Abstract:The double permanent-magnet vernier motor operates based on the bi-directional magnetic field modulation effect principle. With the improvement of torque density, there is a problem of significant motor loss. By taking the rated point as the optimization object, the traditional optimization method can only improve the performance of the rated operating point, but has difficulty in efficiently operating multiple working points under the actual operation condition of the motor. Therefore, this paper designs a low-loss modular dual permanent-magnet vernier motor and proposes a multi-operating points optimization method considering operation condition. The representative working points and their weights are extracted using the K-clustering method. To make the optimization procedure more efficient, the sensitivity analysis method is used to qualitatively optimize the variables to reduce the design space. The optimal global solution of susceptible parameters is determined by combining the response surface method and high-convergence multi-objective differential evolution with a ranking-based mutation operator (MODE-RMO). And then, an efficient and accurate motor parameter optimization under operation condition is realized. The proposed method is verified by simulation and experiment.
[1] 颜建虎, 汪盼, 费晨. 模块化开关磁阻式横向磁通电机设计与分析[J]. 中国电机工程学报, 2018, 38(22): 6723-6730. Yan Jianhu, Wang Pan, Fei Chen.Design and analysis of modular switch reluctance transverse flux machines[J]. Proceedings of the CSEE, 2018, 38(22): 6723-6730. [2] 张岳, 曹文平, John Morrow.电动车用内置式永磁电机(PMSM)设计[J]. 电工技术学报, 2015, 30(14): 108-115. Zhang Yue, Cao Wenping, Morrow J.Design of an interior permanent magnet synchronous motor (PMSM) for EV traction[J]. Transactions of China Electrotechnical Society, 2015, 30(14): 108-115. [3] Kwon J W, Kwon B I.Investigation of dual-stator spoke-type vernier machine for EV application[J]. IEEE Transactions on Magnetics, 2018, 54(11): 1-5. [4] 鲍晓华, 刘佶炜, 孙跃, 等. 低速大转矩永磁直驱电机研究综述与展望[J]. 电工技术学报, 2019, 34(6): 1148-1160. Bao Xiaohua, Liu Jiwei, Sun Yue, et al.Review and prospect of low-speed high-torque permanent magnet machines[J]. Transactions of China Electrotechnical Society, 2019, 34(6): 1148-1160. [5] 石玉君, 程子活, 蹇林旎. 两种典型的场调制型永磁电机的对比分析[J]. 电工技术学报, 2021, 36(1): 120-130. Shi Yujun, Cheng Zihuo, Jian Linni.Comparative analysis of two typical field modulated permanent- magnet machines[J]. Transactions of China Electro- technical Society, 2021, 36(1): 120-130. [6] 张邦富, 程明, 王飒飒, 等. 基于改进型代理模型优化算法的磁通切换永磁直线电机优化设计[J]. 电工技术学报, 2020, 35(5): 1013-1021. Zhang Bangfu, Cheng Ming, Wang Sasa, et al.Optimal design of flux-switching permanent magnet linear machine based on improved surrogate-based optimization algorithm[J]. Transactions of China Electrotechnical Society, 2020, 35(5): 1013-1021. [7] Xiang Zixuan, Zhu Xiaoyong, Quan Li, et al.Multilevel design optimization and operation of a brushless double mechanical port flux-switching permanent-magnet motor[J]. IEEE Transactions on Industrial Electronics, 2016, 63(10): 6042-6054. [8] Zhang Jingwei, Wang Honghua, Chen Ling, et al.Multi-objective optimal design of bearingless switched reluctance motor based on multi-objective genetic particle swarm optimizer[J]. IEEE Transa- ctions on Magnetics, 2018, 54(1): 1-13. [9] Zhu Xiaoyong, Xiang Zixuan, Quan Li, et al.Multimode optimization design methodology for a flux-controllable stator permanent magnet memory motor considering driving cycles[J]. IEEE Transa- ctions on Industrial Electronics, 2018, 65(7): 5353-5366. [10] Zhou Xue, Zhu Xiaoyong, Wu Wenye, et al.Multi- objective optimization design of variable-saliency- ratio PM motor considering driving cycles[J]. IEEE Transactions on Industrial Electronics, 2021, 68(8): 6516-6526. [11] Diao Kaikai, Sun Xiaodong, Lei Gang, et al.System- level robust design optimization of a switched reluctance motor drive system considering multiple driving cycles[J]. IEEE Transactions on Energy Conversion, 2021, 36(1): 348-357. [12] Carraro E, Morandin M, Bianchi N.Traction PMASR motor optimization according to a given driving cycle[J]. IEEE Transactions on Industry Applications, 2016, 52(1): 209-216. [13] 林俐, 潘险险, 张凌云, 等. 