3664 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 50, NO. 6, NOVEMBER/DECEMBER 2014

High-Power-Factor VernierPermanent-Magnet Machines

Dawei Li, Student Member, IEEE, Ronghai Qu, Senior Member, IEEE, andThomas A. Lipo, Life Fellow, IEEE

Abstract—Vernier permanent-magnet (VPM) machines are wellknown for high torque density but low power factor. This paperdeals with the low power factor of VPM machines. The goal is notobtained by reducing the electrical loading or adjusting currentadvance angle but by proposing a novel vernier topology, i.e., adual-stator spoke-array (DSSA) VPM topology. In this paper, thecharacteristics of the DSSA VPM topology, such as active part,auxiliary mechanical structure, and rotor anisotropy, are analyzedin detail. Performances are evaluated based on finite-element anal-ysis, including power factor, torque density, and cogging torque.The results show that the DSSA VPM topology exhibits high powerfactor, viz., ∼0.9, and significantly high torque capability. Theverification of the mechanical structure scheme is also done in thispaper. Finally, theoretical analyses are validated by the experimen-tal results by a 44-rotor pole 24-slot DSSA VPM prototype.

Index Terms—Dual-stator spoke-array vernier permanent-magnet (DSSA VPM) machine, high power factor.

I. INTRODUCTION

IN recent years, due to the booming direct-drive applications,such as wind power, electric propulsion, etc., low-speed

high-power electrical machines are attracting more and more at-tention. However, the low speed and high power demand makesdirect-drive machines suffer from bulky size and large materialconsumption. Therefore, researchers have mostly concentratedon high-torque-density electrical machines, and many novelhigh machine topologies with high torque density are proposedduring the past couple of years.

Transverse flux permanent-magnet machines have becomevery popular recently due to their high torque density, [1], [2].Nevertheless, their power factor is really low (sometimes evenclose to 0.3), which means that the larger capability converteris required for the fixed output power [3].

Manuscript received October 15, 2013; revised February 14, 2014; acceptedMarch 19, 2014. Date of publication April 3, 2014; date of current versionNovember 18, 2014. Paper 2013-EMC-812.R1, presented at the 2013 IEEEEnergy Conversion Congress and Exposition, Denver, CO, USA, September16–20, and approved for publication in the IEEE TRANSACTIONS ON INDUS-TRY APPLICATIONS by the Electric Machines Committee of the IEEE IndustryApplications Society. This work was supported by the National Natural ScienceFoundation of China under Project 51337004.

D. Li and R. Qu are with the School of Electrical and Electronic Engineer-ing, Huazhong University of Science and Technology, Wuhan 430074, China(e-mail: lidawei_zs@163.com; ronghaiqu@hust.edu.cn).

T. A. Lipo is with the University of Wisconsin-Madison, Madison, WI 53706USA (e-mail: lipo@engr.wisc.edu).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIA.2014.2315443

Atallah et al. [4] proposed a so-called pseudo permanent-magnet (PM) machine. This machine can be regarded as themasterly combination of a magnet gear and an electrical ma-chine in one frame, and its excellent performances are reported.As illustrated in [4], the torque density of the air-cooled pseudoPM machine can be larger than 60 (kN · m)/m3 with lessthan 2 A/mm2 current density, whereas its power factor canreach as high as 0.9. However, the two air-gap structures andlow magnet usage ratio lead to large magnet consumption. Inaddition, there are two rotors (one is low speed and the otherone is high speed), and the low-speed rotor is combined withoutput shaft to export torque, whereas the high-speed rotoris encircled by the low-speed rotor. Hence, its mechanicalstructure is relatively complex, particularly for the low-speedhigh-power applications.

Vernier permanent-magnet (VPM) machines have simplestructure and high torque density due to the so-called mag-netic gear effect [5]–[8]. In addition, the VPM machine haslow pulsing torque due to its more sinusoidal electromotiveforce (EMF) waveform, as compared to that of a regular PMmachine [9]; thus, it is very attractive for low-speed direct-driveapplications. VPM machines have attracted more and moreattention, and many novel VPM topologies have been proposed.A vernier machine with a concentrated winding was presentedin [10]. Dual-rotor and dual-stator vernier topologies have beenproposed in [11], in which higher torque density of thesetopologies is reported. These papers focus on the performancessuch as torque density, core losses, etc., and these analysisresults show the advantages of VPM machine on torque densityand efficiency over that of the traditional PM machine.

