Design Optimization of an Electric Variable Transmission for Hybrid Electric Vehicles

Transcription

1 energies Article Design Optimization of an Electric Variable Transmission for Hybri Electric Vehicles Qiwei Xu 1, *, Jing Sun 1, Wenjuan Wang 1, Yunqi Mao 1 an Shumei Cui 2 1 State Key Laboratory of Power Transmission Equipment & System Security an New Technology, Chongqing University, Chongqing , China; sunjingzzx@cqu.eu.cn (J.S.); irenewangwj@gmail.com (W.W.); myq2016@cqu.eu.cn (Y.M.) 2 Department of Electrical Engineering, Harbin Institute of Technology, Harbin , China; cuism@hit.eu.cn * Corresponence: xuqw@cqu.eu.cn; Tel./Fax: Receive: 20 April 2018; Accepte: 30 April 2018; Publishe: 2 May 2018 Abstract: An electric variable transmission (EVT) for hybri electric vehicles (HEVs) is investigate in this paper. With a special ouble rotor structure, EVT splits an reintegrates output power of internal combustion engine (ICE) to run at its optimum working efficiency. However, high electromagnetic coupling egree causes torque ripple an affects ynamic performance of EVT. After introucing configuration an working principle, torque mamatical moel of EVT in an ABC three-phase coorinate system is propose to analyze cause of this torque ripple. Besies, a finite element metho-base (FEM) structural optimization esign for reucing torque ripple an improving working stability is presente. The magnetic fiel istribution, inuce voltage an torque property valiate rationality of optimization. Keywors: hybri electric vehicles; electric variable transmission; torque ripple; torque mamatical moel; structural optimization esign 1. Introuction In recent years, with rapi evelopment of inustry an continuous increase of population, energy crisis has become an urgent problem that nees to be solve immeiately, refore, new-energy vehicles came into being [1]. Battery-base electric vehicles (EVs), which have benefits of zero irect emissions, non-pollution, high efficiency an energy-saving, are future evelopment irection of automobile inustry. Due to low energy ensity, low power ensity of batteries, an fact auxiliary charging facilities are not pervasive, wiely popularization of battery-base EVs is hampere at present. The research on hybri electric vehicles (HEVs) is more mature than battery-base EV as y are cleaner than traitional vehicles, an have avantages of high riving force, strong enurance, high fuel economies, an less eman for external facilities [2,3]. Therefore, common view of new-energy vehicles is that HEVs must be evelope first, an one cannot jump irectly from ICE to zero emissions with battery-base EVs. The fuel economies of parallel-series HEVs are best among all kins of HEVs, which makes m more suitable for urban working conitions with frequent starting an stopping [4]. One of powertrain system in parallel-series HEVs is EVT system, which combines two electric machines [5]. The structure particularity of EVTs can make ICE running in its efficiency region. However, two electric machines are not only mechanically couple, but also interact with each or through electromagnetic fiel. Compare with traitional motors (a stator an a rotor), electromagnetic coupling in EVT will increase control ifficulty. On or han, magnetic coupling can also reuce power factor, power ensity, an increase electromagnetic Energies 2018, 11, 1118; oi: /en

2 Energies 2018, 11, of 18 loss, which is one of ifficult problems to be solve in any EVT system. At present, national an international scholars are mainly focuse on following aspects to research magnetic fiel ecoupling of EVT [6 11]: (1) stuying mamatical moel of EVTs base on coorinate transformation. The expressions of flux linkage, voltage an electromagnetic torque are etermine uner a transforme coorinate system to ientify ecoupling control algorithm an select new state variables. The ecoupling control effect is relate to accuracy of parameters; (2) Changing magnetic fiel istribution in EVTs to reuce egree of mutual interference. A flux-insulation ring is installe in mile of outer rotor, or a magnetic fiel moulation ring is arrange between stator an rotor. The flux-insulation ring is mae of some non-magnetic material, so inner an outer magnetic circuits are isolate from each or. Then two excitation sources of EVT ( magnetic potential of inner rotor an stator) are chaine with inner an outer squirrel cage separately to form two inepenent close magnetic circuits. The magnetic fiel moulation ring aopts magnetic block to change air-gap magnetic conuctance base on flux-moulate effect. It prouces a large number of harmonic components in air-gap to moulate magnetic fiel istribution an transfer electromagnetic energy; (3) Stuying effect of iron core material an lamination metho on magnetic flux fluiity to reuce egree of mutual interference between inner an outer magnetic fiel of EVT. The main factors to be consiere when selecting core material are working flux ensity, magnetic permeability, mechanical strength, loss, working environment an material prices. Different core lamination methos will affect value of air-gap magnetic flux ensity, an thus affect working performance of machine; (4) Stuying factors that influence inuctance, back EMF, flux linkage an torque parameters by using FEM. The magnetic fiel coupling makes inuctance an output torque of EVT fluctuate seriously. The parameters can be selecte accoring to factors affecting parameter variation to optimize structural esign of EVT. This paper stuies operation stability of EVTs use for HEVs. By introucing configuration an working principle it can be known that EVT base on electromagnetic energy conversion rule can be split an output power of ICE reintegrate to make it operate in optimum efficiency area inepenent of roa conitions, which ecreases emissions an fuel consumption. Neverless, high egree of electromagnetic coupling between inner an outer magnetic fiel causes torque ripple, thus reucing running stability of HEVs. Next, to analyze reason for torque ripple, a torque mamatical moel of an EVT in an ABC three-phase coorinate system is propose. From mamatical moel it can be seen that magnetic fiel oversaturation an small magnetic co-energy result in nonlinear variation of machine parameters, an effect can be weakene by proper parameters. Base on analysis results, influence of structural parameters an excitation current on torque ripple are analyze using FEM. Finally, magnetic fiel istribution, inuce voltage an torque properties valiate rationality of structural esign optimization, which reuces torque ripple of EVT to an acceptable range to guarantee running stability of HEVs. 2. Configuration an Working Principle 2.1. Configuration A sectional view of EVT an structure of a HEV base on EVT are shown in Figure 1. The EVT has a stator, an outer rotor, toger with an inner rotor, as shown in Figure 1a. The stator an inner rotor are installe three-phase winings, which are linke with two inverters to complete energy transmission [12]. Two layers of squirrel-cage are place on both sies of outer rotor. The EVT can be seen as a combination of an inner machine (IM) an an outer machine (OM). The IM comprises outer rotor an inner rotor, which connects to ICE as well as final gear, an also be calle electric machine1 (EM1). The OM comprises stator an outer rotor, which is calle electric machine1 (EM2) an have same spee as HEVs.