基于免疫离群数据和敏感初始中心的K-means算法的风电场机群划分[J]. 中国电机工程学报, 2016, 36(20): 5461-5468, 5722. Lin Li, Pan Xianxian, Zhang Lingyun, et al.The K-means clustering algorithm for wind farm based on immune-outlier data and immune-sensitive initial center[J]. Proceedings of the CSEE, 2016, 36(20): 5461-5468, 5722. [14] Xu Liang, Zhao Wenxiang, Wu Mengmeng, et al.Investigation of slot-pole combination of dual- permanent-magnet-excited vernier machines by using air-gap field modulation theory[J]. IEEE Transactions on Transportation Electrification, 2019, 5(4): 1360-1369. [15] Dajaku G, Xie Wei, Gerling D.Reduction of low space harmonics for the fractional slot concentrated windings using a novel stator design[J]. IEEE Transa- ctions on Magnetics, 2014, 50(5): 1-12. [16] 刘永锋, 徐磊, 朱孝勇, 等. 基于多运行区域的磁场增强型内置永磁电机电流分段控制研究[J]. 中国电机工程学报, 2021, 41(10): 3611-3619, 3685. Liu Yongfeng, Xu Lei, Zhu Xiaoyong, et al.Research on current segment control of flux-intensifying interior permanent magnet motor based on multi- operating region[J]. Proceedings of the CSEE, 2021, 41(10): 3611-3619, 3685. [17] Zhao Wenxiang, Yao Tian, Xu Liang, et al.Multi- objective optimization design of a modular linear permanent-magnet vernier machine by combined approximation models and differential evolution[J]. IEEE Transactions on Industrial Electronics, 2021, 68(6): 4634-4645. [18] 刘国海, 王艳阳, 陈前. 非对称V型内置式永磁同步电机的多目标优化设计[J]. 电工技术学报, 2018, 33(增刊2): 385-393. Liu Guohai, Wang Yanyang, Chen Qian.Multi- objective optimization of an asymmetric V-shaped interior permanent magnet synchronous motor[J]. Transactions of China Electrotechnical Society, 2018, 33(S2): 385-393. [19] Zhao Wenxiang, Ma Anqi, Ji Jinghua, et al.Multiobjective optimization of a double-side linear vernier PM motor using response surface method and differential evolution[J]. IEEE Transactions on Industrial Electronics, 2020, 67(1): 80-90. [20] Xiang Zixuan, Pu Weiling, Zhu Xiaoyong, et al.Design and analysis of a V-shaped permanent magnet vernier motor for high torque density[J]. CES Transactions on Electrical Machines and Systems, 2022, 6(1): 20-28. [21] 赵玫, 于帅, 邹海林, 等. 聚磁式横向磁通永磁直线电机的多目标优化[J]. 电工技术学报, 2021, 36(17): 3730-3740. Zhao Mei, Yu Shuai, Zou Hailin, et al.Multi- objective optimization of transverse flux permanent magnet linear machine with the concentrated flux mover[J]. Transactions of China Electrotechnical Society, 2021, 36(17): 3730-3740. [22] 罗玉涛, 卢若皓. 基于结构参数分级优化的电机电磁噪声抑制[J]. 电工技术学报, 2021, 36(14): 2957-2970. Luo Yutao, Lu Ruohao.Hierarchical optimization of structural parameters for motor electromagnetic noise suppression[J]. Transactions of China Electrotechnical Society, 2021, 36(14): 2957-2970. [23] Du Longxin, Liu Xiping, Fu Jiesheng, et al.Design and optimization of reverse salient permanent magnet synchronous motor based on controllable leakage flux[J]. CES Transactions on Electrical Machines and Systems, 2021, 5(2): 163-173. [24] Ren Ziyan, Sun Yuan, Peng Baoyang, et al.Optimal design of electrical machines assisted by hybrid surrogate model based algorithm[J]. CES Transa- ctions on Electrical Machines and Systems, 2020, 4(1): 13-19. [25] 李雄松, 崔鹤松, 胡纯福, 等. 平板型永磁直线同步电机推力特性的优化设计[J]. 电工技术学报, 2021, 36(5): 916-923. Li Xiongsong, Cui Hesong, Hu Chunfu, et al.Optimal design of thrust characteristics of flat-type permanent magnet linear synchronous motor[J]. Transactions of China Electrotechnical Society, 2021, 36(5): 916-923. [26] 张文晶, 徐衍亮, 李树才. 新型盘式横向磁通永磁无刷电机的结构原理及设计优化[J]. 电工技术学报, 2021, 36(14): 2979-2988. Zhang Wenjing, Xu Yanliang, Li Shucai.Structure principle and optimization of a novel disk transverse flux permanent magnet brushless motor[J]. Transa- ctions of China Electrotechnical Society, 2021, 36(14): 2979-2988. [27] Pan Zhenbao, Fang Shuhua, Wang Hui.LightGBM technique and differential evolution algorithm-based multi-objective optimization design of DS-APMM[J]. IEEE Transactions on Energy Conversion, 2021, 36(1): 441-455.