EVS28 KINTEX, Korea, May 3-6, 2015

Magnetic Equivalent Circuit Model of Interior Permanent-Magnet Synchronous Machine Considering Magnetic Saturation Zaimin Zhong, Shang Jiang1 , Guangyao Zhang 1School

of Automotive Studies, Tongji University, 4800 Cao’an Road, Shanghai, China, [email protected]

Abstract This paper improves an analytical model for interior permanent-magnet synchronous machine (IPMSM) by a magnetic equivalent circuit (MEC) approach. The proposed MEC model consists of three major regions: the stator, the rotor, and the air gap. The conventional reluctance approach is applied to the first two regions. Since the magnetic field in air gap region is supposed to distribute unevenly, this model employs a function of rotor electrical angle to describe the flux density distribution. Firstly, the permeability of all iron is assumed to be infinite, so the reluctance of the iron core is close to zero and can be ignored. Then the air gap flux density in the direct-axis and quadrature-axis caused by armature currents are calculated in the d-q reference frame respectively, which are used to acquire the direct and quadrature axes inductances Ld and Lq. Open-circuit voltage E0 can be obtained by the air gap flux density caused by the magnets. A finite element model (FEM) is developed to validate the analytical model, and the comparison results indicate that the accuracy of the analytical model is acceptable only in the condition of low armature currents. When the armature currents exceed a certain value, magnetic saturation of the iron core must be taken into account. Therefore, a modification model considering the magnetic saturation is proposed by adding the reluctance of iron core parts to the previous one. The permeability of iron is nonlinear and presented as a function by fitting the BH-characteristic curve with a cubic polynomial. Finally, through numerical calculation, the air gap flux density is derived from the equations of the analytical model. The result of the modification model is validated with the FEM in the saturated condition. Keywords: Analytical Model, Magnetic equivalent circuit (MEC), Interior permanent-magnet synchronous machine (IPMSM), Saturation, Finite element model (FEM)

1

Introduction

The main trend of clean energy automobile is developing Electric vehicles (EVs). As one of the key components in EVs, the driving motor system deserves more attentions. IPMSM is a type of motor and widely applied in EVs due to

its high power density, reliability, very good efficiency, and their reduced maintenance costs[1]. In project design phase, it’s important to build an efficient and accurate model of IPMSM [2][3]. Generally, accurate modelling of electric machines requires the use of finite-element method[4]. However, finite-element analysis is too time

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consuming, especially for the parametric studies at the first stages of the design process. In order to reduce the pre-design stages duration, MEC model[6]-[8] is usually applied. Especially when regardless of saturation, the simulation speed is much higher due to absence of iterative process. MEC method divides the magnetic field into a network of flux tubes with homogenous distribution of flux density and strength through each cross section [5]. The accuracy of MEC model of IPMSM usually meets the design requirement. In first section, this paper builds conventional MEC models of IPMSM with PMs, d- and q-axis armature currents exciting alone respectively based on the distribution form of PMs, and obtains the distribution function of airgap flux density which takes into counting slotting effects. Then, the synchronous inductances are computed based on their definitions and the proposed MEC model. Furthermore, a MEC network model considering saturation is presented. At last, both the conventional and new MEC model are resolved and validated through comparison with the simulation results of FEM.

2 2.1

0  m 

Br Hc

(2)

B Br

B

H Hc

H

O

Figure 1: Demagnetization curve of PMs

Conventional MEC Model Assumptions

Considering the complexity of motor structure and field distribution, the conventional MEC model is based on the following hypotheses: (1) The permeability of rotor and stator iron core is assumed infinite and the saturation is neglected. (2) Only radial fluxes in airgap are counted. (3) The MMFs produced by stator windings are sinusoidally-distributed in circumferential space around the airgap. (4) The fields distribute evenly in the surface of PMs.

