material-efﬁcient permanent-magnet shape for torque …lipo.ece.wisc.edu/2015pubs/2015-10.pdf ·...

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 10, OCTOBER 2014 5779

Material-Efficient Permanent-Magnet Shapefor Torque Pulsation Minimization in SPM

Motors for Automotive ApplicationsWenliang Zhao, Thomas A. Lipo, Life Fellow, IEEE, and Byung-Il Kwon, Senior Member, IEEE

Abstract—This paper focuses on the design and analysis ofa novel material-efficient permanent-magnet (PM) shape forsurface-mounted PM (SPM) motors used in automotive actuators.Most of such applications require smooth torque with minimumpulsation for an accurate position control. The proposed PMshape is designed to be sinusoidal and symmetrical in the axialdirection for minimizing the amount of rare earth magnets as wellas for providing balanced axial electromagnetic force, which turnsout to obtain better sinusoidal electromotive force, less coggingtorque, and, consequently, smooth electromagnetic torque. Thecontribution of the novel PM shape to motor characteristics is firstestimated by 3-D finite-element method, and all of the simulationresults are compared with those of SPM motors with two conven-tional arched PM shapes: one previously reported sinusoidal PMshape and one step skewed PM shape. Finally, some finite-elementanalysis results are confirmed by experimental results.

Index Terms—Electrical machines, electromagnetic force,finite-element analysis (FEA), finite-element method (FEM),permanent-magnet (PM) machines, sinusoidal electromotiveforce (EMF).

NOMENCLATURE

λ Flux linkage of a phase winding.Nc Number of coil turns per phase.kw Winding factor.Bg Airgap flux density.τp Magnet pole pitch.Lst Motor stack length.p Number of magnet pole pairs.ωr Mechanical angular speed.e Induced phase back electromotive force (EMF).φf Magnetic flux.fe Electrical frequency.θe Electrical rotor position angle.Te Electromagnetic torque.

Manuscript received June 26, 2013; revised October 10, 2013; acceptedDecember 2, 2013. Date of publication January 21, 2014; date of currentversion May 2, 2014. This work was supported by the BK21PLUS programthrough the National Research Foundation of Korea funded by the Ministry ofEducation.

W. Zhao and B.-I. Kwon are with the Department of Electronic Systems En-gineering, Hanyang University, Ansan 426-791, Korea (e-mail: [email protected]; [email protected]).

T. A. Lipo is with the Department of Electrical and Computer Engineering,University of Wisconsin, Madison, WI 53706-1691 USA (e-mail: [email protected]).

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

Digital Object Identifier 10.1109/TIE.2014.2301758

E0 Fundamental amplitude of back EMF.ea, eb, ec Phase back EMF.ia, ib, ic Phase current.Piron Iron loss.Nelement Element number.Phi(B, fe) Hysteresis loss of each element.Pei(B, fe) Joule loss of each element.B Magnetic flux density of each element.Irms RMS value of the armature current.R Stator resistance.Pcopper Copper loss.η Motor efficiency.Nc Cogging torque periods during a slot pitch.n Step skewing number.Q Number of stator slots.HCF Highest common factor.

I. INTRODUCTION

E LECTRIC actuators are proving to be an alternative tohydraulic types due to their reliability, energy efficiency,

precise controllability, and environmental considerations [1],[2]. The main automotive applications include electric powersteering, electromechanical brakes, active suspensions, damp-ing and stabilization actuators, clutch and shift actuators, airconditioning, and ventilation systems [3].

High-performance permanent-magnet (PM) motors combin-ing high power density and good efficiency by using rare earthmagnets are favored for these applications. However, rare earthmaterials included in the rare earth PM motors have the problemof high cost and limited supply. Therefore, the development ofhigh-performance motors with less or no rare earth magnetsis needed. There exists a wealth of literature about designingtraction motors for high torque/power density with less or norare earth magnets [4], [5]. As to automotive actuators, themajor trend is to design the motors to be free of vibrationand acoustic noise, to obtain smooth torque with minimumpulsation for an accurate position control, and to improve thedrive comfort. Thus, the research and development of machinesfree of torque pulsation with less or no rare earth magnets maybe considered as an important research direction.