3 Energies 2018, 11, 1118 Energies 2018, 11, x FOR PEER REVIEW Energies 2018, 11, x FOR PEER REVIEW 3 of 18 3 of 20 3 of 20 squirrel-cage squirrel-cage inner rotor inner rotor wining wining stator stator stator stator wining wining outer rotor outer rotor inner rotor inner rotor (a) (a) ICE ICE stator stator outer rotor outer rotor EM2 EM2 EM1 EM1final gear Pout final gear PICE P Pout Toutωout Toutωout ICE ωice TICE ωicerotor TICE inner inner rotor squirrel-cage squirrel-cage PEM2 PEM1 PEM1 VSI1 ~ VSI1 ~= = Pb VSI2 PEM2 =VSI2 =~ ~ + PbBattery + Battery (b) (b) Figure Figure Structures Structures of of (a) (a) sectional sectional view view of of EVT EVT an an (b) (b) HEV HEV base base on on EVT. EVT. Figure 1. Structures of (a) sectional view of EVT an (b) HEV base on EVT. The EVT is mounte between ICE an final gear, as shown in Figure 1b. The inner rotor The mountebetween between ICE ICEan an final gear, as shown in Figure 1b. inner The inner The EVT is mounte final gear, as shown in Figure 1b. The rotor is linke with ICE an outer rotor is connecte to vehicle. To keep ICE running in rotor is linke ICE anouter outer is connecte vehicle. To keep running ICE running is linke with with ICE an rotor rotor is connecte to tovehicle. To keep ICE in efficiency region, EM1 changes spee of outer rotor referring to spee of ICE, an at in efficiency changes EM1 changes spee of rotor outerreferring rotor referring to of spee ICE, efficiency region,region, EM1 spee of outer to spee ICE,of an at same time, transmits torque of ICE [13]. The EM2 provies spee an torque ifference an at time, sametransmits time, transmits of torque of [13]. ICE EM2 provies torque same torque ICE The[13]. EM2The provies spee anspee torquean ifference between ICE an vehicle, refore, spee an torque of ICE are ajuste ifference between an vehicle, refore, spee torque ICE ICE are ajuste between ICE anice vehicle, refore, spee an an torque of of ajuste simultaneously. The EVT combines two machines toger, making transmission system of simultaneously. simultaneously. The The EVT EVT combines combines two two machines machines toger, toger, making making transmission transmission system system of of HEV more straightforwar. However, control strategies are complex, which nee two iniviual HEV more straightforwar. However, control strategies are complex, which nee two iniviual HEV more straightforwar. However, control strategies are complex, which nee two iniviual conventional controllers, precise rotor position, as well as proper control strategies. A 3D view of conventional conventionalcontrollers, controllers,precise preciserotor rotorposition, position,as aswell wellas as proper propercontrol controlstrategies. strategies.a A3D 3D view view of of EVT is shown in Figure 2. EVT EVT isis shown shownin infigure Figure2.2. Figure 2. 3D view of EVT. Figure Figure D 3D view view of of EVT. EVT.

4 Energies 2018, 11, of 18 Energies 2018, 11, x FOR PEER REVIEW 4 of Working Principle In a typical operation moe, EVT alters output spee an torque of ICE by converting an transforming mechanical energy of ICE [14]. It achieves splitting an reintegration of output power of ICE, which not only meets requirements of HEV riving force, but also optimizes operation area of ICE. The power split in HEV base on EVT is shown in Figure 3. P Fuel ICE P ICE Electrical Coupler VSI1 VSI2 P EM1 Battery Figure 3. Power split of HEV base on EVT. VSI: voltage source inverter. Figure 3 shows operating mechanism of EVT. The output power of ICE is ivie into two parts by EM1, as as shown in in Equation (1). (1). In In orer to to escribe process clearly, PPICE_out,, PEVT_out are use to express of TICE P EVT_out are use to express output power of ICE an EVT; T ICE expresses output torque of PEVT_in is PLoa is P ICE; P EVT_in is input power of EVT; P Loa is power require for roa loa; P to via fiel. PEM1 represents power transmitte to output shaft via magnetic fiel. P EM1 is output power of EM1. P ICE_out = ω PICE_out = T ωice ICE ICE P ICE_out = P EVT_in = P + P EM1 (1) P PICE_out = PEVT_in = P + PEM1 EVT_out = P Loa = ω EM2 (T EM1 + T EM2 ) (1) PEVT_out = PLoa = ωem2 ( TEM1 + TEM2 ) The P EM1 is transporte to battery an stator by using collector ring, an brush as well as The voltage PEM1 is source transporte inverters: to voltage battery source an inverter1 stator by (VSI using 1) an collector voltage source ring, an inverter2 brush (VSI as well 2). The as voltage rest ofsource power, inverters: i.e., P, isvoltage use tosource rive inverter1 HEV irectly. (VSI 1) an voltage source inverter2 (VSI 2). The rest of Due power, to i.e., fact P, is inner use rotor rive is mechanically HEV irectly. connecte to output shaft of ICE, inner rotordue has to same fact spee inner as rotor ICE is mechanically (ω ICE ) [15]. Inconnecte aition, to electromagnetic output shaft of torque ICE, ifference inner between rotor has inner same an spee outer as rotor ICE is (ωice) equal [15]. to that In of aition, ICE in steay electromagnetic case. The output torque shaft ifference of EVT is between connecte inner to final an gear outer ofrotor HEVs, is equal i.e., to spee that of of ICE EM2 in steay (ω EM2 ) case. is etermine The output by shaft of spee EVT of is HEV. connecte The output to final torque gear of of HEVs, outeri.e., rotor combines spee of EM2 torque (ωem2) of is etermine EM1 (T EM1 ) by an EM2 spee (T EM2 of HEV. ). Table The 1 summarizes output torque of operation outer rotor state combines of EM1, EM2 torque an of EM1 battery (TEM1) uring an EM2 power (TEM2). split Table moe. 1 summarizes operation Ieally, state battery of EM1, oesem2 not supply an battery power uring when P ICE_out power = Psplit Loa moe.. However, battery nees to provie Ieally, electrical battery oes energy not insupply actual circumstances, power when because PICE_out = PLoa. EVT However, system hasbattery losses uner nees ifferent to provie working electrical conitions. energy Accoring actual tocircumstances, above analysis, because EVT EVT combines system has output losses power uner of ifferent EM1 an working EM2 toconitions. promote Accoring smooth operation to above of analysis, HEV uner EVT ifferent combines roa conitions. output power The EVT of EM1 canan improve EM2 to promote system efficiency smooth ue operation to fact of HEV output uner power ifferent of roa ICEconitions. is ivie into The two EVT parts, can improve i.e., P EM1 an system P. The efficiency EM1 works ue in to generator fact output or transmission power of moe ICE is toivie accomplish into two power parts, i.e., split. PEM1 The an P EM1 P. will The make EM1 works ICEin inepenent generator of or loas transmission an operate moe into accomplish optimum efficiency power region, split. The which PEM1 iswill treate make as series ICE inepenent hybri power of system. loas an operate in optimum efficiency region, which is treate as series hybri power system.

