A Novel Triple-Permanent-Magnet-Excited Vernier Machine with Double-Stator Structure for Low-Speed and High-Torque Applications

energies

Article A Novel Triple-Permanent-Magnet-Excited Vernier Machine with Double-Stator Structure for Low-Speed and High-Torque Applications

Xinbo Liu 1,2, Xu Zhong 2, Yi Du 1,* ID and Xun Chen 2

1 School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China; [email protected] 2 School of Electronics and Information, Jiangsu University of Science and Technology, Zhenjiang 212013, China; [email protected] (X.Z.); [email protected] (X.C.) * Correspondence: [email protected]; Tel.: +86-139-1455-7920

Received: 23 May 2018; Accepted: 27 June 2018; Published: 1 July 2018

Abstract: In this paper, a novel triple-permanent-magnet-excited vernier (TPMEV) machine with double-stator (DS) is proposed, of which the power density and the torque density are effectively improved to satisfy the operating requirements of low speed and high torque density for direct drive systems. Three sets of permanent magnets (PMs) are placed on the two stators and the rotor, respectively, and the magnetic fields excited by these PMs are modulated to effective magnetic field harmonics with low pole-pair numbers and high speeds based on bi-directional field modulation effect of the non-uniform airgap permeance. Then two sets of armature windings respectively accommodated in two stators are designed according to the effective magnetic field harmonics, thus achieving the coupling between the PM magnetic fields produced by three sets of PMs and armature windings. Firstly, the topology of the TPMEV-DS machine is introduced. Secondly, the airgap flux density of the machine is analyzed based on the equivalent magnetic circuit method, which proves the improvement potentiality of power density and torque density due to the bi-directional field modulation effect. Finally, the performance of the TPMEV-DS machine is calculated and analyzed by the finite element method, verifying the advantages of high power density and high torque density for the direct drive systems.

Keywords: triple-permanent-magnet-excited; bi-directional ﬁeld modulation effect; equivalent magnetic circuit method; ﬁnite element analysis

1. Introduction Due to their low speed and high torque density performance, field-modulation (FM) permanent magnet (PM) machines, such as PM vernier machines [1,2], magnetic-geared PM machines [3,4], and vernier hybrid machines [5], have been widely used for direct drive applications. FMPM machines operate based on the field-modulation theory [6], in which the PM magnetic field is modulated by the non-uniform airgap permeance, so that a series of space harmonics with different pole-pair numbers and rotation speeds are generated in the airgap. Different from conventional PM machines, the armature windings of FMPM machines are connected according to one of the effective harmonic components with low pole-pair number and high speed. Thus, the rotation speed of armature reaction magnetic field is much higher than the rotor speed generally, so that the so called self-deceleration capability is realized [7,8], which can be expressed as

Nst ∓ pa pPM va = ve f = vt = vt = Grvt (1) pa pa

Energies 2018, 11, 1713; doi:10.3390/en11071713 www.mdpi.com/journal/energies Energies 2018, 11, 1713 2 of 18

in which va and vef are the rotation speeds of the armature reaction magnetic ﬁeld and the effective harmonic component, respectively; pa and Nst are the pole-pair number of armature windings and the number of modulating poles, respectively; pPM is the pole-pair number of PMs; Gr is named the magnetic gear ratio which is the rotation speed ratio between the armature reaction magnetic ﬁeld and the rotor; and vt is the rotation speed of the rotor. Then the torque output of an FMPM machine can be written as

µAsBgmaxGr T = (2) kd in which µ is the coefficient relative to the machine structure, As is the stator electrical loading, Bgmax is the amplitude of the effective harmonic magnetic flux density and kd is the leakage coefficient. It can be seen from (2) that the torque of FMPM machines is in proportion to the product of Bgmax and Gr when As and kd are determined. Thus, two methods can be adopted for the design of FMPM machines to further improve the torque density. (a) Selecting a magnetic gear ratio as high as possible.

According to (1), Gr equals the ratio between pPM and pa, so the higher Gr can be obtained by increasing the pole-pair number of PMs or reducing the pole-pair number of armature windings [9,10].

(b) Increasing Bgmax. Although high torque density performance can be achieved in FMPM machines based on its FM operating principle, the amplitude of effective magnetic field harmonics contributing to electromechanical energy conversion is much lower than that of conventional PM machines, so it is necessary to find an appropriate way to improve Bgmax [11,12]. However, the machine tooth-pole arrangement, especial the pole-pair of rotor PMs, is usually decided by the application requirements. Furthermore, the power factor may be reduced when the higher Gr is selected [13,14]. Thus, the torque density of FMPM machines can be improved by increasing the utilization ratio or consumption of PMs to increase Bgmax [15,16]. The armature windings of FMPM machines are connected according to the effective harmonic component of the magnetic field in the airgap rather than the fundamental one generated by PMs directly, so it is possible to obtain effective harmonics with same pole-pair number by modulated multiple sets of PMs with different pole-pair numbers according to (1). Thus, the resultant magnetic field Bgmax can be increased due to the contributions of each set of PMs. In [17], a dual-PM harmonic machine employing two sets of PMs located on stator and rotor, respectively, was proposed. The effective coupling between the magnetic field excited by these two sets of PMs and the armature windings is achieved by the so-called bi-directional field modulation effect. Thus, this dual-PMs harmonic machine has the capability to offer much higher torque owning to the utilization of two sets of PMs. According to the quantitative comparison between the dual-PMs machine and a conventional PM synchronous machine with the same rotor pole-pair number and overall dimension [18], the dual-PMs machine has a 125% higher torque output capability. However, it is still desirable to find more effective methods for the further power density and torque density enhancement of FMPM machines because of the requirements of direct-drive systems. Actually, the operation principle of FMPM machines is similar to that of co-axial magnetic gears (MGs) and FMPM machines can be obtained from any co-axial MGs by replacing one set of PMs with armature windings [19] or just by adding armature windings directly on stators or rotors of co-axial MGs [20]. In [21], a triple-permanent-magnet-excited (TPME) MG was proposed and analyzed. Due to the adoption of a triple-permanent-magnet, the TPME MG can achieve a 20% higher torque density compared with conventional co-axial MGs, which provides a new design concept to increase the torque density of FMPM machines. Energies 2018, 11, x FOR PEER REVIEW 3 of 18

Energies 2018, 11, 1713 3 of 18 higher torque density compared with conventional co-axial MGs, which provides a new design concept to increase the torque density of FMPM machines. In thisthis paper,paper, aa novelnovel triple-permanent-magnet-excitedtriple-permanent-magnet-excited verniervernier (TPMEV)(TPMEV) machinemachine withwith double-stator (TPMEV-DS)(TPMEV-DS) is proposed,is proposed, which which is composed is composed of two coaxialof two stators coaxial and stators an intermediate and an rotor.intermediate Three sets rotor. ofPMs Three are sets located of PMs on theare double-statorlocated on the (DS) double-stator and rotor, respectively.(DS) and rotor, The respectively. adopted DS structureThe adopted enables DS higher structure power enables and torque higher density powe duer and to the torque utilization density improvement due to the of the utilization machine space.improvement Furthermore, of the themachine bi-directional space. Furthermore, effects of the th twoe bi-directional airgaps are artfullyeffects of engaged the two to airgaps guarantee are theartfully coupling engaged between to guarantee the effective the harmoniccoupling between magnetic the fields effective excited harmonic by the three magnetic sets of fields PMs andexcited the armatureby the three reaction sets of magnetic PMs and fieldthe armature excited by reaction the two magnetic sets of armature field excited windings, by the sotwo the sets power of armature density andwindings, torque so density the power are further density improved. and torque The detaileddensity machineare further topology improved. and operation The detailed principle machine will betopology discussed. and Besides,operation two-dimensional principle will be finite discussed. element Besides, analysis two-dime (2D-FEA)nsional will be finite used element to calculate analysis and analyze(2D-FEA) the will machine be used performances. to calculate and analyze the machine performances.

2. Machine ConﬁgurationConfiguration andand OperationOperation PrinciplePrinciple

2.1. Machine ConfigurationConfiguration The structurestructure ofof proposed proposed TPMEV-DS TPMEV-DS machine machine is presentedis presented in Figure in Figure1, in which1, in which the outer the statorouter accommodatingstator accommodating a set of a three-phaseset of three-phase windings, windings, named named “primary “primary windings”, windings”, provides provides the main the power main ofpower the machine. of the machine. The other The set ofother three-phase set of three-ph windings,ase named windings, “secondary named windings”, “secondary is accommodated windings”, is inaccommodated the inner stator. in the Two inner sets ofstator. PMs Two are mounted sets of PMs in theare slotmounted openings in the of outerslot openings stator and of innerouter stator,stator respectively,and inner stator, while respectively, the intermediate while rotor the composedintermedia ofte segmentedrotor composed iron pieces of segmented and PMs areiron sandwiched pieces and betweenPMs are sandwiched two stators. between Based on two the stators. bi-directional Based on field the modulationbi-directional effect field ofmodulation the two airgaps effect of with the non-uniformtwo airgaps with permeance, non-uniform the magnetic permeance, fields the excited magnetic by the fields three excited sets of by PMs the canthree be sets coupled of PMs with can the be fieldscoupled produced with the by fields two sets produced of three-phase by two windings, sets of three-phase which is helpful windings, for the which improvement is helpful of for power the densityimprovement and torque of power density. density and torque density.