Two components of torque pulsation can be defined asfollows: 1) cogging torque, which arises from the interactionbetween the rotor PMs and stator slotted iron structure and 2)torque ripple, which occurs as a result of the field distributionand the armature magnetomotive force (MMF). In SPM

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5780 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 10, OCTOBER 2014

motors, torque ripple is mainly due to the interaction of theMMF caused by the stator windings and the MMF caused bythe rotor magnets, which is closely related to the harmonics inthe back EMF. There exists an extensive literature with varioustechniques for minimizing torque pulsation. Some researchersdeal with the torque pulsation problem from the control side[6]–[9], while some others rely on machine design concepts[11]–[28]. Among the various approaches, modification ofthe PM shape has been recognized as an effective method forreducing torque pulsation [12]–[17], [19]–[28]. One of the mostcommon techniques is skewing, which can be either continuousor stepwise [13], [21]–[23], [26]–[28]. Skew can reduce thecogging torque to zero theoretically with one slot pitch skewingand can improve the back EMF waveform as well. However,the skewing technique has some drawbacks such as reducingthe useful magnet flux linking the stator windings as well as in-creasing the leakage inductance and stay losses [25]. Moreover,conventional continuous and step skewing techniques exhibitunbalanced axial electromagnetic force, inevitably leading tosome vibration and acoustic noise as well as damage on bearingsystems resulting from the axially asymmetrical structure. In[28], the unbalanced axial electromagnetic force can be literallyeliminated by the alternative herringbone rotor skewing tech-nique, while it leads to more complex structure and ineffective-ness of improving back EMF waveform. Based on the fact thatthe PM shape substantially affects the back EMF waveform andconsequently the cogging torque, a sinusoidal PM shape wasdesigned and verified by two preliminary models through 3-Dfinite-element analysis (FEA), and it has been proposed forobtaining smooth output torque in [15]. However, those modelsstill exhibit unbalanced axial electromagnetic force. Thus, thereis no literature providing a technique which gives an overallconsideration of minimized torque pulsation, sinusoidal backEMF waveform, and balanced axial electromagnetic force.

This paper presents a novel PM shape designed to be sinu-soidal and symmetrical in the axial direction for SPM motors.Due to the symmetrical structure of a sinusoidal PM shape, theunbalanced axial electromagnetic force is totally eliminated.Meanwhile, the proposed PM shape achieves a combination ofboth reducing PM material to a minimum and also reducing theharmonics in the back EMF, which consequently reduces thecogging torque and realizes a smooth electromagnetic torque.In order to highlight the contribution of the proposed PM shapeto motor characteristics, the analysis results are compared withthose of SPM motors having two conventional arched PMshapes: one previously reported sinusoidal PM shape and onestep skewed PM shape. Section II discusses the modeling ofSPM motors in detail. Sections III and IV show the comparisonof both 3-D FEA results and experimental results. Finally,concluding remarks are given in Section V.

II. MODELING OF SPM MOTORS

A. Basic Model-SPM Motor With Arched PM Shape

The two conventional SPM motors, shown in Fig. 1, arereferred to as the basic models in this paper. They have a verysimple structure that is compatible with its commercial use inautomotive and other low-cost applications. The motors share

Fig. 1. Configuration of the basic models. (a) Stator and windings. (b) Rotorof basic model 1 with 180◦ magnet span. (c) Rotor of basic model 2 with 120◦

magnet span. 1-Stator core. 2-Windings. 3-Rotor core. 4-Magnets.

TABLE ISPECIFICATIONS OF THE BASIC MODELS

the same stator with six slots, as shown in Fig. 1(a), and three-phase concentrated-coil windings are placed in the slots. Therotor is mounted with radially magnetized NdFeB PMs. Themotor with PMs which cover 180 electric degrees per pole isreferred to as basic model 1, shown in Fig. 1(b), and the motorwith PMs which cover 120 electrical degrees per pole is referredto as basic model 2, shown in Fig. 1(c). The specifications forthe two basic models are listed in Table I.

B. Proposed Model—SPM Motor With Sinusoidal PM Shape

1) Design Principle: The conventional SPM motor is usu-ally adopted with the arched PM shape, as shown in Fig. 1(b)and (c). In this paper, this PM shape is regarded as rectangulardue to the radial magnetization, as shown in Fig. 2(a). As isdiscussed in [10], the SPM motor with arched PMs generatesa rectangular magnetic flux distribution in the airgap, whichresults in a rectangular back EMF waveform in a full pitchwinding as shown in Fig. 2(b). Fig. 2(c) shows the resulting har-monics of the back EMF. As is known, these harmonics producetorque ripple and have a detrimental effect on efficiency due tothe iron loss [29], [30]. Moreover, magnets spanning 180 elec-trical degrees result in magnet material waste because the flux atthe transitions between the North and South poles does not con-tribute materially to the torque. It has been shown that the PMshape can be designed to be sinusoidal, which eliminates theharmonics of back EMF and saves on magnet material as illus-trated in Fig. 3(a) [15]. A novel improved PM shape [Fig. 3(b)]is the subject of this paper. The PM shapes in Fig. 3(a) and (b)follow the same principle of producing sinusoidal back EMF.The flux linkage of a phase winding is equal to