However, different with the traditional PM machine, theVPM machine suffers from low power factor. Spooner andHardock [12] showed that the power factor of the vernier hybridmachine may be lower than 0.4. As well known, the low-power-factor electrical machine requires a large-capacity converter,which results in high cost in the converter. Therefore, theimprovement of power factor of the VPM machine is eagerlyrequired.

High power factor was reported to be obtained by theHalbach VPM (HAVPM) machine in [13]. However, for theHAVPM machine, the rotor iron is still the main flux path due tothe specified slot–pole structure of VPM machines. Therefore,the absence of rotor iron heavily reduces the output torque, andthis feature is different from traditional HAVPM machines [14].

The object of this paper is to propose a new VPM topologywith advantages of high torque density and low torque ripple,

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Fig. 1. DSSA VPM machine.

Fig. 2. Phasor diagram of VPM machines.

which overcomes the low power factor of the state-of-the-artVPM machine. The novel topology, i.e., the dual-stator spoke-array (DSSA) VPM machine, is shown in Fig. 1. The powerfactor of the VPM machine is analyzed in Section II. Thetopology of DSSA VPM is introduced in Section III. Basedon the finite-element analysis (FEA), the DSSA machine’sfeature on power factor is highlighted in Section IV, and theother performance indexes, such as torque waveform and torquedensity, are investigated in Section V. The auxiliary mechanicalstructures are proposed in Section VI. The prototype specifi-cations and mechanical stress checking process are shown inSection VII. Finally, the conclusion is drawn in Section VII.

II. POWER FACTOR OF VPM MACHINES

Although the operation principle of the VPM machine isdifferent from the PM machine, the relationship among theelectrical parameters can be also derived by the classicalsynchronous machine phasor diagram. Therefore, the phasordiagram is employed to study power factor.

The surface-mounted VPM machine is often driven by thezero d-axis current Id = 0. If the resistance is neglected, asshown in Fig. 2, the power factor can be given by

PF =1√

1 +(

LsIψm

) (1)

where Ψm is the magnet flux linkage, I is the RMS phase cur-rent, and Ls is the synchronous inductance. Therefore, powerfactor is determined by LsI/Ψm.

Due to the special stator slot and rotor pole combinationof the VPM machine, the armature field pole pitch is much

Fig. 3. VPM machine stator teeth effect on the flux density distribution.

TABLE IMAIN SPECIFICATIONS OF A SINGLE-SIDED VPM MACHINE

Fig. 4. Flux plot excited by the stator windings. (a) Forty-four-rotor pole four-armature pole VPM machine. (b) Four-pole PM machine.

larger than the rotor pole pitch. There are only half magnetscontributing to the flux per armature field pole pitch duringone armature field pole, as shown in Fig. 3, and the other halfmagnets mainly produce flux leakage. All these reasons reducethe fundamental flux density Bg and the power factor of VPMmachines.

In order to quantitatively investigate the power factor of VPMmachines, two FEA models have been built, with one 44-rotorpole four-armature pole VPM machine and one regular four-pole PM machine, and the VPM machine’s size data are listedin Table I. These two machines have the same stator structure,winding configuration, and magnet thickness. Assuming thatthe permeance of magnet is same as air and the steel saturationis neglected, it is shown in Fig. 4 that the VPM and PM

3666 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 50, NO. 6, NOVEMBER/DECEMBER 2014

Fig. 5. Flux plot excited by magnets. (a) Forty-four-rotor pole four-armaturepole VPM machine. (b) Four-pole PM machine.

Fig. 6. Flux density distribution of the PM and VPM machines.

Fig. 7. Flux linkage of the PM and VPM machines.

TABLE IIPERFORMANCE OF SINGLE-SIDED VPM MACHINE

machines have the same armature field. Therefore, the induc-tances of the two machines should be the same.

The magnet flux of the VPM machine is much smaller thanthat of the PM machine, as shown in Figs. 5 and 6, respectively.It is shown in Fig. 7 that the flux linkage of the PM machine isalmost 3 times that of the VPM machine. Therefore, the powerfactor of the VPM machine is low. Table II shows that the powerfactor of the VPM machine is lower than 0.66, although theratio of magnet thickness to air-gap length reaches almost 9.5.