2.2

Where, μ m is relative permeability of PM and μ 0 is the absolute permeability of vacuum. When B equals to zero, it is deduced as:

MEC Model with PMs Acting Alone

PMs are made of hard magnetic materials and usually work along the demagnetization curve. There are two important quantities associated with the demagnetization curve that are the residual flux density B r and the coercive force Hc. PMs are designed to operate on the linear part of the demagnetization curve between B r and Hc, which is illustrated in Figure 1. Such recoil line is usually approximated by: B  0 m H  Br (1)

Figure 2: Rotor configuration of IPMSM with tangentially magnetized PMs

Based on the rotor configuration and geometric parameters in Figure 2, the reluctances of PM_1 and PM_2 are calculated by[9]:

Rm1 

L1 2 L2 , Rm 2  0 mls h1 0 mls h2

(3)

Where denotes the active length of the rotor. PMs are equivalent to MMF source and the MMF produced by PM_1 and PM_2 respectively are calculated by:

Fc1  H c L1 ,

Fc 2  Hc  2L2

(4)

The leakage reluctance of magnetic bridge is deduced by:

R 

2 L2 0ls (2t2 )

(5)

Since the space MMF produced by PMs is supposed to be evenly distributed along the airgap, the airgap can be equivalent to a hollow cylindrical reluctance element and its resistance is calculated by:

EVS28 International Electric Vehicle Symposium and Exhibition

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R 

1

 0 ls



 ln(

rg ) r

2.3 (6)

2p

Where g denotes the thickness of airgap, r external radius of the rotor, p number of magnetic pole pairs. Figure 3 shows the MEC model when PMs acting alone.

MEC Produced by D-axis Armature Current

When a symmetrical set of three sinusoidal currents is inserted to the three-phase stator winding, the armature currents are expressed as:

 ia  2 I s cos( wr t   )  2  ib  2 I s cos( wr t     ) 3  4  ic  2 I s cos( wr t    3  )

(11)

Where denotes the effective value of currents, angular velocity of the rotor, the torque angle. The currents in dq frame are deduced based on MMF conservation and power equivalent principle:

I d  3I s  cos  , I q  3I s  sin 

(12)

Considering the previous assumption about MMF waveform, the MMFs produced by d- and q-axis armature currents are calculated respectively by: Figure 3: MEC model when d-axis current exciting alone

Considering the previous hypotheses, Ampere’s theorem and flux conservation, the equation set of MEC model is written in:

 Fc1  Rm1m1  Fc 2  Rm 2m 2  Fm         m1 m 2     R  Fm   2 R  Fm

(7)

Nkw1 I d cos( p ) (13) p Nk Fq ( )  Fqm sin( p )  0.9 s w1 I q sin( p ) (14) p

Fd ( )  Fdm cos( p )  0.9

Where, Ns denotes the number of series winding turns of each phase in abc reference frame, the winding factor. When PMs are considered as reluctance elements without remanence and the armature current in qaxis is neglected, the MEC model of IPMSM is illustrated in Figure 4.

The airgap flux is given in:

 

( Rm1Fc 2  Rm 2 Fc1 ) R (8) Rm1Rm 2 ( R  2R )  ( Rm1  Rm 2 )2 R

The flux density distributed along airgap with respect to the mechanical angle of the rotor θ is deduced by:

B f ( ) 



 g (r  )ls 2p 2

;  [

  , ] 2p 2p

(9)

Due to the symmetry of fields in airgap between adjacent poles, the flux density with respect to from to is written in:

B f ( )  





g  (r  )ls 2p 2

(10)

Figure 4: MEC model when d-axis current exciting alone

Considering the previous hypotheses, Ampere’s theorem and flux conservation, the equation set of MEC model is written in:

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u ( )  H d ( )  2 g  0 g    ls  0 H d ( )(r  )d 2 2p   B ( )   H ( ) 0 d  d

3.1 (15)

30ls (r  g / 2) Fdm (16) g 8 g  0ls (r  )( Rm1 / / Rm 2 / / R ) 2

The flux density distributed along airgap with respect to is deduced by:

Bd ( )  0

Fd ( )  ( Rm1 / / Rm 2 / / R ) (17) 2g

And the flux density with respect to to is written in:

Bd ( )   Bd (

2.4



p

 )

from (18)

MEC Produced Armature Current

by

Q-axis

When the field is excited only by q-axis armature current, the flux doesn’t flow through the PMs. Therefore, the MEC model is depicted in Figure 5 and the flux density is deduced as:

Bq ( )  0

Fq ( ) 2g

;   [



The slots increase the resistance of airgap and is employed to correct the airgap thickness[11].

