impact of the inverter dc bus voltage on the iron losses

IEEJ Journal of Industry ApplicationsVol.6 No.6 pp.346–352 DOI: 10.1541/ieejjia.6.346

Paper

Impact of the Inverter DC Bus Voltage on the Iron Losses of a PermanentMagnet Synchronous Motor at Constant Speed

Nicolas Denis∗a)Non-member, Yenyi Wu∗ Non-member

Keisuke Fujisaki∗ Senior Member

(Manuscript received Dec. 26, 2016, revised May 24, 2017)

In this paper, the impact of the DC bus voltage on the iron losses of a permanent magnet synchronous motor (PMSM)fed by a pulse-width modulation inverter is evaluated. Under constant speed operation, the modulation index decreaseswhen the DC bus voltage increases. This modifies the harmonic content of the PMSM input voltage and then affectsthe motor iron losses. The experimental measurements results show that, for the conditions considered in this paper,the total iron losses are 1.8 times larger at the lowest modulation index than at the highest one.

Keywords: inverter, iron loss, magnetic material, permanent magnet synchronous motor

1. Introduction

Many researches demonstrate that the output voltage of apulse-width modulation (PWM) inverter fed to any woundsoft magnetic material tends to increase its iron losses com-pared to the case of sinusoidal voltage fed operation. Earlyliterature assumes that the high frequency harmonic compo-nents in the PWM supplied voltage are responsible for extraeddy current losses only, implying that the hysteresis lossesare only slightly impacted (1). More thorough investigationsshow that high frequency magnetic flux density occurs insidethe magnetic material, which is responsible for a skin effectthat has a strong impact on the material iron losses (2). More-over, some researchers point out that those high frequencymagnetic flux density variations can also cause minor hys-teresis loops which increase the hysteresis losses in a some-times non-negligible way (3).

PWM gate signal generation has several parameters whichcan influence the iron losses in their own way. The impactof the modulation index in particular, has been studied onwound laminated ring cores (4). The authors conclude that thematerial specific iron losses tend to increase when the mod-ulation index decreases. One of the cause of this increase isthat reducing the modulation index has for effect to widen theminor hysteresis loops in the material (5).

Under the assumption that the harmonic content of thePWM supplied voltage is only responsible for extra eddy cur-rent losses, some authors are able to propose analytical for-mulas of the iron losses caused by PWM in transformers (6).As a result, they propose an analytical characterization of theimpact of the PWM modulation index on the iron losses.

As for the permanent magnet synchronous motors(PMSM), numerical analysis allows evaluating the iron losses

a) Correspondence to: Nicolas Denis. E-mail: [email protected]∗ Toyota Technological Institute

2-12-1, Hisakata, Tenpaku-ku, Nagoya, Aichi 468-8511, Japan

caused solely by PWM (7). The physical repartition of theselosses in the motor parts (rotor, stator and magnets) can alsobe evaluated by numerical analysis (8). In particular, authorsconclude that the magnet losses are almost only due to theeddy current caused by the PWM and that the effect of statorslots on the magnet losses is comparatively small. The addi-tional iron losses caused by PWM can also be approximatedusing analytical formulas (9) (10). In (9), the study focuses ona synchronous motor with surface-mounted permanent mag-nets (SPMSM). Both experiment and numerical calculationshow that the motor iron losses decrease when the modula-tion index increases. However, the derivative is not consid-ered in the motor equation used for the analytical model, eventhough the derivative has a significant impact on the currenthigh order harmonics. In (10), the increasing rate of eddycurrent losses due to PWM is evaluated on a synchronousmotor with interior permanent magnets (IPMSM). The mo-tor uses ferrite magnets with high resistivity, which allowsneglecting the magnet eddy current losses. Both the analyt-ical calculation and the experiment show lower eddy currentlosses increasing rate at high modulation index. However, thehigh frequency content of the motor current due to the PWMcarrier signal is considered using an rms value that dependson the PWM control parameters. Then the analytical modeldoes not consider each harmonic of the voltage and current.