5 Energies 2018, 11, x FOR PEER REVIEW 5 of 20 Energies 2018, 11, of 18 Table 1. Design parameters of EM1 an EM2. Power Spee Table 1. Design parameters EM1 of EM1 an EM2 EM2. Battery Relationship Relationship generation Power ωice Spee > ωem2 electric operation operation EM1 EM2 Battery Relationship Relationship PICE_out = PLoa ωice = ωem2 ICE irect-riven moe stop operation ω ICE > ω EM2 generation operation electric operation generation P ICE_out = P Loa ωice ω ICE < = ωem2 ω EM2 electric operation ICE irect-riven moe stop operation operation ω ICE < ω EM2 electric generation operation generation operation PICE_out < PLoa - electric operation operation P ICE_out < P Loa - generation operation operation electric operation operation generation operation operation an charge an PICE_out P ICE_out > PLoa > P Loa - - generation operation electric electric operation operation operation charge by EM1 by EM1 The Theelectromagnetic energy P P has has properties propertiesof ofhigh highefficiency, which whichresembles resembles parallel hybri hybri power system. system. However, However, P P is transferre is transferre to to outer rotor outer by rotor electromagnetic by electromagnetic coupling coupling effect between effect between electromagnetic electromagnetic fiels offiels EM1 an of EM1 EM2. an The EM2. high The electromagnetic high electromagnetic coupling coupling egree egree between between EM1 anem1 EM2an willem2 weaken will weaken output torque, output causing torque, torque causing ripple, torque impeing ripple, cooling, impeing an cooling, ecreasing an ecreasing ynamic performances ynamic performances of EVT. of EVT. 3. Torque Mamatical Moel of EVT in ABC Three-Phase Coorinate System To analyze factors that affect output torque stability uring EVT operation, torque mamatical moel of EVT base on virtual isplacement metho is propose. Ignoring magnetic circuit saturation, iron consumption, winings parameters changing with temperature, an self-inuctance coefficient of ofeach wining is isconstant, n sketch map of of EVT in a three-phase coorinate system is shown in Figure 4. A i A L1 u A a(u) U θ 1 θ 2 W L3 iw L2 uc uw ic c(w) L4 u V i V V B b(v) C Figure 4. Sketch map of EVT in ABC three-phase coorinate system. Figure 4. Sketch map of EVT in ABC three-phase coorinate system.

6 Energies 2018, 11, of 18 Energies 2018, 11, x FOR PEER REVIEW 6 of 20 In Figure 4, equivalent winings of stator, outer rotor an inner rotor are converte into stator sie to to simplify simplify analysis, analysis, an an electromagnetic electromagnetic relationship relationship in EVT in remains EVT unchange. remains The unchange. stator winings The stator are winings Y connecte are an Y connecte representean by represente A, B, C., an by A, inner B, C., rotor an winings inner arerotor also Ywinings connecte are an also represente Y connecte by U, an V, W. represente The equivalent by U, winings V, W. The of outer equivalent squirrel-cage winings are expresse of outer squirrel-cage by a, b an c. are Theexpresse equivalent by winings a, b an of c. The inner equivalent squirrel-cage winings are of expresse inner bysquirrel-cage u, v an w. The are expresse relationship by of u, self-inuctance v an w. The relationship an mutual-inuctance of self-inuctance between an stator, mutual-inuctance outer rotor an between inner rotor stator, is outer shownrotor in Figure an inner 5. rotor is shown in Figure 5. X C Y A Z B X C Y A Z B L1σ L2σ b x c y a z b x c y a z MAR MAa Mσ v r w r u t v r w s u t L3σ L4σ T V R W S U T V R W S U Figure Figure Relationship Relationship of of inuctance inuctance an an mutual-inuctance. mutual-inuctance. To simplify equations, we use L1 L4 an M1 M6 to escribe sum of self-inuctance an To simplify equations, we use L mutual-inuctance, as shown in Equations 1 L (2) 4 an M an (3), 1 M where 6 to escribe sum of self-inuctance an express that squirrel-cages have mutual-inuctance, as shown in Equations (2) an (3), where same turns as stator winings after wining reuction: express that squirrel-cages have same turns as stator winings after wining reuction: L1 = L1σ + MAa + MAR = L1σ + Lms L L 1 = L 2 L 1σ + M 2σ Aa + M Aa AR = L AR 1σ + L ms 2σ + L ms L 2 = L 2σ + M Aa + M AR + M σ = L 2σ + L ms (2) L L 3 3= L 3σ + M Aa + M AR + M σ = L 3σ + L ms (2) ms L L 4 = 4 L 4σ + 4σ M AR AR M 1 = (M + M ( MAa AR ) = AR) 1 2 L ms ms M 2 = M2 3 = M 4 = M 5 = 1 2 (M Aa + M AR + M σ ) = 2 1 L ms (3) M 6 = M2 = M M AR 3 = M4 = M5 = ( MAa + MAR + Mσ) = L ms (3) Then voltage equations of stator (u A, u B, u2 C ), outer squirrel-cage (u2 a, u b, u c ), inner squirrel-cage (u u, u v, u w ) an inner rotor (u1 U, u V, u W ) in ABC three-phase coorinate system are shown in Equations (4) (7): M6 = MAR 2 i Then u A voltage = R 1 equations i A + L A i 1 t of stator M B i 1 t (ua, MuB, C 1 t uc), + (M outer Aa + squirrel-cage M AR ) (ua, ub, uc), inner squirrelcage (uu, uv, uw) an inner t [i a cos rotor θ 1 + (uu, i b cos(θ uv, uw) 1 + in 120 ) ABC + i c cos(θ three-phase coorinate ) + i u cos θ 1 system are shown in Equations (4) (7): +i v cos(θ ) + i w cos(θ )] +M AR t [i U cos θ 2 + i V cos(θ ) + i W cos(θ )] i u B = R 1 i B M A i 1 t + L B i 1 t M C 1 t + (M Aa + M AR ) t [i a cos(θ ) + i b cos θ 1 + i c cos(θ ) + i u cos(θ ) +i v cos θ 1 + i w cos(θ (4) )] +M AR t [i U cos(θ ) + i V cos θ 2 + i W cos(θ )] i u C = R 1 i C M A i 1 t M B i 1 t + L C 1 t + (M Aa + M AR ) t [i a cos(θ ) + i b cos(θ ) + i c cos θ 1 + i u cos(θ ) +i v cos(θ ) + i w cos θ 1 ] +M AR t [i U cos(θ ) + i V cos(θ ) + i W cos θ 2 ]

