volume | PIER Journals

Abstract

Robust optimization design of brushless electrically excited synchronous machines (BEESMs) is a problem that has received extensive attention. The increase in finite element calculation cost due to the increase in the number of motor parameters is one of the main problems faced by optimization. In this paper, a robust multi-objective optimization design method of BEESM based on an improved hill-climbing algorithm is proposed. All design parameters are divided into three subspaces according to the sensitivity by the sensitivity analysis method combined with Kendall's rank coefficient, thereby reducing the consumption required for FEM calculation. The screening problem of Pareto frontier solutions is solved by an improved hill-climbing algorithm. The candidate points to be optimized are screened through the improved climbing algorithm, and only the candidate points located on the Pareto frontier will be optimized, which ensures the high performance of the candidate points. Based on the noise problems that may occur in actual production and processing, the candidate points are robustly analyzed, and the optimal design is screened out. The robust optimization design method proposed in this paper can reduce the computational cost and improve the robustness of the motor based on improving the performance of the motor.

1. Zhang, F. G., G. L. Jia, Y. Zheng, and T. Guan, "Analysis and experimental study of brushless electrically-excited synchronous generator with hybrid rotor," 2015 IEEE International Conference on Applied Superconductivity and Electromagnetic Devices (ASEMD), 332-333, Nov. 2015. Google Scholar

2. Pallantla, M., P. Kumar, and N. Mohan, "Comparison and evaluation of the different brushless excitation topologies for synchronous machines --- A literature survey," 2020 IEEE International Conference on Power Electronics, Smart Grid and Renewable Energy (PESGRE2020), 1-6, Jan. 2020. Google Scholar

3. Berweiler, B. and B. Ponick, "Current and average temperature calculation for electrically excited synchronous machines in case of contactless energy supply," 2020 International Conference on Electrical Machines (ICEM), Vol. 1, 1730-1735, Aug. 2020. Google Scholar

4. Hsieh, M.-F., Y.-H. Chang, and D. G. Dorrell, "Design and analysis of brushless doubly fed reluctance machine for renewable energy applications," IEEE Trans. Magn., Vol. 52, No. 7, 1-5, Jul. 2016. Google Scholar

5. Zhang, F., H. Wang, G. Jia, D. Ma, and M. G. Jovanovic, "Effects of design parameters on performance of brushless electrically excited synchronous reluctance generator," IEEE Trans. Ind. Electron., Vol. 65, No. 11, 9179-9189, Nov. 2018. Google Scholar

6. Zhang, F., J. Xu, G. Jia, and S. Jin, "Electromagnetic design and dynamic performance study of electrically excited brushless synchronous motor," 2013 International Conference on Electrical Machines and Systems (ICEMS), 699-702, Oct. 2013. Google Scholar

7. Chakraborty, C. and Y. T. Rao, "Performance of brushless induction excited synchronous generator," IEEE J. Emerg. Sel. Top. Power Electron., Vol. 7, No. 4, 2571-2582, Dec. 2019. Google Scholar

8. Gorginpour, H., H. Oraee, and R. A. McMahon, "Electromagnetic-thermal design optimization of the brushless doubly fed induction generator," IEEE Trans. Ind. Electron., Vol. 61, No. 4, 1710-1721, Apr. 2014. Google Scholar

9. Hussain, A., S. Atiq, and B. Kwon, "Optimal design and experimental verification of wound rotor synchronous machine using subharmonic excitation for brushless operation," Energies, Vol. 11, No. 3, Art. No. 3, Mar. 2018. Google Scholar

10. Sun, L., X. Gao, F. Yao, Q. An, and T. Lipo, "A new type of harmonic current excited brushless synchronous machine based on an open winding pattern," 2014 IEEE Energy Conversion Congress and Exposition (ECCE), 2366-2373, Sep. 2014. Google Scholar

11. Usinin, Yu. S., M. A. Grigorjev, K. M. Vinogradov, and S. P. Gladyshev, "New brushless synchronous machine for vehicle application," SAE Trans., Vol. 116, 270-276, 2007. Google Scholar

12. Zhang, F., G. Jia, Y. Zhao, Z. Yang, W. Cao, and J. L. Kirtley, "Simulation and experimental analysis of a brushless electrically excited synchronous machine with a hybrid rotor," IEEE Trans. Magn., Vol. 51, No. 12, 1-7, Dec. 2015. Google Scholar

13. Long, Q., Z. Zhou, X. Lin, and J. Liao, "Investigation of a novel brushless electrically excited synchronous machine with arc-shaped rotor structure," Energy Rep., Vol. 6, 608-617, Dec. 2020. Google Scholar

14. Ali, Q., T. A. Lipo, and B.-I. Kwon, "Design and analysis of a novel brushless wound rotor synchronous machine," IEEE Trans. Magn., Vol. 51, No. 11, 1-4, Nov. 2015. Google Scholar

15. Yao, F., Q. An, L. Sun, and T. A. Lipo, "Performance investigation of a brushless synchronous machine with additional harmonic field windings," IEEE Trans. Ind. Electron., Vol. 63, No. 11, 6756-6766, Nov. 2016. Google Scholar

16. Spielmann, H. and H. E. Friedrich, "Method to optimize NVH-behaviour of a brushless electrically excited synchronous machine," 2018 Thirteenth International Conference on Ecological Vehicles and Renewable Energies (EVER), 1-8, Apr. 2018. Google Scholar