Fig. 8. Relative position of the two stators. (a) Proposed relative position.(b) Variation of the back EMF with the relative position.

Fig. 9. Main flux path of the DSSA VPM machines.

For the current-controlled voltage source inverter (VSI)-fedPM machine, it is possible to improve power factor by thecurrent phase advance for regular PM machines. However, thestate-of-the-art VPM machine power factor is so low that thiscontrol strategy leads to heavy reduction of output power.

III. TOPOLOGY AND OPERATION PRINCIPLE

OF THE DSSA VPM MACHINE

The proposed DSSA VPM machine has two stators and onerotor that is sandwiched by the two stators, as shown in Fig. 1.

The relative position angle of the two stators is defined aszero, when the inner teeth axis is coincident with the outer statorteeth axis. The relative position that the inner stator tooth hashalf teeth pitch displacement compared to the outer stator toothis proposed, as shown in Fig. 8(a). The special relative positionof the two stators is the optimal design to get the maximumback-EMF amplitude, as shown in Fig. 8(b).

The rotor adopts the spoke-array magnets with flux acrossthe outside/inside air gap, whereas the adjacent rotor poledrives flux across the inside/outside air gap. After the fluxgoes through the outside/inside air gap, the flux travels in theoutside/inside stator iron, back across the air gap into the rotor,as shown in Fig. 9. Briefly, the specified relative position of thetwo stators and magnet array combine the two stators togetherfrom the view of magnetic field. Fig. 10 shows the 3-D con-figuration of the DSSA VPM machine active part. In addition,there is also another stator configuration whose inner stator isnonwinding and only works as a flux guide, as shown in Fig. 11.The magnet can be also trapezoidal, as shown in Fig. 12, whichcan make the pole shoe rectangular, and the rotor pole iron nearthe two air gaps has a similar saturation level. However, thistrapezoidal-magnet rotor structure does not significantly affect

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Fig. 10. Configuration of the DSSA VPM machine. (a) Outside stator.(b) Rotor. (c) Inside stator. (d) Global model.

Fig. 11. One of the stator configurations.

the back EMF, as illustrated in Fig. 12, whereas the magnetshape is more complex than that of the rectangular magnet.Hence, the rectangle-magnet rotor is preferred.

Fig. 13 shows the magnet flux density distributions of theDSSA VPM machine. It can be seen that the PMs excite a44-pole field density, as shown in Fig. 13(a) and (c), in both airgaps. The space harmonics with four poles in both side statoryokes, as depicted in Fig. 13(b) and (d), become the highestflight due to the modulation effect of the stator teeth on themagnetic field, and then, the four-pole space harmonics interactwith the four-pole armature field to produce steady torque. Itis clear that the stator teeth of VPM machines work as a “polenumber transformer.”

IV. POWER FACTOR OF DSSA VPM MACHINES

A. Open-Circuit Field Distribution

The DSSA VPM topology is not just a double-sided VPMmachine but a novel topology, which employs the inside/outsidestator teeth flux paths to replace the outside/inside slot paths, asshown in Fig. 14(b), and then all magnets produce the main fluxat the same time. Therefore, the magnet leakage flux is muchreduced, and the main flux is boosted.

Fig. 12. Magnet topologies. (a) Rectangular magnet. (b) Trapezoidal magnet.(c) Back-EMF comparison of the two DSSA VPM machine models.

Fig. 13. Magnet flux density distribution. (a) Inner air gap. (b) Inner statoryoke. (c) Outer air gap. (d) Outer stator yoke.

Moreover, since the flux focusing effect can be obtainedby the spoke-array rotor structure, the air-gap flux density isgreatly improved.

3668 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 50, NO. 6, NOVEMBER/DECEMBER 2014

Fig. 14. Flux plot at the no-load condition. (a) Single-sided, (b) dual-sided,and (c) DSSA VPM machines.