λ =NckwBg

τp∫0

Lst sin

(π

τpx− pwrt

)dx (1)

=2

πNckwBgLstτp cos(pwrt). (2)

ZHAO et al.: MATERIAL-EFFICIENT PM SHAPE FOR TORQUE PULSATION MINIMIZATION IN SPM MOTORS 5781

Fig. 2. PM shape and back EMF waveform of basic model 1. (a) RectangularPM shape and airgap flux distribution. (b) Back EMF waveform. (c) FFTanalysis of back EMF.

Fig. 3. Proposed PM shapes and back EMF waveform. (a) Sinusoidal PMshape and airgap flux distribution. (b) Axially symmetrical sinusoidal PM shapeand airgap flux distribution. (c) Ideal back EMF waveform.

Fig. 4. Design sketch of practical PM shapes and rotor topologies. (a) Previ-ous sinusoidal PM shape and rotor. (b) Proposed axially symmetrical sinusoidalPM shape and rotor. 1-Rotor core. 2-PMs.

From the Lenz’s law, the induced back EMF is

e = − dλ

dt=

2

πNckwBgLstτp sin(pwrt) (3)

=2πfeNckwφf sin(θe) (4)

where φf = (2/π)BgLstτp and fe = p(wr/2π).Based on (4), the back EMF waveform varies in a sinusoidal

manner due to the sinusoidal PM shape as shown in Fig. 3(c).The instantaneous torque for a three-phase SPM motor with-

out magnetic saturation is given by

Te = (eaia + ebib + ecic)/wr (5)

when three-phase balanced sinusoidal currents are injected intothe stator coils, smooth output torque production with virtuallyno torque ripple can be obtained.

2) Topology of the Proposed Model: Because of the pro-duction volume, an actuator motor should necessarily be easyto manufacture. Obviously, the ideal sinusoidal PM shape ofFig. 3(b) introduces difficulty in manufacturing. Instead, in thispaper, the magnets are segmented into stepwise stacks. Fig. 4(a)and (b) shows a relatively cost-effective quasi-sinusoidal PMshape design for practical use, and the two models with sinu-soidal PM shape for investigation in this paper are named asmodel 3 and model 4, respectively. It is evident that more stepslead to progressive improvement in obtaining a sinusoidal backEMF waveform.

The selection of step numbers depends on a compromisebetween accuracy and complexity/cost considerations. It isnoted that model 4 adopts more stack segments for producinga more sinusoidal PM shape, which is used for estimating theeffects of the sinusoidal quality of PM shape on the back EMFwaveform when compared with model 3.

C. Analysis Condition for Comparison

In order to verify the contribution of proposed model 4, twobasic models and one previously reported model 3 have been


TABLE IIDESIGN PARAMETERS OF THE ANALYSIS MODELS

first adopted for comparison, as listed in Table II. The analysisconditions for comparison are as follows.

1) The four models have the same specification; the samegrade PMs and iron materials. Basic model 1 has a largeramount of PM material, while the other three modelscontain similar amounts of PM material.

2) In order to obtain reasonable comparative results, therms values of back EMF are kept the same by adjustingthe number of turns per coil in the four models. Thecopper wire was selected with the proper diameter toobtain similar stator copper weight for the four models.Consequently, the current density was increased from4.1 to 4.8 Arms/mm2 in models 2–4.

3) Due to the axial geometry design of sinusoidal PM shapefor the proposed models, 3-D finite-element method(FEM) is utilized to analyze all of the models for ob-taining relatively accurate results for comparison. Theback EMF and cogging torque are analyzed for the no-load case. The electromagnetic torque and iron loss areobtained by feeding with a three-phase balanced sinu-soidal current source for the sake of a simple performancecomparison.

III. THREE-DIMENSIONAL FEM ANALYSIS

A. Magnetic Field Distribution

Fig. 5 shows the open circuit magnetic field distribution forthe four models. The red rectangular shape shows the leakageflux distribution between two poles. As shown in Fig. 5(a),model 1 with rectangular PMs which cover 180 electricaldegrees contains more leakage flux than model 2 which covers120 electric degrees in Fig. 5(b). Although spaces also existbetween North and South poles in model 3, the PM shape pro-duces significant leakage flux as shown in Fig. 5(c). Proposedmodel 4 with an axially symmetrical PM shape shows goodability to reduce the leakage flux in Fig. 5(d).

