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In this paper, subdivided kriging multi objective optimization (SKMOO) is proposed for the optimal design of interior permanent magnet synchronous motor (IPMSM). The SKMOO with inverse searching can obtain uniform and accurate pareto front set with reduced computation cost compared to conventional algorithms. In the SKMOO algorithm, Fill blank method is applied to prevent premature convergence. In addition, the subdivided kriging grid is proposed to make well distributed and precise pareto front set. Superior performance of the SKMOO is confirmed the by compared conventional MOO algorithms with the test function and applied it to the optimal design of IPMSM for electric vehicle.&lt;br/&gt;&lt;br/&gt;I. Introduction&lt;br/&gt;&lt;br/&gt;The interior permanent magnet synchronous motor (IPMSM) has the torque caused by the magnet and reluctance torque. Therefore, the IPMSM torque greater than surface mounted PMSM [1]. However, such a permanent magnet type motor has a disadvantage of high cogging torque and torque ripple which causes in the motor’s noise, vibration, and efficiency reduction. This is important to electric vehicle for comfortable driving [2]. Therefore, we aim to design the IPMSM with reduced cogging torque and torque ripple.&lt;br/&gt;Finite element method (FEM) analysis is required since the accurate analysis is difficult by using simple mathematical models due to the nonlinear characteristic of the IPMSM [3]. However, the actual motor design using FEM analysis should meet several requirements. It takes a lot of time and effort to simultaneously consider multi objective functions in motor design that require FEM interpretation [4],[5]. To solve this problem, a lot of studies are in progress [6],[7]. The most widely used algorithms are multi objective particle swarm optimization (MOPSO) and non-dominated sorting genetic algorithm-II (NSGA-II). However, the MOPSO and NSGA-II still need many function calls to get the accurate and well distributed pareto front set. Therefore, subdivided kriging multi objective optimization (SKMOO) is proposed which applies the surrogate model to reduce function calls.&lt;br/&gt;Outstanding performance of the proposed algorithm is verifyverified through comparison of results with the MOPSO and NSGA-II. And the optimal design was derived by applying the SKMOO to design of the IPMSM with reduced cogging torque and torque ripple.&lt;br/&gt;&lt;br/&gt;II. Proposed Algorithm&lt;br/&gt;&lt;br/&gt;MOO performance can be determined based on the accuracy, uniform distribution, and number of function calls while consisting the SKMOO uses the following methods to improve algorithm performance.&lt;br/&gt;Pareto front set are extracted from samples using non-dominated sorting and sorted one objective function. The Euclidean distance of adjacent solutions is calculated to obtain a uniform pareto front set and predicted solution is added directly between the two solutions with the longest distance. The spline interpolation is used to increase the accuracy of the solution as shown in Fig. 1.&lt;br/&gt;Design variables are inversely searched to generate a real solution. The most similar combination of design variables is found by comparing the objective function value of the surrogate model with the predicted value and the function call is executed to the explored design variables. Fill blank method is used to prevent premature convergence. This method is greatly efficient because it does not overlap the area already explored.&lt;br/&gt;When the algorithm converges after the set number of iterations, subdivided kriging grid is proposed to improve performance. The same methods are used to adds solutions, but more accurate solutions can be added because the kriging grid is finely divided. Also, the solution with the closest distance is deleted, if the distance is less than a set distance and if it is more than a set distance, a new solution is added as the intermediate point of before and after solution to obtain more uniform distribution.&lt;br/&gt;Fig. 1 shows that the solution is directly added in objective function area. However, the solution is added only at the grid points. Therefore, there is a difference between predicted and real solution. In this case, solutions are uneven and inaccurate. Subdivided grid is a method to solve this problem by dividing kriging grid finely as shown in right of Fig. 1.&lt;br/&gt;&lt;br/&gt;III. verification of proposed algorithm&lt;br/&gt;&lt;br/&gt;The SKMOO, the NSGA-II and MOPSO are applied to the test functions. GD indicates how similar the pareto set to the real pareto set and SP indicates how uniformly the solution is distributed. GD and SP value mean better performance if values close to zero. Table. I summarize the results and shows that the SKMOO has superior performance on GD, SP, and the number of function calls than NSGA-II and MOPSO.&lt;br/&gt;&lt;br/&gt;IV. Conclusion&lt;br/&gt;&lt;br/&gt;In this paper, SKMOO based on surrogate model is presented to solve MOO problems. The SKMOO can reduce computation cost and show superior performances in the MOO problems. The proposed algorithm is validated by comparing with MOPSO and NSGA-II. Finally, we applied the SKMOO to the optimal design of IPMSM. Taguchi method is used to select variables among several variables that are sensitive to the objective function. The application of the SKMOO to optimal design of the IPMSM will be covered in full paper.&lt;br/&gt;&lt;br/&gt;V. Acknowledgment&lt;br/&gt;&lt;br/&gt;This research was supported by Korea Electrotechnology Research Institute (KERI) Primary research program through the National Research Council of Science &amp; Technology (NST) funded by the Ministry of Science and ICT (MSIT) (No. 21A01082).

**References:**

[1] Guo Hong, Tian Wei, and Xiaofeng Ding, IEEE Access, Vol. 6, pp. 23568-23581, (2018).&lt;br/&gt;[2] Young-Rok Kang, Ji-Chang Son, and Dong-Kuk Lim, IEEE Access, Vol. 8, (2020).&lt;br/&gt;[3] M. Caruso, A. O. Di Tommaso, L. Ferraris, R. Miceli, F. Viola,2017 Twelfth International Conference on Ecological Vehicles and Renewable Energies (EVER)., (2017)&lt;br/&gt;[4] Min Li, Fabien Gabriel, Maria Alkadri, IEEE Transactions on Magnetics, Vol. 52, (2016)&lt;br/&gt;[5] Siguang An, Shiyou Yang, Osama A. Mohammed, IEEE Transactions on Magnetics, Vol. 54, (2018)&lt;br/&gt;[6] Khalil Alkebsi, Wenli Du, IEEE Access., Vol. 8, (2020)&lt;br/&gt;[7] Vikas Palakonda, Rammohan Mallipeddi, IEEE Access, Vol. 8, (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/de072cbbc28eead8bddd09747917a1f9.jpg)
Fig.1 Conceptual diagram of SKMOO

![](https://assets.underline.io/uploads/markdown_image/1/image/51d55f48cade1a8cf8b2cc9ec7346562.jpg)
Table. I Test function results

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 Optimal Design of IPMSM for EV using Subdivided Kriging Multi Objective Optimization