1

01 

The airgap flux is given in:

 

Correction of airgap thickness due to slotting effect

3 ] 2p 2p

(19)

1  5 / b01 t1 Kc  t1  01b01

(20) (21)

Where, denotes the pitch of the stator tooth, the inner diameter of the stator, the number of stator teeth, the width of each stator slot. holds:

t1 

 Di1 Z1

(22)

Based on Carter’s coefficient thickness is corrected by:

g '  Kc  g 3.2

, the airgap (23)

Correction of the Flux Density Distribution along the Airgap

Since stator slot openings change the airgap reluctance in front of the slots, it is noted that the presence of stator slots have a large influence on the air-gap magnetic field distribution and therefore on the electromagnetic torque. Figure 6 shows the geometric model of the airgap thickness variation[12].

Figure 6: Airgap variation in slot region Figure 5: MEC model when q-axis current exciting alone

3

Modification of MEC Model Considering Slotting Effect

The slotting influences the magnetic field in two ways. First, it reduces the total flux per pole, an effect which is usually accounted by introducing the Carter’s coefficient [10] into the calculation. Second, it affects the distribution of the flux density in the air-gap of the electric machines.

The thickness of slotted airgap region is changed as:

g ( )  g 

 rw 2

(24)

Based on the distribution of the stator slot openings, the circumferential variation airgap thickness is written in:

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       [(k  1)t  t 0 ,(k  1)t  t 0 ]  g 2 2 g ( )          g  r   [(k  1)  t 0 ,(k  1)  t  0 ] t t  2 w 2 2 (25) Where and denote the radian corresponding to tooth pitch and slot space respectively, and they are calculated by:

t 

 t  b0 rg

, 0 

b0 rg

(26)

The radius is the airgap thickness increase caused by slot openings, and it holds:

rw  [  (k  0.5)t ](r  g )

(27) The range of k is determined by the slot number. Then the distribution coefficient of airgap field due to slotting effect is calculated by:  ( )  g / g ( ) (28) The modified distributed flux densities along the airgap are obtained by multiplying the previous function of them by distribution coefficient .

4

Back EMF Calculation

and

Torque

In order to obtain the synchronization parameters of the motor, the fast Fourier transform (FFT) is introduced to formulate the airgap flux density considering slotting effect. Then we get the fundamental component of the flux density distributed along airgap.

 B f 1 ( )  B f 1m  cos( p )   Bd 1 ( )  Bd 1m  cos( p )  B ( )  B  sin( p ) q1m  q1

(29)

Where B f 1m , Bd 1m , Bq1m denote the amplitude of fundamental wave caused by PMs, d- and qaxis armature currents respectively.

4.1

Back EMF

Airgap flux linkage produced by PMs can be calculated by the corresponding flux density function:

E0 

wr f 3

Where

4.2



2 2 g wr kw1 N s ls B f 1m (r  ) (31) 3p 2

denotes the angular speed of rotor.

Electromagnetic Torque

Similarly, by choosing appropriate integrating range, the airgap flux linkage produced by the armature current could be obtained:

d 

2 2 g  kw1 Nsls Bd 1m (r  ) 3 p 2

(32)

2 2 g q   kw1 Nsls Bq1m (r  ) 3 p 2 Then the inductance of d- and q-axis is:

g 2 2kw1 Nsls Bd 1m (r  ) 2 Ld   Id 3 pI s g q 2 2kw1 Nsls Bq1m (r  2 ) Lq   Iq 3 pI s

d

(33)

(34)

With the inductance parameters and flux linkage of PMs, the electromagnetic machine torque can be presented by the following formula. The first item in the bracket is the excitation torque produced by the interaction between the armature currents and PMs while the second item shows the reluctance torque caused by the different reluctance between d- and q-axis.

Te  p[ f I q  ( Ld  Lq ) I d I q ]

5

Simulation Results Conventional MEC Model

(35)

of

In the previous sections, a conventional analytical model of IPMSM in the form of MEC has been developed. It is necessary to validate this model by comparing it to professional software results based on the FEM. The materials in the FEM have linear behavior, so that the analytical and FE results are compared under the same working conditions without saturation.



2 g f  kw1 N s ls  2 p B f 1m cos( p )(r  )d  3 2 2p 

2 2 g  kw1 N s ls B f 1m (r  ) 3 p 2

5.1

Main Parameters

The motor presented in this paper is an IPMSM with tangential magnetized, and the main structure and material parameters are listed in Table 1. Figure 7 shows its FEM.

