基于有限元降阶泛化的扁线绕组交流损耗快速计算方法

doi:10.19595/j.cnki.1000-6753.tces.241262

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Abstract Due to its excellent characteristics, such as low DC resistance, flat wire winding has become the mainstream technical solution for new energy vehicle drive motors. However, the complex AC loss calculation poses significant challenges in the design of flat wire winding motors. The accurate and rapid computation of losses in flat conductors is pivotal for electromagnetic optimization design, multi-physics coupling analysis, and cooling structure design. The finite element method (FEM) has high calculation accuracy, but its protracted solution time makes it unsuitable for rapid calculation requirements. Analytical methods have been proposed to solve the loss faster, but their application range and accuracy need to be improved. This paper introduces a reduced order model, integrating the proper orthogonal decomposition (POD) method with neural networks (NN) to enhance the generalization of magnetic field solutions.
Firstly, this study analyzes the analytical expression of eddy current losses in the conductor within the slot under the influence of an alternating magnetic field and refines the analytical formula for conductor end losses. The updated formula incorporates additional eddy current losses due to end magnetic leakage, enhancing the precision of flat wire winding loss calculations. Secondly, the reduced order method endowed with generalization capabilities is proposed. A neural network generalizes the magnetic fields at various operating points of the conductors based on the POD reduction algorithm. The NN model is integrated with the refined loss solution formula to compute the conductor losses. Finally, an experimental scheme is proposed for winding loss separation.
Compared with the FEM results, the average error of the magnetic field resolved by the proposed method is less than 0.008T, with the majority of errors falling below 0.002 T. The slot loss’s maximum relative error is less than 4.3% compared to two-dimensional (2D) FEM results, while the end loss is less than 6.2% compared to three-dimensional (3D) FEM. The simulation time of the 2D FEM and 3D models is 85 seconds and more than 30 hours, respectively. After the NN training, including the pre-processing of the input data file, the code running time of the proposed order reduction method is about 0.79 seconds. The proposed method is verified through winding loss separation experiments. The error between the experimental separation loss and analytical results is within 40 W, and the deviation is less than 8% at most operating points and less than 4% at operating points with high current values.
The following conclusions can be drawn. (1) Compared with the FEM, the speed of the proposed method is significantly improved. (2) The reduced order method has good generalization and meets the requirement of magnetic field reconstruction at different operating points. (3) This paper introduces a testing method for the loss separation of flat wire windings, achieving loss separation in flat wire windings.

Key words： Permanent magnet synchronous machine reduced order algorithm neural network flat wire winding semi-analytical algorithm

Received: 16 July 2024

PACS:

TM351

Fund:黑龙江省重点研发计划（JD22A002）和重庆市自然科学基金（cstc2021jcyj-msxmX1012）资助项目

Corresponding Authors: 程远男,1979年生,教授,博士生导师,研究方向为永磁同步电机稳健优化与高精度损耗分析、基于宽禁带器件的高功率密度电机控制器、高压高频扁线永磁同步电机轴电流抑制、复杂机电系统多物理建模技术。E-mail: chengyuan@hit.edu.cn

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Cite this article:

Wang Yao,Cheng Yuan,Gao Bo等. Fast Calculation of AC Losses in Flat Wire Windings Based on Finite Element Reduced Order Generalization Method[J]. Transactions of China Electrotechnical Society, 2025, 40(18): 5832-5844.

