Performance Enhancement of the IPMSM for HEV Applications Using Grain-Oriented Electrical Steel and Design Optimization

This paper proposes a method for enhancing the performance of an interior permanent magnet synchronous motor (IPMSM) using grain-oriented electrical steel (GO) and design optimization. As the GO has superior magnetic characteristics in the rolling direction, the GO is applied to the stator teeth to increase the torque and reduce the iron loss of the IPMSM. However, such an approach leads to higher saturation on the core, resulting in worse pulsation characteristics. To handle with pulsation problem on the IPMSM, design optimization is conducted. In this paper, the interpolation multi-objective robust optimization algorithm (IMROA) was proposed. The IMROA can reduce the calculation time by interpolating the objective region and utilizing a stepwise sampling strategy. Moreover, the IMROA considers the robustness of the found solution and can derive a robust global solution that has robustness on the manufacturing tolerance and deformation during the operation and prevents unexpected results on the IPMSM.


I. INTRODUCTION
Electric vehicles (EVs) and hybrid electric vehicles (HEVs) have rapidly developed in recent years and are commonly regarded as one of the promising solutions for emission reduction and energy conservation [1]- [3]. From the environmental standpoint, the EV, which is only driven by an electric motor, seems to be the better option. However, EVs still have problems with long charging times and the expensive cost of establishing a charging infrastructure, and further research and development is needed for increasing the battery capacity and efficiency to extend their driving range [4]- [7].
Unlike EVs, the HEV is a vehicle using both an internal combustion engine (ICE) and an electric motor, which is called as hybrid power source [8]. As a result, the HEV could optimize the power distribution and maximize the energy efficiency by using the motor at the starting sequence and lower-speed region and using the engine in the high-speed operating region. Therefore, HEVs are considered as solution for increasing energy efficiency without compromising vehicle performance [9], [10].
For the traction motors, which is one of the major components of the HEV application, high efficiency, high power density, and wide speed range control is required, and therefore, permanent magnet synchronous motors (PMSMs) are widely used [11], [12]. Especially, interior PMSMs (IPMSMs) are suitable for traction motor as the magnets are embedded inside the rotor core and have superior mechanical stability. Moreover, as the IPMSMs have both magnet torque and reluctance torque, high torque density can be obtained [13].
When designing the traction motor, various performance factors should be considered. Designed motor should have robustness against the manufacturing tolerances and deformation during operation to avoid unexpected results, and the pulsation component of the torque waveform that can affect the driving comfort and control stability should be small [14]- [16]. In addition, the output characteristics of the motor should be improved, because the increased torque enables reducing the stacking length and downsizing the motor or improves the thermal characteristic by reducing the input current.
In this paper, grain-oriented electrical steel (GO) is applied to an IPMSM to acquire torque improvement. Especially, as the magnetic characteristics of the GO vary according to the angle of the flux, the GO is partially applied to the stator teeth, where the direction of the flux path is uniform, and the effect of the GO can be maximized [17].
In addition, design optimization was conducted to further improve various performances of the IPMSM, including the torque pulsation characteristic. The interpolation multiobjective robust optimization algorithm (IMROA) was newly proposed for the design optimization of the IPMSM. The IMROA can reduce the number of function calls to convergence by utilizing the interpolated objective region. Moreover, by considering the robustness of the found solutions, the optimal design with robustness, while improving the various performances, can be obtained.

II. TORQUE ENHANCEMENT OF THE IPMSM USING GRAIN-ORIENTED ELECTRICAL STEEL
In this section, the GO is applied to the target IPMSM model for the HEV application for the purpose of improving the performance of the motor. The characteristic curves of the non-grain-oriented electrical steel (NO) and GO are compared, and the specifications of the target IPMSM are introduced. Through the magnetic flux path analysis of the IPMSM obtained by finite element analysis (FEA), the stator part that maximizes the effect of the GO was selected. Finally, by comparing the FEA results of the NO model and the GO applied model, the superiority of the GO was confirmed.