(30) And then the back EMF is:

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Figure 9 and 10 shows the flux density distribution with respect to the rotor angle in the motor obtained by MEC model and FEM. They show a good general agreement between the two results. Nevertheless, there are still two major differences: (1) MEC model considers the airgap EMF distributes sinusoidally while it should be ladder distribution as for a PMSM with double layer distributed winding in FEM. (2) All flux flow through PMs are supposed to be perpendicular to their surfaces, while there are fluxes oblique crossing the PMs in FEM, which results in the difference of flux density around the angle of 40°. 3 MEC model FEM

2

Figure 7: FEM of IPMSM 1

Pole pair number Stator slot number Stator external diameter Stator inner diameter Rotor external diameter Slot space Tooth width Inductances per slot Size of PM_1 Size of PM_2 Br

5.2

Value 2 36 200mm 118.4mm 117mm 2.2mm 8.13mm 24 5mm*16.5mm 3.5mm*26.2mm 1.23T 1.09978

-2 -3 -50

100

150

MEC model FEM

2 0 -2 -4 -50

0

50 100 Electrical angle α[°]

150

Figure 10: Airgap flux density produced by q-axis current

1.5 MEC model FEM

The inductance matrix Labc in abc frame is obtained from the FEM simulation results, and the inductance matrix Ldq in dq frame is calculated by:

0.5 B[T]

50 Electrical angle α[°]

4

The spatial distribution of airgap flux density produced by PMs is illustrated in Figure 8. It is noted that the variations between analytical and FEM simulation results are limited, less than 5%.

Ldq  C T LabcC

0

(36)

Where,

-0.5 -1 -1.5 -50

0

Figure 9: Airgap flux density produced by d-axis current

Comparison of Simulation Results

1

0 -1

B[T]

Quantity

B[T]

Table 1: Main parameters of IPMSM

Labc 0

50 Electrical angle α[°]

100

150

 Laa   Lba  Lca

Lab Lbb Lcb

Lac  Lbc  Lcc 

(37)

Figure 8: Airgap flux density produced by PMs

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 sin( )   cos( )  2 2  2 cos(   )  sin(   )  C 3 3  (38)  3 2 2  cos(   )  sin(   )  3 3   The results of synchronous inductances obtained from MEC are compared with the results from FEM in Table 2.

6.1.1

Reluctance Calculation of Stator Iron Core The stator iron core is composed of yoke, tooth and tooth shoe from view of flux flow paths, as is shown in Figure 12. The reluctances of three components of the stator are calculated based on their shapes, geometric parameters and flux directions.

Table 2: Comparison of synchronous motor parameters

Quantity Back EMF(V) Ld(mH) Lq(mH)

MEC model 184.88

FEM

variation

183.86

0.55%

103.7 288.5

111.5 272.2

-7% 4.9%

Figure 12: Geometric figure of the stator

 flux tube of stator yoke reluctance: The curves of electromagnetic torque versus rotor position from MEC model and FEM are illustrated in Figure 11. Due to the results in Table 2, the offset of the two torques mainly derives from the error of Ldq. MEC model FEM

Te[N.m]

-100

0

100

200 Torque angle β[°]

300

400

Figure 11: Electromagnetic torque versus rotor position characteristic

6.1

(39)

 flux tube of tooth reluctance:

hd u0uFels ld

(40)

 f ln(lepld )   lep  Rdb   //  u u l (l  l )   u u l b  (41)  0 Fe s ep d   0 Fe s 

0 -50

6

rc 2 ) rc1

 Flux tube of tooth shoe relctance:

50

-150

u0uFels (ln

Rdh 

150 100

d

Rc 

MEC Model Saturation

for

Magnetic

6.1.2 Nonlinear Relative Permeability The relative permeability for each point of a ferromagnetic material is not constant but depends on the actual magnetic field strength H respectively the actual magnetic flux density B of this point. The communication curve H(B) of ferromagnetic material DW310_35_2DSF0.950 is shown in Figure 13.

Nonlinear Reluctance Elements

When working in saturated region, the reluctances of elements with nonlinear permeability characteristics change with respect to the flux density. Saturation usually happens in stator iron core, so this paper take stator yoke, teeth and teeth shoes as nonlinear reluctance elements. Figure 13: Fitting curve of relationship of B and H

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In order to obtain the analytical MEC model, the relationship H(B) in saturated region is approximated with a cubic polynomial function by fitting. (42) Because the relative permeability is get by dividing flux density by magnetic field strength, it is deduced that：

Since the MMF produced by armature currents is supposed to be sinusoidal wave along the airgap, the values of the MMF elements are calculated as: (44) Where is the amplitude of the fundamental harmonic. Then, the system state equation of the MEC network model is obtained based on Kirchhoff laws: (45) AX  b