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[1] 王晓远, 高鹏, 赵玉双. 电动汽车用高功率密度电机关键技术[J]. 电工技术学报, 2015, 30(6): 53-59.
Wang Xiaoyuan, Gao Peng, Zhao Yushuang.Key technology of high power density motors in electric vehicles[J]. Transactions of China Electrotechnical Society, 2015, 30(6): 53-59.
[2] 王道涵, 彭晨, 王秀和. 电动汽车高性能永磁电机转矩脉动与电磁振动抑制方法研究[J]. 电气工程学报, 2021, 16(4): 42-50.
Wang Daohan, Peng Chen, Wang Xiuhe.Research on different design approaches to mitigate torque ripple and electromagnetic vibration for high-performance electric vehicle traction machine[J]. Journal of Electrical Engineering, 2021, 16(4): 42-50.
[3] 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.
[4] 王柄东, 王道涵, 王晓姬, 等. 交流调磁型永磁同步电机磁通协同调控最大转矩铜耗比控制[J]. 电工技术学报, 2024, 39(12): 3630-3645.
Wang Bingdong, Wang Daohan, Wang Xiaoji, et al.A maximum torque per copper loss control for AC flux-regulation permanent magnet synchronous motor with magnetic flux co-regulation[J]. Transactions of China Electrotechnical Society, 2024, 39(12): 3630-3645.
[5] 朱洒, 曾峰, 陆剑波, 等. 考虑PWM谐波损耗的车用扁线内嵌式永磁同步电机效率图简化工程计算[J]. 电工技术学报, 2022, 37(22): 5687-5703.
Zhu Sa, Zeng Feng, Lu Jianbo, et al.Simplified engineering calculation of efficiency map of interior permanent magnet synchronous machines with hairpin windings considering PWM-induced harmonic losses[J]. Transactions of China Electrotechnical Society, 2022, 37(22): 5687-5703.
[6] 崔刚, 熊斌, 顾国彪. 新能源汽车扁铜线绕组电机槽内绝缘等效导热系数分析与计算[J]. 电机与控制学报, 2022, 26(11): 1-13.
Cui Gang, Xiong Bin, Gu Guobiao.Analysis and calculation of equivalent thermal conductivity of slot insulation system of flat copper wire winding motor for new energy vehicle[J]. Electric Machines and Control, 2022, 26(11): 1-13.
[7] 史俊旭, 吴霜, 陈致初, 等. 电动汽车用扁线异步电机性能分析与计算[J]. 微电机, 2024, 57(4): 52-59.
Shi Junxu, Wu Shuang, Chen Zhichu, et al.Perfor-mance analysis and calculation of flat wire induction motors for electric vehicles[J]. Micromotors, 2024, 57(4): 52-59.
[8] 李响, 郭鹏涛, 丁远. 基于场路结合的大功率直线超声波电机压电-热-结构多物理场分析[J]. 电工技术学报, 2024, 39(2): 423-433.
Li Xiang, Guo Pengtao, Ding Yuan.Piezo-thermal-structure coupling analysis for high-power linear ultrasonic motor based on field-circuit combination method[J]. Transactions of China Electrotechnical Society, 2024, 39(2): 423-433.
[9] 于占洋, 胡旭阳, 李岩, 等. 新型强迫风冷散热结构在高功率密度外转子表贴式PMSM上应用分析[J]. 电工技术学报, 2023, 38(24): 6668-6678.
Yu Zhanyang, Hu Xuyang, Li Yan, et al.Application analysis of novel forced air-cooled in outer rotor surface-mounted PMSM with high power density[J]. Transactions of China Electrotechnical Society, 2023, 38(24): 6668-6678.
[10] 陶飞, 张辰源, 戚庆林, 等. 数字孪生成熟度模型[J]. 计算机集成制造系统, 2022, 28(5): 1267-1281.
Tao Fei, Zhang Chenyuan, Qi Qinglin, et al.Digital twin maturity model[J]. Computer Integrated Manu-facturing Systems, 2022, 28(5): 1267-1281.
[11] Du Bochao, Huang Wan, Cheng Yuan, et al.Fault diagnosis and separation of PMSM rotor faults using search coil based on MVSA and random forests[J]. IEEE Transactions on Industrial Electronics, 2024, 71(11): 15089-15099.
[12] Stoll R L.The analysis of eddy currents[M]. Clarendon, U K: Oxford, 1974.
[13] Pinhal D B, Gerling D.A review of the analytical calculation of the AC-resistance of armature windings[C]//2020 23rd International Conference on Electrical Machines and Systems (ICEMS), Hamamatsu, Japan, 2020: 906-911.