In this paper, an experimental methodology to evaluate theinfluence of the PWM modulation index on a synchronousmotor with interior sintered NdFeB magnets is proposed. Ananalytical model is then developed to give the motor voltageand current harmonics as a function of the PWM control pa-rameters, and especially the modulation index. In section 2,the motor geometry and the cores material characteristics arepresented. The section 3 explains the experimental method-ology and provides the IPMSM total iron losses measurementresults. The experiments are conducted at constant speed andthe DC bus voltage is changed so that a fairly wide rangeof modulation index is covered. The section 4 develops an

c© 2017 The Institute of Electrical Engineers of Japan. 346

PWM Modulation Index and PMSM Iron Losses（Nicolas Denis et al.）

Table 1. Material characteristics

Fig. 1. B-H characteristic of the 35H300 material

Fig. 2. Specific iron loss density of the 35H300 material

analytical model of the IPMSM voltage and current harmon-ics as functions of the PWM control parameters. Finally,measurements of the magnetic flux density in the stator areshown in section 5.

2. Material Characteristics and Motor Geometry

2.1 Material Characteristics The stator and rotorof the proposed IPMSM are made of non-oriented electri-cal steel sheets 35H300. The permanent magnets are sin-tered NdFeB. The important characteristics of the materialsare shown in Table 1. The B-H and specific iron loss charac-teristics of the soft-magnetic material are given in Fig. 1 andFig. 2 respectively.2.2 Motor Geometry The cross-section view of the

motor is illustrated in Fig. 3. The geometry characteristicsand the motor electrical characteristics are listed in Table 2and Table 3 respectively.

3. Experimental Methodology and MeasurementResults

3.1 Experimental Methodology The experimentaltest bench is illustrated in Fig. 4. The IPMSM is driven by

Fig. 3. Quarter cross-section view of the IPMSM

Table 2. IPMSM geometry characteristics

Table 3. IPMSM electrical characteristics

Fig. 4. Experimental test bench for the iron loss mea-surement

a three-phase two-level voltage source inverter (VSI) withIGBTs. The inverter input voltage Vdc is provided by a DCpower source. A standard vector control using a fixed fre-quency PWM with a triangular wave carrier signal is imple-mented for the speed control. The d-axis current reference isset to zero in the vector control scheme. No load is connectedto the IPMSM rotor shaft but an encoder is still needed for thefeedback of the shaft rotational speed.

The IPMSM input active electrical power P3Φ is mea-sured using a power analyzer with a sampling frequencyof 2.2 MHz and a bandwidth from DC to 2 MHz. On the

347 IEEJ Journal IA, Vol.6, No.6, 2017


measurement window, the power analyzer performs the cal-culation

P3Φ =1N

N−1∑k=0

(iu(k)vun(k) + iv(k)vvn(k)+iw(k)vwn(k)

)· · · · · · · · · · · (1)

where N is the sample number of the measurement window,iu,v,w are respectively the u, v and w phase currents, and vu,v,wn

are respectively the u, v and w phase to neutral voltages. Inorder to calculate the copper losses, the rms current is ob-tained from the current waveform using the equation

Ixrms =

√√√1N

N−1∑k=0

i2x(k) · · · · · · · · · · · · · · · · · · · · · · · · · · · · (2)

where x can be u, v or w depending in the considered phase.The inverter-fed IPMSM iron losses under no-load condi-

tion can then be calculated using the following equation

Pi nol = P3Φ − Rs(I2urms + I2

vrms + I2wrms) − Pf · · · · · · (3)

where Pf are the mechanical losses of the IPMSM and theencoder that are measured beforehand using a rotor with de-magnetized magnets. With this equation, it is assumed thatthe measured iron losses are the sum of the hysteresis lossesand the eddy current losses in the stator core, rotor core andmagnets.