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In this paper, subdivided kriging multi objective optimization (SKMOO) is proposed for the optimal design of interior permanent magnet synchronous motor (IPMSM). The SKMOO with inverse searching can obtain uniform and accurate pareto front set with reduced computation cost compared to conventional algorithms. In the SKMOO algorithm, Fill blank method is applied to prevent premature convergence. In addition, the subdivided kriging grid is proposed to make well distributed and precise pareto front set. Superior performance of the SKMOO is confirmed the by compared conventional MOO algorithms with the test function and applied it to the optimal design of IPMSM for electric vehicle. I. Introduction The interior permanent magnet synchronous motor (IPMSM) has the torque caused by the magnet and reluctance torque. Therefore, the IPMSM torque greater than surface mounted PMSM [1]. However, such a permanent magnet type motor has a disadvantage of high cogging torque and torque ripple which causes in the motor’s noise, vibration, and efficiency reduction. This is important to electric vehicle for comfortable driving [2]. Therefore, we aim to design the IPMSM with reduced cogging torque and torque ripple. Finite element method (FEM) analysis is required since the accurate analysis is difficult by using simple mathematical models due to the nonlinear characteristic of the IPMSM [3]. However, the actual motor design using FEM analysis should meet several requirements. It takes a lot of time and effort to simultaneously consider multi objective functions in motor design that require FEM interpretation [4],[5]. To solve this problem, a lot of studies are in progress [6],[7]. The most widely used algorithms are multi objective particle swarm optimization (MOPSO) and non-dominated sorting genetic algorithm-II (NSGA-II). However, the MOPSO and NSGA-II still need many function calls to get the accurate and well distributed pareto front set. Therefore, subdivided kriging multi objective optimization (SKMOO) is proposed which applies the surrogate model to reduce function calls. Outstanding performance of the proposed algorithm is verifyverified through comparison of results with the MOPSO and NSGA-II. And the optimal design was derived by applying the SKMOO to design of the IPMSM with reduced cogging torque and torque ripple. II. Proposed Algorithm MOO performance can be determined based on the accuracy, uniform distribution, and number of function calls while consisting the SKMOO uses the following methods to improve algorithm performance. Pareto front set are extracted from samples using non-dominated sorting and sorted one objective function. The Euclidean distance of adjacent solutions is calculated to obtain a uniform pareto front set and predicted solution is added directly between the two solutions with the longest distance. The spline interpolation is used to increase the accuracy of the solution as shown in Fig. 1. Design variables are inversely searched to generate a real solution. The most similar combination of design variables is found by comparing the objective function value of the surrogate model with the predicted value and the function call is executed to the explored design variables. Fill blank method is used to prevent premature convergence. This method is greatly efficient because it does not overlap the area already explored. When the algorithm converges after the set number of iterations, subdivided kriging grid is proposed to improve performance. The same methods are used to adds solutions, but more accurate solutions can be added because the kriging grid is finely divided. Also, the solution with the closest distance is deleted, if the distance is less than a set distance and if it is more than a set distance, a new solution is added as the intermediate point of before and after solution to obtain more uniform distribution. Fig. 1 shows that the solution is directly added in objective function area. However, the solution is added only at the grid points. Therefore, there is a difference between predicted and real solution. In this case, solutions are uneven and inaccurate. Subdivided grid is a method to solve this problem by dividing kriging grid finely as shown in right of Fig. 1. III. verification of proposed algorithm The SKMOO, the NSGA-II and MOPSO are applied to the test functions. GD indicates how similar the pareto set to the real pareto set and SP indicates how uniformly the solution is distributed. GD and SP value mean better performance if values close to zero. Table. I summarize the results and shows that the SKMOO has superior performance on GD, SP, and the number of function calls than NSGA-II and MOPSO. IV. Conclusion In this paper, SKMOO based on surrogate model is presented to solve MOO problems. The SKMOO can reduce computation cost and show superior performances in the MOO problems. The proposed algorithm is validated by comparing with MOPSO and NSGA-II. Finally, we applied the SKMOO to the optimal design of IPMSM. Taguchi method is used to select variables among several variables that are sensitive to the objective function. The application of the SKMOO to optimal design of the IPMSM will be covered in full paper. V. Acknowledgment This research was supported by Korea Electrotechnology Research Institute (KERI) Primary research program through the National Research Council of Science & Technology (NST) funded by the Ministry of Science and ICT (MSIT) (No. 21A01082).

**References:**

[1] Guo Hong, Tian Wei, and Xiaofeng Ding, IEEE Access, Vol. 6, pp. 23568-23581, (2018). [2] Young-Rok Kang, Ji-Chang Son, and Dong-Kuk Lim, IEEE Access, Vol. 8, (2020). [3] M. Caruso, A. O. Di Tommaso, L. Ferraris, R. Miceli, F. Viola,2017 Twelfth International Conference on Ecological Vehicles and Renewable Energies (EVER)., (2017) [4] Min Li, Fabien Gabriel, Maria Alkadri, IEEE Transactions on Magnetics, Vol. 52, (2016) [5] Siguang An, Shiyou Yang, Osama A. Mohammed, IEEE Transactions on Magnetics, Vol. 54, (2018) [6] Khalil Alkebsi, Wenli Du, IEEE Access., Vol. 8, (2020) [7] Vikas Palakonda, Rammohan Mallipeddi, IEEE Access, Vol. 8, (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/de072cbbc28eead8bddd09747917a1f9.jpg)
Fig.1 Conceptual diagram of SKMOO

![](https://assets.underline.io/uploads/markdown_image/1/image/51d55f48cade1a8cf8b2cc9ec7346562.jpg)
Table. I Test function results

poster

I. Introduction Recently, permanent magnet (PM) motors have been widely applied in various application fields, such as electric vehicles, aerospace, and household appliances, owing to the inherent advantages of high torque density, high energy efficiency, and compact structure. With the increasingly severe and diversified application scenarios of PM motors, higher and more complicated requirements are raised for optimization design. It is noted that the motor system is actually a multi-disciplinary, nonlinear, strong coupled system, hence the objectives are often in conflict with each other in the design process. In previous studies, multi-objective optimization design is considered as an effective solution for obtaining high-performance PM motors, and some optimization methods are often utilized, such as a multi-objective genetic algorithm (MOGA) [1]. However, the traditional optimization method is a deterministic design approach and has not investigated the uncertainties in engineering manufacturing, such as material diversity, manufacturing error, and assembly inaccuracy. These will result in design parameter fluctuation affecting the reliability and quality of the machine. To deal with this problem, the robust optimization design approach is proposed and gradually becomes a hotspot in machine design research orientation. Generally, the design for the six sigma (DFSS) technique is an effective optimization approach, which is often adopted to provide direct and reliable evaluation for the assessment of robustness. In [2], a soft magnetic composite (SMC) motor is optimized based on DFSS, which takes robustness into consideration in not only motor but also integrated control schemes. In [3], the robust design of a surface-mounted permanent magnet (SPM) motor is realized by the particle swarm optimization (PSO) instead of genetic algorithm (GA) due to long computational time of DFSS. Yet, it is noted that in the DFSS method, the mean and variance of the optimization objectives should be optimized at the same time, which greatly improves the dimension and complexity of the motor optimization model. Thus, for the machine robust design, ensuring the optimization convergency is a big challenge. It is necessary to propose an optimization method to improve the efficiency and accuracy of DFSS, effectively achieving machine robust design. To address this problem, this paper proposes an efficient machine robust design approach, where the dimension of the robust optimization model can be reduced according to the assessment of the relationship between objectives. To better clarify the proposed method, an interior PM machine with a multi-layer flux barrier is investigated as a design example. By implementing the proposed optimization method, it can be found that the performance and design reliability of the machine can be effectively improved. II. Proposed optimization method As is shown in Fig. 1, the design concept from the traditional deterministic optimization to robust design optimization is described for better presentation. Fig. 2(a) gives the configuration of the design example, an interior PM motor with a multi-layer flux barrier. It can be seen that the motor adopts the 36/8 slot/pole combination and NdFeB-PM is embedded in the middle of each arc-shaped magnetic barrier. Fig. 1(b) shows the parameter model of the motor and structural parameters for optimization is marked. Based on the parametric model, the process of robust optimization is given as the flowchart in Fig. 3. Firstly, in order to reduce the computation of FEA, Latin hypercube sampling (LHS) was utilized to approximate random sampling from multivariate parameter distributions. Then, parameters are divided into two layers by the result of sensitivity analysis. In Layer 1, the parameters with low sensitivity are optimized for objectives that have relatively strong relevance with them by parameter sweeping. In addition, robust factors of the performance fluctuation caused by sensitive parameters are considered in Layer 2. And then, a non-parametric measure of conflict method is adopted for objective reduction, then, the objectives with high conflict have remained for multi-objective optimization. Finally, the filtered objectives are optimized by NSGA-II (Non-Dominated Sorting Genetic Algorithm-II). III. Analysis and results Based on the robust optimization method proposed above, the analysis results are obtained. According to spearman's rank correlation coefficient, five objectives with relatively high assessed conflict value are remained in the process of multi-objective optimization, and the result is shown in Fig. 4 (a). In addition, the solution set corresponding to all objectives based on parameters determined above is shown in Fig. 4 (b). The torque and torque ripple of the proposed interior PM motor are calculated and compared in Fig. 5 (a), it can be seen that the average torque has been improved from 23.56 Nm to 25.95 Nm, while the torque ripple decreases from 10.14% to 9.50%. In order to evaluate the robust performance, 1000 points are sampled separately around initial and optimized parameters by Monte Carlo analysis method, as is shown in Fig. 5 (b), the variance μ of the distribution is decreased from 0.43 Nm to 0.27 Nm. Additionally, the improvement of core loss performance is given in Fig. 6. In conclusion, it can be seen that deterministic and robust performances of the proposed motor are improved simultaneously. More detailed design process description and experimental verification will be given in the full paper.