Figure 1.1. ConﬁgurationConfiguration of proposedproposed triple-permanent-magnet-excitedtriple-permanent-magnet-excited vernier with double-statordouble-stator (TPMEV-DS)(TPMEV-DS) machine. machine.

The TPMEV-DS machine operates on a field modulation effect, according to which the machine The TPMEV-DS machine operates on a ﬁeld modulation effect, according to which the machine stator/rotor pole combination among stator teeth, PMs on stator, rotor teeth, PMs on rotor and the stator/rotor pole combination among stator teeth, PMs on stator, rotor teeth, PMs on rotor and the two two sets of windings can be arranged. When the TPMEV-DS machine is excited only by PMs on DS, sets of windings can be arranged. When the TPMEV-DS machine is excited only by PMs on DS, the the stator/rotor pole combination is governed by stator/rotor pole combination is governed by

pppPMs= r a (3) pPMs = pr ± pa (3) in which pa is the pole-pair numbers of primary windings and secondary windings, pPMs is the

r inpole-pair which numberspa is the of pole-pair PMs on numberseach stator, of and primary p is the windings number and of rotor secondary teeth. windings, pPMs is the pole-pair numbers of PMs on each stator, and pr is the number of rotor teeth.

Energies 2018, 11, x FOR PEER REVIEW 4 of 18 Energies 2018, 11, 1713 4 of 18 When the machine is excited only by PMs on the rotor, the stator/rotor pole combination is governed by When the machine is excited only by PMs on the rotor, the stator/rotor pole combination is governed by pppPMr= s a (4) pPMr = ps ∓ pa (4) where ps is the number of stator teeth, pPMr is the pole-pair number of PMs on rotor. whereTheps isstator/rotor the number pole of statorcombination teeth, p adoptedPMr is the by pole-pair the TPMEV-DS number machine of PMs on in rotor.this paper is The stator/rotor pole combination adopted by the TPMEV-DS machine in this paper is pa = 2 (5)

pa = 2 (5) ppsPMs==24 (6)

pspprPMr===pPMs =2224 (7) (6)

pr = pPMr = 22 (7) 2.2. Operation Principle 2.2. Operation Principle According to (3) and (4), the TPMEV-DS machine can be divided into two parts according to the differentAccording excitations to (3) of and PMs. (4), Figure the TPMEV-DS 2 shows the machine magnetic can befield divided distributions into two due parts to accordingthe different to theexcitations different of excitations PMs. The ofsegmented PMs. Figure iron2 showspieces theof the magnetic rotor and field the distributions salient teeth due of toDS the lead different to the excitationsnon-uniform of airgap PMs. permeance, The segmented thus irona number pieces of of asynchronous the rotor and space the salient harmonics teeth ofcan DS be leadproduced. to the non-uniformWhen the machine airgap is permeance, excited only thus by PMs a number on DS, of the asynchronous stationary magnetic space harmonics field with can24 pair be produced. pole-pair Whennumbers the is machine modulated is excited by the only rotating by PMs 22 rotor on DS, teeth, the stationaryand the effective magnetic harmonic field with magnetic 24 pair field pole-pair with numbers2 pole-pair is numbers modulated is bygenerated the rotating in two 22 airgaps, rotor teeth, as shown and the in effective Figure 2a. harmonic Simultaneously, magnetic the field rotating with 2 pole-pairmagnetic field numbers with is22 generated pole-pair innumbers two airgaps, excited as by shown PMs on in Figurethe rotor2a. is Simultaneously, modulated by 24 the stationary rotating magneticteeth of two field stators, with 22 respectively, pole-pair numbers then excitedthe effective by PMs harmonic on the rotor magnetic is modulated field with by 24 2 stationarypole-pair teethnumbers of two is stators,achieved respectively, in two airgaps then theas shown effective in harmonic Figure 2b. magnetic Comparing field withFigure 2 pole-pair 2a,b, the numbers magnetic is achievedfield distributions in two airgaps and flux as shown linked in by Figure two2 b.sets Comparing of windings Figure are2 consistent.a,b, the magnetic So the field PMs distributions respectively andlocated flux on linked the stators by two and sets rotor of windings can contribute are consistent. to the energy So the PMsconversion respectively together. located In Figure on the stators2c, the andmagnetic rotor canfield contribute is excited toby the three energy sets conversionof PMs toge together.ther, which In Figure is equivalent2c, the magnetic to the superposition field is excited of bymagnetic three sets fields of PMs excited together, by DS which PMs is and equivalent rotor toPMs. the Compared superposition with of magneticthe conventional fields excited FMPM by DSmachines, PMs and the rotor amount PMs. of ComparedPMs is increased, with the so conventional the airgap flux FMPM density machines, as well theas power amount density of PMs and is increased,torque density so the can airgap be improved. flux density as well as power density and torque density can be improved.

Figure 2. No-load magnetic field ﬁeld distributions. ( a) Excited by double-stator (DS) permanent magnets (PMs); (b) excited byby rotorrotor PMs;PMs; ((cc)) excitedexcited byby DSDS PMsPMs andand rotorrotor PMsPMs together.together.

2.3. Harmonic Analysis To moremore clearly clearly reveal reveal the operationthe operation principle principle and torque and generationtorque generation mechanism mechanism of the TPMEV-DS of the machine,TPMEV-DS the machine, ﬂux density the influx the density airgap isin analyzedthe airgap based is analyzed on the equivalent based on magneticthe equivalent circuit magnetic method. Somecircuit assumptions method. Some are assumptions made to simplify are ma thede process to simplify of analysis. the process of analysis. ➣ TheThe relative relative permeability permeability of of PM PM is 1.is 1.  TheThe magnetic magnetic ﬁeld field changes changes only only in in a radiala radial direction. direction.  Ignore the magnetic saturation in iron cores.

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➣ Ignore the magnetic saturation in iron cores. Ignore the magnetic leakage.

All the PMs are uniformly arranged in the outer stator slots, and each PM and its adjacent outer stator tooth constitutes a pair of magnetic poles. When only PMs on the out stator are considered, the corresponding PM magnetomotive force (MMF) can be expressed as

+∞ 2FPMs_out θPMs FPMs_out(θ) = ∑ sin(mpPMs ) cos(mpPMsθ) (8) m=1,3... mπ 2 where the FPMs_out is the MMF amplitude of a single PM pole, pPMs is the pole number of the PMs and the θPMs is the arc of outer stator PMs. The intermediate rotor is composed of segmented iron pieces and PMs. Because of the different permeance of PMs and segmented iron, a non-uniform airgap is established. Considering the rotation of the rotor, the rotor permeance can be expressed as

+∞ 2λppr θr λr(θ, t) = λr0 + ∑ sin(npr ) cos[npr(θ − θ0 − ωrt)] (9) n=1 nπ 2 where λr0 and λppr are the average value and peak-to-peak value of the rotor permeance, respectively, pr is the number of rotor iron poles, θr is the arc of single rotor iron pole, θ0 and ωr are the initial mechanical angle and the mechanical angular velocity of the rotor. Thus, according to (8) and (9), the ﬂux density in the inner airgap can be expressed as

 +∞ +∞ +∞   B(θ, t) = FPMs_out(θ)λr(θ, t) = A1 ∑ ε1 cos(mpPMsθ)+A2 ∑ ∑ ε1ε2[cos α1 + cos α2]  n=1,3,5... n=1,3... m=1   2λr pPMs out FPMs 2λppr pPMs FPMs_out  A = 0 _ , A =  1 π 2 π2 1 θPMs 1 θr ε1 = m sin(mpPMs 2 ), ε2 = n sin(npr 2 ) (10)  h i  npr(θ0+ωrt)  α1 = (mpPMs + npr) θ − mp +np  PMs r  h i  npr(θ0+ωrt)  α2 = (mpPMs − npr) θ +  mpPMs−npr

From (10), it can be found that the airgap flux density has both stationary and rotating components, and the spatial orders, amplitudes and rotational velocities of the corresponding harmonics in the inner airgap are summarized in Table1. At the same time, the flux density harmonics are also generated in the outer airgap, of which the spatial order and the rotation velocities are consistent theoretically with those in the inner airgap; however, the amplitudes are different. It should be mentioned that the flux density produced by the PMs on the inner stator and its corresponding harmonic analysis are similar to those due to the PMs on outer stator, so it is not presented in this paper.

