eﬃciency optimization of spm motor considering carrier

IEEJ Journal of Industry ApplicationsVol.3 No.6 pp.422–427 DOI: 10.1541/ieejjia.3.422

Paper

Efficiency Optimization of SPM Motor Considering Carrier HarmonicsBased on Electric and Magnetic Networks

Yukihiro Yoshida∗a)Member, Kenji Nakamura∗∗ Member

Osamu Ichinokura∗∗ Member, Katsubumi Tajima∗∗∗ Member

(Manuscript received March 3, 2014, revised Aug. 7, 2014)

This paper presents a method for optimizing the efficiency of a surface permanent magnet (SPM) motor taking intoaccount the carrier harmonics based on magnetic and electric networks. The eddy current loss in the magnets of theSPM motor, including carrier harmonics, is calculated with an electric network model. Then, an efficiency map of theSPM is created by using the proposed electric and magnetic network models to evaluate the motor efficiency. Finally,the efficiency of the SPM motor is optimized by changing the stator structure.

Keywords: reluctance network analysis (RNA), surface permanent magnet (SPM) motor, eddy current loss, carrier harmonics

1. Introduction

Nowadays, permanent magnet (PM) motors are widelyused in various applications for their high performance char-acteristics. It has become more important for loss analy-sis of PM motors taking into account the carrier harmonicssince they are driven by a PWM inverter with high frequencyswitching (1) (2). However, estimating motor efficiency consid-ering carrier harmonics and eddy current loss in the PMs iscomputationally expensive.

The most conventional optimum design for PM motors isshape optimization by finite element analysis (FEA). How-ever, to calculate the eddy current loss in magnets, three-dimensional (3D) FEA should be used and it takes much timeto obtain the calculation results in general. Therefore, morepractical solution for the PM motor analysis in reasonabletime with high accuracy is strongly required.

Reluctance network analysis (RNA) can be useful for sav-ing calculation time to estimate characteristics of PM mo-tors. It can be taken into account the magnetic saturation andthe rotor motion (3)–(8). In previous papers, we have proposeda method for calculating characteristics of PM motors basedon RNA (3)–(5). The proposed RNA model of the PM motor canbe coupled with the motor drive circuit and mechanical sys-tem. Using the proposed model, iron loss in the stator coreof the PM motor was calculated accurately (4). In addition,eddy current loss in permanent magnets of a surface perma-nent magnet (SPM) motor can be calculated by coupling with

a) Correspondence to: Yukihiro Yoshida. E-mail: [email protected]∗ Department of Electrical and Electronic Engineering, Akita

University1-1, Tegata Gakuen-machi, Akita 010-5802, Japan

∗∗ Department of Electrical Engineering, Tohoku University6-6-05, Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan

∗∗∗ Department of Cooperative Major in Life Cycle Design Engi-neering, Akita University1-1, Tegata Gakuen-machi, Akita 010-5802, Japan

an electric network model of the magnet (9).In the study, losses of SPM motor including carrier fre-

quency are estimated based on reluctance and electric net-works. To verify the accuracy of proposed models, the cal-culation results are compared with calculated values obtainedfrom FEA. And an efficiency map of the SPM is created byusing proposed models to evaluate the motor efficiency. Fi-nally, the efficiency of the SPM motor is optimized by chang-ing the stator structure.

2. Analysis Model of SPM Motor

Figure 1 shows shape and specifications of an SPM mo-tor used in the consideration. The material of the magnets issintered Nd-Fe-B. The coercive force Hc and the recoil per-meability μr are 920 kA/m and 1.038, respectively.

Fig. 1. Shape and specifications of SPM motor

c© 2014 The Institute of Electrical Engineers of Japan. 422

Efficiency Optimization of SPM Motor Considering Carrier Harmonics（Yukihiro Yoshida et al.）

Fig. 2. A part of reluctance network model of the SPMmotor

(a) Division of a magnet. (b) Electric network model.