7 Energies 2018, 11, of 18 u a = u b = u c = u u = u v = u w = u U = u V = u W = i R 2 i a + L a 2 t M 2 i b t M 2 i c t + M 4 i u i t M v i 5 t M w 5 t +M Aa t [i A cos θ 1 + i B cos(θ ) + i C cos(θ )] +M AR t [i U cos(θ 2 θ 1 ) + i V cos(θ 2 θ ) + i W cos(θ 2 θ )] i R 2 i b M a 2 t + L 2 i b t M 2 i c t M 5 i u i t + M v i 4 t M w 5 t +M Aa t [i A cos(θ ) + i B cos θ 1 + i C cos(θ )] +M AR t [i U cos(θ 2 θ ) + i V cos(θ 2 θ 1 ) + i W cos(θ 2 θ )] i R 2 i c M a 2 t M 2 i b t + L 2 i c t M 5 i r t M 5 i s t + M 4 i t t +M Aa t [i A cos(θ ) + i B cos(θ ) + i C cos θ 1 ] +M AR t [i U cos(θ 2 θ ) + i V cos(θ 2 θ ) + i W cos(θ 2 θ 1 )] i R 3 i u + L u i 3 t M v i 3 t M w i 3 t + M a 4 t M 5 i b t M 5 i c t +M Aa t [i A cos θ 1 + i B cos(θ ) + i C cos(θ )] +M AR t [i U cos(θ 2 θ 1 ) + i V cos(θ 2 θ ) + i W cos(θ 2 θ ) i R 3 i v M u i 3 t + L v i 3 t M w i 3 t M a 5 t + M 4 i b t M 5 i c t +M Aa t [i A cos(θ ) + i B cos θ 1 + i C cos(θ )] +M AR t [i U cos(θ 2 θ ) + i V cos(θ 2 θ 1 ) + i W cos(θ 2 θ )] i R 3 i w M u i 3 t M v i 3 t + L w i 3 t M a 5 t M 5 i b t + M 4 i c t +M Aa t [i A cos(θ ) + i B cos(θ ) + i C cos θ 1 ] +M AR t [i U cos(θ 2 θ ) + i V cos(θ 2 θ ) + i W cos(θ 2 θ 1 )] i R 4 i U + L U i 4 t M S 6 t M 6 i T t +M AR t [i A cos θ 2 + i B cos(θ ) + i C cos(θ )] +M AR t [(i a + i u ) cos(θ 2 θ 1 ) + (i b + i v ) cos(θ 2 θ ) +(i c + i w ) cos(θ 2 θ )] i R 4 i V M U i 6 t + L V i 4 t M W 6 t +M AR t [i A cos(θ ) + i B cos θ 2 + i C cos(θ )] +M AR t [(i a + i u ) cos(θ 2 θ ) + (i b + i v ) cos(θ 2 θ 1 ) +(i c + i w ) cos(θ 2 θ ) i R 4 i W M U i 6 t M V i 6 t + L W 4 t +M AR t [i A cos(θ ) + i B cos(θ ) + i C cos θ 2 ] +M AR t [(i a + i u ) cos(θ 2 θ ) + (i b + i v ) cos(θ 2 θ ) +(i c + i w ) cos(θ 2 θ 1 ) The matrix expression of flux linkage (Ψ) of stator, outer rotor an inner rotor is: Ψ = L ss L sr1 L sr2 L sr3 L r1s L r1r1 L r1r2 L r1r3 L r2s L r2r1 L r2r2 L r2r3 L r3s L r3r1 L r3r2 L r3r3 i s i r1 i r2 i r3 (5) (6) (7) (8)

8 Energies 2018, 11, of 18 where: L ss = L r2r2 = L 1 M 1 M 1 M 1 L 1 M 1 M 1 M 1 L 1 L 3 M 3 M 3 M 3 L 3 M 3 M 3 M 3 L 3 L sr1 = L T r1s = L sr2 = L T r2s = L m L sr3 = L T r3s = M AR L r1r2 = L T r2r1 = M 4 L r1r3 = L T r3r1 = L r2r3 = L T r3r2 = M AR L r1r1 = L r3r3 = L 2 M 2 M 2 M 2 L 2 M 2 M 2 M 2 L 2 L 4 M 6 M 6 M 6 L 4 M 6 M 6 M 6 L 4 cos θ 1 cos(θ ) cos(θ ) cos(θ ) cos θ 1 cos(θ ) cos(θ ) cos(θ ) cos θ 1 cos θ 2 cos(θ ) cos(θ ) cos(θ ) cos θ 2 cos(θ ) cos(θ ) cos(θ ) cos θ = M 4 M 5 M 5 M 5 M 4 M 5 M 5 M 5 M 4 cos(θ 2 θ 1 ) cos(θ 2 θ ) cos(θ 2 θ ) cos(θ 2 θ ) cos(θ 2 θ 1 ) cos(θ 2 θ ) cos(θ 2 θ ) cos(θ 2 θ ) cos(θ 2 θ 1 ) (9) Accoring to virtual isplacement metho, electromagnetic torque is equal to partial erivative of magnetic co-energy to rotor mechanical angle. The magnetic co-energy in system uner linear conition is: W m = 1 2 it Ψ = 1 2 it Nφ = 1 2 it Li (10) The relationship of electromagnetic torque between stator, outer rotor an inner rotor is given in Figure 6. The electromagnetic torques generate by inner rotor on outer rotor (T 12 ) an generate by outer rotor on inner rotor (T 21 ) are a pair of acting forces an reaction forces, so T 12 is equal to T 21. Then electromagnetic torque of outer rotor (T r1r2sr3 ) an inner rotor (T r3sr1r2 ) can Energies be obtaine 2018, 11, x FOR as follows: PEER REVIEW 10 of 20 T2 T1 T1 T12 T2 ω1 T21 ω2 Figure 6. Torque relationship in in EVT. T T T p W W - m m r1r2sr3 = 1 12 = n θ1 ( θ2 θ1) = p ( M + M ){ i [( i + i )sin θ + ( i + i )sin( θ ) n Aa AR A a u 1 b v 1 + ( i + i )sin( θ 120 )] + i [( i + i )sin( θ 120 ) + ( i + i )sinθ c w 1 B a u 1 b v 1 + ( i + i )sin( θ )] + i [( i + i )sin( θ ) c w 1 C a u 1

