Development of Drive System Using Switched Reluctance Motor for Electric Vehicle

In recent years, the necessity for energy saving increases the demand of efficient motors using rare earth permanent magnets. However, the deposits of rare earth are small, and the problems of price jump and unstable supply are worried. As one of the solution for these problems, the Switched Reluctance Motors (SRMs), which do not use the rare earths, attract attention. The SRMs have advantages of robustness, low cost, and high speed operation, since the rotors do not have windings. Moreover, the problems of heat demagnetization and cracks do not exist, since the rotors do not have permanent magnets. However, the efficiency is low as compared with that of permanent magnet synchronous motors, since the energy for magnetizing the rotor is required. Therefore the efficiency improvements of drive system using SRMs are examined. First the high efficient SRM is designed by using the magnetic field analysis with finite element method. Next the single pulse control, which magnetizes at the positions where the inductance derivative is the maximum, is proposed. The effectiveness of them is confirmed by the MATLAB/Simulink simulations and experiments using real machine.


Introduction
A rotor of switched reluctance motor (SRM) is an extremely simple construction using the only laminated silicon steel sheets.The SRMs have characteristics of strong and low cost due to this feature.In addition, the SRMs have no problem of demagnetization under high temperature environments, since permanent magnets are not used.High-speed variable speed drives are possible, since the torque/inertia ratios of SRMs are high (1) .
Because of these characteristics, practical utilizations under heavy loads and poor external environments such as electric vehicles (EVs) and motorcycles are expected.However, the SRMs are driven by the only reluctance torques, and the additional excitation currents for stator windings are needed to excite the rotors.Therefore, the efficiencies of SRMs are inferior to that of permanent magnet synchronous motors used for EVs and motorcycles (2,3) .This paper proposes the design of switched reluctance motor to obtain high motor efficiency.The first step of design makes the principle improving motor efficiency clear.Next the cross sections and axial shapes of rotor and stator cores are designed with the magnetic field analysis using 2D and 3D finite element methods.Also this paper proposes three magnetization modes which shift the modes according to the load.The modes are based on the linear torque equation of SRM.The efficiency comparison tests between the proposed method and the conventional method are conducted with the real machine examinations.

Basic Design of Cores
The magnetic field analysis using finite element method (FEM) and transient analysis for newly designed cores need to be iterated in order to optimize the core shapes of SRMs.The magnetic field analysis using FEM takes a lot of time.Therefore, the transient analysis using the mathematical model of SRM, mechanical system, and inverter is iterated to evaluate the relationships between the motor efficiencies and the core shapes as shown in fig. 1.The design principles are derived from the evaluations.Then the core shapes are designed with 2D and 3D FEMs to meet the design principles.
Fig. 2 shows the motor efficiency of standard 6/4 SRM with 6 stator poles and 4 rotor poles.The data are obtained from transient simulations using MATLAB Simulink.The conditions of simulations are the constant battery voltage of 96V, the excitation method of constant turn-on and commutation angles, and the torque control system with voltage pulse width modulation (PWM).
Fig. 3 shows the 6 types of inductance shape changes of SRMs.The influences of inductance changes upon the motor efficiencies are studied to obtain the design principles for designing core shapes.The inductance change of I increases the maximum value of inductance.The inductance change of II decreases the minimum value of inductance.The inductance change of III has small value of first half period and large value of latter half period.The inductance change of IV has large value of first half period and small value of latter half period.The inductance change of V forwards the position of maximum inductance.The inductance change VI postpones the position of maximum inductance.
Table 1 shows the influences of inductance changes upon the motor efficiencies of SRMs.The inductance change of I is most effective.The inductance change of II, III, and V are effective.The motor efficiencies must be improved when the differences between maximum and minimum inductances become large because of the torque generation principle.The inductance changes of III and V are effective, since the voltage PWM with constant turn-on and commutation angles is applied for the excitation of SRMs, and the current is distributed averagely.The inductance change of I and II are considered firstly for designing the stator and rotor cores of SRMs, since effects of the inductance change of III and V will change depend on the excitation methods.Transient analysis using mathematical models of SRM, mechanical system, and inverter is executed.
Inductance change is applied for induction function.SRM model using inductance function is composed.