Fig. 3. An example division and electric network modelof a magnet

Figure 2 illustrates a part of RNA model. Each elementin air gap is divided in one degree intervals in the circum-ferential direction and the magnets are divided into three inthe radial direction. The stator tooth tip is divided into threeregions and the reluctances in these regions are directly con-nected with the air gap reluctances as shown in the figure.

Figure 3 shows an explanation of derivation of an electricnetwork model for calculating eddy current loss in a pieceof magnet. The magnet is divided into multiple elements asshown in Fig. 3(a). Then, the electric network is expressedby resistances and electromotive forces as shown in Fig. 3(b).Figure 4 is one pole of the magnet of the SPM motor and itsdivision. The magnet is divided into three in the radial di-rection, 36 in the circumferential direction, four in the axialdirection, respectively.

Coupling between magnetic network of the SPM motorand electric network of the magnet, iron loss and eddy currentloss in the magnet can be calculated at the same time.

3. Carrier Frequency Dependence of Losses

To take into account the carrier harmonics, input currentwaveforms are calculated by a motor drive circuit shown inFig. 5. In the figure, the winding resistances, inductances, in-duced voltage by the magnets and phase current are rU , rV ,rW , LU , LV , LV , eU , eV , eW and iU , iV , iW , respectively. vUV isline voltage between U-V phases. In this circuit, the induced

Fig. 4. Shape of one pole of the magnet and its divisionfor the electric network model

Fig. 5. Equivalent electric circuit of the SPM motor

Fig. 6. Voltage waveforms of the PWM inverter

voltages eU , eV , eW and the Inductances LU , LV , LV are cal-culated by the magnetic network model of the SPM motor.Figure 6 shows the voltage waveforms of the PWM inverter.In Fig. 6(a), vtri is carrier wave and vUr,vVr, vWr are modu-lating waves of each phase. Comparing the carrier wave andmodulating waves, the switching patterns of the transistor aredetermined. Since ideal power devices are used in the circuit,the terminal voltage waveforms of the inverter vU0, vV0 andthe line voltage between terminals U and V vUV0 = vU0 − vV0

are calculated as shown in Fig. 6(a), (b) and (c), respectively.Figure 7 shows the comparison of the line voltage vUV

waveforms calculated by the motor drive circuit when thecarrier frequency is 2.5 kHz and 10 kHz. Figure 8 shows thecomparison of phase current waveforms when the carrier fre-quency is 2.5 kHz and 10 kHz. The current amplitude of fun-damental wave is 5 A at both carrier frequency conditions.

423 IEEJ Journal IA, Vol.3, No.6, 2014


(a) Line voltage vUV ( fc = 2.5 kHz).

(b) Line voltage vUV ( fc = 10 kHz).

Fig. 7. Comparison of voltage waveforms

(a) Input Current ( fc = 2.5 kHz).

(b) Input Current ( fc = 10 kHz).

Fig. 8. Comparison of current waveforms

Comparing the phase current waveforms of these two dif-ferent carrier frequencies, the phase current waveform at acarrier frequency of 2.5 kHz is distorted while the waveformat a carrier frequency of 10 kHz are more close to sinusoidalwave.

To investigate the influence of the carrier harmonics, theeddy current loss in the magnets and iron loss in the statorcore corresponding to various carrier frequencies are calcu-lated by using the proposed method. Figure 9(a) providesthe carrier frequency versus iron loss in the stator core at an

(a) Iron loss in the stator core.

(b) Eddy current loss in the magnet.

