hown in Table 3. Table 3. Chaacteitic of moto toque cuve. Paamete Value Rie Time Settling Time Settling Min Settling Max Ovehoot Undehoot Peak Peak Time

17 Enegie 2017, 10, of 21 Figue 15c demontate tato flux diagam on α axe of tationay fame. It hould be noted that efeence flux i equal to moto pemanent magnet flux and i conideed to be 0.5 (wb). Thi figue how that tato flux will follow it efeence value popely. The infomation wa obtained fom imulation i hown in Table 4. Table 4. Chaacteitic of moto flux cuve. Paamete Value Rie Time Settling Time 3 Settling Min Settling Max Ovehoot Undehoot 0 Peak Peak Time Figue 16 how ame chaacte of moto a in Figue 15 unde ame input condition, Enegie but without 2017, 10, uing 1509 imbalance coection method. 17 of 21 (a) (b) (c) Figue 16. Chaacteitic of moto compaed with efeence (without coection). (a) Speed of Figue moto; 16. Chaacteitic (b) electomagnetic of toque; moto (c) compaed tato flux with in efeence α axi of (without tationay coection). fame. (a) Speed of moto; (b) electomagnetic toque; (c) tato flux in α axi of tationay fame. Figue 16a illutate moto peed without uing coection method. The infomation Table 5. Chaacteitic of moto peed cuve without uing coection method. obtained fom imulation i hown in Table 5. Paamete Value Rie Time Settling Time Settling Min Settling Max Ovehoot Undehoot Peak Peak Time

18 Enegie 2017, 10, of 21 Table 5. Chaacteitic of moto peed cuve without uing coection method. Paamete Value Rie Time Settling Time Settling Min Settling Max Ovehoot Undehoot Peak Peak Time A hown in Table 5, a lot of moto peed chaacteitic a ettling time, ettling max, ovehoot and peak value ae moe than Figue 15a. Figue 16b how load toque in compaion with electomagnetic toque without uing coection method. The infomation obtained fom imulation i hown in Table 6. Table 6. Chaacteitic of moto toque cuve without uing coection method. Paamete Value Rie Time Settling Time Settling Min Settling Max Ovehoot Undehoot Peak Peak Time A hown in Table 5, alo a lot of moto toque chaacteitic a ettling time, ettling max, ovehoot and peak value ae moe than Figue 15b. Figue 16c demontate tato flux diagam on α axe of tationay fame without uing coection method. The infomation obtained fom imulation i hown in Table 7. Table 7. Chaacteitic of moto flux cuve without uing coection method. Paamete Value Rie Time Settling Time 3 Settling Min Settling Max Ovehoot Undehoot 0 Peak Peak Time Accoding to Table 7, ovehoot of moto flux i inceaed and e i a woe ituation than peviouly. To evaluate moto pefomance with popoed method in dynamic condition, a tep load at efeence peed of 600 (RPM) i applied to moto (Figue 17).

19 Peak Time Accoding to to Table 7, 7, ovehoot of of moto flux i i inceaed and e i i a a woe ituation than peviouly. To To evaluate moto pefomance with popoed method in in dynamic condition, a a tep load at at efeence peed of of (RPM) i i applied to to moto (Figue 17). Enegie 2017, 10, of The to Figue Figue The The tep tep load load applied applied to to moto. moto. Accoding to to thi figue, toque load diection wa changed between to to Accoding 18 to thi figue, toque load diection wa changed between 0.3 to 0.6. Figue 18 illutate moto chaacteitic. Figue 18 illutate moto chaacteitic. Enegie 2017, 10, of 21 (a) (a) (b) Figue Figue Chaacteitic Chaacteitic of of moto moto compaed compaed with with efeence efeence (with applying (with applying tep load). tep (a) load). Speed (a) of Speed moto; of (b) moto; electomagnetic (b) electomagnetic toque. toque. A A hown in in Figue Figue 18a, 18a, moto moto peed peed follow follow it efeence it efeence value value popely. popely. The efeence The efeence peed value peed ivalue 600 R.P.M. i 600 R.P.M. infomation infomation obtained obtained fom imulation fom imulation i howni inhown Table in 8. Table 8. Table 8. Chaacteitic of moto peed cuve. Paamete Value Rie Time Settling Time Settling Min 540 Settling Max Ovehoot