TABLE IIIMAIN SPECIFICATIONS OF A DSSA VPM MACHINE

The FEA model of the DSSA VPM machine has been built,and its size data are listed in Table III. Fig. 14 shows thecomparison of the open-circuit field distribution of regular,dual-sided, and DSSA VPM machines that were investigated byFEA. It is clearly demonstrated that the DSSA VPM machinecan greatly improve the flux density. Specifically, the fluxdensity of the machine can reach almost 1.8 T in both sidesof the air gap, as shown in Fig. 15. If the DSSA VPM machinewas regarded as the proposed two separated VPM machines,the relative position of the two stators boosts the performancesfor both of them.

Fig. 15. Flux density distribution of the DSSA VPM machine.

TABLE IVPERFORMANCE OF A DSSA VPM MACHINE

Fig. 16. Variation of torque and power factor versus gamma angle.

The FEA results are summarized in Table IV. It is clear thatthe power factor of the proposed machine is 0.91, although themagnet thickness is only 3 times the air-gap length.

B. Reluctance Torque of DSSA VPM Machines

The spoke-array magnets introduce rotor anisotropy for theDSSA VPM topology. Therefore, the DSSA VPM machine hastwo torque components, i.e., a reluctance torque component anda magnet torque component.

As shown in Table IV, the d- and q-axis inductances are5.6 and 5.2 mH, respectively, and in other words, the ratio ofq-to-d inductance is small, viz., 1.08. This rotor anisotropicfeature can be explained that the stator slot opening can evenbe larger than the rotor pole pitch, and the stator tooth works asan “anisotropic filter” to smooth the rotor anisotropic; thus, thesaliency ratio is heavily reduced. Fig. 16 shows the variationsof torque and power factor with gamma angle, which is theelectrical angle between open-circuit EMF E0 and input phasecurrent I , and the gamma angle is positive when the currentphase leads the EMF phase. It can be seen that the optimal

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Fig. 17. Variation of reluctance torque/magnet torque versus gamma angle.

Fig. 18. Back-EMF waveform of the DSSA VPM machine.

gamma angle for maximum torque is at ∼18◦, whereas thepower factor is larger than 0.86. If the gamma angle varies from0◦ to 30◦, the power factor would increase from 0.76 to 0.91with almost 2% torque improvement, and the reluctance torquecomponent contributes from 0 to 13% of the total torque, asshown in Fig. 17.

The inside/outside stator teeth cooperate with the out-side/inside stator teeth to provide the main flux path, whichreplaces the flux leakage paths introduced by stator slots. Thespecified structure heavily reduces magnet flux leakage andincreases air-gap flux density. In addition, although the saliencyratio of the DSSA VPM machine is small, the reluctance torqueof the DSSA VPM machine also contributes the output torque.As a result of all the aforementioned reasons, the power factorof the DSSA VPM topology is boosted to a higher level.

V. ELECTROMAGNETIC PERFORMANCE

OF DSSA VPM MACHINES

This section analyzes other important electromagnetic per-formance indexes of the DSSA VPM machine, including theback-EMF waveform, cogging torque, and torque density.

A. Back-EMF Waveform and Cogging Torque

Benefited from the large rotor poles, few slots, and harmoniccouple effect, the back-EMF waveform of the regular VPMmachine is more sinusoidal than that of the regular PM machine[9], and it is also true for the DSSA VPM topology, as shownin Fig. 18.

Fig. 19. Torque waveform of the DSSA VPM machine.

TABLE VELECTROMAGNET PERFORMANCE COMPARISON

OF SINGLE-SIDED AND DSSA VPM MACHINES

Cogging torque results from the interaction of rotor magnetsand stator teeth, and many methods have been presented toreduce its value, such as skewing slot or pole, using fractional-slot concentrated winding, and so on.

In terms of the interaction of rotor magnets and stator teeth,the DSSA machine can be regarded as a PM machine with asmall number of slots per phase per pole, and its “goodnessfactor” CT [15] is small. Therefore, it is an inherent feature thatthe DSSA VPM topology has a small cogging torque.

Fig. 19 shows the FEA results of torque ripple and coggingtorque. It can be seen that the torque ripple percentage, i.e., theratio of peak-to-peak value to average value, of the DSSA VPMmachine is ∼3.5%, and the cogging torque is 42 N · m.

In summary, the DSSA VPM machine has more sinusoidalback-EMF waveform than that of the regular PM machine,while the pulsing torque of the DSSA VPM machine is smalldue to the more sinusoidal back-EMF waveform and the speci-fied slot–pole combination.