**References:**

[1] X. Zhu, W. Wu, L. Quan, Z. Xiang, and W. Gu, “Design and Multi-objective Stratified Optimization of a Less-rare-earth Hybrid Permanent Magnets Motor with High Torque Density and Low Cost,” IEEE Trans. Energy Convers., vol. 34, no. 3, pp. 1178-1189, Sept. 2019. [2] G. Lei, T. Wang, J. Zhu, Y. Guo and S. Wang, "System-Level Design Optimization Method for Electrical Drive Systems—Robust Approach," IEEE Trans. Ind. Electron., vol. 62, no. 8, pp. 4702-4713, Aug. 2015. [3] V. Rafiee and J. Faiz, "Robust Design of an Outer Rotor Permanent Magnet Motor Through Six-Sigma Methodology Using Response Surface Surrogate Model," IEEE Trans. Magn., vol. 55, no. 10, pp. 1-10, Oct. 2019, Art no. 8107110.

**Images:**
![](https://assets.underline.io/uploads/markdown_image/1/image/781807121d046ecd03abb1172884bca0.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/4e85477824084c91ec3418285d50a0cb.jpg)

 Robust Multi-Objective Optimization Design of Permanent Magnet Motors Based on Objective-Dimension-Reduced Method

I.INTRODUCTION PM machines have obtained wide applications in the last several decades because of the high efficiency, high torque and high power density. Most PM machines adopt rare-earth PMs as magnetic potential source for high performance. However, due to the unstable supply of rare-earth PMs, the price of PMs is becoming a major issue. Therefore, many machines with less or no PM have been developed in the last a couple of years. Although less or no PM machines such as hybrid PM motors and synchronous reluctance motors can reduce the usage of PMs significantly, they still suffer from poor torque density. Adopting consequent-pole(CP) structure in PM machines is another solution to save PMs[1]-[3]. However, the rotors in CP motors are difficult to design and there is seldom design experience for reference. Topology optimization(TO) is an approach for shape optimization. It searches optimal shape by making free modifications in the distribution of material, and has potentialities to provide novel design. In this paper, The TO method based on ON/OFF method and immune algorithm (IA) was applied on the rotor core of a consequent-pole permanent magnet synchronous motor (CP-PMSM) to improve its torque quality. II.STRUCTURE AND OPERATION PRINCIPLE OF CP-PMSMS Fig.1(a) shows the 1/4 models of PMSMs with surface-mounted PM(SPM) and CP. For a CP-PMSM, the magnetic direction of all the PMs are the same, and each PM pole is set between two silicon steel poles. The magnetic circuits of two motors are established to explain the working principle of the CP motor. Then, torque waveforms are simulated for comparison. The average torque of SPM motor and CP motor are 3.25N and 2.09N, respectively. The average thrust will not reduce half with the missing of half PM poles, which means the PM has higher utilization in the CP-PMSM. Additionally, the motors still have potential to be optimized for better torque quality. III.TOPOLOGY OPTIMIZATION BASED ON ON/OFF METHOD AND IMMUNE ALGORITHMS The authors have proposed a TO method based on ON/OFF method with IA [4]. The ON/OFF method divides the search space into numerous finite element meshes to represent material distribution, each finite element mesh is associated with a binary value, indicating either the presence or absence of material. The area to be optimized is the search space of ON/OFF method. Consequently, the optimized shape could be represented by the presence (silicon steel) or absence (air) of silicon steel material. IA is used to search the optimal shape by changing the material distribution in the meshes. The TO procedures of ON/OFF method based on IA can be summarized as follows:1)Generate initial antibodies of Npop candidate solutions, create random initial shapes;2)Smoothen surface and eliminate holes by filter process;3)Evaluate the objective function for each antibody, list them up from high value to low value;4)Generate clones for each antibody, the antibodies with high evaluation function will be cloned more to generate more offspring;5)Apply affinity maturation (small modifications) on material surface to the clones;6)Smoothen surface and eliminate holes by filter process;7)Evaluate each clone and list them up, if one clone is better than its parent, it will replace its parent;8)Keep Ns%(0＜Ns＜1) clones with high ranking and weed others out. Then add randomly generated antibodies as step 1-2 to keep the population size constant;9) Back to step 4 until the optimization targets are met. IV.OPTIMIZATION RESULT OF THE CP-PMSM The rotor core is chosen to be the search space of ON/OFF method. The search space is defined in 0°–45°range, the optimized shape of this range is reversing copied to 45°–90°range, so as to make the rotor symmetrical and reduce computation cost. Both the average torque and torque ripple were considered in the evaluation function in optimization. Fig.1(b) shows the evolution of the rotor topologies during optimization. At first, the profile of silicon steel poles emerged in the surface of rotor core, and there were many big holes inside the rotor. Then, the holes inside the core gradually decreased and became smaller, and the shape of the silicon steel poles became more obvious. Finally, the holes inside the rotor core almost disappeared, and the silicon steel poles gradually became a‘W’shape. Torque characteristics before and after optimization are compared in Fig.2. The components of output torque, i.e., electromagnetic torque and cogging torque, are simulated for analysis. It can be found that the output torque of the CP-PMSM is greatly improved after optimization, the average torque is increased from 2.09N to 2.32N, and the torque ripple is reduced from 126.6% to 13.7%. Moreover, the improvement of output torque is contributed by both the improvement of cogging torque and electromagnetic torque. In the future, we plan to extend this TO method to PM poles and stator core so as realize comprehensive TO.

**References:**

[1]S. U. Chung, J. W. Kim, and Y. D. Chun,“Fractional slot concentrated winding PMSM with consequent pole rotor for a low-speed direct drive: reduction of rare earth permanent magnet,”IEEE Transactions on Energy Conversion, Vol.30, No.1, pp. 103–109, Mar. 2015. [2]L. Wei and T. Nakamura, "Optimization Design of a Dual-Stator Switched Flux Consequent Pole Permanent Magnet Machine With Unequal Length Teeth," IEEE Transactions on Magnetics, Vol. 56, No. 2, pp. 1-5, Feb. 2020. [3]S. Teymoori, A. Rahideh, and H. Moayed-Jahromi,“2-D analytical magnetic field prediction for consequent-pole permanent magnet synchronous machines,” IEEE Transactions on Magnetics, Vol.6, No.6, pp. 1–14, Jun.2016. [4]K. Watanabe, T. Suga and S. Kitabatake, "Topology Optimization Based on the ON/OFF Method for Synchronous Motor," IEEE Transactions on Magnetics, Vol. 54, No. 3, pp. 1-4, March 2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/643715c3ce09d6801d0368701f2223ca.png)
Fig. 1.(a) Comparison of surface-mounted PM motor and consequent-pole motor. In consequent-pole motor, each PM pole is set between two silicon steel poles, so as to save PM volume. (b)Variation of rotor topologies during evolution(Evolutions takes 15 hours in total). The rotor shape varies sharply in the beginning generations and gradually tends to be fixed in a 'W' shape.