20 Enegie 2017, 10, of 21 Table 8. Chaacteitic of moto peed cuve. Paamete Value Rie Time Settling Time Settling Min 540 Settling Max Ovehoot Undehoot Peak Peak Time Figue 18b how load toque in compaion with electomagnetic toque. The load toque value i 10 N.M. infomation obtained fom imulation i hown in Table 9. Table 9. Chaacteitic of moto toque cuve. Paamete Value Rie Time Settling Time Settling Min Settling Max Ovehoot Undehoot Peak Peak Time Concluion In thi pape, a new technique i popoed to eliminate unbalanced e-phae ouce effect on a five-phae pemanent magnet moto pefomance that ue a matix convete in it dive tuctue. Thi method i baed on diect powe contol. Becaue of imbalance in ouce, moto toque and peed will fluctuate. By identifying toque ocillation facto and by eliminating e facto, moto powe efeence change. A efeence geneato ha tak of geneating a new powe efeence evey time. With a contol unit, active and eactive powe of moto popely follow new active and eactive powe efeence. Each time efeence powe change, howeve, toque and peed chaacteitic emain contant. Autho Contibution: Bozou Youefi uveyed backgound of eeach and popoed main idea. Soodabeh Soleymani, Babak Mozafai and Seid Agha Gholamian contibuted to imulation and modeling and contolle deign. The autho woked collectively on manucipt pepaation. Conflict of Inteet: The autho declae no conflict of inteet. Refeence 1. Zhao, J.; Liu, W.; Li, B.; Liu, X.; Gao, C.; Gu, Z. Invetigation of Electomagnetic, Themal and Mechanical Chaacteitic of a Five-Phae Dual-Roto Pemanent-Magnet Synchonou Moto. Enegie 2015, 8, [CoRef] 2. Yu, F.; Cheng, M.; Chau, K.T.; Li, F. Contol and Pefomance Evaluation of Multiphae FSPM Moto in Low-Speed egion fo Hybid Electic Vehicle. Enegie 2015, 8, [CoRef] 3. Wu, X.; Wang, H.; Huang, S.; Huang, K.; Wang, L. Senole Speed Contol with Initial Roto Poition Etimation fo Suface Mounted Pemanent Magnet Synchonou Moto Dive in Electic Vehicle. Enegie 2015, 8, [CoRef] 4. Kazmiekowki, M.P.; Buja, G. Review of diect toque contol method fo ouce invete-fed induction moto. In Poceeding of 29th Annual Confeence of IEEE Indutial Electonic Society, 2003; IECON 03, Roanoke, VA, USA, 2 6 Novembe 2003.