Table 1. Excited harmonic components by the PMs on outer stator.

Group Spatial Amplitude Rotating Velocity

1 mpPMs A1ε1 0 −np ω 2 |mp − np | A ε ε r r PMs r 2 1 2 |mpPMs −npr | npr ωr 3 mpPMs + npr A2ε1ε2 mpPMs +npr

Energies 2018, 11, 1713 6 of 18

Secondly, all the PMs are uniformly arranged between the adjacent segmented irons on the rotor. Each PM and its neighboring iron core constitute a pair of magnetic poles. Taking the rotation of the rotor into account, the corresponding MMF produced by the PMs on the rotor can be indicated as:

+∞ 2pPMr FPMr θPMr FPMr(θ, t) = ∑ sin(ipPMr ) cos[ipPMr(θ − θ0 − ωrt)] (11) i=1,3... iπ 2 where FPMr is the MMF amplitude of a single PM pole, pPMr is the pole-pair number of rotor PM magnetic fields, and θPMr is the PM arc. To the magnetic field produced by the rotor PMs, the teeth of two stators function as modulation poles, and the modulation functions of the outer and inner stators are similar to generate flux density harmonics in outer airgap and inner airgap, respectively. Thus, only the modulation function of inner stator teeth is presented. The inner stator permeance can be expressed as

+∞ 2λpps θs_inner λs_inner(θ) = λ0_inner + ∑ sin(jps ) cos(jpsθ) (12) j=1 jπ 2 where the λ0_inner and the λpps are the average value and the peak-to-peak value of inner stator permeance, and θs_inner is the arc of stator teeth. So the harmonics in the inner airgap can be expressed as

 +∞ +∞ +∞  B(θ, t) = F (θ, t)λ (θ) = A ∑ ε cos[ip (θ − θ − ωrt)]+A ∑ ∑ ε ε [cos α + cos α ]  PMr s_inner 3 3 PMr 0 4 3 4 3 4  i=1,3... i=1,3,5... j=1  2λ p F 2λpps pPMr FPMr  A = 0_inner PMr PMr A =  3 π , 4 π2 1 θPMr 1 θs_inner (13) ε3 = i sin(ipPMr 2 ), ε4 = j sin(jps 2 )  h i  ipPMr(θ0+ωrt)  α = (jps + ip ) θ −  3 PMr jps+ipPMr  h i  ipPMr(θ0+ωrt)  α = (jps − ip ) θ +  4 PMr jps−ipPMr

The spatial orders, amplitudes and rotational velocities of the corresponding harmonics in inner airgap are summarized in Table2.

Table 2. Excited harmonic components by the PMs on the rotor.

Group Spatial Amplitude Rotating Velocity

1 ipPMr A3ε3 ωr −ipr ωr 2 |ips − jp | A ε ε PMr 4 3 4 |ipPMs −jpr | 3 ip + jp A ε ε ipr ωr s PMr 4 3 4 ipPMs +jpr

From Tables1 and2, it can be seen that a series of harmonics are produced by modulating the magnetic fields excited by the PMs on the DS and rotor, respectively. In Table1, there are three kinds of main harmonics, which can be divided into stationary and rotating components. The harmonics of group 1 are stationary and are produced by PMs on the stator without modulation. The harmonics of group 2 and group 3 are the components produced by the modulation of rotor iron poles to the magnetic field of group 1. In Table2, the harmonics of group 1 are directly excited by the PMs on the rotor which rotates synchronously with the rotor. The harmonics of group 2 and group 3 are generated by the modulation of stator teeth to the components of group 1. Furthermore, the speed of the harmonic components of group 1 in Table1 is 0; therefore, it cannot induce back electromotive force (EMF) in two sets of windings and no energy conversion is achieved. The harmonic components of group 1 in Table2 is directly excited by rotor PMs and synchronously rotates with the rotor, which are used to achieve energy conversion in conventional PM machines. The harmonic components of group 2 and group 3 in Tables1 and2, respectively, have the same pole-pair Energies 2018, 11, x FOR PEER REVIEW 7 of 18 Energies 2018, 11, x FOR PEER REVIEW 7 of 18 PM machines. The harmonic components of group 2 and group 3 in Tables 1 and 2, respectively, PM machines. The harmonic components of group 2 and group 3 in Tables 1 and 2, respectively, Energieshave the2018 same, 11, 1713 pole-pair numbers and speeds, so they can contribute to produce torque output7 of 18 have the same pole-pair numbers and speeds, so they can contribute to produce torque output together when the magnetic fields of two sets of armature windings have the same spatial order and together when the magnetic fields of two sets of armature windings have the same spatial order and rotating speed. In order to achieve the low speed and high torque performances, the armature numbersrotating speed. and speeds, In order so theyto achieve can contribute the low to sp produceeed and torque high torque output performances, together when the magneticarmature windings is designed according to the effective harmonic component with the lowest pole-pair fieldswindings of two is designed sets of armature according windings to the haveeffective the same harmonic spatial component order and rotatingwith the speed. lowest In pole-pair order to number and the highest rotating speed. So the harmonic components of group 2 in Tables 1 and 2 are achievenumber theand low the speedhighest and rotating high torque speed. performances, So the harmon theic components armature windings of group is 2 designed in Tables according 1 and 2 are to selected and the pole-pair number of the effective harmonic is 2 with m = n = i = j = 1. theselected effective and harmonicthe pole-pair component number withof the the effective lowest harmonic pole-pair is number 2 with andm = n the = i highest= j = 1. rotating speed. On the other hand, in order to achieve effective coupling between the armature magnetic field So theOn harmonic the other components hand, in order of group to achieve 2 in Tables effectiv1 ande coupling2 are selected between and thethe pole-pairarmature numbermagnetic of field the and the effective PM harmonic magnetic field, the frequency of current injected into the armature effectiveand the effective harmonic PM is 2harmonic with m = nmagnetic= i = j = 1.field, the frequency of current injected into the armature windings is obtained as windingsOn the is otherobtained hand, as in order to achieve effective coupling between the armature magnetic field and the effective PM harmonic magnetic field,ωω the frequencyω of current injected into the armature ppefs efs efr efr p f = ppωω==prrω (14) windings is obtained as a = efsπππ efs== efr efr rr fa 222 (14) pe f sω222eπππ f s pe f rωe f r prωr fa = = = (14) where the pefs and ωefs are the pole-pair number2π of effective2π harmonics2π excited by PMs on the stator where the pefs and ωefs are the pole-pair number of effective harmonics excited by PMs on the stator whereand its the correspondingpefs and ωefs are mechanical the pole-pair angular number speed, of effective respectively; harmonics and excited pefr and by ω PMsefr are on the statorpole-pair and and its corresponding mechanical angular speed, respectively; and pefr and ωefr are the pole-pair itsnumber corresponding of the effective mechanical harmonic angular excited speed, by PMs respectively; on rotor and and itsp correspondingand ω are the mechanical pole-pair numberangular number of the effective harmonic excited by PMs on rotor and itsefr correspondingefr mechanical angular ofvelocity, the effective respectively. harmonic It can excited be seen by PMsthat onthe rotor rotati andonal its speed corresponding of armature mechanical reaction magnetic angular velocity, field is velocity, respectively. It can be seen that the rotational speed of armature reaction magnetic field is respectively.different from It the can rotating be seen speed that the of the rotational rotor, but speed the offrequency armature of reaction armature magnetic current is field the issame different with different from the rotating speed of the rotor, but the frequency of armature current is the same with fromtraditional the rotating PM synchronous speed of the machines. rotor, but the frequency of armature current is the same with traditional traditional PM synchronous machines. PM synchronous machines. 3. Performance Analysis 3. Performance Analysis 3. Performance Analysis 3.1. Magnetization Patterns 3.1. Magnetization Patterns The TPMEV-DS machine possesses three sets of PMs. According to (10) and (13), the The TPMEV-DS machine possesses three sets of PMs. According to (10) and (13), the TPMEV-DSThe TPMEV-DS machine machinecan operate possesses when these three PMs sets ofare PMs. magnetized According in different to (10) and directions, (13), the TPMEV-DSnamely the TPMEV-DS machine can operate when these PMs are magnetized in different directions, namely the machineradial outward can operate direction when or these radial PMs inward are magnetized direction, inrespectively. different directions, Thus, four namely possible the radialmagnetization outward radial outward direction or radial inward direction, respectively. Thus, four possible magnetization directionpatterns can or radialbe achieved, inward as direction, shown in respectively. Figure 3. Dimension Thus, four parameters possible magnetization are defined in patterns Figure can4 and be patterns can be achieved, as shown in Figure 3. Dimension parameters are defined in Figure 4 and achieved,listed in Table as shown 3. in Figure3. Dimension parameters are defined in Figure4 and listed in Table3. listed in Table 3. Back-EMF waveforms of the phase A in four modelsmodels with different magnetization patterns are Back-EMF waveforms of the phase A in four models with different magnetization patterns are shown in Figure 55.. ComparedCompared FigureFigure5 5a,b,a,b, it it can can be be seen seen that that the the maximum maximum peak peak value value is is achieved achieved shown in Figure 5. Compared Figure 5a,b, it can be seen that the maximum peak value is achieved when the magnetization directions of the three sets of PMs are same, as shown in Model 1, so the when the magnetization directions of the three sets of PMs are same, as shown in Model 1, so the magnetization pattern of Model 1 is adopted in this paper. magnetization pattern of Model 1 is adopted in this paper.