![](https://assets.underline.io/uploads/markdown_image/1/image/d441845f21330cb640be24a1e761dd93.jpg)
Fig. 2.(a)Torque characteristics before optimization. (b)Torque characteristics after optimization. It can be found the improvement of output torque is contributed by both the improvement of cogging torque and electromagnetic torque

 Topology Optimization of Consequent-Pole PMSM Using ON/OFF Method

I. Introduction Permanent magnet (PM) machines have been extensively investigated and employed in various industrial applications due to their inherit merits of high torque and high efficiency. Nevertheless, because of the ever-increasing price and unstable supply, the rare-earth material cost is a major concern [1]. In order to address above-mentioned issue, the electrical machines with no or less rare-earth PM material are widely developed [1]. Because half of magnetic poles are replaced by iron core, the consequent-pole PM (CPM) machines [2]-[13] exhibit higher PM utilization ratio and comparable torque capability compared with conventional surfaced-mounted PM (SPM) structures. Therefore, various CPM machines in terms of surface-inset [2] [3], interior [4]-[7] and hybrid pole [8]-[10] configurations are reported and extensively investigated, which shows that the CPM design exhibits better field-weakening capability, higher PM utilization ratio, similar torque capability and efficiency compared with SPM machines. Recently, the field modulation effect (FME) concept has been extended to the CPM machines [11]-[13]. It can be found that the CPM machines exhibit more air-gap field harmonics responsible for torque generation compared with the SPM counterparts [11]-[13], which is mainly due to its doubly salient structure, unipolar PM magneto-motive force (MMF) distribution. The split ratio is a key design parameter of the PM machines, which significantly reflects the torque capability, iron loss, efficiency and thermal behavior [14]. However, the influences of split ratio on the FMEs in CPM machines remain unreported hitherto. Therefore, in order to provide an in-depth understanding of their torque production mechanism, the influence split ratio on FME of the CPM machines is investigated in this paper. II. Machine Topology and Preliminary Electromagnetic Performance The topology of the proposed CPM with 12-stator-slot/14-rotor-pole is illustrated in Fig. 1(a). The fractional slot concentrated windings are adopted to reduce the end winding length and improve the efficiency. The split ratio γ can be defined as γ=rsi/rso (1) where rsi and rso are the stator inner and outer diameters, respectively. The average torque variations of the CPM machine with different split ratios are illustrated in Fig. 1(b). It can be seen that the average torque is rises first, and then drops steadily when split ratio exceeds 0.55, which is mainly due to the increased first and then decreased electrical load. In order to quantify the torque contributions of the various working harmonics, the Maxwell stress tensor method is employed. The electromagnetic torque can be expressed as Τe=∑(πlstkrg2/μ0)BrkBtkcos[θrk(t)-θtk(t)]=∑Tk(t) (2) where rg is the air-gap radius. lstk is the active stack length. Tk is the electromagnetic torque generated by the kth harmonics of radial and tangential air-gap flux densities, respectively. Thus, the contributions of the kth field harmonics to the total electromagnetic torque can be separated when the kth radial and tangential air-gap field harmonics are obtained. The average torque proportion can be defined as λ=(Tk/Te)×100% (3) The torque contributions of FME can be expressed as λFME=(1-TZr/Te)×100% (4) where TZr is the average torque generated by Zr order air-gap field harmonic. The corresponding torque proportions of the various air-gap flux density harmonics can be obtained (2)-(4), as shown in Figs. 2(c) and (d). Due to the slightly increased air-gap flux density amplitudes, the torque proportions of 5th, 19th and 21th are increased with split ratio, as shown in Fig. 2(c). Similarly, the torque proportion of 7th harmonic is decreased with split ratio, which is mainly due to its decreased 7th air-gap flux density amplitude. The corresponding torque proportion of FME can be obtained by (4), as shown in Fig. 1(e). Because of the decreased amplitude and torque proportion of the Zr order air-gap flux density, the torque proportion of FME is increased with split ratio, which indicates that the more pronounced FME can be obtained in relatively higher split ratio. III. Experimental Validation In order verify the FE simulation, a 12-slot/14-pole CPM machine prototype is manufactured, as shown in Figs 2. The test results are illustrated in Figs. 2(c) and (d), respectively. It can be seen that the measured back-EMF values are slightly lower than FE predictions, as shown in Fig. 2(d), which is mainly due to the fact that the end-winding effect and mechanical tolerance are not considered in FE analysis. The detailed analysis and experimental measurements will be presented in the full paper.

**References:**

[1] H. Tahanian, M. Aliahmadi and J. Faiz, IEEE Transactions on Magnetics, Vol. 56, Art. no. 900120, (2020) [2] S. U. Chung, S. H. Moon and D. J. Kim, IEEE Transactions on industrial Electronics, Vol. 63, p.302-309, (2016) [3] J, Li, K. Wang and F. Li, IEEE Transactions on industrial Electronics, Vol. 66, p.1736-1747, (2019) [4] M. Onsal, B. Cumhur and Y. Demir, IEEE Transactions on Magnetics, Vol. 54, Art. no. 8206005, (2018) [5] W. Liu and T. A. Lipo, IEEE Transactions on Industry Application, Vol. 54, p.5918-5929, (2018) [6] X. Ren, D. Li and R. Qu, IEEE Transactions on Energy Conversion, Vol. 33, p.2112-2121, (2018) [7] J. Li, K. Wang and H. Zhang, IEEE Transactions on industrial Electronics, Vol. 67, p.3374-3385, (2020) [8] K. Wang, J. Li and S. S. Zhu, IEEE Transactions on industrial Electronics, Vol. 66, p.6811-6823, (2019) [9] G. Dajaku, IEEE Transactions on Magnetics, Vol. 56, Art. no. 8200409, (2020) [10] G. Xu, W. Zhao and G. Liu, IEEE Transactions on Transportation Electrification, accepted, (2020) [11] Y. Li, H. Yang and H. Lin, in Proc. XIII International Conference Electrical Macine (ICEM), pp.65-71, (2018) [12] D. Jang and J. Chang, IEEE Transactions on Energy Conversion, Vol. 34, p.2019-2028, (2019) [13] Y. Li, H. Yang and H. Lin, IEEE Transactions on Energy Conversion, accepted, (2020) [14] Y. Shen and Z. Q. Zhu, IEEE Transactions on Magnetics, Vol. 47, p.4187-4190, (2011)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9549b4f93fc46a47e02517de642ae14b.png)
Fig. 1. (a) Configuration of 12-stator-slot/14-pole CPM. Torque characteristics of the CPM machine with different split ratio. (b) Average torque. Torque proportions of the various working harmonics (c) field modulated harmonics, (d) 7th, (d) FME.

![](https://assets.underline.io/uploads/markdown_image/1/image/a93893e2c93e7f9a334ca1037de1cbd4.jpg)
Fig. 2. 12-slot/14-pole CPM machine prototype and measured results. (a) Stator. (b) Rotor. (c) Measured open-circuit back-EMFs. (d) Comparison of the measured and FE predicted open-circuit fundamental amplitudes of back-EMFs.