(43)

6.2

Reluctance Network Model with D-axis Currents

The constant vector is:

b

The proposed MEC network model of the IPMSM in Figure 7 is depicted in Figure 14. 0.5fd1

Rc

Rc

Rc

Rc

Rc

Rc

Rc

0.5fd2

0.5fd3

0.5fd4

0.5fd5

0.5fd6

0.5fd7

0.5fd8

0.5fd9

0.5fd10

Rd

Rd

Rd

Rd

Rd

2Rd

Rg

Rg

Rg

Rg

Rg

2Rg

Rd

Rd

2Rg

Rg

Rg

Rg

Linear reluctance element

Nonlinear reluctance element

Figure 14: Reluctance network model each pole   Rdg 1  Rc  1 Rm 2 2 1 1 R  R A   2 c 2 m 1 1  Rc  Rm 2 2  1 1  2 Rc  2 Rm

6.3

fd 5 

Rdg  Rc

Rc

Rc

1 3 Rdg  Rm  Rc 2 2 1 3 Rm  Rc 2 2 1 3 Rm  Rc 2 2 1 3 Rm  Rc 2 2

1 3 Rm  Rc 2 2 1 5 Rdg  Rm  Rc 2 2 1 5 Rm  Rc 2 2 1 5 Rm  Rc 2 2

1 3 Rm  Rc 2 2 1 5 Rm  Rc 2 2 1 7 Rdg  Rm  Rc 2 2 1 7 Rm  Rc 2 2

Model Solution and Simulation Results

The algorithm for solution[13] of the MEC network model is concluded based on the researches on the nonlinear equations’ solution: First, the dimensions and material properties of motor are initialized. Variables and airgap permeances and flux sources are calculated. Then, using a constant permeability for iron the permeance matrix of system is developed and solved. Flux density values in different parts of the motor are then computed and permeabilities of saturated parts are updated using curve of iron parts and flux densities are recomputed for these regions.

T

(46)

(47)

The coefficient matrix A is listed in equation (48): The five state varibles correspond to the radial fluxes through five stator teeth, and the airgap flux density along each stator tooth can be obtained based on its definition. Futhermore, all reluctances are replaced by their corresponding formulas with geometric parameters and the relative permeability of stator iron core is expressed as the fitted function. Then, a nonlinear equation set to calculate distributed airgap flux density is obtained.

Rm2 Magnetomotive force source

fd 4

Where, the states denote:

Rm1

Flux tube

fd 3

T

Rc

2Rd

fd 2

X  1 2 3 4 5 

Rc

Rd

1  fd1 2

Rc   1 3 Rm  Rc  2 2   1 5 Rm  Rc  2 2   1 7 Rm  Rc  2 2  1 9  Rdg  Rm  Rc  2 2 

(48)

Last, the convergence of flux density is then provided through an iterative process. However, since the high accuracy of fitting for the permeability of the iron core only holds when the flux density B doesn’t exceed 2.1T, the error will be not accepted in working conditions of large currents. Therefore, this paper introduces the constrained optimization method to solve the nonlinear MEC equations. The MEC equation set in (45) is used to define the error vector f:

f  [ f1 , f 2 , f3 , f 4 , f5 ]T  AX  b

(49) The objective function is based on least squares criterion, and holds:

Minimize

EVS28 International Electric Vehicle Symposium and Exhibition

f12  f 2 2  f32  f 42  f52 (50)

8

Considering the limitation of the flux density B in the iron core due to the fitting accuracy, the constraint condition holds: B(Fe)≤2.1 (51) The optimization process is implemented using the optimization toolbox of Matlab, and it takes 13 iterations to satisfy the convergence criteria within a few seconds. Noted that the MEC method saves much time compared to FEA. Figure 15 and Figure 16 illustrate the comparison of airgap flux densities with 15A and 200A armature currents from MEC model and FEM

density. At last, the two proposed MEC models are validated by comparing the solution results with the simulation results of FEM, which indicates the feasibility of the conventional MEC model and the limitation of the proposed network model considering saturation.

References [1]

Renyuan Tang. Modern Permanent Motor: Theory and Design, ISBN 978-7-111-06010-9, Beijing: China Machine Press, 1997.

[2]

Tiegna H, Amara Y, Barakat G. Overview of analytical models of permanent magnet electrical machines for analysis and design purposes, Mathematics and Computers in Simulation, ISSN 03784754, 90(2013): 162-177.