Figure 3. Magnetization patterns. (a) Model 1; (b) Model 2; (c) Model 3; (d) Mode 4. Figure 3. Magnetization patterns. ( a) Model 1; ( b) Model 2; (c) Model 3; (d) Mode 4.

Figure 4. Dimension parameters of the TPMEV-DS machine. Figure 4. Dimension parameters of the TPMEV-DS machine. Figure 4. Dimension parameters of the TPMEV-DS machine.

Energies 2018, 11, x FOR PEER REVIEW 8 of 18

Table 3. Dimension parameters of TPMEV-DS Machine. Energies 2018, 11, 1713 8 of 18 Symbol Parameter Unit Value h1 Thickness of inner stator PMs mm 2 h2 Table 3. Dimension Width ofparameters inner stator of teeth TPMEV-DS Machine. mm 4.4 h3 Height of inner stator yoke mm 6 Symbol Parameter Unit Value h4 High of inner stator shoes mm 1 h1 h5 Thickness Width of of inner inner stator stator PMs shoes mm mm 3.3 2 h2 Width of inner stator teeth mm 4.4 h6 Thickness of outer stator PMs mm 2 h3 Height of inner stator yoke mm 6 h7 Width of outer stator teeth mm 5.6 h4 High of inner stator shoes mm 1 h5 h8 WidthWidth of inner of outer stator stator shoes shoes mm mm 4.3 3.3 h6 h9 ThicknessHeight of outerof outer stator stator PMs yoke mm mm 7 2 h Width of outer stator teeth mm 5.6 7 h10 High of outer stator shoes mm 1 h Width of outer stator shoes mm 4.3 8 r1 Inner radius of inner stator mm 20 h9 Height of outer stator yoke mm 7 h10 r2 HighOuter of outer radius stator of inner shoes stator mm mm 40 1 r1r3 Inner Inner radiusradius of of inner intermediate stator rotor mmmm 40.5 20 r2r4 Outer Outer radiusradius of of inner intermediate stator rotor mm mm 46 40 r 3r5 Inner radiusOuter ofradius intermediate of outer rotor stator mmmm 70 40.5 r4 Outer radius of intermediate rotor mm 46 r5 Series Outer turns radius per phase of outer of statorprimary windings mm 150 70 SeriesSeries turns turns per per phase phase of primary of secondary windings windings 100 150 Series turns per phaseStack of secondary length windingsmm 50 100 Stack Length length of airgap mm mm 0.5 50 Length of airgap mm 0.5 Remanence Remanence of PMs of PMs T T 1.2 1.2 Volume Volume of outer of outer stator stator PMs PMs mm mm3 3 16,40016,400 Volume Volume of rotor of rotor PMs PMs mm mm3 3 37,35037,350 Volume Volume of inner of inner stator stator PMs PMs mm mm3 3 13,90013,900

60 Model 1 Model 2 Model 3 Model 4 40 20 0 -20 Back-EMF (V) Back-EMF -40 -60 0 60 120 180 240 300 360 Electrical angle (°) (a) 40 Model 1 Model 2 Model 3 Model 4 30 20 10 0 -10

Back-EMF(V) -20 -30 -40 0 60 120 180 240 300 360 Electrical angle (°) (b)

FigureFigure 5. Back-electromotiveBack-electromotive force force (EMF) (EMF) waveforms waveforms in inphase phase A Aof offour four magnetization magnetization patterns. patterns. (a) (Primarya) Primary windings; windings; (b) (secondaryb) secondary windings. windings.

Energies 2018, 11, 1713 9 of 18

3.2. RelativeEnergies 2018 Position, 11, x FOR of InnerPEER REVIEW Stator and Outer Stator 9 of 18 Energies 2018, 11, x FOR PEER REVIEW 9 of 18 TheEnergies3.2. Relative TPMEV-DS 2018, 11 Position, x FOR machine PEER of Inner REVIEW adoptsStator and a coaxialOuter Stator double stator, and the magnetic circuit may be9 of changed 18 with the change of relative position of inner stator and outer stator. The electrical angle between the 3.2. RelativeThe TPMEV-DS Position of machineInner Stator adopts and Outer a coaxial Stator double stator, and the magnetic circuit may be centerlines3.2. Relative of outer Position stator of Inner teeth Stator and and inner Outer stator Stator teeth is defined as β, as shown in Figure6. Figure7 changedThe withTPMEV-DS the change machine of relati adoptsve position a coaxial of innerdouble stator stator, and and outer the stator. magnetic The electricalcircuit may angle be shows the magnetic field distributions when β = 0◦, β = 60◦, β = 120◦ and β = 180◦. It can be seen that betweenchangedThe thewithTPMEV-DS centerlines the change machine of outerof relati adoptsstatorve positionte aeth coaxial and of inner innerdouble stator stator stator, teeth and andis outer defined the stator. magnetic as β ,The as shown circuitelectrical in may Figure angle be shortedchanged6.between Figure magnetic thewith7 shows centerlines fluxthe thechange around magnetic of ofouter airgaps relati field statorve distributions byposition teeth the and stators’ of inner innerwhen teethstator statorβ = 0°, and teeth andβ = rotor 60°, isouter defined β iron = stator.120° coresas and β The, as isβ shown =electrical increased 180°. inIt Figurecan angle with be the improvementbetweenseen6. Figure that the7shorted of shows βcenterlines, and magneticthe the magnetic magneticof outer flux field aroundstator flux distributions te coupled airgapseth and by byinner when the the statorstators’ armatureβ = 0°, teeth teethβ = is windings60°, anddefined β =roto 120° asr is iron andβ decreased, as coresβ shown = 180°. is as increasedin It well, Figurecan be which can be6.withseen Figure seen thethat from improvement 7shorted shows the themagnetic reduced magnetic of β, fluxand magnetic field aroundthe magneticdistributions fieldairgaps densityflux by whencoupled the instators’ β the= by 0°, outerthe βteeth = armature60°, and stator β = roto 120° windings yoke.r ironand Thus,coresβ = is 180°. decreased is the increased It can maximum beas back-EMFseenwell,with thatthewhich is improvement obtainedshorted can be magnetic seen under of from β ,flux βand =the around 0the ◦reduced. magnetic Figure airgaps magnetic8 fluxshows by coupled the field the stators’ density variation by theteeth armaturein andthe trend outerroto windings ofr ironstator back-EMF cores yoke. is decreased is increasedThus, peak the valuesas inductedwithmaximumwell, theinwhich twoimprovement back-EMF can sets be of seen windings is of obtained from β, and the andthe underreduced magnetic the β peak-to-peak= magnetic 0°. flux Figure coupled field 8 shows value density by the the of armature in coggingvariation the outer windings trend torque stator of versus back-EMFyoke.is decreased Thus, the peak changesthe as well, which can be seen from the reduced magnetic field density in the outer stator yoke. Thus, the of β,values respectively.maximum inducted back-EMF It canin two beis obtainedsets seen of that windings under the back-EMF β and= 0°. theFigure peak-to-peak peak 8 shows values the value of variation the of two cogging trend sets of torqueof windingsback-EMF versus peak reach the the maximumchanges of back-EMFβ, respectively. is obtained It can beunder seen β that = 0°. the Figure back-E 8 showsMF peak the values variation of the trend two of sets back-EMF of windings peak maximumvalues values inducted and in the two peak-to-peak sets of windings value and of the cogging peak-to-peak torque isvalue relatively of cogging small torque when versusβ equals the zero, valuesreachchanges the inducted of maximum β, respectively. in two values sets It and ofcan windings the be peak-to-peakseen thatand thethe back-E valuepeak-to-peak ofMF cogging peak value values torque of ofco is thegging relatively two torque sets small of versus windings when the β respectively. So β is selected to be zero in this paper. changesequalsreach the zero, of maximum β ,respectively. respectively. values So It and βcan is theselectedbe seenpeak-to-peak thatto be the zero back-Evalue in this ofMF paper.cogging peak values torque of is the relatively two sets small of windings when β reachequals the zero, maximum respectively. values So and β is theselected peak-to-peak to be zero value in this of paper.cogging torque is relatively small when β equals zero, respectively. So β is selected to be zero in this paper.