A. MAGNETIC CHARACTERISTIC OF THE GRAIN-ORIENTED ELECTRICAL STEEL
Electrical steel can be classified into two categories according to the magnetic anisotropy characteristics; one is NO, and the other is GO. The magnetic characteristics of the former are uniform regardless of the direction of the magnetic flux flowing through the NO. Therefore, NO has been widely used for the core material of the rotation machine, such as the motor, that the direction of the magnetic flux of the core changes according to the position of the rotor or the instantaneous input current of each phase [18]. On the other hand, the later has strong magnetic anisotropy, and the magnetic characteristic varies according to the direction of the magnetic flux to the rolling direction of the GO. The GO shows superior magnetic characteristics when a direction of the magnetic flux matches the rolling direction. However, it shows inferior characteristics when the flux is perpendicular to the rolling direction, which is the transverse direction [19]. Due to such magnetic orientation  characteristics, the GO is suitable for enhancing the performance of electrical machines with a uniform flux path, especially transformers [20].
The magnetic characteristics of the NO and GO are compared in Fig. 1. The compared materials are 35JN230 and 35ZH135 for the NO and GO, respectively. Fig. 1(a) and Fig. 1(b) show the magnetic flux density-magnetic field curve (B-H curve) and the magnetic flux density-iron loss density (B-W curve) of the NO and GO. As shown in Fig. 1, the GO shows superior performance in the rolling direction, and inferior performance in the transverse direction compared with the NO. Therefore, in order to improve the performance of the IPMSM, it is critical to properly place the GO where the magnetic flux flows in the rolling direction.

B. TARGET IPMSM FOR HEV APPLICATION
The IPMSM is a suitable type of motor for the traction motor for the HEV applications, as the IPMSM satisfies the requirements on high torque density, superior power factor, and high efficiency [21]- [24]. The target model benchmarked the model of the [25]. The specifications and requirements of the IPMSM are tabulated in Table I, and configuration of the target model is shown in Fig. 2.
To determine where to apply the GO, FEA is conducted to confirm the magnetic flux path of the target model. The JMAG, which is the commercial FEA analysis tool, is used to analyze the load and no-load conditions of the IPMSM. Fig. 3 shows the load condition flux path on the core according to the rotor position. The flux path on the rotor core is uniform regardless of the rotor position. However, the rotor is not suitable for GO application, as the flux path highly relies on the array of the magnet, and there is a mechanical stability problem at high-speed rotation.   The stator core can be divided into two parts, the yoke and the teeth. The flux path on the yoke part varies greatly depending on the position of the rotor. However, the flux path on the teeth part is constant in the radial direction regardless of the rotor position. Therefore, when the GO is applied to the teeth part, magnetic flux flows in the rolling direction of the core, and the effect of improving the performance of the motor can be high, which can be confirmed from Fig. 1.

C. PERFORMANCE COMPARISON OF THE NO MODEL AND THE GO MODEL
Based on the magnetic flux path analysis results of the NO model, the GO is applied to the stator teeth part to enhance the performance of the IPMSM. The configurations of the NO and GO models are shown in Fig. 4. The GO model has a connection part at the boundary of the NO and GO, so that the teeth can be fixed to the attraction between the rotor and the stator.
The load and no-load condition analysis using FEA is conducted, and the detailed analysis results and comparison are tabulated in Table II. In detail, for the no-load condition, the iron loss of the GO model was 25.40% reduced compared with the NO model. The line to line back-electromotive force (B-EMF) was 0.53% increased, the B-EMF total harmonic distortion (THD) was 5.56% reduced, and the cogging torque was 7.42% increased. For the load condition, the average torque was 5.50% increased, the iron loss was 9.64% reduced, and the efficiency was 0.25% increased. However, the torque ripple was 43.89% increased.
The torque increase and iron loss decrease effect of applying the GO was confirmed by the results in Table II. Fig. 5 shows the magnetic flux density contour plots of the NO and GO models at the load and no-load condition. As shown in Fig. 1(a), the GO has superior B-H curve characteristics in the rolling direction. Therefore, the GO model shows higher saturation (Fig. 5(c)) compared with the NO model ( Fig. 5(a)), and the reason for the torque increase was higher saturation on the stator. However, due to the severe saturation on the core, the torque ripple of the GO model was 43.89% higher compared with the NO model. In    this paper, design optimization is conducted to handle the pulsation problem.