B. Torque Density

The FEA results show that the DSSA VPM machine canproduce 1.73 times torque compared to that of a single-sidedVPM machine; thus, the machine has larger torque density. Asshown in Table V, the DSSA VPM machine has impressivetorque density and magnet-saving capability.

This high torque density of the proposed machine is at-tributed to three reasons.

1) Special structure significantly improves magnet usageratio and greatly reduces magnet flux leakage.

2) Spoke-array magnet structure can be used to improve air-gap flux density.

3670 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 50, NO. 6, NOVEMBER/DECEMBER 2014

Fig. 20. Proposed machine configuration. (a) Front view. (b) Subdivisiongraph.

3) Output torque components include magnet torque andreluctance torque.

VI. AUXILIARY MECHANICAL STRUCTURE

OF DSSA VPM MACHINES

The frame and outer stator are assembled together by theshrinkage fit process as the traditional PM machine does. Asshown in Fig. 20, the support structure of the rotor and innerstator uses a cantilever structural model. The rotor active partcombines with the output shaft by the rotor support, and theinner stator support is fixed on the frame by bolts. In orderto reduce the deformation of the inner stator support shaft, areinforcing ring is employed in this paper.

Rotor support is used to transfer torque from the rotor activepart to the output shaft; thus, the rotor support should haveenough mechanical strength. In addition, since the spoke-arraymagnets produce heavy-end magnet flux leakage, as shown inFig. 21, the rotor support should be manufactured by nonmag-netic material.

VII. PROTOTYPE AND EXPERIMENTAL MEASUREMENTS

A three-phase DSSA VPM prototype has been designed,built, and tested here.

The design parameters and size data of the prototype arelisted in Table VI, and Table VII gives out the materials ofmechanical parts. The stator uses the traditional distributed

Fig. 21. End leakage flux of the proposed machine configuration.

TABLE VISPECIFICATION AND DESIGN PARAMETERS OF THE PROTOTYPE

TABLE VIIMATERIAL OF DSSA VPM MACHINE PARTS

winding configuration and short-pitched, viz., 5/6, to reduce thestator MMF harmonics. As a principle verification prototype,the machine is designed to be flat shaped, which simplifies theprocessing difficulty but makes the machine tend to have largeend-winding length. For the specific design cases of DSSAVPM machines, the end-winding length can be reduced byoptimizing the ratio of diameter to stack length and that ofrotor and armature pole number. As illustrated in the foregoingsection, the DSSA VPM machine has high torque density andsmooth torque waveform. Therefore, it is suitable to the direct-drive applications. However, the direct-drive machine alwaysmeans large mass and volume, and the inner stator has to usea cantilever structural model, due to the sandwich structure ofdual stators and rotor.

A. Mechanical Checking

As a result, the stiffness of the inner stator support shaft mustbe checked. As shown in Fig. 22, the maximum mechanicalstress of inner stator support due to gravity is almost 59 MPa,which is smaller than the yield strength of carbon steel, viz.,100–200 MPa. The maximum vertical deformation due to

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Fig. 22. Mechanical stress distribution plot. (a) Inner stator support andReinforcing ring. (b) Rotor support.

Fig. 23. Deformation plot. (a) Inner stator support and reinforcing ring.(b) Rotor support.

Fig. 24. Dynamic eccentricity fault for 1/5 air-gap length. (a) Mechanicalstress. (b) Deformation plot.

gravity of inner stator and rotor support are 0.0025 and0.12 mm, respectively, as shown in Fig. 23. If there is a 1/5 air-gap length dynamic eccentricity, the mechanical stress will besignificantly increased, and the maximum stress reaches almost125 MPa, as shown in Fig. 24, and the maximum deformationis almost 0.1 mm. Therefore, the dynamic eccentricity shouldbe made as small as possible.

B. Loss Calculation and Thermal Checking

Losses in electrical machines can be classified into thefollowing:

1) copper loss;2) magnet loss;3) core losses, including stator and rotor iron losses;4) stray loss;5) mechanical loss.This section focuses on the copper, magnet, and core loss

calculation, and the results will be treated as the thermal sourceto do the thermal dissipation process.

Fig. 25. Flux route excited only by armature winding.