Figure 6. The relative position between outer stator and inner stator. Figure 6. The relative position between outer stator and inner stator. Figure 6. The relative position between outer stator and inner stator. Figure 6. The relative position between outer stator and inner stator.

Figure 7. Magnetic field distributions. (a) β = 0; (b) β = 60; (c) β = 120; (d) β = 180.

Figure 7. Magnetic field distributions. (a) β = 0; (b) β = 60; (c) β = 120; (d) β = 180. FigureFigure 7. Magnetic7. Magnetic40 ﬁeld field distributions. distributions. (a )(aβ) =β = 0; 0; ( b(b))β β == 60; ( (cc)) β0.4β = =120; 120; (d () dβ) =β 180.= 180. 40 0.4 4030 0.40.3 30 0.3 3020 0.30.2 20 Primary windings 0.2 Secondly windings Back-EMF(V) 2010 Primary windings 0.20.1 Cogging torque torque(T) Cogging PrimarySecondly windings windings

Back-EMF(V) 10 0.1

0 SecondlyCogging torquewindings 0 torque(T) Cogging

Back-EMF(V) 10 0.1

-180 -120 -60Cogging 0 torque 60 120 180 torque(T) Cogging 0 Electrical angle (°) 0 0-180 -120 -60 0 60 120 1800 Electrical angle (°) Figure-180 8. Back-EMF -120 -60 and cogging 0 torque 60 with 120 different 180 β. Electrical angle (°) Figure 8. Back-EMF and cogging torque with different β. Figure 8. Back-EMF and cogging torque with different β. Figure 8. Back-EMF and cogging torque with different β.

Energies 2018, 11, 1713 10 of 18 Energies 2018, 11, x FOR PEER REVIEW 10 of 18

3.3. Airgap Flux Density In order to verify the harmonic analysis in Section 2.3,2.3, the airgap airgap flux ﬂux density in the outer outer airgap airgap and inner airgap are calculated by FEA. Figure 99 showsshows thethe airgapairgap densitydensity waveformswaveforms inin thethe outerouter airgap in 0 to 180 mechanical degrees due to different excitation sources and the corresponding harmonic spectra. The The amplitudes amplitudes of of the the main main harmonics harmonics are are listed in Table 4 4.. Firstly,Firstly, thethe mainmain harmonics ofof thethe airgapairgap ﬂuxflux density density due due to to outer outer stator stator PMs PMs and and inner inner stator stator PMs PMs are, are, respectively, respectively, the the2nd 2nd and and the 24ththe 24th components, components, where where the 24th theharmonic 24th harmonic component component is directly is directly excited excited by PMs by with PMs 24 pole-pairwith 24 pole-pair number andnumber the 2nd and harmonic the 2nd component harmonic iscomponent generated byis modulationgenerated by of segmentedmodulation iron of segmentedcores of the iron intermediate cores of the rotor. intermediate When the machinerotor. When is excited the machine by PMs ison excited the rotor, by PMs the mainon the harmonics rotor, the mainin the harmonics outer airgap in arethe theouter 22nd airgap and are the the 2nd 22nd components, and the 2nd where components, the 22nd harmonic where the is 22nd directly harmonic excited isby directly rotor PMs excited whilst by the rotor 2nd PMs harmonic whilst componentthe 2nd harmonic is generated component by the is modulation generated by of the the modulation outer stator ofteeth. the So,outer the primarystator teeth. windings So, the are primary designed windin accordinggs are to thedesigned 2nd harmonic according component to the 2nd to couple harmonic with componentthree sets of to PMs couple together. with It three can be sets seen of that PMs the toge amplitudether. It ofcan the be resultant seen that 2nd the harmonic amplitude component of the resultantexcited by 2nd the harmonic three sets component of PMs is 0.309T, excited which by the is almostthree sets the sumof PMs of theis 0.309T, 2nd harmonic which is components almost the sumrespectively of the 2nd excited harmonic by the components three sets of respecti PMs. vely excited by the three sets of PMs.

Figure 9. Outer airgap flux ﬂux density with different excitationexcitation sources and corresponding harmonic spectra. ( a) Flux density waveforms; ( b) corresponding harmonic spectra.

Table 4. Main outer airgap ﬂuxflux density harmonics amplitude (T). Harmonic Order Outer Stator PMs Inner Stator PMs Stator PMs Rotor PMs All PMs Harmonic Order Outer Stator PMs Inner Stator PMs Stator PMs Rotor PMs All PMs 2nd 0.09 0.053 0.144 0.177 0.309 2nd 0.09 0.053 0.144 0.177 0.309 22nd22nd 0.050.05 0.0150.015 0.0650.065 0.6790.679 0.7350.735 24th24th 0.5870.587 0.0160.016 0.6040.604 0.0810.081 0.6770.677

The airgapairgap ﬂuxflux densitydensity waveforms waveforms in in the the inner inner airgap airgap excited excited by differentby different excitation excitation sources sources and andcorresponding corresponding harmonic harmonic spectra spectra are shown are shown in Figure in Fi 10gure. The 10. amplitudes The amplitudes of the of main the harmonicsmain harmonics in the ininner the airgapinner airgap are listed are in listed Table in5. Table It can be5. It seen can that be seen the modulation that the modulation functions offunctions the stator of teeththe stator and teeth and rotor segmented iron cores to the airgap flux density due to different PM arrays are similar to those presented in Figure 9, namely all of the flux density in the inner airgap due to the three sets

Energies 2018, 11, 1713 11 of 18

rotorEnergies segmented 2018, 11, x FOR iron PEER cores REVIEW to the airgap ﬂux density due to different PM arrays are similar to11 those of 18 presented in Figure9, namely all of the ﬂux density in the inner airgap due to the three sets of PMs containof PMs thecontain 2nd harmonicthe 2nd harmonic component. component. So the secondary So the secondary winding canwinding be connected can be connected with 2 pole-pair with 2 numbers.pole-pair numbers. Furthermore, Furthermore, the 2nd harmonic the 2nd harmonic amplitude am isplitude 0.348T, is which 0.348T, is which close to is theclose sum to the of the sum 2nd of harmonicthe 2nd harmonic components components respectively respectively excited by excited different by different PMs. PMs.

Figure 10.10. InnerInner airair gapgap ﬂuxflux densitydensity withwith differentdifferent excitationexcitation sourcessources andand correspondingcorresponding harmonicharmonic spectra.spectra. (a) FluxFlux densitydensity wavefroms;wavefroms; ((bb)) correspondingcorresponding harmonicharmonic spectra.spectra.

Table 5.5. Main inner airgap ﬂuxflux densitydensity harmonicsharmonics amplitudeamplitude (T).(T).

Harmonic Order Outer Stator PMs Inner Stator PMs Stator PMs Rotor PMs All PMs Harmonic Order Outer Stator PMs Inner Stator PMs Stator PMs Rotor PMs All PMs 2nd 0.062 0.097 0.161 0.202 0.348 2nd 0.062 0.097 0.161 0.202 0.348 22nd 0.019 0.049 0.068 0.698 0.755 22nd 0.019 0.049 0.068 0.698 0.755 24th24th 0.0190.019 0.6080.608 0.6270.627 0.080.08 0.6940.694

3.4. Flux Linkage and No-Load Back-Electromotive ForceForce (EMF)(EMF) Figure 11a shows flux linkage waveforms in the primary windings due to different excitation Figure 11a shows flux linkage waveforms in the primary windings due to different excitation sources, and the corresponding back-EMF waveforms are presented in Figure 11b. It can be seen sources, and the corresponding back-EMF waveforms are presented in Figure 11b. It can be seen that that the phases of flux linage and back-EMF waveforms due to different excitation sources are the the phases of flux linage and back-EMF waveforms due to different excitation sources are the same, so same, so it can be concluded that the three sets of PMs play a positive role for energy conversion. it can be concluded that the three sets of PMs play a positive role for energy conversion. Firstly, when PMs on the two stators are excited, the peak values of flux linkage in primary Firstly, when PMs on the two stators are excited, the peak values of flux linkage in primary windings excited by outer stator PMs and inner stator PMs are 0.0086 Wb and 0.0045 Wb, windings excited by outer stator PMs and inner stator PMs are 0.0086 Wb and 0.0045 Wb, respectively, respectively, and its corresponding back-EMF are 9.57 V and 6.48 V, respectively. According to the and its corresponding back-EMF are 9.57 V and 6.48 V, respectively. According to the analysis of airgap analysis of airgap flux density in part 3.3, the flux linkage and the back-EMF excited by two sets of flux density in part 3.3, the flux linkage and the back-EMF excited by two sets of PMs on the stator can PMs on the stator can be calculated as be calculated as ( ψìsyy==+ψs_outer + yψs inner ï s s__ outer s_ inner í (15)(15) EïsEE==+Es_outer + E s_inner îï s souter__ sinner

where ψs_outer and ψs_inner are the flux linkage excited by PMs on the outer stator and inner stator, respectively, and the Es_outer and Es_inner are the corresponding back-EMF, respectively. It can be seen that the theoretical peak values of flux linkage and back-EMF in the primary windings due to two sets of stator PMs are 0.0131 Wb and 16.05 V, which are almost the same as the