III. OPTIMAL DESIGN OF THE IPMSM USING IMROA
For the traction motors of the HEVs, high pulsation characteristics can cause mechanical vibration and acoustic noise in the vehicles [26]. Such torque ripple problems can be solved through the optimal design of the motor structure.
Since the FEA, which requires a huge computational burden, is required to analyze the motor, an optimization algorithm that can find an exact solution within a small number of function calls is required. However, when the designed motor is manufactured, expected performances may not be achieved due to manufacturing tolerance issues and the deformation of the motor [27]. In this paper, to avoid the influence of uncertainty of design parameters and to ensure the robustness of the solution, the novel optimization algorithm, that finds all the solutions including global and local solutions and checks the robustness, is proposed.

A. INTERPOLATION MULTI-OBJECTIVE ROBUST OPTIMIZATION ALGORITHM
The optimal design of the electrical machine is a multiobjective optimization problem as the various aspects, such as torque, torque ripple, and THD, of the motor should be considered. One of the methods of considering multiobjectives is the weighted sum method (WSM), which multiplies the assigned weight of each objective and adds them together. The IMROA utilizes the WSM and can consider multi-objectives as a single objective.
To reduce the number of function calls, the IMROA utilizes a surrogate model interpolated by samples on the problem domain such that computation time can be saved compared with standard approaches [28]. The flow chart of the IMROA is shown in Fig. 6. The IMROA effectively adjusts the number of generated samples using a stepwise sampling strategy that consists of peripheral search sampling (PSS), regional search sampling (RSS), and robust test sampling (RTS).
The PSS generates samples that are spread out while maintaining randomness throughout the entire problem domain. In addition, PSS repeatedly adds the sample at the farthest point from the existing samples until all local solutions are roughly found. In RSS, samples are added considering the distances of the existing samples and moving direction of the solutions of surrogate model at each generation. At the end of the algorithm, when the solutions are obtained, RTS is added to test the tolerance for each variable, and the robust optimal solution is determined.

1) PERIPHERAL SEARCH SAMPLING
At the beginning of the IMROA, PSS is conducted to roughly interpolate the entire problem domain without missing local solutions. Firstly, the initial samples are generated using the Latin hypercube sampling method, which is an efficient sampling method that generates uniformly distributed samples with randomness [29], [30]. The objective region is interpolated using the generated initial samples. Then, to find all the solutions without omission, a new sample is added at the farthest point from the existing samples. The process is repeated until the number of the found solutions in the interpolated region does not change.    7 shows the principle of the PS. The green and black dashed lines are surrogate models of the previous and current iteration. On the contour plot, which indicates the current surrogate model, the solution of the surrogate model is moved to the (+) direction. Therefore, the position of the actual solution is likely to be located to the right of the solution of the current surrogate model. Accordingly, the PS is generated on the blue triangle, which is in the (+) direction on the red circle line.

3) ROBUST TEST SAMPLING
When enough iterations have passed and all the solutions are found by PSS and RSS, RTS is conducted to determine the robust optimal solution. Fig. 8 shows an example of the robustness test. The red star (v1os, v2os) is the optimized solution of the algorithm. Considering the manufacturing tolerance of each variable, the orange line represents the uncertainty band of the solution, and samples are added at the red points (v1os±dv1, v2os±dv2). For the maximization problem, among the red points, the point with the minimum function value, which is the same as the worst case of the uncertainty band, becomes a robust solution. Finally, the point with the largest value among other robust solutions is selected as the robust optimal solution.