TABLE VIIIFEA CALCULATION RESULTS OF LOSSES

Fig. 26. No-load three-phase short-circuit current.

Fig. 25 shows the armature flux route, and it can be seenthat the magnet is not exposed to the armature flux. Therefore,the low magnet losses can be predicted. Table VIII summarizesthe results of FEA loss calculation at the rated load. It can beobtained that the magnet loss is really small.

The radial-field dual-stator PM machines are always troubledby the inner stator thermal issues, and there are many papersdiscussing on this topic, such as Sun and Cheng [16].

In order to make sure that the prototype can operate undera permissible range of temperature rising, it is necessary to testthe temperature of the inner stator end-winding temperature riseunder at least 7-h continuous rated load operation and shouldguarantee that the temperature rise is no more than 90◦.

C. Demagnetization Investigation

The fault tolerance of electrical machines is one of theimportant performance indexes for the drive machines. Thereare many fault tolerance indexes, such as ability to resistshort current, demagnetization, etc. Due to space limitations,this section focuses on evaluating the risk of demagnetizationduring the no-load three-phase short-circuit fault. As shown inFig. 26, the short-circuit current reaches its maximum value ataround 41 ms, and the flux density is given out in Fig. 27. It canbe seen that there is almost no demagnetization part during theno-load three-phase short circuit.

3672 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 50, NO. 6, NOVEMBER/DECEMBER 2014

Fig. 27. FEA result of demagnetization.

Fig. 28. Prototype. (a) Outer stator. (b) Rotor. (c) Inner stator. (d) Test bed.

D. Test

The prototype and its test setup are shown in Fig. 28. Theback-EMF waveform of inner and outer stators is measured at33.5 r/min. The back EMF waveforms shown in Figs. 29 and30 illustrate that the measured back EMFs match simulationswell. The discrepancy between the measured and simulatedline back-EMF amplitudes of outer and inner stators is about0.5% and 0.2%, respectively. Moreover, the experiments showthat the total harmonic distortion (THD) of the line back-EMFwaveform is only 1.24%.

Fig. 29. Back-EMF waveforms of the prototype machine.

Fig. 30. Comparison of the 2-D FE predicted and measured phase amplitudesof the fundamental back EMF.

Fig. 31. DSSA VPM machine. (a) Air-gap flux density. (b) Winding function.

The back EMF of the DSSA VPM machines can be ex-pressed as

e =d

dtλ =

d

dt

2π∫0

N(θs)Bgm(θs, t) dθs (2)

where e is the phase back EMF, λ is the magnet flux linkage,N(θs) is the winding function of one-phase winding, andBgm(θs) is the air-gap flux density.

The harmonics of back EMF is dependent on the coupleeffect between the flux density distribution and the windingconfiguration, i.e., the winding function.

For the DSSA VPM machine, its rotor pole number is muchlarger than that of the stator pole number, e.g., for the 22-rotorpole, 12-stator teeth VPM machine, the pole number of magnetfield harmonic arrays excited by the interaction between magnetMMF and fundamental air-gap permeance harmonics is shownin Fig. 31. It is clearly seen that the harmonics arrays of thetwo fields are staggered. Therefore, the DSSA VPM has lowerback-EMF harmonic distortion.

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Fig. 32. Measured line voltage and current waveform (curve 1: line voltage;curve 3: line current).

TABLE IXCOMPARISON OF SIMULATION AND MEASURED PERFORMANCE INDEXES

Fig. 32 shows the measured line current and voltage wave-form, and Table IX summarizes the comparison of the designedand measured electromagnetic performances of the prototype. Itcan be seen that the measured line current to produce the sameamount of torque as simulated is larger by 4% compared to thatof the designed value, which would lead to larger copper lossand lower efficiency in response. The error between measuredand FEA values is attributed to the relative complex mechan-ical structure and immature manufacture, which introduces alarge no-load loss. In addition, a commercial converter is usedto drive the prototype machine, and it is not good enoughfor the DSSA VPM machine. The measured power factor is0.83, which is slightly lower than the foregoing prediction.It is also shown in Table IX that the torque density can belarger than 66 (kN · m)/m3 with less than 1.2 A/mm2 currentdensity.