 Influence of Split Ratio on Field Modulation Effect in Consequent-Pole Permanent Magnet Machine

This work focuses on the analysis of rotor geometry parameters and added flux barriers design to improve the anti-demagnetization capability of fractional slot concentrated windings interior permanent magnet motor (IPM) for electric vehicle (EV) traction applications. A 2.5kW V-shape IPM motor (12 slots and 8 poles) is designed to achieve high torque density and wide constant power speed range (CPSR), which is selected to study in this paper. The influence of rotor geometry parameters variation (such as the magnet position and angle, the width and thickness of magnet) on the relation of characteristic current (Ich) and demagnetization in wide-speed range operation is firstly investigated under high-temperature and high current density operation. Then, the impact of added flux barriers design on the anti-demagnetization capability of the IPM motor is evaluated. The analysis results show that the increase of magnet angle of V-shape IPM would improve the anti-demagnetization capability but would reduce Ich; meanwhile, the increase of magnet thickness would increase Ich and simultaneously improve the anti-demagnetization capability. In addition, the added flux barriers design significantly affects the anti-demagnetization capability of the V-shape IPM motor. Finally, a unique multi-objective genetic algorithm is applied for the rotor geometry optimization of the V-shape IPM motor to achieve good anti-demagnetization capability, excellent CPSR, and high efficiency. Finite element analysis (FEA) is used for evaluation, and experiments are conducted to validate the analysis. I.Introduction In order to achieve the power and torque requirements of an EV motor, magnetic loading and electrical loading need to be improved. However, due to the saturation of the electrical steel sheet, a high current density design is unavoidable. In a high current operating environment, due to the high temperatures and strong armature magnetic field presented in the motor, the magnetic field provided by the magnet is usually reduced. Under these conditions, the magnet can suffer from irreversible demagnetization. For this reason, a higher current will be required to achieve the originally expected performance. To avoid this type of problem is very important to design a motor with high resistance to demagnetization for the safety and reliability of the product. II.Target Models and Analysis Method A 2.5 kW fractional slot concentrated windings V-shape IPM motor with 12 slots and 8 poles is applied to study here. The rotor configuration of V-shape IPM with the design parameters is shown in Fig. 1(a) and the design of different flux barriers is presented in Fig. 1(b). Finite element analysis (FEA) is utilized to comprehensively evaluate the impact of rotor geometry parameters variation and design characteristic of added flux barriers on the relation of characteristic current (Ich) and the anti-demagnetization capability of the V-shape IPM motor. The details will be reported in the full paper. III.Analysis Results and Experiments Fig. 2 shows the comparison of magnetic flux density distribution on PM without and with added flux barriers design during no-load and load conditions. It can be seen that the added flux barriers design significantly affects the demagnetization risk on PM. Fig. 3 presents the comparison of back EMF of V-shape IPM motor without and with the added flux barriers design before and after demagnetization. The result shows that the added flux barriers design significantly reduces the demagnetization risk on PM of V-shape IPM motor. Fig. 4(a) shows the rotor configuration after optimized of the V-shape IPM motor which is made as a prototype for validating the analyses. Fig. 4(b) shows the comparison of back EMF of V-shape IPM motor between the simulation and experiment at 1500 rpm speed. The phase voltage of back EMF is 13.45 V in the simulation, thus the peak-to-peak of back EMF is 23.3 V; meanwhile, the measured back EMF is 24.8 V. The error between the simulation and experiment is only 6%, thus the analysis results are reliable. Fig. 5(a) shows the torque and power versus speed curves of the V-shape IPM motor. The output torque of the motor is 9.17 Nm for simulation and 8.9 Nm for the experiment, respectively. Fig. 5(b) presents the comparison of back EMF of IPM motor before and after demagnetization in the experiment. The back EMF of the motor after fully demagnetized magnets only has an error of 2%. The accuracy of the simulation is thus verified by the experiment results. Detail analysis and experiment will be reported in the full paper. IV.Conclusion This digest has analyzed the impact of rotor geometry parameters variation and design characteristic of added flux barriers on the performance and the anti-demagnetization capability of fractional slot concentrated windings V-shape IPM motor. The added flux barriers design significantly affects the performance and anti-demagnetization capability of the V-shape IPM motor. The detail analysis and experimental results will be reported in the full paper.

**References:**

[1] H. Chen, R. Qu, J. Li and D. Li, "Demagnetization Performance of a 7 MW Interior Permanent Magnet Wind Generator With Fractional-Slot Concentrated Windings," IEEE Transactions on Magnetics, vol. 51, no. 11, pp. 1-4, Nov. 2015. [2] K. Imamura, M. Sanada, S. Morimoto, and Y. Inoue, "Improvement of Demagnetization by Rotor Structure of IPMSM with Dy-Free Rare-Earth Magnet," in Proceeding of IEEE International Electrical Machines and Systems Conference, Sapporo, 2012.

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 Design and Optimization of Fractional Slot Concentrated Windings Interior Permanent Magnet Traction Motor Considering Anti-Demagnetization Capability

I. Introduction With the large-scale application of rare-earth permanent magnet motors, the consumption of rare-earth PM material has increased sharply [1]. As a non-renewable resource, such excessive consumption increases the potential risks of further larger scale application of rare-earth PM motors. Recently, to alleviate the dependence on the rare-earth PMs, a type of less rare-earth permanent magnet (LRE-PM) machines has attracted much attention since the adoption the low cost of non-rare-earth Ferrite-PMs [2]. In this paper, a new asymmetric-PM-placed rotor topology is applied to the conventional LRE hybrid magnet machine, where such new placement of hybrid magnets can be designed to improve the torque performance effectively. Considering the complexity of rotor structure and the difference between two magnetic materials, the relationship among the size of the hybrid magnets (NdFeB-PMs and Ferrite-PMs), torque density and torque ripple is investigated through theoretical derivation and finite element analysis. And, some key size parameters are optimized to improve torque performances. II. Optimization Design and Analysis of Torque Performance In this paper, a new frozen permeability method is used to separate the components of total torque [3], and the design factors influencing torque ripple are deduced theoretically. According to the principle of equivalent magnetomotive force, the initial design of hybrid magnets is carried out. Then for the key size of hybrid magnets, the sensitivity analysis of multiple optimization objectives is conducted to obtain the optimal solution [4]. The effectiveness of the proposed method is verified by comparing the torque performance and anti-demagnetization property of the initial machine with that of the optimized one. Fig. 1(a) shows the proposed asymmetric-hybrid-PM machine structure. In the rotor, the NdFeB-PMs and Ferrite-PMs are asymmetric arranged in mixed series-parallel connection. It can be seen that the permanent magnet torque (Tpm) decreases due to the coupling effect of the two different magnets. However, by properly designing the size of spoken hybrid magnet element arranged asymmetrically, the reluctance torque (Tr) can be improved and the maximum torque approximation angle can be optimized to improve the torque density. Fig. 1(b) shows the sensitivity analysis results of key parameters and the optimal solution. The improvement of torque capabilities and anti-demagnetization ability is shown in Fig. 2, which verifies the validity of the proposed optimal method. III. Verification by FEM and Experimental Results In order to further verify the feasibility of the motor topology and the effectiveness of the proposed optimal method, an experimental prototype is fabricated, and more detailed electromagnetic performance analysis and experimental results will be presented in the full paper.

**References:**

Xianxian Zeng , Li Quan, Xiaoyong Zhu, et al., Investigation of an asymmetrical rotor hybrid permanent magnet motor for approaching maximum output torque. IEEE Trans. Appl. Supercond., 2019, vol. 29, no. 2, Article No. 0602704. Qian Chen, Gaohong Xu, Guohai Liu, et al., Reduction of torque ripple caused by slot harmonics in FSCW spoke-type FPM motors by assisted poles, IEEE Trans. Ind. Electron., 2020, Vol. 67, No. 11, pp. 9613-9622. Xiaoyong Zhu, Deyang Fan, Zixuan Xiang, et al., Systematic multi-level optimization design and dynamic control of less-rare-earth hybrid permanent magnet motor for all-climatic electric vehicles. Appl. Energy, 2019, 253, 113549. B.Ma, G. Lei, J. Zhu,Y. Guo, et al., Application-oriented robust design optimization method for batch production of permanent-magnet motors, IEEE Trans. Ind. Electron., vol. 65, no. 2, pp. 1728-1739, Feb. 2018.

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The asymmetric-hybrid-PM machine structure and the optimal design.

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The performance improvement of the proposed machine.