In order to get an approximation of the impact of the PWMon the total iron losses by experiment, a test at no-current isdone. The methodology of this test is explained in detailsin (11). During this test, an auxiliary brushless DC motor isused to rotate the IPMSM externally. The three phases of theIPMSM stator are in open circuit. Therefore, no current isflowing through the stator windings and the iron losses arecaused by the rotating magnets only. In this condition, theIPMSM total iron losses is equal to Pi noc and the contribu-tion of the PWM to the total iron losses is estimated using thesimple equation

Pi PWM = Pi nol − Pi noc · · · · · · · · · · · · · · · · · · · · · · · · · (4)

3.2 Iron Loss Measurement Results The PWM car-rier frequency is 1 kHz and the inverter dead-time 3500 ns. Inorder to evaluate the influence of the PWM modulation indexon the iron losses, the measurements are made at a constantspeed of 750 rpm (50 Hz) with different values of Vdc. Whenchanging Vdc, the speed control loop modifies the value of themodulation index in order to adjust the inverter output volt-age so that the speed is maintained constant. The values ofVdc range from 180 V to 43 V, which corresponds to a varia-tion of modulation index ma from 0.230 to 0.975.

The Fig. 5 shows the evolution of the DC bus voltage, theIPMSM total iron losses under no-current condition Pi noc,no-load condition Pi nol and the IPMSM iron losses causedby the PWM Pi PWM . Pi noc does not depend on the modula-tion index because the IPMSM is not driven by the inverter inno-current condition. At a modulation index ma of 0.230, thePWM carrier frequency is responsible for as much as 66%of the total iron losses. At a modulation index of 0.975, thisratio becomes 37%.

Fig. 5. IPMSM iron loss measurement

Fig. 6. PWM sampled modulation signal and triangularcarrier signal (upper), and IGBT upper gate signal (bot-tom). Example for u phase with ma = 0.8, Fc = 1 kHz andFe = 50 Hz

4. Analytical Model of Motor Voltage and Cur-rent

4.1 Calculation of Motor Phase Voltage HarmonicsAs explained section 3, the PWM uses a triangular wave

shape of frequency Fc and a sinusoidal modulation signalwhose amplitude is given by the modulation index ma andfrequency is equal to the IPMSM electrical frequency Fe.The modulation signal is sampled at two times the carrier fre-quency, which gives the IGBT gate signal illustrated in Fig. 6.The switch OFF points θk,off ,u and switch ON points θk,on,u (inrad) of the u phase upper gate signal can be calculated as afunction of the electrical frequency, the carrier frequency andthe modulation index (6). They are given by

θk,off ,u =θc4

(masin((k − 1)θc) − 3 + 4k) · · · · · · · · · · · (5)

θk,on,u = −θc4(masin

((k − 1

2

)θc

)+ 1 − 4k

)· · · · · · · (6)

where θc is equal to 2πFe/Fc, k is an integer from 1 to mc

and mc is equal to Fc/Fe. The switch OFF and switch ONpoints of the two other phases can be obtained by a simple2π/3 phase shift in (5) and (6).

By performing a Fourier transformation, it is possible toobtain the Fourier series of the u phase upper gate signal. It



follows

Cu(θ) =12+

∞∑n=1

(an(Cu)cos(nθ) + bn(Cu)sin(nθ))

· · · · · · · · · · · · · · · · · · · · (7)

where n is the harmonic order, θ is the electrical angle (be-tween 0 and 2π) and an(Cu) and bn(Cu) are the Fourier coeffi-cients of the signal. The coefficients depend on the switchingtimes obtained in (5) and (6) and are given by

an(Cu) =1πn

mc∑k=1

(sin(nθk,off ,u) − sin(nθk,on,u))

· · · · · · · · · · · · · · · · · · · · (8)

bn(Cu) = − 1πn

mc∑k=1

(cos(nθk,off ,u) − cos(nθk,on,u))

