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轴向磁通永磁同步电机多层准三维等效模型研究
Multi-layer Quasi Three-dimensional Equivalent Model of Axial-Flux Permanent Magnet Synchronous Machine
Author：Mingjie He; Weiye Li; Jun Peng; Jiangtao Yang
DOI: 10.30941/CESTEMS.2021.00002
https://ieeexplore.ieee.org/document/9393746
A multi-layer quasi three-dimensional equivalent model of the AFPMSM is investigated in this paper, which could take the end leakage into consideration. Firstly, the multi-layer quasi three-dimensional equivalent model of the AFPMSM with single stator and single rotor is derived in details, including the equivalent processes and conversions of structure dimensions, motion conditions and electromagnetic parameters. Then, to consider the influence of end leakage on the performance, a correction factor is introduced in the multi-layer quasi three-dimensional equivalent model. Finally, the proposed multi-layer quasi three-dimensional equivalent model is verified by the 3D FEM based on an AFPMSM under different structure parameters. It demonstrates that the errors of flux linkage and average torque obtained by the multi-layer quasi three-dimensional equivalent model and 3D FEM are only around 2% although the structure parameters of the AFPMSM are varied. Besides, the computation time of one case based on the multi-layer quasi three-dimensional equivalent model is only 6 min, which is much less than that of the 3D FEM, 1.8 h, under the same conditions.
Firstly, a multi-layer quasi three-dimensional equivalent model of the AFPMSM, which could take the end leakage into consideration, is proposed. Secondly, the proposed multi-layer quasi three-dimensional equivalent model is verified by the 3D FEM based on an AFPMSM under different structure parameters.
A. Equivalent Process
The equivalent process of the multi-layer quasi three-dimensional equivalent model is illustrated in Fig. 1. The main steps of the equivalent process are given as follows.
Step1: Divide the AFPMSM into several layers along the radial direction. Thus, each layer could be regarded as a small AFPMSM.
Step2: Unfold each layer along the circumference direction and several linear machines with three-dimensional structures can be obtained.
Step3: Establish the two-dimensional equivalent models for the linear machines obtained by Step2, as shown in Fig. 2.
Step4: Analyze the performance indexes of the linear machines using 2D FEM based on the two-dimensional equivalent models established in Step3. Then, the performance indexes of the AFPMSM can be obtained by adding those of the linear machines together.
Fig. 1. Equivalent process of the quasi three-dimensional equivalent model.
Fig. 2. Equivalent linear machine.
B. Correction Factor and Calculation of Leakage Permeance
The correction factor considering the effect of end leakage flux is defined and can be calculated based on Fig. 3, as given by
where Λpm , Λg and Λend as the permeances of PM, air gap and end leakage magnetic circuit under one PM pole, respectively, Λmm as the leakage permeance between the adjacent PMs, Λmr as the leakage permeance between the PM and rotor yoke of one side.
(a) Magnetic circuit
(b) Equivalent model
Fig. 3. Magnetic circuit of PM and the equivalent model.
C. Verification
To verify the effectiveness of the proposed multi-layer quasi three-dimensional equivalent model, the comparison of the flux linkage and average torque calculated by the proposed equivalent model and 3D FEM is made under different structure parameters, as given by Fig. 4. It could be found that the flux linkage and torque errors between the results calculated by the equivalent model and 3D FEM would be smaller than 2% when the number of layers N is larger than four.
(a)
(b)
(c)
(d)
(e)
(f)
Fig. 4. Flux linkage and torque calculated by the proposed equivalent model and 3D FEM. (a). Flux linkage under different airgap length. (b). Flux linkage under different split ratio. (c). Flux linkage under different pole arc coefficient of PM. (d). Average torque under different airgap length. (e). Average torque under different split ratio. (f). Average torque under different pole arc coefficient of PM.
D. Computation Time
The computation time of one case based on the multi-layer quasi three-dimensional equivalent model and 3D FEM is given in Table I. It could be found that the computation time for the equivalent model is about 6 min, which is much less than that of the 3D FEM, 1.8 h.
Table I
Simulation Time
This paper has proposed and investigated the multi-layer quasi three-dimensional equivalent model of the AFPMSM with single stator and single rotor. It indicates that the errors between the analysis results obtained by the multi-layer quasi three-dimensional equivalent model and 3D FEM are only around 2% when the number of layers N is larger than four. Besides, the computation time of one case based on the multi-layer quasi three-dimensional equivalent model, 6 min, is much less than that of the 3D FEM, 1.8 h, under the same conditions. Thus, the proposed multi-layer quasi three-dimensional equivalent model can be used to analyze and optimize the AFPMSM and much time could be saved by this method compared with the 3D FEM.
引用本文
M. He, W. Li, J. Peng and J. Yang, "Multi-layer quasi three-dimensional equivalent model of axial-flux permanent magnet synchronous machine," in CES Transactions on Electrical Machines and Systems, vol. 5, no. 1, pp. 3-12, March 2021.
doi: 10.30941/CESTEMS.2021.00002.
本文作者
Mingjie He received the B.E. degree from the School of Hydropower & Information Engineering, Huazhong University of Science and Technology, Wuhan, China, in 2014. He received the Ph.D. degree with the State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, China, in 2019.
He is now working at the CRRC Zhuzhou Institute CO., LTD. His current research interest includes the design of doubly salient permanent magnet machine, axial flux permanent magnet machine, hybrid excited machine and magnetic gear.
Weiye Li received the B.E. degree from the School of Automation and Information Engineering, Xi'an University of Technology, Xi'an, China, in 2009. He received the M.E. degree from the School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, China, in 2012.
He has joined the CRRC Zhuzhou Institute CO., LTD from 2012 and he has been engaged in the research and product development of permanent magnet machine.
Jun Peng received the B.Eng. degree in mechanical design from Huazhong Agricultural University, Wuhan, China, in 2007, and the M.Sc. degree in electrical engineering from Huazhong University of Science and Technology, Wuhan, China, in 2016.
Since 2007, he has been with CRRC Zhuzhou Institute Co., Ltd., Changsha, China. His major research interests include design and application of permanent magnet machine for electrical vehicle application.
Jiangtao Yang (S’18-M’19) received the B.E. degree from the Wuhan University of Technology, Wuhan, China, in 2014, and the Ph.D. degree from the Huazhong University of Science and Technology, Wuhan, in 2019, both in electrical engineering.
He is currently an Assistant Professor with the College of Electrical and Information Engineering, Hunan University, Changsha, China. His research interests include the design and analysis of high-speed electrical machine, pulsed alternator, and flywheel energy storage system.
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