[14] Bellara A, Amara Y, Barakat G, et al.Two-dimensional exact analytical solution of armature reaction field in slotted surface mounted PM radial flux synchronous machines[J]. IEEE Transactions on Magnetics, 2009, 45(10): 4534-4538.
[15] Amara Y, Reghem P, Barakat G.Analytical prediction of eddy-current loss in armature windings of permanent magnet brushless AC machines[J]. IEEE Transactions on Magnetics, 2010, 46(8): 3481-3484.
[16] Zhang Wanjun, Jahns T M.Analytical model for predicting AC losses in form-wound machine windings due to stator current interactions[C]//2015 IEEE International Electric Machines & Drives Conference (IEMDC), Coeur d’Alene, ID, USA, 2015: 1131-1137.
[17] 王晓光, 尹浩, 余仁伟. 轴向磁通无铁心永磁电机多层矩形扁线绕组涡流损耗解析计算及优化[J]. 电工技术学报, 2023, 38(12): 3130-3140.
Wang Xiaoguang, Yin Hao, Yu Renwei.Analytical calculation and parameter optimization of eddy current loss for coreless axial flux permanent magnet synchronous machine with multilayer flat wire winding[J]. Transactions of China Electrotechnical Society, 2023, 38(12): 3130-3140.
[18] Preci E, Nuzzo S, Valente G, et al.Segmented hairpin topology for reduced losses at high-frequency operations[J]. IEEE Transactions on Transportation Electrification, 2022, 8(1): 688-698.
[19] Mlot A, Lukaniszyn M, Korkosz M.Influence of an end-winding size on proximity losses in a high-speed PM synchronous motor[C]//2015 Selected Problems of Electrical Engineering and Electronics (WZEE), Kielce, Poland, 2015: 1-6.
[20] Ju Xiaowei, Cheng Yuan, Du Bochao, et al.AC loss analysis and measurement of a hybrid transposed hairpin winding for EV traction machines[J]. IEEE Transactions on Industrial Electronics, 2023, 70(4): 3525-3536.
[21] Zhang Jian, Zhang Zhuoran, Xia Yiwen, et al.Thermal analysis and management for doubly salient brushless DC generator with flat wire winding[J]. IEEE Transactions on Energy Conversion, 2020, 35(2): 1110-1119.
[22] 王晓远, 黄旭东, 李天元. 高频供电条件下的PCB定子盘式永磁电机绕组优化设计[J]. 中国电机工程学报, 2021, 41(6): 1937-1946.
Wang Xiaoyuan, Huang Xudong, Li Tianyuan.Optimal design of winding of permanent magnet motor based on high frequency PCB stator[J]. Pro-ceedings of the CSEE, 2021, 41(6): 1937-1946.
[23] 曹龙飞, 范兴纲, 李大伟, 等. 基于快速有限元的永磁电机绕组涡流损耗半解析高效计算[J]. 电工技术学报, 2023, 38(1): 153-165.
Cao Longfei, Fan Xinggang, Li Dawei, et al.Semi analytical and efficient calculation method of eddy current loss in windings of permanent magnet machines based on fast finite element method[J]. Transactions of China Electrotechnical Society, 2023, 38(1): 153-165.
[24] Xiao D, Heaney C E, Mottet L, et al.A reduced order model for turbulent flows in the urban environment using machine learning[J]. Building and Environment, 2019, 148: 323-337.
[25] Far M F, Martin F, Belahcen A, et al.Real-time control of an IPMSM using model order reduction[J]. IEEE Transactions on Industrial Electronics, 2021, 68(3): 2005-2014.
[26] Mou Changhong, Koc B, San O, et al.Data-driven variational multiscale reduced order models[J]. Computer Methods in Applied Mechanics and Engineering, 2021, 373: 113470.
[27] Hannon B, Sergeant P, Dupré L.Computational-time reduction of Fourier-based analytical models[J]. IEEE Transactions on Energy Conversion, 2018, 33(1): 281-289.
[28] She Z, Liu Y, Cao W,et al.Full-parameter identi-fication of buck converter through bp-nn fitting explicit time-domain relationships[J]. IEEE Transa-ctions on Power Electronics, 2024, 39(6): 7560-7571.