Evaluation of motor efficiency and speed-torque characteristics
Design of stator and rotor core shapes using 3D FEM static magnetic field analysis is executed.The air gap spaces exist inside the coil ends.The motor efficiency is improved if these spaces are used to extend the stator core length, since the inductance increases.The extension of core for 12/8 SRM (SRM having 12 stator poles/8 rotor poles) is longer than that of 6/4 SRM, since the coil ends of 12/8 SRM are small.Fig. 4 shows the 3D FEM analytical model of 6/4 SRM with round teeth end.Its core axial length is 114mm.Table 2 shows the inductance changes for core axial length extensions of 6/4 SRM.The core axial length can be extended by adjusting the shapes of stator teeth ends to the shapes inside coil ends.This core axial length extensions increase the maximum value of inductance L max .The minimum value of inductance L min decreases slightly when the rotor teeth ends are round.However L max also decreases.As a result, the difference of value between L max and L min does not increase.Therefore the stator teeth ends and normal rotor teeth ends are used.Table 3 shows the inductance changes for core axial length extensions of 12/8 SRM shown in fig. 5.The 12/8 SRM have the larger difference of value between L max and L min , since the 12/8 SRMs can extend the core axial length longer than 6/4 SRMs.

Detailed design of cores
(b) Relation between stator and rotor teeth lengths The differences in value between L max and L min are calculated for changing the relation between stator and rotor as shown in fig.6.Table 4 shows the inductance changes for relations between stator and rotor teeth lengths of 6/4 SRM.Table 5 shows the inductance changes for relations between stator and rotor teeth lengths of 12/8 SRM.The inductance of aligned position is not influenced by relations between stator and rotor teeth lengths and the coil currents.However the differences in value between Fig. 5. 12/8 SRM with round stator teeth and normal rotor teeth.L max and L min are increased by extending the rotor teeth length, since the inductances of unaligned position are decreased.These tendencies are recognized both for the 6/4 and 12/8 SRMs.The large differences in value between L max and L min are obtained by extending the rotor teeth length within the range securing coil spaces.(c) Core teeth shapes The differences of value between L max and L min are studied for the core teeth shapes shown in fig. 7. The areas for the cross sections of both shapes are the same to equalize the volumes of iron.Table 6 shows the inductance changes for teeth shapes of 6/4 SRMs.And table 7 shows the Inductance changes for teeth shapes of 12/8 SRMs.Under the low load condition, the inductances of aligned positions for the wide stator cores increase, and inductances of tapered stator cores are similar to the standard stator cores.Under the high load condition, the inductances of unaligned positions for the wide stator cores increase, and the inductances of aligned positions for the tapered core increase without increasing the inductances of unaligned The taper angle of rotor teethes can be designed without considering coil space.Therefore the differences of value between L max and L min are calculated for the taper angles from 0 to 18 degree every 2 degree.Fig. 8 shows the inductance changes for taper angles of rotor teethes.The differences in value between L max and L min increase until the taper angle of 6 degree, and saturate around the taper angle of 8 degree.Therefore the taper angle of 8 degree is used for the rotor teeth to reduce the weight of rotor.
The improvements of motor efficiency are studied with the previous analyzed results.And the improvements for the relation between stator and rotor teeth lengths is same for the 6/4 SRMs and 12/8 SRMs.However the improvements for the core axial length extensions of 12/8 SRMs are significant compared with the 6/4 SRMs.Therefore the 12/8 SRMs are decided to be employed and designed in detail.
The height of connection points of divided cores are designed as shown in fig.9.The height need to be low to make enough coil space.However the low height will cause the magnetic saturation for the high load conditions.
The air gap between the divided cores will be the barrier for the flux in yoke as shown in fig.10.The inductance changes for air gap lengths are studied.The differences of value between L max and L min will increase by adding the core back as shown in fig.11, since the axial cross section of yoke will increase.The inductance changes for the extension of core back are studied.
The inductance of aligned position will increase when the alternate piles of the stator and rotor teeth are used as shown in fig.12.The inductance changes for the various alternate piles of the stator and rotor teeth are studied.

