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

Semi Analytical and Efficient Calculation Method of Eddy Current Loss in Windings of Permanent Magnet Machines Based on Fast Finite Element Method

随着永磁电机朝着高效化和轻质化方向发展,其功率密度和转速越来越高,使得绕组交流铜耗增加,从而导致电机局部过热、效率降低。该文以永磁电机为研究对象,着重研究绕组涡流损耗的产生机理及计算方法,提出基于快速有限元的绕组涡流损耗半解析算法。首先,介绍借助快速有限元提取槽漏磁的方法,并构建导体排布模型;其次,推导了导体涡流损耗的低频和高频解析计算方法,并通过搭建基于Matlab和开源有限元软件FEMM的仿真平台将提出的半解析方法予以实现,并与传统商用有限元软件仿真结果进行对比;最后,通过实验进一步验证了其准确性。结果表明,该方法的计算速度提高了近100倍,在较大频率范围内误差小于5%。

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 1/6electrical 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 R_(ac)/R_(dc) 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.