 Optimization of a New Asymmetric-hybrid-PM Machine with High Torque Density and Low Torque Ripple Considering the Difference of Magnetic Materials

I. INTRODUCTION This paper proposed a new flux-concentrating rotor for PM machine, taking advantages of spoke-type and Halbach array PM flux-concentrating. As shown in Fig. 1 (a), it is the evolution of the proposed rotor. The upper part of tangentially magnetized magnets still remain the spoke-type flux-concentrating property, while the bottom tangentially magnetized magnets and the radially magnetized magnets form a primitive Halbach array [1] [2]. Since the ratio match tangentially/radially magnetized magnets directly affects the effect of flux-concentrating, as well as the saliency ratio and torque performance, this paper focuses on the optimization of the size of permanent magnets on the rotor on the basis of keeping the same amount of PMs and the polar arc coefficient. II. OPTIMAL DESIGN OF NEW FLUX-CONCENTRATING ROTOR Response surface method (RSM) is a set of statistical and mathematical techniques to find the “best fitted” response of the physical system through experiment or simulation [3]. In RSM, a polynomial model, called a fitted model, is generally constructed to represent the relationship between the performance and design parameters. As shown in Fig. 1 (a), it is the evolution of the proposed rotor. Ensuring the same volume of PM in three rotors, the new rotor was optimized. The geometric parameters of the new rotor are shown in Fig. 1 (b). In order to quantitatively compare with the motor whose pole-arc coefficient is 0.8, including in various electromagnetic characteristics. b is determined as 8 mm. The volume of PM is defined as (1). where p is pole pairs, l is stack length, m is the volume of PMs. The optimized objective is formulated to maximize the air-gap flux density under the constraint of keeping the PM volume. Tab. I shows electromagnetic analysis results under various combinations of lx and hy. The relationship between air-gap flux density and lx, hy is shown in Fig. 2 (a). Two optimized points are found, where the analysis result is better than the predicted value. The regression equations of air-gap flux density obtained by RSM analysis is as (2). As shown in Fig. 2 (b), the predicted value and the actual result maintain a high consistency. It can be concluded that the regression equation obtained by the RMS is reliable. As shown in Fig. 3, The result of optimization is to maximize the air-gap magnetic density. . lx is determined as 16.5 mm, and hy is determined as 3.75 mm. Fig. 4 shows the comparison of two rotors. The final optimized model is built by 2-D FEA, as shown in Fig.5. III. FEA AND EXPERIMENTAL VERIFICATION Tab. II gives the main parameters of optimized rotor. Fig. 6 (a) compares the air-gap flux density of the motors with optimized rotor and the original rotor. The air-gap flux density in the motor with optimized rotor is higher than that in the initial one. As shown in Fig. 6 (b), the line back electromotive force (EMF) of the motor with optimized rotor increases slightly due to the higher air gap flux density. Fig. 6 (c) shows the C-T relationship under maximum torque per ampere (MTPA) control and id=0 control. The results show that under MTPA control and id=0 control, the output torque of the optimized rotor is higher than the initial model. In Fig. 6 (d), the saliency ratio is higher in the optimized rotor than in the original one. so the flux-weakening ability is stronger. Considering the manufacturing process, the actual rotor structure is shown in Fig. 7 the shape of the radially magnetized PMs are rectangular. The stator, rotor and test platforms are shown in Fig. 8. Fig. 9 compares the experimental and FEA results. Fig. 9 (a) is the comparison between the experimental and analytical result about back EMF without load, Fig. 9 (b) shows the C-T relationship of the motors with original rotor and optimized rotor under MTPA control and the results present a high consistency and error is less than 2%. But the error is large in the relationship between experiment and analysis under id=0 control due to the reluctance torque is fully utilized with the large current. IV. CONCLUSION In this paper, a new flux-concentrating rotor for PM machines is designed to combing spoke-type IPM rotor and Halbach PM array The size parameters of PM of the new rotor are optimized by the response surface method for the maximum air-gap flux density and torque capacity considering the constant pole-arc coefficient and the volume of PM.The 72-slot/16-pole PM motor with the optimized rotor is developed by 2-D FEA and experiments. The experimental result the air-gap flux density is increased by 6.7%and the torque is increased by 7.5%.

**References:**

[1]Igor P. Wiltuschnig, Paulo R. Eckert, David G. Dorrell ,“A Study of the influence of quasi-Halbach arrays on a torus machine,” IEEE Trans. Magn.,.vol. 52, no. 7, pp. 1325-1328. July 2016. [2]M. M. Rahman, K.-T. Kim, and J. Hur, “Design and optimization of neodymium-free spoke-type motor with segmented wing-shaped PM,” IEEE Trans. Magn., vol. 50, no. 2, Feb. 2014, Art. ID 7021404. [3]Byeong-Hwa Lee;Jung-Pyo Hong;Jung-Ho Lee ,“Optimum Design Criteria for Maximum Torque and Efficiency of a Line-Start Permanent-Magnet Motor Using Response Surface Methodology and Finite Element Method,” IEEE Trans. Magn. .vol. 48, no. 2, pp. 863-866. Feb. 2012.

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 Design and Optimization of New Flux-Concentrating Rotors combining Halbach PM array and spoke-type IPM for PMSM

I. Introduction Interior permanent magnet (IPM) machines are very attractive for the electric vehicle (EV) traction applications due to its excellent performance such as high torque density, and good flux-weakening capability. The multi-layered magnet rotors are more and more adopted in IPM machines, such as the 2008 Lexus LS600H, 2012 Nissan Leaf, 2016 BMW i3, and 2017 Prius which are delta-shape and 2U-shape magnet configuration. A multi-objective tradeoff design method is proposed in a multi-layered IPM machine for EV applications. The multi-objective including the cogging torque, average torque at different loads, torque ripple at different loads, iron loss, and magnet eddy-current loss. Firstly, the single-objective according to the variation of rotor flux-barriers are investigated individually. It is hard to tradeoff design between them, because there have seven targets. Then, a novelty method synthesize the torque on different loads, torque ripple on different loads, and total iron loss which can reduce the targets number from seven to three. The center of gravity of the three points are selected as the eventual angles of rotor flux-barriers. Finally, the multi-layered IPM machine is prototyped and experimented to verify the tradeoff design results. II. Main Body Fig. 1(a) shows the multi-layered magnet configurations. The rib1-rib5 are the bridges and ribs, PMa2 - PMa3 are the angle of magnets, ba1 - ba3 are the angle of barriers. The magnets are inserted in the rotor barriers. Multi-layer magnet has adopted to enhancing saliency ratio for improving reluctance torque. The rated power of the machines is 48 kW, the continuous rated current (rated load) is 200 A, the maximum current (over load) is 400 A, and the maximum speed of the machines is 12000 r/min. The torque ripple is generated by the harmonic interaction of the stator magnetic force harmonic and the rotor magnetic field. It will also cause the vibration, and noise, affecting the comfort of passengers in the EV. In the design of IPM machines, it is desire to minimize the torque ripple. Not only just about the rated load, also about over load condition. The torque ripple at different loads according to the variation of ba3 and ba6 are shown in Fig. 2(a) and Fig. 2(b). The minimum torque ripple under rated load condition is located at point A. The minimum torque ripple under over load condition is located at point B. With different loads, the location of point A, and B are different. To considerate the overall torque ripple, synthesize the rated load, and the over load condition. In the design of IPM machines, it is desire to minimize the core loss and magnet eddy-current loss. The core loss and magnet eddy-current loss at 12000 r/min according to the variation of ba3 and ba6 are shown in Fig. 2(c) and Fig. 2(d). The minimum core loss is located at point C. The minimum magnet eddy-current loss is located at point D. Therefore, it is hard to achieve minimum core loss and magnet eddy-current loss simultaneously. In order to verify the results of the previous analysis, a prototype machine with multi-layered magnet rotor is manufactured. Fig. 1(b) shows photographs of the rotor. The FEA predicted and measured no-load phase EMF at 1500 r/min of multi-layered IPM machines are compared. It can be seen that the measured EMF waveforms consist of three steps corresponding to the pole-arc to pole-pitch ratios of three PM layers, which agrees well with the results of the FEA. The torque and efficiency are measured by a digital meter, the measured results are also agrees well with the results of the FEA. III. Conclusion This paper has presented a multi-objective tradeoff design method in a multi-layered IPM machine for EV traction applications. The novelty method synthesize the torque on different loads, torque ripple on different loads, and total iron loss, which can reduce the targets numbers. The selected of the center of gravity of the three targets can consider the global performances simultaneously, it is a reasonable tradeoff design. It is demonstrated that the effects of angles of rotor flux-barriers on torque ripple and core loss is significant. Therefore, rotor flux-barrier angles is an important issue in the design of multi-layered IPM machine. Finally, the prototype machine with multi-layered magnet rotor is fabricated and experimented.

