Fast Calculation of AC Losses in Flat Wire Windings Based on Finite Element Reduced Order Generalization Method
Wang Yao1, Cheng Yuan1, Gao Bo1, Li Yukuan2, Cui Shumei1
1. School of Electrical Engineering and Automation Harbin Institute of Technology Harbin 150001 China; 2. Global R&D Center of China FAW Corporation Limited Changchun 130000 China;
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.
王耀, 程远, 高博, 李育宽, 崔淑梅. 基于有限元降阶泛化的扁线绕组交流损耗快速计算方法[J]. 电工技术学报, 2025, 40(18): 5832-5844.
Wang Yao, Cheng Yuan, Gao Bo, Li Yukuan, Cui Shumei. Fast Calculation of AC Losses in Flat Wire Windings Based on Finite Element Reduced Order Generalization Method. Transactions of China Electrotechnical Society, 2025, 40(18): 5832-5844.
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