9 Energies 2018, 11, of 18 T r1r2sr3 [ ] = T 1 T 12 = p W m n θ 1 W m (θ 2 θ 1 ) = p n (M Aa + M AR ){i A [(i a + i u ) sin θ 1 + (i b + i v ) sin(θ ) T r3sr1r2 +(i c + i w ) sin(θ )] + i B [(i a + i u ) sin(θ ) + (i b + i v ) sin θ 1 +(i c + i w ) sin(θ )] + i C [(i a + i u ) sin(θ ) +(i b + i v ) sin(θ ) + (i c + i w ) sin θ 1 ]} p n M AR {i U [(i a + i u ) sin(θ 2 θ 1 ) + (i b + i v ) sin(θ 2 θ ) +(i c + i w ) sin(θ 2 θ )] + i V [(i a + i u ) sin(θ 2 θ ) +(i b + i v ) sin(θ 2 θ 1 ) + (i c + i w ) sin(θ 2 θ )] +i W [(i a + i u ) sin(θ 2 θ ) + (i b + i v ) sin(θ 2 θ ) +(i c + i w ) sin(θ 2 θ 1 )]} [ ] = T 2 + T 21 = p W m n θ 2 + W m (θ 2 θ 1 ) = p n M AR {(i A i U + i B i V + i C i W ) sin θ 2 + (i A i U + i B i V + i C i W ) sin(θ ) + (i A i W + i B i U + i C i V ) sin(θ )} + p n M AR {i U [(i a + i u ) sin(θ 2 θ 1 ) + (i b + i v ) sin(θ 2 θ ) + (i c + i w ) sin(θ 2 θ )] + i V [(i a + i u ) sin(θ 2 θ ) + (i b + i v ) sin(θ 2 θ 1 ) +(i c + i w ) sin(θ 2 θ )] + i W [(i a + i u ) sin(θ 2 θ ) +(i b + i v ) sin(θ 2 θ ) + (i c + i w ) sin(θ 2 θ 1 )]} (11) (12) where P n number of pole-pairs of EVT; θ 1 angle between axis of wining A an wining a; θ 2 angle between axis of wining A an wining R; i A, i B, i C current instantaneous value of stator winings; i a, i b, i c, i u, i v, i w current instantaneous value of outer an inner squirrel-cage; i U, i V, i W current instantaneous value of inner rotor winings; R 1, R 2, R 3, R 4 total equivalent resistance of stator winings, outer an inner squirrel-cage, inner rotor winings; L 1σ, L 2σ, L 3σ, L 4σ leakage inuctance of stator, outer an inner squirrel-cage, inner rotor generate by leakage flux; s stans for stator parameters, r 1 an r 2 express parameters of inner an outer squirrel cage, respectively, r 3 is parameters for inner rotor; L ss, L r1r1, L r1r1, L r1r1 phase wining self-inuctance of stator winings, outer an inner squirrel-cage, inner rotor winings; L sr1, L r1s T, L sr2, L r2s T, L sr3, L r3s T mutual-inuctance between stator an outer squirrel-cage, inner squirrel cage, inner rotor, respectively; L r1r2, L r2r1 T mutual-inuctance between outer an inner-squirrel cage; L r1r3, L r3r1 T mutual-inuctance between outer-squirrel an inner rotor; L r2r3, L r3r2 T mutual-inuctance between inner squirrel an inner rotor; L m mutual-inuctance between stator, outer rotor when axis of m coincience; M Aa, M AR mutual-inuctance between stator an outer rotor, inner rotor, M σ leakage mutual-inuctance between outer an inner squirrel-cage. The torque ripple is an important inex to evaluate operation stability of EVT, which has a great influence on comfort of HEVs. When torque ripple frequency coincies with working frequency, it will cause a resonance phenomenon an affect output efficiency of EVT. It can be seen from Equations (11) an (12) that P n is a constant, torque of outer rotor is relate to M Aa, M AR, an torque of inner rotor is associate with M AR, so torque ripple is mainly prouce in two aspects. Firstly, both of EM1 an EM2 are compose by outer rotor. Their magnetic circuits are close through outer rotor, which makes outer rotor easily saturate. When magnetic fiel is saturate, mutual-inuctance will be in a nonlinear state. The erivative of mutual-inuctance to position is not 0, which oes not change linearly an makes torque of outer rotor ripple serious. Seconly, output torque cannot change with symmetric current excitation when magnetic fiel is seriously saturate. Both of torques of outer rotor an stator are relate to instantaneous current of stator, outer rotor an inner rotor, so it is necessary to investigate influence of ifferent currents on torque ripple.

10 Energies 2018, 11, of 18 The harms of torque ripple are big electromagnetic noise, poor output torque an control accuracy. The interference between inner an outer magnetic fiels can be eliminate from proper structure parameters, which greatly improves torque property an reuces size of EVT. The next part of article stuies optimal esign of structure parameters to weaken coupling egree an enhance torque stability. 4. Optimal Design There are two magnetic potential sources in EVT, which complicate structure an lea to serious coupling. Therefore, structural parameters of EVT have a great influence on electromagnetic performance. The mutual-inuctance linearity egree changes with magnetic conuctance, which is relate to magnetic circuit length, area an saturation egree. The magnetic circuit length an area are influence by slot with, yoke thickness of stator, outer rotor an inner rotor etc. The wining turns an excitation current impact magnetic co-energy, an have a certain effect on magnetic fiel saturation egree. We can optimal esign se factors to improve torque stability. The outer rotor s output torque is compose by that of EM1 an EM2, so we separately analyze ir torque ripple to reuce total ripple Slot With In orer to stuy effect of outer rotor yoke thickness, stator yoke height on torque ripple, inner an outer iameters of inner rotor are limite to 61 mm an 113 mm, respectively. The inner iameter of outer rotor is chosen as 114 mm. For ifferent slot withs of inner rotor an stator, torque ripple percentage curve is calculate. The analysis result is given in Figure 7. As can be seen, an increase in slot with will a torque ripple for EM1 an EM2, an ue to fact istance of air-gap in tangential is raise, magnetic flux leakage an harmonic content in air-gap are also raise. However, slot withs of two machines have no appreciable influence on torque ripple within analysis range. The torque ripple percentage only increase by 1.5% when slot with change from 1.6 mm to 3 mm of EM1. In EM2, torque ripple only changes about 3.5% uner slot with is 3.4 mm 4.8 mm. Therefore, torque ripple improvement for EM1 an EM2 is not obvious by optimizing slot with. Then effect of or structural parameters on torque ripple are researche Outer Rotor Outer Diameter The esign of yoke thickness of stator an rotor shoul be able to avoi phenomenon of electromagnetic super-saturation in m. The outer iameter of outer rotor influences on torque ripple of EM1 an EM2 are shown in Figure 8, where it can be seen that change of outer rotor size has significant influence on torque ripple of EM1 an EM2. The rise of outer rotor size reuces torque ripple of two machines until outer iameter reaches 166 mm. This is because when outer iameter of outer rotor is increasing, magnetic fiels coupling egree of EM1 an EM2 in outer rotor will be reuce. The increase of magnetic circuit linearity results in ecrease of harmonic content in air-gap, so torque ripple is weaken. However, change range of torque ripple is small when outer iameter of outer rotor increases to a certain egree, namely, more than 166 mm. It shows that magnetic fiels of two machines is in a state of non-interference Stator Outer Diameter The tren of change of torque ripple uner ifferent stator outer iameters is very similar to that in ifferent outer rotor sizes, as given in Figure 9. The torque ripples of EM1 an EM2 ecrease with increase of stator outer iameter until iameter reaches 228 mm. Neverless, when iameter excees 228 mm, saturation issue becomes non-ominant an torque ripple percentage is basically stable.