· · · · · · · · · · · · · · · · · · · · (9)

The Fourier series of motor phase to neutral voltage canthen be obtained from (8) and (9) using

⎛⎜⎜⎜⎜⎜⎜⎜⎝Vun(θ)Vvn(θ)Vwn(θ)

⎞⎟⎟⎟⎟⎟⎟⎟⎠ =⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

23−1

3−1

3

−13

23−1

3

−13−1

323

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

⎛⎜⎜⎜⎜⎜⎜⎜⎝Cu(θ)Cv(θ)Cw(θ)

⎞⎟⎟⎟⎟⎟⎟⎟⎠ · · · · · · · · · · · · (10)

The voltage harmonics amplitudes obtained using the de-veloped model are presented in Fig. 7 and Fig. 8 for two val-ues of ma. The harmonics are compared with the FFT per-formed on the voltage waveforms obtained by measurement.It can be seen that the model gives results relatively close tothe experimental data. Moreover, the fundamental remainsthe same for both modulation index values because the rota-tional speed is constant. Consequently, only the high orderharmonics change. Knowing the harmonics amplitudes, cal-culating the voltage total harmonic distortion (THD) is quitestraightforward. The THD values obtained from experimen-tal measurements and model calculation are compared in Ta-ble 4.4.2 Calculation of Motor Phase Current HarmonicsAs explained in the previous section, the IPMSM rotates

without load. Consequently, the fundamental of the phasecurrent can be considered null as an approximation. Thismeans that the fundamental of the phase voltage and the fun-damental of the IPMSM back-EMF have no phase or ampli-tude difference. According to a preliminary measurement,the back-EMF of the u phase can be approximated using thefollowing equation.

eu(θ) = 2πFe(Ψ f 1 sin(θ) + Ψ f 5 sin(5θ + φ f 5)

+ Ψ f 7 sin(7θ + φ f 7)) · · · · · · · · · · · · · · · · · · · (11)

where Ψ f 1 is equal to 0.0641 V.s/rad, Ψ f 5 is equal to0.00232 V.s/rad, Ψ f 7 is equal to 0.00440 V.s/rad, and ϕ f 5 andϕ f 7 are almost equal to −π. Moreover, given the known re-lation between the inverter output voltage fundamental, Vdc

and ma, it is possible to write

2πFeΨ f 1 = maVdc

2· · · · · · · · · · · · · · · · · · · · · · · · · · · · · (12)

Fig. 7. Phase voltage harmonics amplitudes for ma =0.230, Fc = 1 kHz and Fe = 50 Hz

Fig. 8. Phase voltage harmonics amplitudes for ma =0.975, Fc = 1 kHz and Fe = 50 Hz

Table 4. Voltage THD comparison

In order to find an analytical expression of the phase cur-rent harmonics, it is proposed to perform a Clarke-Park trans-formation on the voltage expression found in (10) in order toobtain their expression in the rotating (d, q) frame. By firstperforming the Clarke transformation, the phase voltage inthe (α, β) frame is equal to(

Vα(θ)Vβ(θ)

)=

∞∑n=1

(an(Vα) cos(nθ) + bn(Vα) sin(nθ)an(Vβ) cos(nθ) + bn(Vβ) sin(nθ)

)· · · · · · · · · · · · · · · · · · · (13)

with

an(Vα) =

√23

(an(Vu) − 1

2an(Vv) − 1

2an(Vw)

)· · · · (14)

bn(Vα) =

√23

(bn(Vu) − 1

2bn(Vv) − 1

2bn(Vw)

