Analytical Magnetic Field Method of Permanent Magnet Synchronous Machine Considering Step-Skewed Magnets and Magnetic Slot Wedge
Zhang Shoushou1, Guo Siyuan2
1.Bangor College Central South University of Forestry and Technology Changsha 410018 China; 2.State Grid Hunan Electric Power Company Limited Research Institute Changsha 410007 China
Abstract：The use of step-skewed magnets along axis and magnetic slot wedge are two effective ways to reduce the torque ripple of permanent magnet synchronous machine. The magnetic field analytical model of the surface permanent magnet synchronous machine is established, taking into account the influence of step-skewed magnets and magnetic slot wedge. Aiming at the shortcomings of the current accurate subdomain magnetic field analytical model, the periodic boundary condition is introduced to resolve the general solution of the stator slot, magnetic slot wedge, air gap and permanent magnet four kinds of subdomains, so as to improve the computational efficiency of the analytical model and save computing resources. Based on the magnetic field analytical model, the back-EMF and electromagnetic torque are calculated considering the step-skewed magnets and magnetic slot wedge. Through the finite element simulation analysis, the correctness of the proposed method is verified.
张守首, 郭思源. 考虑分段斜极和磁性槽楔的永磁同步电机磁场解析方法[J]. 电工技术学报, 2019, 34(1): 11-22.
Zhang Shoushou, Guo Siyuan. Analytical Magnetic Field Method of Permanent Magnet Synchronous Machine Considering Step-Skewed Magnets and Magnetic Slot Wedge. Transactions of China Electrotechnical Society, 2019, 34(1): 11-22.
[1] 陈丽香, 解志霖, 王雪斌. 低速大转矩永磁电机的转子散热问题[J]. 电工技术学报, 2017, 32(7): 40-48.Chen Lixiang, Xie Zhilin, Wang Xuebin. The rotor heat dissipation problem of low speed and high torque permanent magnet motor[J]. Transactions of China Electrotechnical Society, 2017, 32(7): 40-48. [2] 高闯, 赵文祥, 吉敬华, 等. 低谐波双三相永磁同步电机及其容错控制[J]. 电工技术学报, 2017, 32(增刊1): 124-130. Gao Chuang, Zhao Wenxiang, Ji Jinghua, et al. Low harmonic dual three-phase permanent magnet synchronous motor and fault-tolerant control[J]. Transactions of China Electrotechnical Society, 2017, 32(S1): 124-130. [3] Tapia J A, Pyrhönen J, Puranen J, et al.Optimal design of large permanent magnet synchronous generators[J].IEEE Transactions on Magnetics, 2012, 49(1): 642-650. [4] 张岳, 王凤翔, 周浩, 等. 极槽匹配对直驱式永磁风力发电机性能的影响[J]. 电工技术学报, 2009, 24(6): 12-16. Zhang Yue, Wang Fengxiang, Zhou Hao, et al. Effect of pole number and slot number on performance of permanent magnet generator directly driven by wind turbine[J]. Transactions of China Electrotechnical Society, 2009, 24(6): 12-16. [5] 程辉, 杨克立, 王克军, 等. PMSG 风力发电系统转速估计算法的研究[J]. 电力系统保护与控制, 2016, 44(5): 24-29. Cheng Hui, Yang Keli, Wang Kejun, et al. Study on a rotor speed estimation algorithm of PMSG wind power system[J]. Power System Protection and Control, 2016, 44(5): 24-29. [6] 张彦兵, 谢文龙, 王伟, 等. 永磁直驱风机直流并网的启停控制[J]. 电力系统保护与控制, 2017, 45(13): 143-148. Zhang Yanbing, Xie Wenlong, Wang Wei, et al. Start/stop control of permanent magnet direct drive wind turbine on DC grid connection[J]. Power System Protection and Control, 2017, 45(13): 143-148. [7] 朱永彬, 林珍. 电动汽车用永磁同步电动机弱磁研究综述[J]. 电气技术, 2015, 16(10): 1-7. Zhu Yongbin, Lin Zhen. Summarization for flux-weakening performance of permanent magnet synchronous motors applied in electric vehicle[J]. Electrical Engineering, 2015, 16(10): 1-7. [8] Guemes J A, Iraolagoitia A M, Del Hoyo J I, et al. Torque analysis in permanent-magnet synchronous motors: a comparative study[J]. IEEE Transactions on Energy Conversion, 2011, 26(1): 55-63. [9] Islam R, Husain I, Fardoun A, et al.Permanent-magnet synchronous motor magnet designs with skewing for torque ripple and cogging torque reduction[J]. IEEE Transactions on Industry Applications, 2009, 45(1): 152-160. [10] 石松宁, 王大志. 消弱永磁驱动器齿槽转矩的斜极优化方法[J]. 