**References:**

[1] Burak Ozpineci, “Oak Ridge National Laboratory Annual Progress Report for the Electric Drive Technologies Program,” Oak Ridge National Laboratory, ORNL/SR-2016/640, Oct. 2016. [2] Rodrigo Silva, Armin Salimi1, Min Li, “Visualization and Analysis of Tradeoffs in Many-Objective Optimization: A Case Study on the Interior Permanent Magnet Motor Design, ” IEEE Trans. Magn., vol. 52, no. 3, pp. 8102404, Mar. 2016.

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 Multi-Objective Tradeoff Designs of Rotor Flux-Barrier in a Multi-layered IPM Machines for EV Applications

I. Introduction There has been a growing demand for permanent magnet electric machines with high torque and power density per unit current. Furthermore, electric machines are increasingly required to have high efficiency by regulation of energy efficiency. Many optimization algorithms are being studied to achieve high efficiency of IPMSM. Practically, manufactured electric machines can’t expect high performance for all products due to material deviations and dimensional tolerances. Therefore, we must consider the problems that occur while manufacturing to perform an optimization algorithm. However, considering the manufacturing tolerances along with many of the design variables of IPMSM requires a lot of time and cost. Therefore, we propose to apply multiple regression method to improve the performance of the conventional particle swarm optimization (PSO) algorithm. In addition, we can estimate the function formula for the design variables and derive the global solution by using estimated function formula. The convergence speed of the conventional PSO algorithm is improved by using the information of the solution obtained by performing the multiple regression. In addition, we will ensure the robustness of the design by estimating the appropriate regression equation for each design space. II. Particle Swarm Optimization with Multiple Regression Method Since the PSO algorithm finds the optimal solution using the information of each individual, the optimal solution can be found only when the particle moves. In this paper, multiple regression analysis is performed on the accumulation data obtained through the PSO algorithm. Then, an approximate solution can be obtained by using multiple regression. PSO with multiple regression algorithm has the same main loop as conventional PSO algorithm. First, initial particles are created with random locations, and update the velocity and position to find the global solution every iteration. If the amount of data for multiple regression is considered to be sufficient, then regression analysis is performed. We iterate this process until we reach the defined objective function. We selected seven numerical test functions to validate the proposed algorithm. The data obtained from performing the PSO algorithm is used to construct the Multiple Regression Model. Multiple regression is performed within the overall design space, and the result is a rough model. However, it is not a problem because it is used to improve the convergence speed. III. Robust Design Optimization of IPMSM A robust solution is the solution that has the lowest variability of the objective function in the design space that meets the requirements of the objective function. Constraints are needed to solve the problem of finding a robust solution. Constraints are obtained through multiple regression analysis. In particular, in order to consider the variability of design variables, the surrogate model must be configured in all solutions to find a robust solution. However, multiple regression analysis over the entire design space can improve the convergence of the algorithm, but it is challenging to construct an accurate surrogate model. Therefore, we used a method of reducing the design space into limited space that can be explained by multiple regression. A detailed procedure to find a robust solution is as follows. First, perform the modified PSO algorithm to save the data of the particles and find the first solution. When finding a solution, convergence speed is improved by performing multiple regression in the total design space. Second, Construct a multiple regression model around the first solution. The construct region of the multiple regression model limits the region to the adjusted coefficient of determination above 0.95. Multiple regression models verify the variability of the objective function. Third, the first and second process is repeated except for the multiple regression areas obtained in the second section. This procedure is repeated to the extent that it does not violate the constraints of the objective function. We have applied the proposed algorithm to the robust design optimization of IPMSM. We considered the variability of the objective function according to manufacturing tolerances. Target model was selected as IPMSM with eight poles and 48 slots as the target model for driving a vehicle. The constraint condition is over 165 Nm of average torque at 3000 RPM and objective function is minimization of the torque ripple. The central case torque and central case torque ripple are the average torque and torque ripple at the reference point. The worst case torque and worst case torque ripple are the average torque and torque ripple at the design variable values that represent the largest variation within the manufacturing tolerances. As a result of optimization using proposed algorithm, global solution and robust solution were found as shown in Fig. 1, 2. The robust solution has smaller torque ripple variability in Fig. 1. however, global solutions are large variability when considering manufacturing tolerance in Fig. 2. The engineers have the problem of selecting a global solution with higher torque at a similar torque ripple level without considering manufacturing tolerances. However, considering manufacturing tolerances, engineers can choose a robust solution with low variability.

**References:**

B. D. S. G. Vidanalage, M. S. Toulabi, S. Filizadeh, IEEE Transactions on Energy Conversion., vol. 33, p.1547 (2018) C. Ma, L. Qu, IEEE Transactions on Energy Conversion., vol. 30, p.1144 (2015) J. Ou, Y. Liu, R. Qu, IEEE Transactions on Industrial Electronics., vol. 65, p.3772 (2018) J. H. Lee, J. Song, D. Kim, IEEE Transactions on Industrial Electronics., vol. 65, p.1791 (2018) B. Ma, G. Lei, C. Liu, IEEE Transactions on Magnetics., vol. 54, p.8102404 (2018)

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Average torque variability of robust solution

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Average torque variability of global solution

