2026-08-08
Multi-Objective Optimization of Rare-Earth-Saving Permanent Magnet Generator with Asymmetric Poles Based on Sensitivity Analysis
By
Progress In Electromagnetics Research B, Vol. 118, 87-103, 2026
Abstract
To cut rare-earth consumption and suppress cogging torque of conventional symmetrical pole permanent magnet generators (PMGs), this paper presents a low-rare-earth composite asymmetric pole topology with hybrid NdFeB-ferrite magnets. The magnetic field modulation of permanent magnet magnetomotive force (MMF) is analyzed, and an energy-method cogging torque formula is derived to elaborate the flux-improving and torque-reducing mechanism of asymmetric poles. Equivalent magnetic circuit and finite element models are built, followed by stratified sensitivity analysis of structural parameters. Taking high induced electromotive force (EMF), low EMF THD, and small cogging torque as targets, magnet arc angle is optimized via an evolutionary algorithm coupled with TOPSIS; magnet width and thickness are further optimized for optimal cost-performance. After optimization, EMF fundamental amplitude rises; EMF THD and cogging torque drop; and NdFeB usage falls by 8.56%. Prototype tests verify the simulation accuracy. The hybrid magnet scheme saves rare-earth materials and enhances overall generator performance.
Citation
Yanhong Gao, Huihui Geng, Xingzhe Pang, Wenyu Li, Junfeng Wang, Xin Zhou, and Xingxv Jin, "Multi-Objective Optimization of Rare-Earth-Saving Permanent Magnet Generator with Asymmetric Poles Based on Sensitivity Analysis," Progress In Electromagnetics Research B, Vol. 118, 87-103, 2026.
doi:10.2528/PIERB26051102
References

1. Darwish, Ahmed, Mohamed A. Elgenedy, and Barry W. Williams, "A review of modular electrical sub-systems of electric vehicles," Energies, Vol. 17, No. 14, 3474, 2024.
doi:10.3390/en17143474        Google Scholar

2. Prakht, Vladimir, Vladimir Dmitrievskii, and Vadim Kazakbaev, "Analysis of performance improvement of passenger car synchronous homopolar generator with the addition of ferrite magnets," Applied Sciences, Vol. 13, No. 6, 3990, 2023.
doi:10.3390/app13063990        Google Scholar

3. Liu, J., X. Zhu, L. Quan, Z. Xiang, and C. Zhang, "Driving control research of less-rare-earth tooth yoke magnetomotive complementary doubly salient permanent magnet motors based on resonance compensation strategy," Proceedings of the CSEE, Vol. 37, No. 22, 6534-6542, 2017.
doi:10.13334/j.0258-8013.pcsee.171124        Google Scholar

4. Si, X., X. Zhu, Y. Zuo, Z. Xiang, and L. Xu, "Research on drive performance of the less-rare-earth hybrid-excitation PM motor based on decoupled SVPWM control strategy," Proceedings of the CSEE, Vol. 40, No. 24, 7899-7909, 2020.
doi:10.13334/j.0258-8013.pcsee.201139        Google Scholar

5. Li, F., K. Wang, X. Song, J. Li, S. Zhu, and C. Liu, "Coordinated control with high efficiency in wide operating region of AC-excited hybrid excitation generator," Proceedings of the CSEE, Vol. 45, No. 10, 4046-4055, 2025.
doi:10.13334/j.0258-8013.pcsee.240930        Google Scholar

6. Ma, X., Q. Zheng, X. Han, and T. Zhou, "Optimal design of the pole structure of low head permanent magnet synchronous generators," Electrical Machinery Technology, No. 3, 5-10, 2024.
doi:10.3969/j.issn.1006-2807.2024.03.002        Google Scholar

7. Zhen, Zhang, Haihua Wang, Xuedong Han, Ying Fan, and Q. U. Guangyu, "Design and analysis of a consequent-pole permanent magnet wind generator," Micromotors, Vol. 52, No. 8, 2019.        Google Scholar

8. Wang, X., H. Yin, and R. Yu, "Magnetic field analysis and rotor optimization for coreless axial flux permanent magnet synchronous machine," Electric Machines and Control, Vol. 28, No. 9, 170-178, 2024.
doi:10.15938/j.emc.2024.09.015        Google Scholar

