Abstract：When calculating the rotor eddy current loss (RECL) by the existing two-dimensional accurate subdomain method, in order to facilitate the solution of the coefficient matrix, the influence of the eddy current reaction is usually ignored. For high-speed permanent magnet synchronous motors (HS-PMSM) powered by converters, the armature current contains a large number of time harmonics, and the eddy current reaction has a great influence on the RECL. Ignoring the eddy current reaction seriously affects the calculation accuracy. Based on the accurate subdomain method, an analytical model for RECL analysis in HS-PMSM is established by solving the diffusion equation including time derivative and conductor motion velocity in the active region. An equation is established in the slot opening considering the influence of the slot opening on the magnetic field to improve the calculation accuracy, and periodic boundary conditions are established using the periodicity of the motor to increase the calculation speed. Then, the eddy current loss changes caused by time-space harmonics are analyzed at different inverter switching frequencies and air gap lengths. Through a loss separation experiment of a 7.5kW amorphous alloy HS-PMSM, the comparison of the analytical results, the finite element results and experimental results verifies the analytical model.
佟文明, 侯明君, 孙鲁, 吴胜男. 基于精确子域模型的带护套转子高速永磁电机转子涡流损耗解析方法[J]. 电工技术学报, 2022, 37(16): 4047-4059.
Tong Wenming, Hou Mingjun, Sun Lu, Wu Shengnan. Analytical Method of Rotor Eddy Current Loss for High-Speed Surface-Mounted Permanent Magnet Motor with Rotor Retaining Sleeve. Transactions of China Electrotechnical Society, 2022, 37(16): 4047-4059.
[1] 沈建新, 韩婷, 尧磊, 等. 提高永磁体电阻率对降低高速永磁交流电机转子涡流损耗的有效性分析(英文)[J]. 电工技术学报, 2020, 35(9): 2074-2078. Shen Jianxin, Han Ting, Yao Lei, et al.Is higher resistivity of magnet beneficial to reduce rotor eddy current loss in high-speed permanent magnets AC machines?[J]. Transactions of China Electrotechnical Society, 2020, 35(9): 2074-2078. [2] 张凤阁, 杜光辉, 王天煜, 等. 高速电机发展与设计综述[J]. 电工技术学报, 2016, 31(7): 1-18. Zhang Fengge, Du Guanghui, Wang Tianyu, et al.Review on development and design of high speed machines[J]. Transactions of China Electrotechnical Society, 2016, 31(7): 1-18. [3] Ma Jie, Zhu Z Q.Optimal split ratio in small high speed PM machines considering both stator and rotor loss limitations[J]. CES Transactions on Electrical Machines and Systems, 2019, 3(1): 3-11. [4] Cheng Xin, Xu Wei, Du Guanghui, et al.Novel rotors with low eddy current loss for high speed permanent magnet machines[J]. CES Transactions on Electrical Machines and Systems, 2019, 3(2): 187-194. [5] Yamazaki K, Fukushima Y, Sato M.Loss analysis of permanent-magnet motors with concentrated windings- variation of magnet eddy-current loss due to stator and rotor shapes[J]. IEEE Transactions on Industry Applications, 2009, 45(4): 1334-1342. [6] Fu Xinghe, Xu Da, Lin Mingyao, et al.Calculation and analysis of rotor eddy current loss of permanent magnet-inductor hybrid excited synchronous gener- ator[J]. IEEE Transactions on Magnetics, 2013, 49(5): 2389-2392. [7] 高锋阳, 齐晓东, 李晓峰, 等. 部分分段Halbach永磁同步电机优化设计[J]. 电工技术学报, 2021, 36(4): 787-800. Gao Fengyang, Qi Xiaodong, Li Xiaofeng, et al.Optimization design of partially-segmented Halbach permanent magnet synchronous motor[J]. Transa- ctions of China Electrotechnical Society, 2021, 36(4): 787-800. [8] Ishak D, Zhu Z Q, Howe D.Eddy-current loss in the rotor magnets of permanent-magnet brushless machines having a fractional number of slots per pole[J]. IEEE Transactions on Magnetics, 2005, 41(9): 2462-2469. [9] Wang Jiabin, Atallah K, Chin R, et al.Rotor eddy- current loss in permanent-magnet brushless AC machines[J]. IEEE Transactions on Magnetics, 2010, 46(7): 2701-2707. [10] Zhu Z Q, Ng K, Schofield N, et al.Improved analytical modelling of rotor eddy current loss in brushless machines equipped with surface-mounted permanent magnets[J]. IEE Proceedings-Electric Power Applications, 2004, 151(6): 641-650. [11] 唐任远, 陈萍, 佟文明, 等. 考虑涡流反作用的永磁体涡流损耗解析计算[J]. 