11 Energies 2018, 11, of 18 Energies 2018, 11, x FOR PEER REVIEW 12 of 20 Torque ripple percentage (%) EM1 3.5 Torque ripple percentage (%) Slot with (mm) EM Slot with (mm) Energies 2018, 11, x FOR Figure PEER REVIEW Effect of of slot slot with with on on torque torque ripple ripple for for EM1 EM1 an an EM2. EM2. 13 of Outer Rotor Outer Diameter 30 EM1 The esign of yoke thickness of stator an rotor shoul be able to EM2 avoi phenomenon of electromagnetic super-saturation 25 in m. The outer iameter of outer rotor influences on torque ripple of EM1 an EM2 are shown in Figure 8, where it can be seen that change of outer rotor size has significant 20 influence on torque ripple of EM1 an EM2. The rise of outer rotor size reuces torque ripple of two machines until outer iameter reaches 166 mm. This is because when 15 outer iameter of outer rotor is increasing, magnetic fiels coupling egree of EM1 an EM2 in outer rotor will be reuce. The increase of magnetic circuit linearity results in ecrease of harmonic content in air-gap, so torque ripple is weaken. 10 However, change range of torque ripple is small when outer iameter of outer rotor increases to a certain egree, namely, more than 166 mm. It shows that magnetic fiels of two machines is 5 in a state of non-interference. Torque ripple percentage (%) Outer iameter of outer rotor (mm) Figure Effect of outer rotor outer iameter on torque ripple for EM1 an EM Stator Outer Diameter The tren of change of torque ripple uner ifferent stator outer iameters is very similar to that in ifferent outer rotor sizes, as given in Figure 9. The torque ripples of EM1 an EM2 ecrease with increase of stator outer iameter until iameter reaches 228 mm. Neverless, when

12 4.3. Stator Outer Diameter The tren of change of torque ripple uner ifferent stator outer iameters is very similar to that in ifferent outer rotor sizes, as given in Figure 9. The torque ripples of EM1 an EM2 ecrease with increase of stator outer iameter until iameter reaches 228 mm. Neverless, when Energies 2018, iameter 11, 1118 excees 228 mm, saturation issue becomes non-ominant an torque ripple 12 of 18 percentage is basically stable. Torque ripple percentage (%) EM1 EM Outer iameter of stator (mm) Figure 9. Figure Effect 9. of Effect stator of stator outer outer iameter on torque ripple ripple for EM1 for an EM1 EM2. an EM Wining Turns per Slot 4.4. Wining Turns per Slot In orer to make output torque change with symmetric excitation phase, wining In orer turns toof make inner rotor output an stator torque are researche change to with increase symmetric magnetic excitation co-energy properly, phase, which wining will turns regulate instantaneous torque waveform. The number of wining turns per slot of inner rotor are of inner rotor an stator are researche to increase magnetic co-energy properly, which will regulate changing from 12 to 36, an that of stator are changing from 8 to 32. The analysis results are given in instantaneous Figure 10. torque waveform. The number of wining turns per slot of inner rotor are changing from 12 to 36, an that of stator are changing from 8 to 32. The analysis results are given in Figure 10. Energies 2018, 11, x FOR PEER REVIEW 14 of 20 Torque ripple percentage (%) Wining turns per slot of inner rotor (a) Torque ripple percentage (%) Wining turns per slot of inner rotor (b) Figure 10. Effect of wining turns on torque ripple for (a) EM1; (b) EM2. Figure 10. Effect of wining turns on torque ripple for (a) EM1; (b) EM2. In Figure 10a, torque ripple of EM1 increases with rise of wining turns slowly an n rapily. The turning point appears when number of wining turns per slot in inner rotor is 24. When number of wining turns per slot in stator is 32, torque ripple increases linearly with ifferent wining turns per slot in inner rotor. The slowest increase in torque ripple occurs when wining turns per slot in stator is 8. This because when wining turns are ae, magnetic co-energy is also ae, which increases magnetic coupling egree. At this time output torque cannot be followe by current change in real time, which makes torque ripple more an more serious. In Figure 10b, influence of wining turns on torque ripple of EM2 is slightly similar to that of EM1. The ifference is with increase of magnetic fiel saturation,

13 Energies 2018, 11, of 18 In Figure 10a, torque ripple of EM1 increases with rise of wining turns slowly an n rapily. The turning point appears when number of wining turns per slot in inner rotor is 24. When number of wining turns per slot in stator is 32, torque ripple increases linearly with ifferent wining turns per slot in inner rotor. The slowest increase in torque ripple occurs when wining turns per slot in stator is 8. This because when wining turns are ae, magnetic co-energy is also ae, which increases magnetic coupling egree. At this time output torque cannot be followe by current change in real time, which makes torque ripple more an more Energies 2018, 11, x FOR PEER REVIEW 15 of 20 serious. In Figure 10b, influence of wining turns on torque ripple of EM2 is slightly similar to that of EM1. The The ifference variation range is with of excitation increase current of initial magnetic phase angle fiel is 0 saturation, to 180 egree in EM1 growth an EM2. rate of torque ripple for EM2 As can is less be seen than in Figure that of 11a, EM1. torque ripple of EM1 increases as current amplitue increases from 225 A to 265 A. At same time, if excitation current amplitue is ientical, magnetic ensity an coupling egree of EM1 an EM2 will change with initial phase angle. The torque ripple also as with rise of uner same current amplitue. In Figure 11b, effect of excitation current on torque properties of EM2 is quite similar to that of EM1. The torque ripple 4.5. Excitation Current with Different Amplitue an Initial Phase Angle The or metho to increase magnetic co-energy is to analyze excitation current with ifferent of EM2 increases with excitation current between 225 A to 265 A. This is because magnetic fiel amplitue an coupling initial state phase an angle. saturation Theegree magneto-motive are ifferent when force of winings EVT given is provie ifferent excitation by winings of EM1 an EM2, currents. an The magnetic inuctance fiel an mutual-inuctance coupling state of inmachine EVT isare ifferent also ifferent. uner The ifferent coupling egree excitation currents. of magnetic circuit has increase, which makes torque ripple serious an precise control of The effects of excitation current on torque ripple of EM1 an EM2 are shown in Figure 11. EVT becomes more ifficult. Torque ripple percentage (%) A 235A 245A 255A 265A Torque ripple percentage (%) Current initial phase angle of inner rotor wining (egree) (a) Current initial phase angle of stator wining (egree) (b) 225A 235A 245A 255A 265A Figure 11. Effect of excitation current on torque ripple for (a) EM1; (b) EM2. Figure 11. Effect of excitation current on torque ripple for (a) EM1; (b) EM2. In summary, base on above analysis, it can be seen that to reuce magnetic fiel coupling egree, ecrease torque ripple to improve output torque performance of EVT following actions are require: (1) A smaller slot with of stator an inner rotor is expecte. However, slot with of machine shoul be a little larger to facilitate coil processing. Generally speaking, slot with is at least The variation range of excitation current initial phase angle is 0 to 180 egree in EM1 an EM2. As can be seen in Figure 11a, torque ripple of EM1 increases as current amplitue increases from 225 A to 265 A. At same time, if excitation current amplitue is ientical, magnetic ensity an coupling egree of EM1 an EM2 will change with initial phase angle. The torque ripple also as with rise of uner same current amplitue. In Figure 11b, effect of excitation current on torque properties of EM2 is quite similar to that of EM1. The torque ripple of EM2 increases