High Efficient SRM
The High efficient SRM is produced experimentally based on the core design described in section 2.2.Fig. 13 shows the rotor core produced experimentally.shows the stator core produced experimentally.The 12 stator division cores are needed to produce the stator core.
The static torque is measured with the real machine examination.The measured static torque is compared with static torque obtained with the magnetic field analysis using FEM.Fig. 15 shows the static torque of the high efficient SRM.The static torque characteristics are calculated for the three types of core materials, and they are similar to the actual value.Fig. 16 shows the experimental results of the rotor speed and stator current between the high efficient SRM and standard SRM.Fig. 17 shows the experimental results of the motor efficiency and output power between the high efficient SRM and standard SRM.The high efficient SRM shows the better results compared with the standard SRM.effects are ignored, and also the saturation of self-inductance are ignored.Hence, the linear torque is given by the following equation.

𝑇(𝜃, 𝑖
where   ,   ,   is the phase currents,  is the rotor position,   () ,   () ,   () is the self-inductances.The equation of (1) implies that the torque of SRM is proportional to the self-inductance space derivative.The self-inductance space derivatives are not constant, and it has the maximum value at the fixed position.Therefore, when the SRM is magnetized in the position where the inductance space derivative is maximum value, the torque can be generated efficiently.

Maximum of Self-Inductance Derivative
In order to clarify the position of maximum self-inductance derivative, the test SRM of 300W, 6 stator poles, and 4 rotor poles is analyzed with magnetic field analysis using FEM.The flux linkages (, ) for each rotor position 0-45° and phase current 0-100A are calculated as shown in fig.19 Where, (, ) is flux linkage,  is phase current, (, ) is self-inductance, and   is self-inductance derivative.
Fig. 21 (b) shows the self-inductance space derivative for the phase current of 15A with which the magnetic pole begins to saturate.In other words, the linear region is below 15A.The peak value of the self-inductance space derivative is almost flat-topped, and the position of the maximum self-inductance space derivative is 54.64deg (elec.).This position is same with the overlap angle of test SRM.The overlap angle   is given by the following equation.
Where,   is the number of rotor poles,   is stator pole arc,   is a rotor pole arc.
However, the yoke begins to saturate for 40A (the magnetic pole is fully saturated) as shown in fig.21(c).The position of the maximum self-inductance space derivative is 89.05deg (elec.), and lags as compared with the position of linear region.
The yoke is saturated for 100A as shown in Fig. 21 (d), Fig. 18.The typical each waveform of SRM.  and the position of maximum self-inductance space derivative becomes 61.43deg (elec.).The self-inductance space derivative is smaller than that of the linear region.The self-inductance space derivative around the aligned position decreases particularly.
The positions of maximum self-inductance space derivative shift for the current.However, in the nonlinear region, the self-inductance space derivative at the overlap angle is almost same with the maximum value of self-inductance space derivative.Therefore, it is predicted that the torque can be generated efficiently by magnetizing around overlap angle 54.64deg (elec.).

Excitation Mode
The diagram of the efficient single pulse control method is shown in fig.22. Three magnetization regions of positive torque region, no torque region, and a reverse torque region are considered according to load.In the low load region, the SRM is magnetized only in the positive torque region, and this mode is defined as the magnetization mode 1.In the middle load region, the SRM is magnetized in the positive torque region and no torque region, and this mode is defined as the magnetization mode 2. In the high load region, the SRM is magnetized in all regions of positive torque, no torque, and reverse torque, and this mode is defined as the magnetization mode 3.
The magnetization mode 1 is the mode which controls only the commutation angle   .The phase current flows only in the positive torque region.In medium speed region around 2000 rpm, the motor efficiency for the turn-on angle  0 was investigated, and the  0 was fixed at 40° (elec.) ) which gave the maximum efficiency.The   is regulated according to the load between the  0 and the optimal commutation angles    (which makes the phase current become zero at the aligned position).The  0 and   in the magnetization mode 1 are given by the following equations. 0 =  0 1 (5)   =  0 +  (6) Where,  is the output of PI controller.The regulation range of   is  0 ~  .
The magnetization mode shifts to the magnetization mode 2 when the torque is insufficient in the magnetization mode 1.The   is fixed at the    .The  0 is regulated according to the load between 0 and the  0 1 .The  0 and   in the magnetization mode 2 are given by the following equations. 0 =   −  (7)   =    (8) A turn-on angle regulation range is 0°~ 0 1 .
The magnetization mode shifts to the magnetization mode 3 when the torque is insufficient in the magnetization mode 2. The  0 is fixed at 0° (= 0 3 ), and the   is regulated according to load between 0 and the commutation angles    .The    is the maximum commutation angle increasing the torque.The  0 and   in the magnetization mode 3 are given by the following equations. 0 =  0 3 (9)   =  (10) The commutation angle regulation range is    ~  .