B. Axial Electromagnetic Force

In many applications, the axial electromagnetic force is animportant issue especially in those which cannot tolerate anyvibration and acoustic noise or in cases where precise positioncontrol is necessary. Fig. 6 shows the axial electromagneticforce without load for the four models. As with the skewingmethod in [26], model 3 exhibits an inherent drawback of un-

Fig. 5. Open circuit magnetic field distribution. (a) Model 1. (b) Model 2.(c) Model 3. (d) Model 4.

Fig. 6. Axial electromagnetic force at the no-load case.

Fig. 7. Axial electromagnetic force at the load case.

balanced axial electromagnetic force, while model 4 combiningthe two basic models contains nearly zero axial electromagneticforce due to the symmetrical PM structure. When the motorsare operated with load, the drawback of model 3 is enlargedas shown in Fig. 7, which demonstrates that a symmetricalstructure for machines will be necessary in some applicationswith stringent operating conditions.


Fig. 8. Phase back EMF of the four models.

Fig. 9. FFT analysis of phase back EMFs.

C. Back EMF and Cogging Torque

The phase back EMFs of the four models are shown inFig. 8. Due to the adjustment of the number of coil turns,the rms values of back EMF are kept the same in four casesfor a reasonable comparison of EMF harmonics and torquepulsations. The two basic models show rectangular back EMFwaveforms, while model 3 and model 4 show good sinusoidalback EMF waveforms. In order to evaluate the sinusoidalquality of the back EMF, a fast Fourier transform (FFT) analysisof back EMFs is shown in Fig. 9, and the dominant back EMFharmonics of the fifth and seventh orders are enlarged. Model 3and model 4 contain almost only a fundamental componentof back EMF by directly utilizing the proposed magnet shapedesign and without any complex optimization procedures. Theharmonic distortions (THDs) of the back EMF of the fourmodels are 23.6%, 22.8%, 3.3%, and 2.8%, respectively, whichare calculated by

THD =

√E2

1 + E22 + E2

3 + · · ·E0

. (6)

It is noted that model 4 shows a better sinusoidal backEMF waveform than model 3 because model 4 adopts morestack steps for a better sinusoidal PM shape. Hence, an evenbetter sinusoidal back EMF waveform is expected when the PMstep number and step size are designed to be more sinusoidal,consistent with an ease of manufacture issue.

Fig. 10 shows the cogging torque comparison for the fourmodels. Proposed model 4 shows the least peak-to-peak valueof cogging torque as 0.0072 N · m, which is reduced by 86.1%,

Fig. 10. Cogging torque of the four models.

Fig. 11. Electromagnetic torque of the four models.

70.3%, and 20.9%, as compared with those of model 1, model 2,and model 3, respectively. It should be mentioned here thatmodel 1 has the largest amount of magnets, while model 2 hasthe least amount of magnets, and it can be concluded that thePM shape is the main contributor to the reduction of coggingtorque.

D. Electromagnetic Torque

In this paper, sinusoidal current excitation has been utilizedto evaluate the torque ripple of the four models. The electro-magnetic torque at the rotational speed of 5000 r/min is shownin Fig. 11. The average output torque of the four models isapproximately the same, resulting in the similar output powerdue to the adjustment of stator winding turns. It is noted thatbasic model 2 is regarded as the preferred reference modelrather than basic model 1 since it has the same current densitywith model 3 and model 4, providing the same operating pointcomparison.

The torque ripple factor defined as the ratio of the peak-to-peak torque value to the average torque value is adopted fortorque ripple calculation, which has the form

KT =Tmax − Tmin

TAVG. (7)

The torque ripple factor of model 4 is 5.6%, which is de-creased by 74.7%, 70.1%, and 5.4%, respectively, as comparedwith model 1, model 2, and model 3. The comparison resultsare summarized in Table III.


TABLE IIITHREE-DIMENSIONAL FEM ANALYSIS RESULTS

E. Iron Loss and Efficiency

As stated in [17], the harmonics of the back EMF havea significant influence on the iron loss. In order to evaluatethe iron loss accurately considering nonlinear phenomena, 3-DFEM modeling was used, employing the commercial softwareJMAG which is based on the equation

Piron =

Nelement∑i

[Ph

i(B, fe) + Pe

i(B, fe)

]. (8)

The iron loss follows the same variation with the THD of theback EMF as shown in Table III. The reduction in iron loss isobtained in spite of the fact that model 3 and model 4 contain aslightly larger amount of PM than basic model 2.