14 Energies 2018, 11, of 18 with excitation current between 225 A to 265 A. This is because magnetic fiel coupling state an saturation egree are ifferent when winings given ifferent excitation currents. The inuctance an mutual-inuctance of machine are also ifferent. The coupling egree of magnetic circuit has increase, which makes torque ripple serious an precise control of EVT becomes more ifficult. In summary, base on above analysis, it can be seen that to reuce magnetic fiel coupling egree, ecrease torque ripple to improve output torque performance of EVT following actions are require: (1) A smaller slot with of stator an inner rotor is expecte. However, slot with of machine shoul be a little larger to facilitate coil processing. Generally speaking, slot with is at least three multiples of wire iameter. As we choose wire iameter of inner rotor an stator is 0.65 mm an 1.3 mm, slot with of EM1 an EM1 is ientifie as 2 mm an 4 mm, separately; (2) A larger outer iameter of outer rotor an stator is esirable consiering torque ripple, but torque ripple graually becomes steay when size increases to a certain egree. For reucing size of EVT an convenience for installing in HEVs, outer iameter of outer rotor is selecte as 166 mm, an yoke thickness of outer rotor is 14 mm. The outer iameter of stator is etermine as 223 mm, an its yoke thickness is 14.5 mm; (3) Fewer wining turns are require to reuce torque ripple. However, with fewer wining turns, excitation reactance is smaller, which will increase excitation current. In orer to make machine nee a smaller excitation current, wining turns per slot in inner rotor an stator are set at 16 an 8, respectively; (4) A smaller excitation current amplitue an initial phase angle can reuce torque ripple. In this optimal esign, excitation current amplitue of EM1 is chosen as 30 A, an initial phase angle is 0 egrees. For EM2, excitation current amplitue is 90 A, an initial phase angle also chosen as 0 egrees. 5. Performance Valiation In this part, an EVT where EM1 is 15 kw an EM2 is 30 kw is esigne. Accoring to above optimization analysis, a FEM moel is constructe for electromagnetic esign of EVT, as shown in Figure 1a. The etaile parameters are given in Table 2. Table 2. Design parameters of EM1 an EM2. Design Parameters EM1 EM2 Rate power (kw) Rate current (A) Rate spee (rpm) Number of phase 3 3 Iron core material DW DW Squirrel-cage material re copper re copper Number of slot Number of squirrel-cage Iron core length (mm) Air-gap length (mm) Slot with (mm) 2 4 Squirrel-cage with (mm) 8 8 Squirrel-cage thickness (mm) 6 6 Inner iameter of inner rotor (mm) 61 Outer iameter of inner rotor (mm) 113 Inner iameter of outer rotor (mm) 114 Outer iameter of outer rotor (mm) 166 Inner iameter of stator (mm) 167 Outer iameter of stator (mm) 223

15 Energies 2018, 11, of 18 The performance of EVT after optimization esign is analyze base on FEM moel an simulation results are given as follows Fiel Distribution The magnetic fiel of EVT is compute using FEM. The magnetic fiel ensity an magnetic flux irection uner rate loa are plotte in Figure 12. In Figure 12a, most parts of EVT are in low magnetic fiel ensity state, such as outer rotor, slot of stator an inner rotor. This inicates that EVT is in a state of unsaturation. The low magnetic circuit saturation egree can not only increase Energies 2018, 11, x FOR PEER REVIEW 17 of 20 power ensity of EVT, but also effectively restrain iron loss when riving at high spee. The larger high spee. magnetic The larger flux ensity magnetic appears flux ensity in appears stator yoke, in inner stator rotor yoke, yoke inner an rotor tooth. yoke an The tooth. maximum flux ensity The maximum is no more flux ensity than 2T, is no which more isthan allowable 2T, which foris allowable iron core for material. iron core material. (a) (b) Figure 12. Magnetic fiel of EVT: (a) magnetic flux ensity; (b) magnetic flux irection. Figure 12. Magnetic fiel of EVT: (a) magnetic flux ensity; (b) magnetic flux irection. From Figure 12b can be seen flow path of magnetic flux lines of EM1 an EM2. In EM2, magnetic flux lines flow in stator yoke, stator tooth, air-gap, outer rotor yoke, n return to stator yoke to form a close magnetic circuit, while in EM1, close magnetic circuit is compose by inner rotor yoke an its teeth, air-gap, outer rotor yoke, n return. The magnetic flux lines of two machines have little interference with each or. Through above structural optimization esign, istribution of whole magnetic fiel in EVT is more reasonable. The magnetic circuit saturation egree an coupling egree between EM1 an EM2 are reuce, so working losses

16 Energies 2018, 11, of 18 From Figure 12b can be seen flow path of magnetic flux lines of EM1 an EM2. In EM2, magnetic flux lines flow in stator yoke, stator tooth, air-gap, outer rotor yoke, n return to stator yoke to form a close magnetic circuit, while in EM1, close magnetic circuit is compose by inner rotor yoke an its teeth, air-gap, outer rotor yoke, n return. The magnetic flux lines of two machines have little interference with each or. Through above structural optimization esign, istribution of whole magnetic fiel in EVT is more reasonable. The magnetic circuit saturation egree Energies 2018, an 11, x coupling FOR PEER egree REVIEW between EM1 an EM2 are reuce, so working losses of 18 EVT of 20 are reuce uner complicate conitions. However, re are some leakage fluxes in stator an inner stator rotor an inner slot, which rotor slot, o not which participate o not participate in electromagnetic in electromagnetic energy transmission energy transmission an shoulan be furr shoul investigate be furr investigate to weaken to m. weaken m Inuce Voltage at Full-Loa Operation The inuce voltage is one of key factors that ecies operating voltage. The sinusoial egree of inuce voltage waveform also also influences efficiency, vibration, vibration, an an noise noise of of EVT. When EVT. When EM1 spee EM1 is spee 5000is rpm 5000 anrpm an EM2 is 2400 EM2 rpm, is 2400 rpm, inuce voltages inuce in voltages stator in winings stator an winings inner an rotorinner winings rotor are winings calculate are calculate by FEM, asby shown FEM, in as Figure shown 13. in Figure 13. Figure 13. Inuce voltage of stator winings an inner rotor winings. Figure 13. Inuce voltage of stator winings an inner rotor winings. After above parameters optimization it can be seen that inuce voltages in two winings After are above similar parameters to a sinusoial optimization wave, which it can be shows seen that that inuce funamental voltages component in two is winings significant are an similar to harmonic a sinusoial content wave, is which non-ominant shows that in funamental air-gap. Goo component air-gap is significant magnetic an properties harmonic can a content to is linearity non-ominant of magnetic in air-gap. circuit. Goo Therefore, air-gap magnetic parameter properties optimization can a to esign linearity of magnetic of magnetic circuit is circuit. reasonable Therefore, to make parameter magnetic optimization fiel be in a low esign coupling of state. magnetic The circuit linearity is reasonable of inuctance to make an mutual-inuctance magnetic fiel be is increase, in a low coupling so output state. torque The linearity smoothness of inuctance an an overloa mutual-inuctance capacity of is EVT increase, are improve, so output which torque makes smoothness EVT more an suitable overloa for use capacity in HEVs. of EVT are improve, which makes EVT more suitable for use in HEVs Output Torque at Full-Loa Operation 5.3. Output Torque at Full-Loa Operation Keeping spee of EM1 an EM2 unchange, ir output torque waves are shown in Figure Keeping spee of EM1 an EM2 unchange, ir output torque waves are shown in Figure In Figure 14, moving1 torque curve represents torque of EM1, which is negative. The moving2 torque curve represents torque of EM2, an its value is positive. This illustrates that one of machines in operating in generating state, or is an electric state. It also can be seen that, torque of EM1 stablilizes at 12 ms, which is about 16 Nm. For EM2, value is about 76 Nm an stablilizes at 24 ms. The torque of EM2 ecreases a little, an n increases an remains smooth. By optimizing structural parameters an excitation current of EVT, torque ripple of EM1 an EM2 is stable at about 5%, which is generally acceptable to fulfil stability an comfortableness emans of HEVs.