)· · · · (15)

an(Vβ) =1√2

(an(Vv) − an(Vw)) · · · · · · · · · · · · · · · · · · (16)

bn(Vβ) =1√2

(bn(Vv) − bn(Vw)) · · · · · · · · · · · · · · · · · · (17)

where an(Vu), an(Vv), an(Vw), bn(Vu), bn(Vv) and bn(Vw) arethe Fourier series coefficients of the phase voltage in the (u,



v, w) frame calculated using (10). Then by performing thePark transformation, the phase voltage in the (d, q) frame isequal to(

Vd(θ)Vq(θ)

)=

(a0(Vd)a0(Vq)

)

+

∞∑n=1

(an(Vd) cos(nθ) + bn(Vd) sin(nθ)an(Vq) cos(nθ) + bn(Vq) sin(nθ)

)· · · · · · (18)

with

a0(Vd) =12

(a1(Vα) + b1(Vβ)) · · · · · · · · · · · · · · · · · · · (19)

a0(Vq) =12

(a1(Vβ) − b1(Vα)) · · · · · · · · · · · · · · · · · · · (20)

an(Vd) =12

(an+1(Vα) + bn+1(Vβ) + an−1(Vα) − bn−1(Vβ))

· · · · · · · · · · · · · · · · · · · (21)

bn(Vd) =12

(bn+1(Vα) − an+1(Vβ) + bn−1(Vα) + an−1(Vβ))

· · · · · · · · · · · · · · · · · · · (22)

an(Vq) =12

(an+1(Vβ) − bn+1(Vα) + bn−1(Vα) + an−1(Vβ))

· · · · · · · · · · · · · · · · · · · (23)

bn(Vq) =12

(bn+1(Vβ) + an+1(Vα) + bn−1(Vβ) − an−1(Vα))

· · · · · · · · · · · · · · · · · · · (24)

It should be noted that when n = 1 in (21) to (24), a0(Vα),b0(Vα), a0(Vβ) and b0(Vβ) are null.

After performing the same transformation on the back-EMF, it is possible to write the phase current in the (d, q)frame by using the IPMSM dynamic equation

ddt

(Id(θ)Iq(θ)

)=

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝−Rs

Ld

2πFeLq

Ld

−2πFeLd

Lq−Rs

Lq

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠(Id(θ)Iq(θ)

)

+

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝1Ld

0

01Lq

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠(Vd(θ) − ed(θ)Vq(θ) − eq(θ)

)· · · · · · · (25)

Since it is quite difficult to derive the expressions of thephase currents directly from (25), the following assumptionis proposed. Since the fundamental of the phase currents havebeen taken null in the previous assumption, this means thatthe DC components of Id and Iq are also null. Consequently,Id and Iq only have high order harmonics due to the PWM andalso a 6th harmonic due to the back-EMF. It is then thoughtthat (25) can be approximated to its expression at high fre-quency.

ddt

(Id(θ)Iq(θ)

)=

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝1Ld

0

01Lq

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠(

Vd(θ) − ed(θ)Vq(θ) − eq(θ)

)· · · · · · · · (26)

In this way, the phase currents can be written(Id(θ)Iq(θ)

)=

∞∑n=1

(an(Id) cos(nθ) + bn(Id) sin(nθ)an(Iq) cos(nθ) + bn(Iq) sin(nθ)

)· · · · (27)

Fig. 9. Phase current harmonics amplitudes for Vdc =180 V, Fc = 1 kHz, Fe = 50 Hz, ma(model) = 0.224 andma(exp) = 0.230

Fig. 10. Phase current harmonics amplitudes for Vdc =43 V, Fc = 1 kHz, Fe = 50 Hz, ma(model) = 0.937 andma(exp) = 0.975

with

an(Id) =1Ld

(−bn(Vd)

2πnFe+ Ψdn

)· · · · · · · · · · · · · · · · · · (28)

bn(Id) =an(Vd)

Ld2πnFe· · · · · · · · · · · · · · · · · · · · · · · · · · · · · (29)

an(Iq) = − bn(Vq)

Lq2πnFe· · · · · · · · · · · · · · · · · · · · · · · · · · · (30)

bn(Iq) =1Lq

(−an(Vq)

