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| Semi Analytical and Efficient Calculation Method of Eddy Current Loss in Windings of Permanent Magnet Machines Based on Fast Finite Element Method |
| Cao Longfei, Fan Xinggang, Li Dawei, Qu Ronghai, Liu Jingyi |
| State Key Laboratory of Advanced Electromagnetic Engineering and Technology Huazhong University of Science and Technology Wuhan 430074 China |
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Abstract Winding eddy current loss is the main component of AC copper loss of permanent magnet machines, and its estimation is an important step in machine design. In the traditional design process, the estimation of winding eddy current loss is generally based on 2D finite element method (FEM) simulation, but it is inevitable to model the conductors and divide them into dense meshes, which will take a lot of computing time. Another method is analytical calculation. Although this method is not time-consuming, the nonlinear characteristic of the ferromagnetic material cannot be considered, and it will result in low calculation accuracy. To achieve a balance between calculation speed and accuracy, this paper studies the generation mechanism of winding eddy current loss of permanent magnet machines, and proposes a semi-analytical algorithm to calculate the winding eddy current loss. On the one hand, the analytical algorithm only depends on slot magnetic leakage flux density, so it is not necessary to establish the conductor model in the FEM model. To further reduce the time cost, the fast FEM is used to extract and reconstruct the slot magnetic leakage flux density. On the other hand, the slot magnetic leakage flux density obtained by FEM has high fidelity, and the analytical algorithm considering high-frequency demagnetization effect in conductor is applied, thus improving the calculation accuracy of winding eddy current loss.
Firstly, the reconstruction algorithm of slot magnetic flux leakage is derived based on the fast FEM theory and the slot/pole configuration of the permanent magnet machine, and the conductor layout model is established to obtain the conductor coordinates. Secondly, the machine FE model without conductors is established, and 1/6 electrical period simulation is carried out. The slot magnetic leakage flux density is extracted based on conductor coordinate, and the entire electrical period slot magnetic leakage flux density is reconstructed. Finally, fast Fourier transform (FFT) is performed for the slot magnetic leakage flux density, and each harmonic magnetic flux density is substituted into the high-frequency analytical algorithm to solve eddy current loss. The total winding eddy current losses can be obtained by summing the losses caused by all harmonic magnetic densities of all conductors.
The proposed semi-analytical method based on fast FEM is implemented by established simulation platform based on Matlab and open source finite element software FEMM, and a 12-slot, 10-pole surface permanent magnet machine was used to verify the proposed method. Firstly, compared with the simulation results obtained by traditional commercial finite element software, the calculation speed of the proposed method is improved by nearly 100 times, and the errors are less than 4% within 50kHz. Secondly, the effectiveness of proposed method is verified through experiments, to separate the winding eddy current loss conveniently, only the stator is used for experimental research. The winding eddy current loss below 5kHz is separated by directly measuring the input power, while the eddy current loss above 5kHz is indirectly characterized by measuring the Rac/Rdc by LCR meter due to the limit of the highest frequency (5kHz) output of the sinusoidal power supply device. The experimental results show that the error of winding eddy current loss calculated by proposed method is generally within 5%, and the maximum error is 6.9% at 50kHz.
The semi-analytical method based on fast FEM proposed in this paper only focuses on the efficient calculation of winding eddy current loss. For multi-stranded winding, it is necessary to study the efficient calculation method of circulating current loss in the future. In addition, the proposed method is only applicable to the machine with cylindrical winding, and the efficient calculation method of hair-pin winding eddy current loss remains to be studied.
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Received: 10 October 2021
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2023, Vol. 38 