Energies 2018, 11, 1713 12 of 18

Energies 2018, 11, x FOR PEER REVIEW 12 of 18 where ψs_outer and ψs_inner are the flux linkage excited by PMs on the outer stator and inner stator, respectively, and the Es_outer and Es_inner are the corresponding back-EMF, respectively. It can be seen that the theoretical peak values of flux linkage and back-EMF in the primary It can be seen that the theoretical peak values of flux linkage and back-EMF in the primary windings due to two sets of stator PMs are 0.0131 Wb and 16.05 V, which are almost the same as the windings due to two sets of stator PMs are 0.0131 Wb and 16.05 V, which are almost the same as the FEA results of 0.0131 Wb and 15.71 V, respectively. Besides, the peak values of the flux linkage and FEA results of 0.0131 Wb and 15.71 V, respectively. Besides, the peak values of the flux linkage and back-EMF excited by the PMs on the rotor are 0.0201 Wb and 23.03V, respectively. Thus, when the back-EMF excited by the PMs on the rotor are 0.0201 Wb and 23.03V, respectively. Thus, when the machine is excited by three sets of PMs, the flux linkage and the back-EMF can be calculated as machine is excited by three sets of PMs, the flux linkage and the back-EMF can be calculated as ìyyy=+ ï asr ( í (16) ïψEEEa ==+ψs + ψr îï asr (16) Ea = Es + Er where ψr and Er are the flux linkage and the back EMF excited by the PMs on rotor, respectively. whereIt ψcanr and be Eseenr are that the fluxthe theoretical linkage and peak theback values EMF of excitedtotal flux by linkage the PMs and on rotor,total respectively.back-EMF in the primaryIt can windings be seen are that 0.0332 the theoretical Wb and 39.08 peak V, values which of agree total fluxwell linkagewith the and FEA total results back-EMF of 0.0315 in Wb the primaryand 38.59 windings V, as shown are 0.0332 in Figure Wb 10b. and 39.08 V, which agree well with the FEA results of 0.0315 Wb and 38.59 V, as shown in Figure 10b.

0.04 Outer stator PMs 0.03 Inner stator PMs 0.02 Stator PMs Rotor PMs 0.01 All PMs 0 -0.01 -0.02 Flux linkage (Wb) linkage Flux -0.03 -0.04 0 60 120 180 240 300 360 Electrical angle (°)

(a)

60 Outer stator PMs 40 Inner stator PMs Stator PMs 20 Rotor PMs All PMs 0 -20 Back-EMF (V) -40 -60 0 60 120 180 240 300 360 Electrical angle (°) (b)

Figure 11.11. FluxFlux linkagelinkage and and Back-EMF Back-EMF in in primary primary windings windings due due todifferent to different excitation excitation sources. sources. (a) Flux (a) linkage;Flux linkage; (b) back-EMF. (b) back-EMF.

Similarly, the flux linkage and the back-EMF in the secondary windings can be calculated and Similarly, the ﬂux linkage and the back-EMF in the secondary windings can be calculated and analyzed. As shown in Figure 12, when the machine is respectively excited by outer and inner stator analyzed. As shown in Figure 12, when the machine is respectively excited by outer and inner stator PMs, rotor PMs and all of the three sets of PMs, the peak values of flux linkage and back-EMF are PMs, rotor PMs and all of the three sets of PMs, the peak values of ﬂux linkage and back-EMF are 0.0031 Wb and 4.27 V, 0.0052 Wb and 6 V, 0.0128 Wb and 14.98 V, and 0.02 Wb and 25.17 V, 0.0031 Wb and 4.27 V, 0.0052 Wb and 6 V, 0.0128 Wb and 14.98 V, and 0.02 Wb and 25.17 V, respectively, respectively, which also agrees well with the results obtained from (15) and (16). which also agrees well with the results obtained from (15) and (16).

Energies 2018, 11, 1713 13 of 18 Energies 2018, 11, x FOR PEER REVIEW 13 of 18

0.03 Outer stator PMs 0.02 Inner stator PMs Stator PMs 0.01 Rotor PMs All PMs 0 -0.01 -0.02 Flux linkage (Wb) linkage Flux -0.03 0 60 120 180 240 300 360 Electrical angle (°)

(a) 30 Outer stator PMs 20 Inner stator PMs Stator PMs 10 Rotor PMs All PMs 0 -10 Back-EMF (V) -20 -30 0 60 120 180 240 300 360 ° Electrical angle ( ) 30 Outer stator PMs 20 Inner stator PMs Stator PMs 10 Rotor PMs All PMs 0 -10 Back-EMF (V) -20 -30 0 60 120 180 240 300 360 Electrical angle (°)

(b)

Figure 12. Flux linkage and back-EMF in secondary windings due to different excitation sources. (a) Figure 12. Flux linkage and back-EMF in secondary windings due to different excitation sources. Flux linkage; (b) back-EMF. (a) Flux linkage; (b) back-EMF.

From the analysis of flux linkage and back-EMF of the primary and secondary windings, it can be seenFrom that the the analysis two sets of of ﬂux windings linkage can and couple back-EMF with the of thethree primary sets of andPMs secondaryon the stator windings, and rotor it cansimultaneously, be seen that which the two is setsconsistent of windings with the can analysis couple withof airgap the three flux setsdensity of PMs in part on the3.3. statorThus, andthe rotorback-EMF simultaneously, and the power which density is consistent can be with improved the analysis effectively of airgap compared ﬂux density with inthose part of 3.3. existing Thus, themachines back-EMF with andsingle-layer the power and density double-layer can be PMs. improved effectively compared with those of existing machines with single-layer and double-layer PMs. 3.5. Torque 3.5. Torque In order to obtain the optimum current phase angle for the maximum output torque, the torque In order to obtain the optimum current phase angle for the maximum output torque, the against current angle characteristics are calculated. As shown in Figure 13a, the maximum torque against current angle characteristics are calculated. As shown in Figure 13a, the maximum electromagnetic torque can be obtained when the current angle equals zero in both armature electromagnetic torque can be obtained when the current angle equals zero in both armature windings. windings. Furthermore, the electromagnetic torque waveforms due to different excitation sources Furthermore, the electromagnetic torque waveforms due to different excitation sources are shown are shown in Figure 13b with different current angles. It can be seen again that the maximum in Figure 13b with different current angles. It can be seen again that the maximum electromagnetic electromagnetic torque is obtained when the current angles of primary windings and secondary torque is obtained when the current angles of primary windings and secondary windings both equal windings both equal zero. Thus, the id = 0 control method is adopted to obtained the high torque current ratio. The magnetic performances of stator PM motor and rotor PM motor is analyzed and