电工技术学报, 2015, 30(24): 1-10. Tang Renyuan, Chen Ping, Tong Wenming, et al.Analytical calculation of eddy current loss accounting for eddy current reaction[J]. Transactions of China Electrotechnical Society, 2015, 30(24): 1-10. [12] Zarko D, Ban D, Lipo T A.Analytical calculation of magnetic field distribution in the slotted air gap of a surface permanent-magnet motor using complex relative air-gap permeance[J]. IEEE Transactions on Magnetics, 2006, 42(7): 1828-1837. [13] Qazalbash A A, Sharkh S M, Irenji N T, et al.Rotor eddy loss in high-speed permanent magnet syn- chronous generators[J]. IET Electric Power Appli- cations, 2015, 9(5): 370-376. [14] Chiodetto N, Bianchi N, Alberti L.Improved analytical estimation of rotor losses in high-speed surface-mounted PM synchronous machines[J]. IEEE Transactions on Industry Applications, 2017, 53(4): 3548-3556. [15] Zhu Z Q, Wu Lijian, Xia Zhenping.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. [16] Wu Lijian, Zhu Z Q, Staton D, et al.Analytical modeling and analysis of open-circuit magnet loss in surface-mounted permanent-magnet machines[J]. IEEE Transactions on Magnetics, 2012, 48(3): 1234-1247. [17] Wu Lijian, Zhu Z Q, Staton D, et al.Analytical model for predicting magnet loss of surface-mounted per- manent magnet machines accounting for slotting effect and load[J]. IEEE Transactions on Magnetics, 2012, 48(1): 107-117. [18] Atallah K, Howe D, Mellor P H, et al.Rotor loss in permanent-magnet brushless AC machines[J]. IEEE Transactions on Industry Applications, 2000, 36(6): 1612-1618. [19] 孙权贵, 邓智泉, 张忠明. 基于齿槽效应的高速永磁电机转子涡流损耗解析计算[J]. 电工技术学报, 2018, 33(9): 1994-2004. Sun Quangui, Deng Zhiquan, Zhang Zhongming.Analytical calculation of rotor eddy current losses in high speed permanent magnet machines accounting for influence of slot opening[J]. Transactions of China Electrotechnical Society, 2018, 33(9): 1994-2004. [20] Pfister P D, Yin Xin, Fang Youtong.Slotted permanent- magnet machines: general analytical model of mag- netic fields, torque, eddy currents, and permanent- magnet power losses including the diffusion effect[J]. IEEE Transactions on Magnetics, 2016, 52(5): 1-13. [21] Chen Liang, Wang Jiabin, Nair S S.An analytical method for predicting 3-D eddy current loss in permanent magnet machines based on generalized image theory[J]. IEEE Transactions on Magnetics, 2016, 52(6): 1-11. [22] Nair S S, Wang Jiabin, Chin R, et al.Analytical prediction of 3-D magnet eddy current losses in surface mounted PM machines accounting slotting effect[J]. IEEE Transactions on Energy Conversion, 2017, 32(2): 414-423. [23] Nair S S, Wang Jiabin, Chen Liang, et al.Prediction of 3-D high-frequency eddy current loss in rotor magnets of SPM machines[J]. IEEE Transactions on Magnetics, 2016, 52(9): 1-10. [24] Tong Wenming, Li Shiqi, Pan Xuelong, et al.Analytical model for cogging torque calculation in surface-mounted permanent magnet motors with rotor eccentricity and magnet defects[J]. IEEE Transactions on Energy Conversion, 2020, 35(4): 2191-2200. [25] 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 mag- netic slot wedge[J]. Transactions of China Elec- trotechnical Society, 2019, 34(1): 11-22. [26] Gonzalez D A, Saban D M.Study of the copper losses in a high-speed permanent-magnet machine with form-wound windings[J]. IEEE Transactions on Industrial Electronics, 2014, 61(6): 3038-3045. [27] Tong Wenming, Li Shiqi, Sun Ruolan, et al.Modified core loss calculation for high-speed PMSMs with amorphous metal stator cores[J]. IEEE Transactions on Energy Conversion, 2021, 36(1): 560-569. [28] Sarri J.Thermal analysis of high-speed induction machines[D]. Finland: Helsinki University of Tech- nology, 1998. [29] Huang Ziyuan, Fang Jiancheng, Liu Xiquan, et al.Loss calculation and thermal analysis of rotors supported by active magnetic bearings for high-speed permanent-magnet electrical machines[J]. IEEE Transa- ctions on Industrial Electronics, 2016, 63(4): 2027-2035. [30] Brändlein J.Ball and roller bearings: theory, design, and application[M]. 3rd ed. Chichester: John Wiley, 1999.
2022, Vol. 37 