 Robust Design Optimization Based on Separated Surrogate Model Method for IPMSM

In this paper, a novel global search algorithm tornado optimization (TO) and its hybridization with pattern search method (PSM) are proposed to solve the multimodal optimization problem. The TO enhances capability of global searching with two strategies, intensification strategy and diversification strategy. The hybridization with PSM supports the exact and fast convergence on adjacent optima from the points that are discovered in global search using TO. Outstanding performance of the proposed algorithm is verified by comparison with niching genetic algorithm at the test function and the algorithm is applied to the optimal design of the interior permanent magnet synchronous motor for electric vehicle. I. Introduction To analyze the accurate characteristics of the electric motors for electric vehicle (EV), finite element method (FEM) analysis, which takes a lot of time, is required because of the nonlinear magnetic saturation of the motors [1]. Computational problem of FEM becomes worse when it is applied to the multimodal optimization problem, such as an optimal design of motor. To solve this problem, several algorithms such as niching genetic algorithm (NGA) have been studied. The NGA is an improved algorithm of GA for the multimodal function [2]. However, the NGA still have a problem with calculation time because it takes a lot of function calls to converge to the accurate peak point [3]. To reduce the number of function calls and to enhance the convergence characteristic, this paper proposes the tornado optimization (TO) hybridized with pattern search method (PSM). The TO is an algorithm to search overall area and to designate some points as candidates for several optima. The performance of the algorithm is maximized with the usage of the PSM, which is a kind of deterministic algorithm. II. TORNADO OPTIMIZATION WITH PSM In hybrid algorithm for the multimodal function, adopting strategy and role sharing of each search algorithm are important. Global search algorithm adopts diversification strategy to search overall area and to find undiscovered candidates. On the other hand, local search algorithm converges candidates to each adjacent optimum quickly and precisely by adopting intensification strategy [4]. In TO, the processes of being sucked into tornadoes and searching the opposite side by Zone 1 are employed as intensification strategy. On the other hand, thunder strike of Zone 2 is used as a diversification strategy to prevent particles from being trapped in a local optimum. First, the superior initial particles are generated by Latin hypercube sampling (LHS), which scatters samples evenly, and search each location [5]. With their results, tornadoes occur with their own zones. The rest of particles are sucked into tornado. When they enter the zone of tornado, they will be moved in two ways. As seen in Fig. 1, if they enter in Zone 1 which is the half of the zone, they are swept away by tornado and fly to the opposite side of the tornado. On the other hand, if they enter in Zone 2 which is the inside of the zone, they will be scattered outside the tornado, just as thunder strikes from inside to outside of the real tornado. They will continue to be sucked into the tornado at the relocated area. And then, the searched tornado extends its zone to the location of the absorbed particle. At the same time, the proportion of Zone 2 increases. Zone 1 reduces the number of function calls in advance before the PSM to be executed and helps to find optima hiding beyond the tornado. Zone 2 prevents meaningless re-discovery of discovered tornado and it helps to find new candidates that has not been found yet. In addition, expansion of Zone 2 increases the weight of thunder strikes instead of being swept away. It means that the proportion of diversification strategy increases with each iteration of the search. After repeating this process, new tornadoes occur in potentially optimal candidates recorded during the process. After enough tornadoes are created by TO, those candidates are converged to adjacent optimum by the PSM. The hybridization with the PSM makes TO to find the accurate peak point without being trapped to the local optima [3]. III. VERIFICATION OF PROPOSED ALGORITHM To verify the performance of the proposed algorithm, TO and NGA are applied to the mathematical test function. Test was carried out 100 times with each algorithm. As shown in Fig. 2, there is no doubt that the TO shows outstanding performance than the NGA. The Dstavg means the average distance from the found peak point to the actual peak point. When the function calls of TO and NGA are 1108 and 1380, respectively, the Dstavg of the TO is 72% less than the result of NGA. The TO consumed 19% less function calls than the NGA, even though the accuracy was higher. The application of the TO to the optimal design of the interior permanent magnet synchronous motor (IPMSM) will be covered in full paper. IV. CONCLUSION This paper introduces a novel hybrid algorithm on the purpose of both reducing function call and increasing accuracy of multimodal problem. The outstanding performance of the TO was confirmed through a test function, compared with NGA. The TO was applied to the optimal design for minimizing the cogging torque of IPMSM for EV and successfully derived the optimum model. Acknowledgement This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (Ministry of Science and ICT) (No. 2019R1F1A1061132).

**References:**

[1] M. Caruso, A. O. Di Tommaso, L. Ferraris, 2017 Twelfth International Conference on Ecological Vehicles and Renewable Energies (EVER)(2017) [2] B.-K. Son, G.-J. Park, J.-W. Kim, IEEE Trans. Magnetics., vol.52, No.3 (2016) [3] Emanuele Dilettoso, Nunzio Salerno, IEEE Trans. Magnetics., vol.42, No.4, pp.1203-1206 (2006) [4] K. Lei, F. Wang, Y. Qiu, Proc. Auto. Decentralized Syst. (ISADS), pp. 513–519 (2005) [5] Y.-R. Kang, J.-C. Son, D.-K. Lim, IEEE Access., vol.8, pp. 117405-117412 (2020)

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Fig 1. Concept of Tornado Optimization

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Fig 2. Result of test function. (a) TO, (b) NGA

 Tornado Optimization with Pattern Search Method for Optimal Design of IPMSM

This paper focuses on designing a optimal novel structure for high power densitiy of a concentric winding integer slots permanent magnet synchronous motor(PMSM). This research shows the motor design possibility with a higher power density than a typical distributed winding model, within the same size. If the number of slots per phase per pole(NSPP) of PMSM is larger than 1, distributed windings are applied mostly. The distributed winding is a winding method that the number of turns is distributed into each slot according to NSPP. The distributed winding can make a sinusoidal magnetomotive force(MMF) waveform. Also, harmonics can be reduced. Distributed Windings can be classified into lap winding and concentric winding according to the number of pitch of each coil. In lap winding, the number of pitch of each coil is same. On the other hand, the number of pitch of each coil is different maintaining same center of each coil in concentric winding. The distinction between the winding methods is shown in Fig. 1. The concentric winding is divided into identical concentric winding and nonidentical concentric winding according to the number of each coil. Identical concentric winding is that the number of turns in each coil is identical. Nonidentical concentric winding, maintaining a sinusoidal waveform even if the number of turns in each coil is nonidentical, has the advantage of adjusting the number of turns in each coil can obtain a higher winding factor than the lap winding[1-3]. The winding factor is the determinant by the MMF at the air gap and is proportional to the fundamental amplitude of back electromotive force (BEMF)[4-5]. Consequently, the nonidentical concentric winding has potential to enhance a power density of motors according to winding factor. In general, all slots in the stator are the identical shape, so if each coil has a different number of turns, slot fill factors vary from each slot. As a result of slot fill factor differences, some slots are inefficient in utilizing space. It affects the BEMF's fundamental wave amplitude as well, which the output performance of the nonidentical concentric winding motors could be worse than the identical concentric winding one. To improve this problem, we need to design the structure of stator with optimization algorithm to make each slot shape efficiently. In this paper, we study about nonidentical slotted concentric winding in the following ways. A concentric winding integer slots model is selected with 3-phase 4-pole 24-slots PMSM that NSPP is 2. the winding factors of identical concentric winding type and various nonidentical concentric winding types are calculated and compared in case of the number of turns distribution for nonidentical one. nonidentical concentric winding is selected to the winding factor higher than identical concentric winding. For improving the above mentioned problem, a new structure of the stator, nonidentical slotted concentric winding, is optimized and designed. the winding factors of identical concentric winding type and various nonidentical concentric winding types are calculated and compared in case of the number of turns distribution for nonidentical one. Variable shown in Fig. 2. for algorithm is composed of factors which control a slot area. The purpose of optimization is power density and performance. Therefore, objective functions are average torque and torque ripple, and they are minimized as the following two objective function equations. obj1= 1/Tavg obj2= Te, ripple = (Te,max-Te,min)/Te * 100 Te, avg is the average torque and Te, ripple is the torque ripple ratio. Te, max and Te, min are the maximum and minimum of the instantaneous torque, respectively. Through a finite element analysis(FEA) of designed models, we ultimately compared the performance of motor models according to identical concentric winding, nonidentical concentric winding and nonidentical slotted concentric winding. Finally, we propose a novel structure of stator with each different slot areas and nonidentical concentric winding. it is called nonidentical slotted concentric winding. This research shows the motor design possibility with a higher power density than a typical distributed winding model, within the same size.

**References:**

[1] T.A.Lipo, "Introduction to AC Machine Design", University of Wisconsin, pp. 53-82, 2004. [2] M. M. Liwschitz, "Distribution Factors and Pitch Factors of the Harmonics of a Fractional-Slot Winding," in Transactions of the American Institute of Electrical Engineers, vol. 62, no. 10, pp. 664-666, Oct. 1943. [3] G. R. Slemon, A. Straughen “Electric Machines” University of Toronto, pp. 369-383, 1980. [4] Wen Ouyang, A. El-Antably, Surong Huang and T. A. Lipo, "Analysis of optimal stator concentric winding patterns design," 2005 International Conference on Electrical Machines and Systems, Nanjing, vol. 1, pp. 94-98, 2005. [5] J.R. Hendershot, T.J.E.Miller, “Design of Brushless Permanent-Magnet Machines” Magna Physics Publishing & Oxford University Press, pp. 180-181, 2010 [6] J. H. Lee, J. Kim, J. Song, Y. Kim and S. Jung, "A Novel Memetic Algorithm Using Modified Particle Swarm Optimization and Mesh Adaptive Direct Search for PMSM Design," in IEEE Transactions on Magnetics, vol. 52, no. 3, pp. 1-4, March, 2016.

**Images:**

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