17 linearity of inuctance an mutual-inuctance is increase, so output torque smoothness an overloa capacity of EVT are improve, which makes EVT more suitable for use in HEVs Output Torque at Full-Loa Operation Keeping spee of EM1 an EM2 unchange, ir output torque waves are shown in Figure Energies 2018, 11, of Figure 14. Output torque of EM1 an EM2. Figure 14. Output torque of EM1 an EM2. 6. Conclusions An EVT with a special ouble rotor structure for HEVs is researche in this paper. It combines two electric machines an has few mechanical issues owing to gearless structure. However, coupling between inner an outer magnetic fiel causes torque ripple an affects working stability of HEVs uner ifferent loa conitions. The torque mamatical moel of an EVT in an ABC three-phase coorinate system is presente to analyze factors that influence it. Base on torque equations of inner rotor an inner rotor it is seen that magnetic fiel coupling causes nonlinear variation of machine parameters, an n leas to torque ripple. A FEM-base structural optimization esign an excitation current for reucing torque ripple is propose. After optimization EVT has a better magnetic fiel performance an a stable output torque, which verifies reasonableness of propose optimal esign. Author Contributions: Conceptualization, Qiwei Xu an Shumei Cui; Data curation, Wenjuan Wang; Formal analysis, Jing Sun; Investigation, Jing Sun; Methoology, Wenjuan Wang; Project aministration, Qiwei Xu; Software, Yunqi Mao; Supervision, Qiwei Xu; Valiation, Yunqi Mao an Shumei Cui; Visualization, Yunqi Mao; Writing original raft, Jing Sun; Writing-review & eiting, Jing Sun. Funing: This work was supporte by National Natural Science Founation of China uner Project No , Chongqing Science an Technology Commission of China uner Project No. cstc2013jcyja60001, an The State Key Laboratory of Power Transmission Equipment & System Security an New Technology in Chongqing University of China uner Project No. 2007DA Conflicts of Interest: The authors eclare no conflict of interest. References 1. Vinot, E.; Reinbol, V.; Trigui, R. Global Optimize Design of an Electric Variable Transmission for HEVs. IEEE Trans. Veh. Technol. 2016, 65, [CrossRef] 2. Xu, Q.W.; Cui, S.M.; Song, L.W.; Zhang, Q.F. Research on power management strategy of hybri electric vehicles base on electric variable transmissions. Energies 2014, 7, [CrossRef] 3. Su, P.; Hua, W.; Zhang, G.; Chen, Z.; Cheng, M. Analysis an evaluation of novel rotor permanent magnet flux-switching machine for EV an HEV applications. IET Electr. Power Appl. 2017, 11, [CrossRef] 4. Arunkumar, J.; Anrew, C.; Tek, T.L. Review of prospects for aoption of fuel cell electric vehicles in New Zealan. IET Electr. Syst. Trans. 2017, 7, Hoeijmakeer, M.J.; Ferreira, J.A. The electric variable transmission. IEEE Trans. In. Appl. 2006, 42, [CrossRef] 6. Xu, Q.W.; Sun, J.; Luo, L.Y.; Cui, S.M.; Zhang, Q.F. A Stuy on Magnetic Decoupling of Compoun-Structure Permanent-Magnet Motor for HEVs Application. Energies 2016, 9, 819. [CrossRef]

18 Energies 2018, 11, of Sinervo, A.; Arkkio, A. Rotor raial position control an its effect on total efficiency of a bearingless inuction motor with a cage rotor. IEEE Trans. Magn. 2014, 50, 1 9. [CrossRef] 8. Cai, H.W.; Xu, L.Y. Moeling an Control for Cage Rotor Dual Mechanical Port Electric Machine Part I: Moel Development. IEEE Trans. Energy Convers. 2015, 30, [CrossRef] 9. Osman, C.S.; Alper, T.; Lale, T.E. Efficiency analysis in three phase squirrel cage inuction motor. In Proceeings of 2016 National Conference on Electrical, Electronics an Biomeical Engineering (ELECO), Bursa, Turkey, 1 3 December 2016; pp Yang, Y.Y.; Schofiel, N.; Emai, A. Integrate Electromechanical Double-Rotor Compoun Hybri Transmissions for Hybri Electric Vehicles. IEEE Trans. Veh. Technol. 2016, 65, [CrossRef] 11. Kim, J.; Kim, T.; Min, B.; Hwang, S.; Kim, H. Moe Control Strategy for a Two-Moe Hybri Electric Vehicle Using Electrically Variable Transmission (EVT) an Fixe-Gear Moe. IEEE Trans. Veh. Technol. 2011, 60, [CrossRef] 12. Liu, Y.L.; Niu, S.X.; Ho, S.L.; Fu, W.N. A New Hybri-Excite Electric Continuous Variable Transmission System. IEEE Trans. Magn. 2014, 50, [CrossRef] 13. Shane, O.; Sumeha, R. A Combine High-Efficiency Region Controller to Improve Fuel Consumption of Power-Split HEVs. IEEE Trans. Veh. Technol. 2016, 65, Ma, Z.T.; Cui, S.M.; Li, S.P. Applying ynamic programming to HEV powertrain base on EVT. In Proceeings of 2015 International Conference on Control, Automation an Information Sciences (ICCAIS), Changshu, China, October Liu, Y.L.; Niu, S.X.; Fu, W.N. Design of an Electrical Continuously Variable Transmission Base Win Energy Conversion System. IEEE Trans. In. Electron. 2016, 63, [CrossRef] 2018 by authors. Licensee MDPI, Basel, Switzerlan. This article is an open access article istribute uner terms an conitions of Creative Commons Attribution (CC BY) license (