9. Afinowi, I. A. A., Z. Q. Zhu, Y. Guan, Jean-Claude Mipo, and P. Farah, "Switched-flux machines with hybrid NdFeB and ferrite magnets," COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 35, No. 2, 456-472, 2016.
doi:10.1108/compel-03-2015-0112        Google Scholar

10. Khazdozian, Helena A., Ravi L. Hadimani, and David C. Jiles, "Development of rare earth free permanent magnet generator using halbach cylinder rotor design," Renewable Energy, Vol. 112, 84-92, 2017.
doi:10.1016/j.renene.2017.05.034        Google Scholar

11. Shao, P., J. Xu, Q. Liang, and Y. Zhang, "Analytical modeling of magnetic field of permanent magnet in surface mounted linear motors based on exact subdomain model method," Journal of Naval University of Engineering, Vol. 36, No. 3, 66-71, 2024.
doi:10.7495/j.issn.1009-3486.2024.03.011        Google Scholar

12. Xing, Z. Z., X. H. Wang, and W. L. Zhao, "Research on reduction methods of cogging torque based on segmented skewing magnetic poles with different combinations of pole-arc coefficients in surface-mounted permanent magnet synchronous motors," Proceedings of the CSEE, Vol. 41, No. 16, 5737-5748, 2021.
doi:10.13334/j.0258-8013.pcsee.201370        Google Scholar

13. Wang, W., X. Zhang, C. Yu, J. Zhang, S. Hua, K. Geng, and W. Hu, "Research on cogging torque weakening method of parallel double-rotor motor based on polar arc coefficient and relative deflection angle of rotor," Journal of Shaanxi University of Science & Technology, Vol. 41, No. 6, 139-144,154, 2023.
doi:10.3969/j.issn.1000-5811.2023.06.019        Google Scholar

14. Bao, M., Y. Sun, C. Chen, and X. Zheng, "Calculation of suspension force of amorphous alloy high-speed maglev linear motor based on distributed magnetic circuit method," Transactions of China Electrotechnical Society, Vol. 38, No. 14, 3678-3688,3732, 2023.
doi:10.19595/j.cnki.1000-6753.tces.221852        Google Scholar

15. Song, Si-Woo, Min-Ki Hong, Ju Lee, and Won-Ho Kim, "A study on reduction of cogging torque and magnet usage through intersect magnet consequent pole structure," Energies, Vol. 15, No. 23, 9255, 2022.
doi:10.3390/en15239255        Google Scholar

16. Geng, Huihui, Xueyi Zhang, Tao Si, Lanian Tong, Qingzhi Ma, and Mingjun Xu, "Analysis of the rotor magnetomotive force of built-in radial permanent magnet generator for vehicle," International Journal of Rotating Machinery, Vol. 2021, No. 1, 5319615, 2021.
doi:10.1155/2021/5319615        Google Scholar

17. Liang, Z. and X. Liu, "Equivalent dynamic magnetic network model of novel disc planetary permanent magnet motor," Journal of Zhejiang University(Engineering Science), Vol. 58, No. 10, 2182-2191, 2024.
doi:10.3785/j.issn.1008-973X.2024.10.022        Google Scholar

18. Mamede, A. C. F. and J. R. Camacho, "Evolutionary algorithms for optimization of 4/4 single phase switched reluctance machine," IEEE Latin America Transactions, Vol. 16, No. 6, 1684-1691, 2018.
doi:10.1109/tla.2018.8444387        Google Scholar

19. Yang, L., J. Xu, J. Chen, J. Li, and S. Xiang, "An analysis model of renewal regulation policy for village-in-city based on pareto optimality theory: A case study of zhuhai city," Urban Development Studies, Vol. 30, No. 8, 68-75, 2023.
doi:10.3969/j.issn.1006-3862.2023.08.020        Google Scholar

20. Zhou, Dawei, Li Lu, Changqing Yang, Yang Dai, and Xi Wang, "Co-simulation optimization of high speed permanent magnet synchronous motor based on genetic algorithm and TOPSIS method," Modular Machine Tool & Automatic Manufacturing Technique, Vol. 11, 69-73, 2023.
doi:10.13462/j.cnki.mmtamt.2023.11.016        Google Scholar

21. Jiang, L., L. Yang, L. Chen, and F. Xie, "Research on less-rare-earth hybrid permanent magnet synchronous motor for industrial robots," Small & Special Electrical Machines, Vol. 53, No. 5, 21-26.
doi:10.3969/j.issn.1004-7018.2025.05.004        Google Scholar