Estimation of Optimal Commutation Angle
As mentioned above, the commutation angles, with which current become zero in the aligned position, was defined as the optimal commutation angles    .As shown in fig.23, the method for estimating the    uses the  principle that the inductance slopes change for the phase current.When the  0 is fixed to the certain value and the load torque increases, the inductance slopes decrease and the    increase.Therefore, when the inductance slopes and the    are tabularized for each load torque, the    can be estimated with the inductance slopes and the  0 .
The look-up table for the    is shown in fig.24.The inductance slope under 0.05mH/deg (elec.) is in the nonlinear region.And the characteristics of the inductance slope and the    is almost linear.However, all the optimal commutation angles are the same regardless of the turn-on angles in the linear region over 0.05mH/deg (elec.).

Control System
The control system is shown in fig.25.As mentioned above, the conduction angle ∆θ is controlled by the PI controller using the input of angular velocity error.The    is calculated with phase currents, rotor position information, and commutation angles.The turn on and commutation angle controller determines the turn-on angle and commutation angle in the next magnetization cycle from phase currents, rotor positions, and optimal commutation angles according to the load torque.These operations are executed in the counter torque region in which the phase current does not flow.
The flow chart of turn-on angle and commutation angles controller is shown in fig.26.The magnetization mode is shifted by three variables of magnetization mode, aligned position current, and a turn-on angle.In the magnetization modes 1 and 3, the magnetization mode for the next magnetization cycle is determined by checking whether the aligned position current is zero.The magnetization mode 2 shifts to the magnetization mode 1 when the turn-on angle is 40° (elec.)(=  0 1 ).And the magnetization mode 2 shifts to the magnetization mode 3 when the turn-on angle is 0° (=  0 3 ).The initial magnetization mode is 3, since the large torque is required for starting,

Experimental Results
The motor efficiencies for the voltage PWM control and proposed method are shown in fig.27  (a) and (b).The PWM frequency of voltage PWM control is 10kHz, and the rotor speed is controlled by the PI controller.The chopping method is the high side soft chopping.The turn-on angle is fixed at 0° (elec.), and the commutation angle is fixed at 120° (elec.).The supply voltage is DC24V.In the low and medium speed region, the proposed method improves the efficiency for the high load range.The improvement is more significant than that of the low load region.However, the region of 60% -65% is narrow, and the region exceeding 65% is lost in the high speed region.

Conclusions
The basic design for the core shapes of SRM was studied, and the design principles to improve motor efficiency were summarized.According to the design principle, the concrete design of the core pole number and core shapes was carried out with the magnetic field analysis using FEM, and the number of core poles and core shapes were decided to improve motor efficiency more than 5%.The designed SRM was produced experimentally and the motor efficiency improvement of more than 5% was confirmed experimentally.
Three magnetization modes, in which a magnetization region was regulated according to the load, was proposed based on the linear torque equation of SRM.The efficiency of the proposed method was compared with that of the voltage PWM control method.The prposed method gave the high efficiency improvement of 8.2% for high load of 1Nm and low-medium speed region of 1000-2000rpm.However, the efficiency falls by 3.5% at the operating points of low-medium speed around 1000rpm and low load region of 0.1-0.2Nm, since the peak value of phase current became large and the conduction angle became too small.

Fig. 1 .Fig. 2 .
Fig. 1.Flow chart of making the principle to improve motor efficiency clear.

Table 1 .
Influence of inductance changes upon motor efficiencies. Fig.14
. The self-inductance of fig.20 and the self-inductance derivatives of fig.21 are calculated with calculated results by the following equations.

Fig. 23 .
Principle of estimation of optimum commutation angle.

Table 3 .
Inductance changes for core axial length extensions of 12/8 SRM.

Table 2 .
Inductance changes for core axial length extensions of 6/4 SRM.

Table 4 .
Inductance changes for relation between stator and rotor teeth lengths of 6/4 SRMs.

Table 5 .
Inductance changes for relation between stator and rotor teeth lengths of 12/8 SRMs.
position.The effects for changing core teeth shapes of 12/8 SRMs are bigger than those of 6/4 SRMs.(d)Taper angle of rotor core teeth