The copper loss can be found by

Pcopper = 3I2rmsR. (9)

Although the copper loss of model 4 is the highest, it stillmaintains high efficiency as the other three models due toreduction of iron loss. The efficiency is herein defined as

η =Pout

Pout + Pcopper + Piron(10)

where the output power Pout is obtained by

Pout = Te2πωr

60. (11)

F. Quantitative Comparison With Step Skewing Method

In order to highlight the advantage of proposed model 4, anSPM motor with step skewed PMs keeping the same specifica-tion as model 4 has been introduced for comparison, as shownin Fig. 12. Since the conventional skewing method improvesthe back EMF waveform by reducing the areas of the backEMF trapezoid, thus reducing the machine performance [22],[25], each step of skewed magnets in the comparative modelis designed to cover 120 electrical degrees per pole to eliminatethe effects of two adjacent poles. The mechanical skewing anglebetween two adjacent steps is given as

θss =2kπ

nNcQ, k = 1, 2, 3 . . . . (12)

Fig. 12. SPM motor with step skewed PMs. (a) Stator. (b) Rotor.

Fig. 13. Comparison of cogging torque.

Fig. 14. Comparison of phase back EMFs.

Normally, k is chosen as unity so that the machine torqueperformance is prevented from degradation. The cogging torqueperiod over a slot pitch is given by

Nc =2p

HCF(2p,Q). (13)

The total SPM motor with step skewed magnets was modeledand analyzed by 3-D FEM. Fig. 13 shows the comparison ofcogging torque. Based on the skewing principle for eliminatingthe cogging torque, the model with step skewed magnets indeedcontains less cogging torque compared with proposed model 4.However, proposed model 4 shows better sinusoidal back EMFwaveform with lower harmonics as indicated in Figs. 14 and 15,which results in less torque ripple as compared with the modelwith step skewed magnets as shown in Fig. 16. Moreover, theunbalanced axial electromagnetic force inevitably occurs inthe model with step skewed magnets due to the skewed axialgeometry as shown in Fig. 17, while it is eliminated in model 4by obtaining a significant cogging torque and torque ripplereduction as well as back EMF improvement. The comparisondata between the two models are summarized in Table IV.


Fig. 15. FFT analysis of phase back EMFs.

Fig. 16. Comparison of electromagnetic torque.

Fig. 17. Comparison of axial electromagnetic force.

TABLE IVTHREE-DIMENSIONAL FEM ANALYSIS RESULTS

IV. EXPERIMENTAL VALIDATION

The 3-D FEM analysis results at no-load case for model 1,model 3, and model 4 have been confirmed by experimentalmeasurements. Fig. 18 shows the prototypes of the manufac-tured SPM motor models. The back EMF was tested as a gener-ator at 1000 r/min. In order to obtain an accurate measurementof cogging torque, it was measured by the commercial cog-ging torque analyzer (ATM-50MN, SUGAWARA Laboratories

Fig. 18. Manufactured prototypes of model 1, model 3, and model 4.

Fig. 19. Back EMF waveforms of model 1, model 3, and model 4 at 1000 r/min.(a), (c), and (e) Simulated waveforms. (b), (d), and (f) Measured waveforms.

Inc.), which measures the torque per angle by rotating the rotorat 1 rad/min and then uploads the angle-torque characteristicsto a computer running windows.

A comparison of simulated and measured back EMF wave-forms is shown in Fig. 19. Fig. 19(a), (c), and (e) showsthe simulated results, while Fig. 19(b), (d), and (f) shows thecorresponding measured results, respectively. The measuredand simulated results show good accordance in back EMFwaveform except that the measured rms value of model 1 hasa slight difference with the simulated rms value due to themanufacturing tolerance, as shown in Table V.