电工技术学报, 2015, 30(11): 27-32. Shi Songning, Wang Dazhi. Magnet skewing optimization method for reducing cogging torque in permanent magnet drive[J]. Transactions of China Electrotechnical Society, 2015, 30(11): 27-32. [11] 李军, 刘颖, 许自贵, 等. 层压磁性槽楔的性能及其对电机性能的影响[J]. 中国电机工程学报, 2005, 25(16): 126-131. Li Jun, Liu Ying, Xu Zigui, et al. Properties of laminated magnetic wedge and their effects on characteristics of motors[J]. Proceedings of the CSEE, 2005, 25(16): 126-131. [12] 梁艳萍, 陈晶, 刘金鹏. 磁性槽楔对高压感应电动机电磁参数和性能的影响[J]. 电机与控制学报, 2010, 14(3): 1-5. Liang Yanping, Chen Jing, Liu Jinpeng. Influence of magnetic slot wedge on electromagnetic parameters and performance of high voltage induction motor[J]. Electric Machines and Control, 2010, 14(3): 1-5. [13] 薛易, 李伟力, 王立坤. 转子导磁导电槽楔材料对汽轮发电机参数和转子表面损耗影响的研究[J]. 中国电机工程学报, 2015, 35(7): 1768-1774. Xue Yi, Li Weili, Wang Likun. Study on influences of magnetic and electric conductive slot wedges on parameters of turbo-generators and losses on rotor surface[J]. Proceedings of the CSEE, 2015, 35(7): 1768-1774. [14] 张海军, 张京军, 高瑞贞. 采用磁性槽楔改善无刷直流电机的气隙磁场[J]. 华北电力大学学报, 2007, 34(3): 17-21. Zhang Haijun, Zhang Jingjun, Gao Ruizhen. Using magnetic slot wedge to improve the air-magnetic field of brushless direct current motor[J]. Journal of North China Electric Power University, 2007, 34(3): 17-21. [15] 何山, 王维庆, 张新燕, 等. 磁性槽楔对大型永磁风力发电机性能的影响[J]. 电力设备, 2008, 9(5): 53-56. He Shan, Wang Weiqing, Zhang Xinyan, et al. Effect of magnetic slot wedge on the performance of large permanent magnet wind power generator[J]. Electrical Equipment, 2008, 9(5): 53-56. [16] 雷银照. 关于电磁场解析方法的一些认识[J]. 电工技术学报, 2016, 31(19): 11-25. Lei Yinzhao. Reviews of analytical methods for electromagnetic fields[J]. Transactions of China Electrotechnical Society, 2016, 31(19): 11-25. [17] 林福, 左曙光, 毛钰, 等. 考虑电流谐波的永磁同步电机电磁振动和噪声半解析模型[J]. 电工技术学报, 2017, 32(9): 24-31. Lin Fu, Zuo Shuguang, Mao Yu, et al. Semi-analytical model of vibration and noise for permanent magnet synchronous motor considering current harmonics[J]. Transactions of China Electrotechnical Society, 2017, 32(9): 24-31. [18] Dubas F, Espanet C.Analytical solution of the magnetic field in permanent-magnet motors taking into account slotting effect: no-load vector potential and flux density calculation[J]. IEEE Transactions on Magnetics, 2009, 45(5): 2097-2109. [19] Zhu Z Q, Wu L J, Xia Z P.An accurate subdomain model for magnetic field computation in slotted surface-mounted permanent-magnet machines[J]. IEEE Transactions on Magnetics, 2010, 46(4): 1100-1115. [20] Lubin T, Mezani S, Rezzoug A.2-D exact analytical model for surface-mounted permanent-magnet motors with semi-closed slots[J]. IEEE Transactions on Magnetics, 2011, 47(2): 479-492. [21] 张凤阁, 陈进华, 刘光伟, 等. 面贴式异向旋转双转子永磁电机的磁场解析计算[J]. 电工技术学报, 2011, 26(12): 28-36. Zhang Fengge, Chen Jinhua, Liu Guangwei, et al. Analytical solution of magnetic field for surface-mounted permanent magnet machines with anti-rotation dual rotors[J]. Transactions of China Electrotechnical Society, 2011, 26(12): 28-36. [22] 李节宝, 井立兵, 周晓燕, 等. 表贴式永磁无刷电机直接解析计算方法[J]. 电工技术学报, 2012, 27(11): 83-88. Li Jiebao, Jing Libing, Zhou Xiaoyan, et al. Exact analytical method for surface-mounted permanent-magnet brushless motors[J]. Transactions of China Electrotechnical Society, 2012, 27(11): 83-88. [23] 郭思源, 周理兵, 齐歌. 双三相永磁同步电机电磁性能解析计算[J]. 电工技术学报, 2014, 29(5): 17-28.Guo Siyuan, Zhou Libing, Qi Ge. Analytical calculation of electromagnetic performance in dual three-phase permanent magnet brushless AC machines[J]. Transactions of China Electrotechnical Society, 2014, 29(5): 17-28. [24] Kalokiris G D, Kefalas T D, Kladas A G, et al.Special air-gap element for 2-D FEM analysis of electrical machines accounting for rotor skew[J]. IEEE Transactions on Magnetics, 2005, 41(5): 2020-2023. [25] Gysen B L J, Meessen K J, Paulides J J H, et al. 3-D analytical and numerical modeling of tubular actuators with skewed permanent magnets[J]. IEEE Transactions on Magnetics, 2011, 47(9): 2200-2212.
2019, Vol. 34 