Fig. 9. Losses versus carrier frequency

input current amplitude of 5 A. The fundamental frequencyis 250 Hz. Figure 9(b) provides the carrier frequency versuseddy current loss in the magnets at the same current condi-tion. In the figures, the calculated value of 0 kHz is obtainedwhen the input current is ideal sinusoidal wave. The calcu-lated values obtained from the proposed models almost agreewell with the ones obtained from 3D-FEA. The iron loss hasless influence from the input current waveforms, since theflux flowing through the stator core is principally producedby the magnets. However, the iron loss is increased by atleast 1.4 times comparing with the one without carrier fre-quency. As for the eddy current loss in the magnets, it isincreased by 3 times when the carrier frequency is 10 kHz.These results tell that it is important to estimate the losses inthe SPM motor considering the carrier harmonics.

4. Efficiency Optimization of the SPM Motor

It is useful to evaluate a motor efficiency map for designingthe motor since the motor efficiency is changed in accordancewith the change of rotor speed and load. In this section, an ef-ficiency map of the SPM motor is obtained by using proposedmodels. Then, the efficiency of the SPM motor is optimizedby changing the structure of stator.

4.1 Efficiency of the SPM Motor To minimize theloss of the SPM motor at an operating point (rotor speed andtorque), the motor should be driven by a suitable current con-dition. Figure 9 shows torque distribution maps when the in-put current amplitude and current phase angle β are changedby 0 to 10 A and 0 to 90 degrees, respectively. Figure 10(a)is a torque distribution map capable of outputting at the rotorspeed of 1000 rpm and Fig. 10(b) is the one at the rotor speedof 3000 rpm. High torque region at 3000 rpm cannot be per-formed because the induced voltage exceeds the source volt-age and the motor is uncontrollable. As shown in the figure,various input current conditions can be chosen for driving the



(a) 1000 rpm.

(b) 3000 rpm.

Fig. 10. Torque map of the SPM motor

motor at an operating point. The processing for minimizingthe motor loss with a suitable condition is described below.

Figure 11(a) shows the relationship between the currentphase angle β and losses of the SPM motor when the rotorspeed and output torque are 1000 rpm and 1.0 N·m, respec-tively. The loss becomes minimum at the current phase angleof 0 degrees whose current amplitude is minimum since thecopper loss is dominant at this operating point. Figure 11(b) shows the relationship between the current phase angleβ and losses of the motor when the rotor speed and outputtorque are 3000 rpm and 1.0 N·m, respectively. To minimizethe total loss of the motor, iron loss is needed to reduce byincreasing current phase angle β. Thus, the total loss can beminimized at the current phase angle β of 10 degrees at thisoperating point.

Figure 12 describes an efficiency map of the SPM motorand breakdown of the losses at representative points. In theefficiency map, all operating points are driven with minimumloss by the above-mentioned method. The maximum effi-ciency is 92.3% when the rotor speed and output torque are3000 rpm and 1.0 N·m, respectively. In Fig. 12(b), copperloss is dominant at the operating point of A, C and E. Partic-ularly at E, copper loss increases since much field weakeningcurrent is required to decrease the induced voltage.

4.2 Efficiency Optimization of the SPM Motor byChanging the Stator Structure The SPM motor hasmuch copper loss in the high torque and high speed regions.

(a) 1000 rpm.

(b) 3000 rpm.

Fig. 11. Current phase versus losses at the output torqueof 1.0 N·m

(a) Efficiency map of the SPM motor.

(b) Breakdown of the losses at representative points.

Fig. 12. Efficiency map and Breakdown of the losses ofthe SPM motor

To improve the motor efficiency, the motor efficiency is opti-mized as the total loss of representative points is minimizedby changing the stator structure.

Figure 13 illustrates original structure of the stator. Re-ducing the copper loss of the motor, it is effective to increase



Fig. 13. Original structure of the stator

Table 1. Shape parameter of the stator

Fig. 14. Calculation results

the cross-sectional area of the wire. It can also be effectivethat the number of winding turns is reduced to decrease in-duced voltage so that the field weakening current is reduced.Therefore, the stator tooth width Wt, stator yoke width Wy

and number of winding turns shown in the figure are changedas the range in Table 1. Because nonlinearity of the core isnot taken into account in the proposed reluctance networkmodel, the minimum values of Wt and Wy are determined bythe maximum flux density in the core of 1.7 T. In all condi-tions, the winding space factor is 55% and input current iscreated using the electric circuit shown in Fig. 5 when thecarrier frequency is 10 kHz.