21 Enegie 2017, 10, of Loncaki, J.; Leijon, M.; Sndovic, M.; Roi, C.; Gandi, G. Compaion of Output Cuent Ripple in Single and Dual Thee-Phae Invete fo Electic Vehicle Moto Dive. Enegie 2015, 8, [CoRef] 6. Cai, X.J.; Wu, Z.X.; Li, Q.F.; Wang, S.X. Phae-Shifted Caie Pule Wih Modulation Baed on Paticle Swam Optimization fo Cacaded H-bidge Multilevel Invete with Unequal DC Voltage. Enegie 2015, 8, [CoRef] 7. Liu, X.; Du, J.; Liang, D. Analyi and Speed Ripple Mitigation of a Space Vecto Pule Wih Modulation-Baed Pemanent Magnet Synchonou Moto with a Paticle Swam Optimization Algoithm. Enegie 2016, 9, 923. [CoRef] 8. Bak, Y.; Lee, E.; Lee, K.B. Indiect Matix Convete fo Hybid Electic Vehicle Application with Thee-Phae and Single-Phae Output. Enegie 2015, 8, [CoRef] 9. Yongchang, J. Diect toque contol of pemanent magnet ynchonou moto with educed toque ipple and commutation fequency. IEEE Tan. Powe Electon. 2011, 26, [CoRef] 10. Otega, C.; Aia, A.; Cauana, C.; Balcell, J. Impoved wavefom quality in diect toque contol of matix-convete-fed PMSM dive. IEEE Tan. Ind. Electon. 2010, 57, [CoRef] 11. Tuyen, N.D.; Dzung, P.Q. Space Vecto Modulation fo an Indiect Matix Convete with Impoved Input Powe Facto. Enegie 2017, 10, 588. [CoRef] 12. Youefi Talouki, A.; Gholamian, S.A.; Youefi Talouki, M. Hamonic elimination in witching-table baed diect toque contol of Five-Phae PMSM uing matix conevet. In Poceeding of 2012 IEEE Sympoium on Humanity, Science and Engineeing Reeach, Kuala Lumpu, Malayia, June 2012; pp Mende, V.F.; Mato, F.F.; Liu, S.Y.; Cupetino, A.F.; Peeia, H.A.; De Soua, C.V. Low Voltage Ride-Though Capability Solution fo Pemanent Magnet Synchonou Wind Geneato. Enegie 2016, 9, 59. [CoRef] 14. Zhao, J.; Gao, X.; Li, B.; Liu, X.; Guan, X. Open-Phae Fault Toleance Technique of Five-Phae Dual-Roto Pemanent Magnet Synchonou Moto. Enegie 2015, 8, [CoRef] 15. Maiuz, M.; Maek, J.; Maian, P. Simple diect powe contol of Thee-Phae PWM ectifie uing pace-vecto modulation (DPC-SVM). IEEE Tan. Ind. Appl. 2004, 51, Liang, P.; Pei, Y.; Chai, F.; Zhao, K. Analytical Calculation of D- and Q-axi Inductance fo Inteio Pemanent Magnet Moto Baed on Winding Function Theoy. Enegie 2016, 9, 580. [CoRef] 17. Abdul Kadi, M.N.; Mekhilef, S.; Ping, H.W. Diect Toque Contol Pemanent Magnet Synchonou Moto dive with aymmetical multilevel invete upply. In Poceeding of th Intenational Confeence on Powe Electonic, Daegu, Koea, Octobe 2007; pp Sun, Z.; Li, S.; Zhang, X. Diect toque contol of induction machine uing finite-time contol and ditubance compenation. In Poceeding of IECON th Annual Confeence of IEEE Indutial Electonic Society, Dalla, TX, USA, 29 Octobe 1 Novembe 2014; pp Chu, J.; Hu, Y.; Huang, W. Diect active and eactive powe contol of PMSM. In Poceeding of 2009 IEEE 6th Intenational Powe Electonic and Motion Contol Confeence, Wuhan, China, May Jacob, B.; Baiju, M.R. Spead pectum modulation cheme fo two-level invete uing vecto quantied pace vecto-baed pule denity modulation. IET Elect. Powe Appl. 2011, 5, [CoRef] 21. Vu, H.G.; Yahoui, H.; Choot, T.; Hammoui, H. Contol active and eactive powe of Voltage Souce Invete (VSI). In Poceeding of nd Intenational Sympoium on Envionment Fiendly Enegie and Application, Newcatle upon Tyne, UK, June LaWhite, N.; Ilic, M.D. Vecto pace decompoition of eactive powe fo peiodic noninuoidal ignal. IEEE Tan. Cicuit Syt. 1997, 44, [CoRef] 2017 by autho. Licenee MDPI, Bael, Switzeland. Thi aticle i an open acce aticle ditibuted unde tem and condition of Ceative Common Attibution (CC BY) licene (