[3]

Vido L, Gabsi M, Chabot F, et al. Interior Permanent-Magnet Synchronous Machine Design by Reluctants Networks Approach for Hybrid Vehicle Applications, In: 3rd IET International Conference on Power Electronics, ISBN 0-86341609-8, 2006, 541-545.

[4]

F. Magnussen, P. Thelin, and C. Sadarangani, Performance evaluation of permanent magnet synchronous machines with concentrated and distributed windings including the effect of field weakening, ISSN 0537-9989, PEMD 2004(2): 679-685.

[5]

J.R. Hendershot, T.J.E. Miller. Design of Brushless Permanent-Magnet Motors, ISBN 9780984068708, Motor Design Books LLC, 2010.

[6]

Hsieh M, Hsu Y. A Generalized Magnetic Circuit Modeling Approach for Design of Surface Permanent-Magnet Machines. IEEE Transactions on Industrial Electronics, ISSN 0278-0046 2012, 59(2): 779-792.

[7]

Sheikh-Ghalavand B, Vaez-Zadeh S, Hassanpour Isfahani A. An Improved Magnetic Equivalent Circuit Model for Iron-Core Linear PermanentMagnet Synchronous Motors, IEEE Transactions on Magnetics, ISSN 0018-9464, 2010, 46(1): 112120.

[8]

Han S, Jahns T M, Soong W L. A Magnetic Circuit Model for an IPM Synchronous Machine Incorporating Moving Airgap and Cross-Coupled Saturation Effects, 2007 International Electric Machines & Drives Conference, ISBN 1-42440742-7, 2007, 21-26.

[9]

Perho J. Reluctance network for analysing induction machines, ISBN 951-666-620-5, Finland: Helsinki University of Technology, 2002.

1.5 MEC network FEM

1

B[T]

0.5 0 -0.5 -1 -1.5 -1

-0.5

0

0.5

1

Electrical angle α[°]

1.5

2

2.5

Figure 15: Airgap flux density with 15A current 3 MEC network FEM

2

B[T]

1 0 -1 -2 -3 -1

-0.5

0

0.5

1

Electrical angle α[°]

1.5

2

2.5

Figure 16: Airgap flux density with 200A current

It is noted that the airgap flux densities from the two simulation methods have a certain deviation. The reasons can be concluded as following:  The error exits in fitting function of the permeability of iron core.  The linkage fluxes are not taken into consideration when modelling.

7

Conclusion

This paper presents a simple MEC model and a MEC network model for IPMSM applied in unsaturated and saturated regions, respectively. Both models take into account the slotting effect. The synchronous inductances and back EMF are obtained by applying FFT to the airgap flux

[10] Dajaku, G. and D. Gerling, Stator Slotting Effect on the Magnetic Field Distribution of Salient Pole Synchronous Permanent-Magnet Machines. IEEE Transactions on Magnetics, ISSN 0018-9464, 2010,

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46(9): 3676-3683. [11] Zhiguang Hu. Analysis and computation of motor field, ISBN 978711128798, Beijing, China Mechanical Press, 1989, 57-79. [12] Zhu, Z.Q. and D. Howe, Instantaneous magnetic field distribution in brushless permanent magnet DC motors. III. Effect of stator slotting. Magnetics, IEEE Transactions on, ISSN 00189464, 1993. 29(1): 143-151. [13] Zhang M, Macdonald A, Tseng K, et al. Magnetic equivalent circuit modeling for interior permanent magnet synchronous machine under eccentricity fault: Power Engineering Conference (UPEC), 48th International Universities, INSPEC Accession Number: 14043562, 2013: 1-6.

Authors Zaimin Zhong, is professor of automotive electronics at school of automotive studies, Tongji University. He received bachelor’s degree in 1995 and doctor’s degree in 2000 for automotive engineering from Beijing Institute of Technology, and has more than ten years in research on design and control of electrified mechanical transmission applied in EV and HEV. Shang Jiang, is studying for doctor’s degree of automotive electronics at school of automotive studies, Tongji University. He received the bachelor’s degree of communication and transportation from Central South University in 2012. His research interests include modelling of electric machines and powertrain control.

Guangyao Zhang, is studying for master’s degree of automotive electronics at school of automotive studies, Tongji University. He received the bachelor’s degree of automotive engineering from Tsinghua University in 2013. His research interest is analysis of vehicular PMSM.

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