EnergiesEnergies 20182018,, 1111,, 1713x FOR PEER REVIEW 1414 ofof 1818

compared in [22], which indicated that the PM utilization ratio with PMs mounted in the stator is zero.significantly Thus, thelowerid =than 0 control that with method PMs in is the adopted rotor. Furthermore, to obtained the it can high be torqueseen from current Table ratio. 3 that The the magneticvolume of performances the three sets of of stator PMs PMare motordifferent, and namely, rotor PM the motor volume is analyzed of outer andstator compared PMs and in inner [22], whichstator PMs indicated are 16 that,400 the mm PM2 and utilization 13,900 mm ratio2, resp withectively, PMs mounted whilst the in the volume stator of is rotor significantly PMs is 37 lower,350 thanmm2. that So, withthe rotor PMs inPMs the provide rotor. Furthermore, the maximum itcan torque be seen and from the inner Table 3stator that theprovides volume the of minimum the three setstorque, of PMs as depicted are different, in Figure namely, 14. the volume of outer stator PMs and inner stator PMs are 16,400 mm2 and 13,900Figure mm 14 2shows, respectively, the average whilst torque the volume waveforms of rotor versus PMs is different 37,350 mm excitation2. So, the source rotor PMss with provide same theslot maximum current density torque of and 6 A/mm the inner2 in the stator outer provides stator and the minimum5 A/mm2 in torque, the inner as depicted stator. Ignoring in Figure the 14 iron. core Figuresaturation, 14 shows the amplitude the average of torquetorque waveforms is linear with versus the differentpeak value excitation of flux sourceslinkage withand the same q-axis slot currentcurrent densityin armature of 6 A/mmwindings.2 in According the outer stator to the and analysis 5 A/mm of flux2 in linkage the inner and stator. back Ignoring-EMF, the the torque iron corecan be saturation, expressed the as amplitude of torque is linear with the peak value of flux linkage and the q-axis current in armature windings. According to the analysis of flux linkage and back-EMF, the torque can TTTssoutersinner__ be expressed as (17) ( TTT T =emsrT + T s s_outer s_inner (17) where Ts_outer and Ts_inner are the torqueT em generated= Ts + T r by PMs on the outer stator and inner stator, respectively, Ts and Tr are the torque generated by two sets of PMs on the stator and the PMs on the where Ts_outer and Ts_inner are the torque generated by PMs on the outer stator and inner stator, rotor. respectively, Ts and Tr are the torque generated by two sets of PMs on the stator and the PMs on the rotor.It can be seen that the average values of the torque are 5.346 Nm and 3.88 Nm when the machineIt can is beexcited seen thatby the the outer average stator values and of inner the torquestator PMs, are 5.346 respectively. Nm and 3.88 Besides, Nm whenthe average the machine value isof excited torque by excited the outer by two stator stator and inner PMs is stator 9.226 PMs, Nm respectively. according to Besides, (17), which the average is consistent value of with torque the excitedsimulation by two value stator of 9.225 PMs isNm. 9.226 Moreover, Nm according the average to (17), value which of is torque consistent due to with the the rotor simulation PMs is 13.926 value ofNm, 9.225 so Nm.the resultant Moreover, torque the average can be valuecalculated of torque to be due 23.152 to the Nm rotor according PMs is13.926 to (17), Nm, which so the agrees resultant well torquewith the can FEA be calculatedresult of 22.01 to be Nm. 23.152 Nm according to (17), which agrees well with the FEA result of

22.01 Nm.

)

(

o T

C ur ren t an ry w gle onda in of f sec din pr gle o gs im t an (°) (°) ary urren ings C wind

(a)

Figure 13. Cont.

Energies 2018, 11, 1713 15 of 18 Energies 2018, 11, x FOR PEER REVIEW 15 of 18 Energies 2018, 11, x FOR PEER REVIEW 15 of 18 30 30 All PMs All PMs Outer stator PMs 25 Outer stator PMs 25 Inner stator PMs Inner stator PMs 20 Stator PMs 20 Stator PMs Rotor PMs 15 Rotor PMs 15 10 Torque (Nm) Torque 10 Torque (Nm) Torque 5 5 0 0 -90 -60 -30 0 30 60 90 -90 -60 -30 0 30 60 90 Electrical angle (°) Electrical angle (°)

30 30 All PMs All PMs Outer stator PMs 25 Outer stator PMs 25 Inner stator PMs Inner stator PMs 20 Stator PMs 20 Stator PMs Rotor PMs 15 Rotor PMs 15 10 Torque (Nm) Torque 10 Torque (Nm) Torque 5 5 0 0 -90 -60 -30 0 30 60 90 -90 -60 -30 0 30 60 90 Electrical angle (°) Electrical angle (°) (b) (b) Figure 13. Torque-current angle characteristics. (a) Torque due to primary windings and secondary Figure 13. Torque-current angleangle characteristics. ( a) Torque duedue toto primaryprimary windingswindings and secondary windings respectively; (b) total torque of two windings. windings respectively; ((bb)) totaltotal torquetorque ofof twotwo windings.windings. 30 30 All PMs Outer stator PMs Inner stator PMs All PMs Outer stator PMs Inner stator PMs 25 Stator PMs Rotor PMs 25 Stator PMs Rotor PMs 20 20 15 15 10 Torque (Nm) Torque 10 Torque (Nm) Torque 5 5 0 0 0 60 120 180 240 300 360 0 60 120 180 240 300 360 ° Electrical angle (°) Electrical angle ( ) Figure 14. Steady torque with different excitation sources. Figure 14. Steady torque with different excitation sources. Figure 15 shows the torque-current characteristics under different slot current density. It can be Figure 15 shows the torque-current characteristics under different slot current density. It can be seen Figurethat the 15 average shows thetorque torque-current increases linearly characteristics with the underslot current different density, slot current which indicates density. It that can the be seen that the average torque increases linearly with the slot current density, which indicates that the seenmachine that has the averagea desirable torque overload increases capability. linearly with the slot current density, which indicates that the machine has a desirable overload capability. machine has a desirable overload capability.

Energies 2018, 11, 1713 16 of 18 Energies 2018, 11, x FOR PEER REVIEW 16 of 18

Energies 2018, 11, x FOR PEER REVIEW 16 of 18

)

(

o T

J o J o f se f se con con da gs (Ada ry indin ( /mry win ry w A/ mw2 i di ima 2 mm 2 ) nd ng f pr ) ) ing s J o /mm2 s (A

Figure 15. Torque-current curve. Figure 15. Torque-currentTorque-current curve. 3.6. Temperature Field Analysis 3.6. Temperature Field Analysis Figure 16 shows the temperature field distribution of the proposed TPMEV-DS machine under Figure 1616 showsshows thethe temperaturetemperature ﬁeld field distribution distribution of of the the proposed proposed TPMEV-DS TPMEV-DS machine machine under under the the rated conditions at 7200 s. Due to the copper loss of primary windings being much higher than therated rated conditions conditions at 7200 at 7200 s. Due s. Due to the to copperthe copper loss lo ofss primary of primary windings windings being being much much higher higher than than that that of secondary windings, the outer stator exhibits higher temperature compared with the inner thatof secondary of secondary windings, windings, the outer the outer stator stator exhibits exhibits higher higher temperature temperature compared compared with thewith inner the stator.inner stator. Figure 17 shows the corresponding temperature curves. It can be seen that the steady stator.Figure 17Figure shows 17 the shows corresponding the corresponding temperature temperat curves.ure It can curves. be seen It thatcan thebe steadyseen that temperatures the steady of temperatures of the primary windings, secondary windings, inner stator PMs, rotor stator PMs and temperaturesthe primary windings, of the primary secondary windings, windings, secondary inner statorwindings, PMs, inner rotor stator stator PMs, PMs androtor outer stator stator PMs PMsand outer stator PMs are 107 °C, 99.9 °C , 99.4 °C , 83.1 °C and 106.5 °C , respectively. outerare 107 stator◦C, 99.9PMs◦ C,are 99.4 107◦ °C,C, 83.199.9 ◦°C,C and 99.4 106.5 °C, 83.1◦C, °C respectively. and 106.5 °C, respectively.

Figure 16. Temperature field distributions at 7200 s. Figure 16. TemperatureTemperature ﬁeldfield distributions at 7200 s.

Energies 2018, 11, 1713 17 of 18 Energies 2018, 11, x FOR PEER REVIEW 17 of 18

120 100 80 60 Primary windings Secondary windings 40 Outer stator PMs Temperature (℃) Temperature 20 Rotor PMs Inner stator PMs 0 0 1200 2400 3600 4800 6000 7200 Time (s)

Figure 17. The temperature curves.

4. Conclusions 4. Conclusions In this paper, a novel TPMEV-DS machine is proposed, in which the DS and intermediate rotor In this paper, a novel TPMEV-DS machine is proposed, in which the DS and intermediate rotor structure are adopted and three sets of PMs are located on the DS and rotor of the machine, structure are adopted and three sets of PMs are located on the DS and rotor of the machine, respectively. respectively. The DS teeth and segmented iron of the rotor lead to non-even airgap magnetic The DS teeth and segmented iron of the rotor lead to non-even airgap magnetic reluctance for magnetic reluctance for magnetic fields produced by three sets of PMs, and thus a series of field harmonic fields produced by three sets of PMs, and thus a series of field harmonic components can be produced components can be produced in the two airgaps based on the modulation effect. By selecting a in the two airgaps based on the modulation effect. By selecting a suitable stator/rotor pole combination, suitable stator/rotor pole combination, all of the flux density in the outer airgap and inner airgap due all of the flux density in the outer airgap and inner airgap due to three sets of PMs contain the 2nd to three sets of PMs contain the 2nd harmonic component, so two sets of windings are connected harmonic component, so two sets of windings are connected according to this effective harmonic according to this effective harmonic component in order to achieve the coupling with three sets of component in order to achieve the coupling with three sets of PMs simultaneously, and thus the PMs simultaneously, and thus the performance of low-speed and high-torque can be performed. performance of low-speed and high-torque can be performed. Based on the equivalent magnetic circuit Based on the equivalent magnetic circuit method, the operation of the machine is analyzed. method, the operation of the machine is analyzed. Furthermore, the static characteristics such as flux Furthermore, the static characteristics such as flux density and corresponding harmonic spectra, flux density and corresponding harmonic spectra, flux linkage and torque are analyzed by 2D-FEA to linkage and torque are analyzed by 2D-FEA to verifying the theory. This confirms that the torque of verifying the theory. This confirms that the torque of the proposed machine can be improved due to the proposed machine can be improved due to the adoption of the triple-permanent-magnet the adoption of the triple-permanent-magnet structure. Finally, thermal behavior is analyzed which structure. Finally, thermal behavior is analyzed which shows the machine can run safely. shows the machine can run safely.