The cogging torque under a no-load condition comparedby FEM simulation and measured results is given in Fig. 20.Fig. 20(a) shows the comparison of simulated results, andFig. 20(b) shows the comparison of measured results. Themeasured cogging torque of model 4 is decreased by 72.0%and 16.5%, as compared with that of model 1 and model 3,


TABLE VCOMPARISON OF SIMULATED AND MEASURED RESULTS

Fig. 20. Comparison of simulated and measured cogging torque. (a) Simu-lated waveform. (b) Measured waveform.

respectively. The measured results retain the same coggingtorque reduction trends as with the simulated results. However,the measured peak-to-peak value of the cogging torque hassome differences with the simulated value. This is presumablybecause the simulation models assume perfect manufacture andassembly of the prototype motors, while there are inevitablymechanical tolerances in manufacture and assembly difficultiesin practice. In particular, each step of the proposed model wasdesigned by special angles for finally sinusoidal PM pole shape,which makes it more difficult for magnets to be cut by designedtolerance. Still, it is satisfied that the cogging torque is highlyreduced in the proposed model in both the simulation andexperimental results.

V. CONCLUSION

In this paper, a novel sinusoidal rotor PM shape has beenproposed to be axially symmetric for the purpose of elimi-nating unbalanced axial electromagnetic force and minimizingtorque pulsation. The proposed PM shape was designed for afundamental waveform of back EMF, which realizes a goodcombination of PM material reduction and back EMF harmonicminimization. In order to facilitate the ease of manufactur-ing, the proposed sinusoidal PM shape was designed to havestepwise stacks approximating a sine wave. A detailed 3-DFEA for the five models to predict the main characteristicswas illustrated by comparison results. Finally, some resultsare confirmed by experimental measurements. The followingconclusion can be obtained from these results.

1) The SPM motors with a sinusoidal PM shape in the axialdirection can produce nearly a pure sinusoidal back EMFeven with full pitched stator windings. The proposedaxially symmetric sinusoidal PM shape appears to have abetter sinusoidal back EMF waveform with less harmoniccomponents than any known designs previously reported.

2) The proposed model with a symmetrically sinusoidalPM shape can effectively eliminate the unbalanced axialelectromagnetic force, which is a prominent advantage

for avoiding extra vibration, acoustic noise, and bearinglosses compared with the previously reported sinusoidalshape and the conventional step skewed magnets, espe-cially in the automotive applications requiring precise po-sition control, such as active steering and brake systems.

3) The SPM motors with a sinusoidal PM shape can ef-fectively minimize the torque pulsation. In the proposedmodel, not only cogging torque but also torque ripple issignificantly reduced compared with the models with theconventional arched PM shape, the previously reportedsinusoidal PM shape, and the conventional step skewedmagnets.

4) The SPM motors with a sinusoidal PM shape sustain lessiron loss due to the minimization of harmonics in theback EMF, which contributes to high efficiency especiallywhen the motors are operated in the high-speed region.

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Wenliang Zhao received the B.S. degree in con-trol science and engineering from Harbin Instituteof Technology, Weihai, China, in 2011. He is cur-rently working toward the Ph.D. degree in electronicsystems engineering at Hanyang University, Ansan,Korea.

His research interests include design, analysis,and optimization of electric machines with analyticalmethod and finite-element method.

Thomas A. Lipo (M’64–SM’71–F’87–LF’06) wasborn in Milwaukee, WI, USA, in 1938. He receivedthe B.E.E. and M.S.E.E. degrees from MarquetteUniversity, Milwaukee, WI, USA, in 1962 and 1964,respectively, and the Ph.D. degree in electrical engi-neering from the University of Wisconsin, Madison,WI, USA, in 1968.

From 1969 to 1979, he was an Electrical Engineerwith the Power Electronics Laboratory, CorporateResearch and Development, General Electric Com-pany, Schenectady, NY, USA. In 1979, he joined

Purdue University, West Lafayette, IN, USA, as a Professor of electricalengineering. In 1981, he joined the Department of Electrical and ComputerEngineering, University of Wisconsin, as a Professor, where he has been anEmeritus Professor since January 1, 2009. He has published over 550 technicalpapers, five books, and 40 patents and has received numerous awards forhis work.

Byung-Il Kwon (M’87–SM’13) was born in 1956.He received the B.S. and M.S. degrees in electricalengineering from Hanyang University, Ansan, Korea,and the Ph.D. degree in electrical engineering fromThe University of Tokyo, Tokyo, Japan, in 1989.

He was a Visiting Researcher with the Faculty ofScience and Engineering Laboratory, University ofWaseda, Tokyo, from 1989 to 2000, a Researcherwith the Toshiba System Laboratory in 1990, aSenior Researcher with the Institute of Machineryand Materials Magnetic Train Business in 1991, and

a Visiting Professor with the University of Wisconsin, Madison, WI, USA, from2001 to 2002. He is currently a Professor with Hanyang University. His researchinterests are design and control of electric machines.

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