Figure 14 shows the calculated total loss of representativepoints. All conditions in Table 1 are plotted in the figure. Thetotal loss is minimized when the stator tooth width Wt, sta-tor yoke width Wy and number of winding turns are 4.8 mm,2.5 mm and 27 turns, respectively. The total loss of represen-tative points is decreased by 31% at that condition comparingwith the original condition. The number of turns is effectiveto reduce the total loss because the field weakening currentis reduced due to reduction of induced voltage as number ofturns is decreased.

Figure 15(a) illustrates the optimized structure of the

(a) Stator stracture.

(b) Comparison of the wire cross-section.

Fig. 15. Optimized structure of the stator

(a) Efficiency map of the optimized SPM motor.

(b) Breakdown of the losses at representative points.

Fig. 16. Efficiency map and Breakdown of the losses ofthe optimized SPM motor

stator. The cross-sectional area of slot is increased by 1.3times. As the result, the winding resistance is reduced by59 % due to increase in cross-sectional area of wire as shownin Fig. 15(b).

Figure 16(a) shows the efficiency map of the optimizedSPM motor. The maximum efficiency is 92.8% when therotor speed and output torque are 5000 rpm and 2.0 N·m, re-spectively. Comparing with the efficiency map of the originalstructure, the point of maximum efficiency moves high speedregion since the copper loss at operating point E is reduced by



about one-fourth as shown in Fig. 16(b). On the other hand,the iron loss in the stator core is increased since the flux den-sity in the core is increased due to diminution of the corewidth.

5. Conclusion

This paper presents the efficiency optimization of an SPMmotor taking into account the carrier harmonics based on re-luctance and electric networks. To take account of the carrierharmonics caused by PWM switching, input current wave-forms are calculated by a motor drive circuit. By using theinput current waveforms with various carrier frequencies, theiron loss in the stator core and eddy current loss in the mag-nets are calculated. It is clarified that the eddy current loss inthe magnet is more affected by the carrier harmonics.

The efficiency map of the SPM motor is made with mini-mum loss at each operating point. In high speed region, thecopper loss increases since much field weakening current isrequired to decrease the induced voltage. Then, the motor ef-ficiency is optimized by changing stator structure. Reducingthe stator core width and number of winding turns, the totalloss of representative points is decreased by 31% comparingwith the one of original structure.

References

( 1 ) K. Yamazaki and A. Abe: “Loss investigation of interior permanent mag-net motors considering carrier harmonics and magnet eddy currents”, IEEETrans. Ind., Vol.45, pp.659–665 (2009)

( 2 ) T. Okitsu, D. Matsuhashi, Yanhui Gao, and K. Muramatsu: “Coupled 2-D and3-D Eddy Current Analyses for Evaluating Eddy Current Loss of a PermanentMagnet in Surface PM Motors”, IEEE Trans. Magn., Vol.48, pp.3100–3103(2012)

( 3 ) K. Nakamura, K. Saito, and O. Ichinokura: “Dynamic Analysis of InteriorPermanent Magnet Motor Based on a Magnetic Circuit Model”, IEEE Trans.Magn., Vol.39, pp.3250–3252 (2003)

( 4 ) K. Nakamura, M. Ishihara, and O. Ichinokura: “Reluctance Network Analy-sis Model of a Permanent Magnet Generator Considering an Overhang Struc-ture and Iron loss”, 17th International Conference on Electrical Machines(ICEM 2006), PSA1-16 (2006)

( 5 ) K. Nakamura and O. Ichinokura: “Dynamic Simulation of PM Motor DriveSystem Based on Reluctance Network Analysis”, 13th International PowerElectronics and Motion Control Conference (EPE-PEMC 2008), 441 (2008)