Author Contributions:Contributions: X.L.X.L. isis thethe main main author author of of this th manuscript.is manuscript. X.Z. X.Z. is theis the main ma authorin author of this of manuscriptthis manuscript who conceivedwho conceived of the ideaof the of theidea research of the and research implemented and impl theemented research. the Y.D. research. provided guidanceY.D. provided and supervision. guidance and X.C. providedsupervision. some X.C. useful provided suggestions some inuseful the construction suggestions of in this the paper. construction All the authors of this havepaper. contributed All the authors signiﬁcantly have tocontributed this work. significantly to this work.

Acknowledgments: ThisThis workwork was was supported supported in in part part by theby the National National Natural Natural Science Science Foundation Foundation of China of China under Project 51677081 and 51777089, in part by the grant from the Priority Academic Program Development of Jiangsu Higherunder Project Education 51677081 Institution, and 51777089, in part by in the part Fund by the Program grant offrom Jiangsu the Priority University Academic for Excellent Program Youth Development Teachers, and of inJiangsu part by Higher Jiangsu Education University Institution, under Project in part 14JDG169. by the WeFund also Program thank Deming of Jiangsu Wang University from Nanjing for Excellent Tech University Youth forTeachers, the contribution and in part to theby improvementJiangsu University of English unde expressionr Project and14JDG169. organization. We also thank Deming Wang from ConflictsNanjing Tech of Interest: UniversityThe for authors the contribution declare no conflictto the improvement of interest. of English expression and organization. Conflicts of Interest: The authors declare no conflict of interest. References References 1. Li, X.L.; Chau, K.T.; Cheng, M. Analysis, design and experimental verification of a field-modulated 1. permanent-magnetLi, X.L.; Chau, K.T.; machine Cheng, forM. direct-driveAnalysis, design wind an turbines.d experimentalIET Electr. verification Power Appl. of a 2015field-modulated, 9, 150–159. permanent-magnet[CrossRef] machine for direct-drive wind turbines. IET Electr. Power Appl. 2015, 9, 150–159. 2. Zhao, W.X.; Zheng, J.Q.; Wang, J.B.; Liu, G.H.; Zhao, Zhao, J.X.; Fang, Fang, Z.Y. Z.Y. Design and analysis of a linear permanent-magnet vernier machine with improvedimproved forceforce density.density. IEEEIEEE Trans.Trans. Ind.Ind. Electron. 20152015,, 6363,, 2072–2082. [CrossRef] 3. Jian, L.N.; Chau, K.T.; Jiang, J.Z. A magnetic-gearedmagnetic-geared outer-rotor permanent-magnet brushless machine for wind power generation. IEEE Trans. Ind. Appl. 2009,, 45,, 954–962. 954–962. [CrossRef] 4. Wang, L.L.; Shen, J.X.; Luk,P.C.K.L.; P.C.; Fei, Fei, W.Z.; W.Z.; Wang, Wang, C.F.; C.F.; Hao, Hao, H. H. Development of a magnetic-gearedmagnetic-geared permanent-magnet brushless motor. IEEEIEEE Trans.Trans. Magn.Magn. 20092009,, 4545,, 4578–4581.4578–4581. [CrossRef]

Energies 2018, 11, 1713 18 of 18

5. Du, Y.; Cheng, M.; Chau, K.T.; Liu, X.X.; Xiao, F.; Zhao, W.X.; Shi, K.; Mo, L.H. Comparison of linear primary permanent magnet vernier machine and linear vernier hybrid machine. IEEE Trans. Magn. 2014, 50, 8202604. [CrossRef] 6. Cheng, M.; Han, P.; Hua, W. A general airgap field modulation theory for electrical machines. IEEE Trans. Ind. Electron. 2017, 64, 6063–6074. [CrossRef] 7. Jian, L.; Xu, G.; Mi, C.C.; Chau, K.T.; Chau, C.C. Analytical method for magnetic field calculation in a low-speed permanent-magnet harmonic machine. IEEE Trans. Energy Convers. 2011, 26, 862–870. [CrossRef] 8. Salihu Mustafa, S.; Misron, N.; Mariun, N.; Othman, M.L.; Hanamoto, T. Torque distribution characteristics of a novel double-stator permanent magnet generator integrated with a magnetic gear. Energies 2017, 10, 2. [CrossRef] 9. Du, Y.; Zhang, C.; Zhu, X.Y.; Xiao, F.; Sun, Y.; Zuo, Y.; Quan, L. Principle and analysis of doubly salient PM motor with Π-shaped stator iron core segments. IEEE Trans. Ind. Electron. 2018.[CrossRef] 10. Du, Y.; Xiao, F.; Hua, W.; Zhu, X.Y.; Cheng, M.; Quan, L.; Chau, K.T. Comparison of flux-switching PM motors with different winding configurations using magnetic gearing principle. IEEE Trans. Magn. 2016, 52, 8201980. [CrossRef] 11. Zhu, X.Y.; Shu, Z.M.; Quan, L.; Xiang, Z.X.; Pan, X.Q. Design and multi-condition comparison of two outer-rotor flux-switching permanent magnet motors for in-wheel traction applications. IEEE Trans. Ind. Electron. 2017, 64, 6137–6148. [CrossRef] 12. Zhu, X.Y.; Xiang, Z.X.; Quan, L.; Wu, W.Y.; Du, Y. Multi-Mode optimization design methodology for a flux-controllable stator permanent magnet memory motor considering driving cycles. IEEE Trans. Ind. Electron. 2018, 65, 5353–5366. [CrossRef] 13. Wang, S.Y.; Zhao, W.X.; Ji, J.H.; Xu, L.; Zheng, J.Q. Magnetic gear ratio effects on performances of linear primary permanent magnet vernier motor. IEEE Trans. Appl. Supercond. 2016, 26, 0610505. [CrossRef] 14. Kim, B. Design of a pm vernier machine with consideration for modulation flux and comparison with conventional PM motors. Energies 2017, 10, 1819. [CrossRef] 15. Zhu, X.Y.; Fan, D.Y.; Mo, L.H.; Chen, Y.Y.; Quan, L. Multi-objective optimization design of double-rotor flux-switching permanent magnet machine considering multi-mode operation. IEEE Trans. Ind. Electron. 2018. [CrossRef] 16. Zhu, X.Y.; Xiang, Z.X.; Quan, L.; Chen, Y.Y.; Mo, L.H. Multi-mode optimization research on a multi-port magnetic planetary gear permanent magnet machine for hybrid electric vehicles. IEEE Trans. Ind. Electron. 2018.[CrossRef] 17. Jian, L.N.; Shi, Y.J.; Liu, C.; Xu, G.Q.; Gong, Y.; Chan, C.C. A novel dual-permanent-magnet-excited machine for low-speed large-torque application. IEEE Trans. Magn. 2013, 49, 2381–2384. [CrossRef] 18. Liu, Y.; Fu, W.N.; Guo, X.; Li, Z.; Fang, R. A dual permanent magnet machine for high-torque low-Speed applications. In Proceedings of the 2017 20th International Conference on Electrical Machines and Systems (ICEMS), Sydney, NSW, Australia, 11–14 August 2017; pp. 1–4. 19. Qu, R.H.; Li, D.W.; Wang, J. Relationship between magnetic gears and vernier machines. In Proceedings of the 2011 International Conference on Electrical Machines and Systems, Beijing, China, 20–23 August 2011; pp. 1–6. 20. Ho, S.L.; Niu, S.X.; Fu, W.N. Transient analysis of a magnetic gear integrated brushless permanent magnet machine using circuit-field-motion coupled time-stepping finite element method. IEEE Trans. Magn. 2010, 46, 2074–2077. [CrossRef] 21. Peng, S.; Fu, W.N.; Ho, S.L. A novel high torque-density triple-permanent-magnet-excited magnetic gear. IEEE Trans. Magn. 2014, 50, 8001704. [CrossRef] 22. Hua, W.; Cheng, M.; Zhu, Z.Q.; Zhao, W.X. Comparison of electromagnetic performance of brushless motors having magnets in stator and rotor. J. Appl. Phys. 2008, 103, 07F124. [CrossRef]

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