2πnFe+ Ψqn

)· · · · · · · · · · · · · · · · · · (31)

and

Ψdn =

⎧⎪⎪⎪⎨⎪⎪⎪⎩−√

32

(Ψ f 5+Ψ f 7

n

)0, n � 6

, n = 6 · · · · · · · · · · · · · · · · (32)

Ψqn =

⎧⎪⎪⎪⎨⎪⎪⎪⎩√

32

(Ψ f 5−Ψ f 7

n

)0, n � 6

, n = 6 · · · · · · · · · · · · · · · · · (33)

Equations (27) to (33) give an analytical form of the phasecurrents harmonics in the (d, q) frame. Similarly to what wasdone from (13) to (24), the harmonics in the (u, v, w) framecan be obtained by inverse Clarke-Park transformation. Theobtained harmonic amplitudes are illustrated in Fig. 9 andFig. 10 for Vdc = 180 V and Vdc = 43 V respectively. It canbe seen that the fundamental component is neglected in themodel due to the no-load approximation but, although low,



it appears in the experimental data. This is due to the lowelectromagnetic torque that is actually needed to balance theiron losses and the mechanical friction losses. Moreover, the5th and 7th harmonics of the current given by the model arehigher than found by experiments. This is thought to be dueto the approximation done in (26).

5. Observation of Stator Magnetic Flux Density

In the former sections, an expression of the high order har-monics caused by the PWM control on the IPMSM phase cur-rents was established. Moreover the link between the PWMmodulation index and the amplitude of these harmonics hasbeen clarified. Those high order harmonics are responsiblefor magnetomotive forces originating from the stator wind-ings and variating at high frequencies. These magnetomo-tive forces are responsible for high frequency variations ofthe magnetic flux density in the rotor, stator and magnets ofthe IPMSM. Ideally, the analysis should include an analyticalcalculation model of the magnetic flux density using a sim-plified linear magnetic model. However, this study is left forfuture work and in this section, measurements of the mag-netic flux density in the stator is shown.

Besides the three-phase armature windings, additionalcoils are also wound on the stator core teeth and yoke parts inorder to measure the average magnetic flux density. The coilhas NB = 10 turns and delimits an open surface S which iseither the yoke or teeth surface. While the motor is rotating,the voltage Vb induced in the coil is measured at a samplingfrequency of 1 MHz. This voltage can be used to estimatethe average magnetic flux density through the teeth or yokesurface using the equation

B(t) =1

NBS

∫ t

0Vb(u)du · · · · · · · · · · · · · · · · · · · · · · · · (34)

The measurements have been done at Vdc equal to 43 V and180 V and are illustrated in Fig. 11 and Fig. 12 for the teeth

Fig. 11. Teeth magnetic flux density

and yoke respectively. On the scale of the carrier frequency,the modulation index has a noticeable influence on the mag-netic flux density waveform. Fig. 13 illustrates the FFT anal-ysis on the teeth magnetic flux density. The fundamentalstays unchanged because it is mainly due to the magnet ro-tation. Moreover, similarly to what is observed on the phasecurrents, the harmonics caused by the PWM control dependon the modulation index. At high modulation index, thestrongest harmonics are around 1 kHz while at low modula-tion index, the strongest harmonics occurs around 2 kHz and4 kHz. As in the voltage and current, the high order harmon-ics are stronger in case of low modulation index. In order toevaluate this phenomenon quantitatively, Table 6 shows thecomparison between the low order harmonic contents andthe high order harmonic contents. These contents are basi-cally the rms value of the magnetic flux density harmonicsin a given frequency range. It can be seen that at low mod-ulation index, the high order harmonic content increases by

Fig. 12. Yoke magnetic flux density

Fig. 13. FFT of the magnetic flux density measured onthe teeth



Table 5. Harmonic content comparison of teeth mag-netic flux density

more than 250% compared the high modulation index.