( 6 ) T. Raminosoa, J.A. Farooq, A. Djerdir, and A. Miraoui: “Reluctance networkmodelling of surface permanent magnet motor considering iron nonlineari-ties”, Energy Conversion and Management, Vol.50, pp.1356–1361 (2009)

( 7 ) J.K. Tangudu, T.M. Jahns, A.M. EL-Refaie, and Z.Q. Zhu: “Lumped Pa-rameter Magnetic Circuit Model for Fractional-Slot Concentrated-WindingPermanent Magnet Machines”, Energy Conversion Congress and Exposition(ECCE 2009), pp.2423–2430 (2009)

( 8 ) S.-H. Han, T.M. Jahns, and W.L. Soong: “A Magnetic Circuit Model for anIPM Synchronous Machine Incorporating Moving Airgap and Cross-CoupledSaturation Effects”, International Electric Machines and Drives Conference(IEMDC 2007), Vol.1, pp.21–26 (2007)

( 9 ) Y. Yoshida, K. Nakamura, and O. Ichinokura: “Consideration of Eddy Cur-rent Loss Estimation in SPM Motor Based on Electric and Magnetic Net-works”, IEEE Trans. Magnetics, Vol.48, No.11, pp.3108–3111 (2012)

Yukihiro Yoshida (Member) was born in 1981 in Fukuoka, Japan.He received the B.E. degrees from Oita University in2003. From 2003 to 2009, he was an electrical engi-neer at MEITEC Corporation. In 2011, He receivedM.E. Ph.D. degrees in electrical engineering from To-hoku University in 2011 and 2013, respectively. Heis currently a research associate of Akita University.His research interests include the design and analy-sis of permanent magnet machines. Dr. Yoshida isa member of the Institute of Electrical Engineers of

Japan (IEEJ), the Magnetic Society of Japan (MSJ).

Kenji Nakamura (Member) was born in 1975 in Nagano, Japan. Hereceived the B.E. and M.E. degrees from Tohoku Uni-versity in 1998 and 2000, respectively. Since 2000, hehas been with the Graduate School of Engineering,Tohoku University. In 2007, he received the Ph.D.degree in electrical engineering from Tohoku Univer-sity, where he is currently an Associate Professor. Hiscurrent research interests include the design and anal-ysis of reluctance machines and permanent magnetmachines. Dr. Nakamura is a member of IEEE, the

Institute of Electrical Engineers of Japan (IEEJ), the Magnetic Society ofJapan (MSJ), and the Japan Society of Applied Electromagnetics and Me-chanics.

Osamu Ichinokura (Member) was born in 1951 in Iwate, Japan. Hereceived his B.S., M.S. and Ph.D. degrees in electricalengineering from Tohoku University in 1975, 1977and 1980, respectively. Since 1980, he has been withthe Electrical Engineering, Tohoku University. He isnow a professor of the Graduate School of Engineer-ing, Tohoku University. His current research interestsare in the areas of power electronics and power mag-netics. Prof. Ichinokura is a member of IEEE, theInstitute of Electrical Engineers of Japan (IEEJ), the

Magnetic Society of Japan (MSJ), the Society of Instrument and ControlEngineers (SICE), and the Institute of Electrical Installation Engineers ofJapan.

Katsubumi Tajima (Member) was born in 1965 in Morioka, Japan.He received his D.Eng. degree in electrical engineer-ing from Tohoku University in 1998. He is a pro-fessor in the Cooperative Major in Life Cycle De-sign Engineering, Graduate School of Engineeringand Resource Science, Akita University. He has beenengaged the reluctance network analysis of the induc-tion motor and stepping motor. He is a member ofThe Institute of Electrical Engineers of Japan, TheMagnetics Society of Japan, IEEE.


eﬃciency optimization of spm motor considering carrier

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