VIII. CONCLUSION

A high-power-factor vernier topology DSSA VPM machinehas been proposed in this paper. Both the structure and perfor-mance characteristics of the DSSA VPM topology have beendiscussed in this paper.

At first, the power factor of normal VPM machines is inves-tigated. The analysis shows that the low power factor is mainlycaused by heavy magnet flux leakage and low magnet utiliza-tion, viz., 50%. It has been proven that the proposed DSSAVPM topology can greatly reduce the magnet flux leakage, andall magnets contribute to the air-gap flux density at same time.This improvement is benefited from the special structure, i.e.,the inner stator tooth has half teeth pitch displacement relativeto the outer stator tooth. Therefore, both inner and outer teeth

compensate with each other. They can provide large permeanceand guide leakage flux for the contribution to the useful fluxfrom one side to the other side.

Moreover, the rotor anisotropy introduces the reluctancetorque, which could lead to high torque density and high powerfactor for the proposed machine.

Furthermore, the DSSA VPM machine has inherent advan-tages, i.e., low cogging torque and low THD of the back-EMFwaveform. Therefore, the DSSA VPM machine is suitable forthe applications with strict requirements of high output torquedensity and low torque ripple.

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Dawei Li (S’12) was born in China. He received theB.Eng. degree in electrical engineering from HarbinInstitute of Technology, Harbin, China, in 2010. Heis currently working toward the Ph.D. degree inthe School of Electrical and Electronic Engineering,Huazhong University of Science and Technology,Wuhan, China.

His research interests include design and analysisof novel permanent-magnet brushless machines.

3674 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 50, NO. 6, NOVEMBER/DECEMBER 2014

Ronghai Qu (S’01–M’02–SM’05) was born inChina. He received the B.E.E. and M.S.E.E. degreesfrom Tsinghua University, Beijing, China, in 1993and 1996, respectively, and the Ph.D. degree in elec-trical engineering from the University of Wisconsin-Madison, Madison, WI, USA, 2002.

In 1998, he joined the Wisconsin Electric Ma-chines and Power Electronics Consortiums as aResearch Assistant. He became a Senior ElectricalEngineer with Northland, a Scott Fetzer Company,in 2002. In 2003, he joined the General Electric

(GE) Global Research Center, Niskayuna, NY, USA, as a Senior ElectricalEngineer with the Electrical Machines and Drives Laboratory. Since 2010, hehas been the “Thousands of People Plan” Professor at Huazhong Universityof Science and Technology, Wuhan, China. He has authored more than 50published technical papers. He is the holder of more than 40 patents/patentapplications.

Prof. Qu is a Full Member of Sigma Xi. He has been the recipient ofseveral awards from the GE Global Research Center since 2003, including theTechnical Achievement and Management Awards. He was the recipient of the2003 and 2005 Best Paper Awards, Third Prize, from the Electric MachinesCommittee of the IEEE Industry Applications Society (IAS) at the 2002 and2004 IEEE IAS Annual Meetings, respectively.

Thomas A. Lipo (M’64–SM’71–F’87–LF’00) wasborn in Milwaukee, WI, USA.

From 1969 to 1979, he was an Electrical Engineerwith the Power Electronics Laboratory, CorporateResearch and Development, General Electric Com-pany, Schenectady, NY, USA. He became a Professorof electrical engineering at Purdue University, WestLafayette, IN, USA, in 1979, and in 1981, he joinedthe University of Wisconsin-Madison, Madison, WI,USA, where he served for 28 years as the W. W.Grainger Professor of Power Electronics and Elec-

trical Machines. He is currently an Emeritus Professor at the University ofWisconsin-Madison.

Dr. Lipo received the Outstanding Achievement Award from the IEEEIndustry Applications Society, the William E. Newell Award from the IEEEPower Electronics Society, and the 1995 Nicola Tesla IEEE Field Awardfrom the IEEE Power Engineering Society for his work. He was elected amember of the Royal Academy of Engineering (U.K.) in 2002, a memberof the National Academy of Engineering (USA) in 2008, and a member ofthe National Academy of Inventors (USA) in 2013. In 2014, he was selectedto receive the IEEE Medal for Power Engineering. For the past 40 years, hehas served the IEEE in numerous capacities, including President of the IEEEIndustry Applications Society in 1994.