6. Conclusion

This paper proposes an experimental evaluation of the de-pendence between an IPMSM iron losses and the PWM mod-ulation index used for inverter control. It is demonstrated thatin no-load condition, the iron losses at a modulation indexof 0.230 are 1.8 times higher than at a modulation index of0.975. An analytical model that relates the PWM control pa-rameters to the phase voltage and current harmonics has beendeveloped and its validity was confirmed by comparison withexperimental data. Using this model, the impact of the modu-lation index on the high order harmonics of the phase currentshas been clarified. It is concluded that low modulation indexincreases the high order harmonic content of the phase cur-rent, which in turn increase the high order harmonic contentof the magnetic flux density in the motor, then increasing theiron losses. In future works, an analytical linear magneticmodel will be developed in order to relate the phase currentharmonics to the high frequency magnetic flux density varia-tions and then to the iron losses. Overall, the aim will be torelate the PWM modulation index to the iron losses of eachpart of the IPMSM.

AcknowledgmentThis work was supported in part by the Ministry of Ed-

ucation, Culture, Sports, Science and Technology program,Japan, for private universities.

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(11) N. Denis, K. Fujitani, Y. Kato, M. Ieki, and K. Fujisaki: “Core loss in-crease due to inverter carrier frequency in an interior permanent magnet syn-chronous motor”, Proc. of 18th Int. Conf. on Electrical Machines and Systems(ICEMS 2015), Pattaya, Thailand, pp.1–7 (2015)

Nicolas Denis (Non-member) was born in France in 1987. He re-ceived the M.Eng. degree and the French Engi-neer Diploma degree in electrical engineering fromthe Ecole Nationale Superieure d’Electricite et deMecanique de Nancy, Nancy, France, in 2010, andthe Dr. Eng. degree in electrical engineering fromSherbrooke University, Sherbrooke, QC, Canada, in2014. He was a Postdoctoral Fellow and Commis-sioned Scientist in the Toyota Technological Insti-tute, Nagoya, Japan, from 2014 to 2017, in which he

worked on electrical motors iron losses and application of efficient magneticmaterials for electrical motors. He is currently engineer at Challenergy Inc.,Tokyo, Japan.

Yenyi Wu (Non-member) was born in Taichung, Taiwan in 1992. Shereceived the B.S. degree in electronic engineeringfrom National Kaohsiung Normal University, Kaoh-siung, Taiwan, in 2014. She is currently working to-ward the M.S. degree at National Chung Hsing Uni-versity, Taiwan, and is now attending the double de-gree program between the Toyota Technological In-stitute, Japan, and National Chung Hsing University.Her research interests include Radio-Frequency inte-grated circuit design and the loss property of the iron

core of the electrical motor.

Keisuke Fujisaki (Senior Member) received the B.Eng., M.Eng., andDr. Eng. degrees in electronics engineering from theFaculty of Engineering, The University of Tokyo,Tokyo, Japan, in 1981, 1983, and 1986, respectively.From 1986 to 1991, he conducted research on elec-tromagnetic force applications to steel-making plantsat the Ohita Works, Nippon Steel Corporation. From1991 to 2010, he was a chief researcher in the Tech-nical Development Bureau, Nippon Steel Corpora-tion, Futtsu, Japan. Since 2010, he was a professor

of Toyota Technological Institute. His current scientific interests are mag-netic multi-scale, electromagnetic multi-physics, high efficient motor drivesystem, electrical motor, and power electronics. In 2002–2003, he was aVisiting Professor at Ohita University. In 2003–2009, he was a Visiting Pro-fessor at Tohoku University. Dr. Fujisaki received the Outstanding PrizePaper Award at the Metal Industry Committee sessions of the 2002 IEEEIndustry Applications Society Annual Meeting.


impact of the inverter dc bus voltage on the iron losses

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