B. PERFORMANCE VERIFICATION AT THE MATHEMATICAL TEST FUNCTIONS
To verify the superiority of the proposed algorithm, three multimodal optimization algorithms are applied to the optimization of two mathematical test functions, and the objective regions of each test function are shown in Fig. 9. The blue and red dots represent the global solution and robust optimal solution, respectively. Two test functions can be expressed as  The criteria for performance comparison are the convergence rate, which is the ratio of the found solution to the actual robust solution, and the number of function calls to converge to the robust optimal solution. The test is repeated 100 times and the average test result is listed in Table III.
Each algorithm is set to terminate when all solutions are found, so that the convergence rates of all tests are over 99%. In the case of test function 1, the number of function calls of the IMROA is reduced by 87.9% and 83.5% compared with RIA and RNGA, respectively. For test function 2, the reduction rate of the number of function calls of IMROA is 89.7% and 90.3%. Therefore, the superiority of the proposed IMROA is verified by comparing the test results.

C. DESIGN OPTIMIZATION OF THE IPMSM FOR HEV APPLICATION USING IMROA
The verified IMROA is applied to design optimization of the IPMSM GO model, which shows high pulsation characteristics. The design variables are shown in Fig. 10 and are selected as the pole arc to pole pitch ratio (alpha) and the angle of the magnet (m θ ), as the torque ripple varies according to the shape of the magnet placement [31], [32].
The considered objectives of the optimization were average torque, torque ripple, B-EMF THD, and cogging torque. After obtaining the initial samples, each objective value is normalized between 0 to 1. The normalized objective value can be calculated as _ ( min ) / (max min ) where obji is the objective value of the i th sample, and maxi and mini are the maximum and minimum values of the initial samples. Then total objective function of the optimization can be calculated as where objt_ave, objt_ripple, objTHD, and objcogging are normalized average torque, torque ripple, B-EMF THD, and cogging torque value. In order to focus on reducing the pulsation characteristics, weights on the torque ripple and B-EMF THD are set as 0.4 and the target of the optimization is maximizing the objfinal.
As a result of design optimization, a robust global solution was derived. The variables of the GO initial model and the robust model are tabulated on Table IV, and the rotor configuration is shown in Fig. 11.
The performance comparison of the GO initial model and robust model is listed in Table V. The average torque, torque ripple, B-EMF THD, and cogging torque, which are considered objectives, are 1.82%, -37.60%, -13.84%, and 29.36% improved, respectively. As the performances of the considered objectives of the robust model were improved compared with GO initial model, the applicability of the IMROA to the practical motor design optimization is verified.     The effect of GO utilization and design optimization is tabulated in Table II and Table V, respectively, and each method improves the performance of the IPMSM of the HEV application. To conduct the overall comparison, the analysis result comparison of the NO model and the robust model is listed in Table VI, and the waveform comparison of the NO and robust models are shown in Fig. 12. The magnetic flux density contour plot comparison is shown in Fig. 13. For the no-load analysis, the B-EMF THD was 18.63% reduced, cogging torque was 24.12% reduced, and iron loss was 28.30% reduced. The load condition results show 7.42% torque increase, 10.21% torque ripple reduction, 6.61% iron loss reduction, and 0.28% efficiency increase.
The detailed comparison of the iron loss is conducted, and the results comparison is tabulated in Table VII. Especially for the stator teeth part, where the GO is applied, the iron loss was 41.45% and 30.34% reduced for the noload and load condition. The reason for the low iron loss on  the stator teeth is superior B-W curve characteristics, shown in Fig. 1(b). The robust model shows superior load and no-load performances compared with the NO model and the GO model. Moreover, the average torque, torque ripple, cogging torque, and B-EMF THD, which were objective functions, were 1.82%, 37.60%, 29.36%, 13.84% improved, respectively, by only changing the position of the magnet. Therefore, superior performance of the IMROA was validated, and the applicability of the IMROA to the practical electrical machine design optimization was conducted.

IV. CONCLUSION
In this paper, the GO was applied at the IPMSM for HEV application. To utilize the superior effect of the GO, the GO was partially applied to the stator teeth, where the direction of the flux path is equal to the rolling direction of the GO, and the torque and iron loss was improved. For further performance enhancement of the IPMSM, design optimization was conducted by the proposed IMROA, which can consider robustness of the solution and reduce the calculation time. The IMROA derives a robust optimal solution with improved performance, and the applicability to the practical electrical machine design optimization was proved.