17. Sun, X., Z. Shi, G. Lei, Y. Guo, and J. Zhu, "Analysis and design optimization of a permanent magnet synchronous motor for a campus patrol electric vehicle," IEEE Trans. Veh. Technol., Vol. 68, No. 11, 10535-10544, Nov. 2019. Google Scholar

18. Salimi, A. and D. A. Lowther, "On the role of robustness in multi-objective robust optimization: Application to an IPM motor design problem," IEEE Trans. Magn., Vol. 52, No. 3, 1-4, Mar. 2016. Google Scholar

19. Sun, X., N. Xu, and M. Yao, "Sequential subspace optimization design of a dual three- phase permanent magnet synchronous hub motor based on NSGA III," IEEE Trans. Transp. Electrification, 1-1, 2022. Google Scholar

20. Shi, Z., X. Sun, G. Lei, X. Tian, Y. Guo, and J. Zhu, "Multiobjective optimization of a five-phase bearingless permanent magnet motor considering winding area," IEEE ASME Trans. Mechatron., 1-10, 2021. Google Scholar

21. Ma, B., G. Lei, C. Liu, J. Zhu, and Y. Guo, "Robust tolerance design optimization of a PM claw pole motor with soft magnetic composite cores," IEEE Trans. Magn., Vol. 54, No. 3, 1-4, Mar. 2018. Google Scholar

22. Sun, X., Z. Shi, and J. Zhu, "Multiobjective design optimization of an IPMSM for EVs based on fuzzy method and sequential taguchi method," IEEE Trans. Ind. Electron., Vol. 68, No. 11, 10592-10600, 2021. Google Scholar

23. Liu, G., Y. Wang, Q. Chen, G. Xu, and C. Song, "Multiobjective deterministic and robust optimization design of a new spoke-type permanent magnet machine for the improvement of torque performance," IEEE Trans. Ind. Electron., Vol. 67, No. 12, 10202-10212, 2020. Google Scholar

24. Kim, K.-S., K.-T. Jung, J.-M. Kim, J.-P. Hong, and S.-I. Kim, "Taguchi robust optimum design for reducing the cogging torque of EPS motors considering magnetic unbalance caused by manufacturing tolerances of PM," IET Electr. Power Appl., Vol. 10, No. 9, 909-915, 2016. Google Scholar

25. Sun, X., Z. Shi, Y. Cai, G. Lei, Y. Guo, and J. Zhu, "Driving-cycle-oriented design optimization of a permanent magnet hub motor drive system for a four-wheel-drive electric vehicle," IEEE Trans. Transp. Electrification, Vol. 6, No. 3, 1115-1125, Sep. 2020. Google Scholar

26. Lee, J.-G., N.-W. Hwang, H. Ryu, H.-K. Jung, and D.-K. Woo, "Robust optimization approach applied to permanent magnet synchronous motor," IEEE Trans. Magn., Vol. 53, No. 6, 1-4, Jun. 2017. Google Scholar

27. Diao, K., X. Sun, G. Bramerdorfer, Y. Cai, G. Lei, and L. Chen, "Design optimization of switched reluctance machines for performance and reliability enhancements: A review," Renew. Sustain. Energy Rev., Vol. 168, 112785, Oct. 2022. Google Scholar

28. Jin, Z., X. Sun, L. Chen, and Z. Yang, "Robust multi-objective optimization of a 3-pole active magnetic bearing based on combined curves with climbing algorithm," IEEE Trans. Ind. Electron., Vol. 69, No. 6, 5491-5501, Jun. 2022. Google Scholar

29. Almansa Malagoli, J., J. R. Camacho, M. Valencia Ferreira da Luz, J. H. Inacio Ferreira, and A. Maximiano Sobrinho, "Design of three-phase induction machine using differential evolution algorithm," IEEE Lat. Am. Trans., Vol. 13, No. 7, 2202-2208, Jul. 2015. Google Scholar

30. Jolly, L., M. A. Jabbar, and L. Qinghua, "Design optimization of permanent magnet motors using response surface methodology and genetic algorithms," IEEE Trans. Magn., Vol. 41, No. 10, 3928-3930, 2005. Google Scholar

31. Lee, J. H., J.-W. Kim, J.-Y. Song, D.-W. Kim, Y.-J. Kim, and S.-Y. Jung, "Distance-based intelligent particle swarm optimization for optimal design of permanent magnet synchronous machine," IEEE Trans. Magn., Vol. 53, No. 6, 1-4, Jun. 2017. Google Scholar

32. Sim, D.-J., D.-H. Cho, J.-S. Chun, H.-K. Jung, and T.-K. Chung, "Efficiency optimization of interior permanent magnet synchronous motor using genetic algorithms," IEEE Trans. Magn., Vol. 33, No. 2, 1880-1883, Mar. 1997. Google Scholar

33. Bokose, F. L., L. Vandevelde, and J. A. A. Melkebeek, "Sequential approximate multiobjective optimisation of switched reluctance motor design using surrogate models and nongradient local search algorithm," IEE Proc. --- Sci. Meas. Technol., Vol. 151, No. 6, 471-475, Nov. 2004. Google Scholar

34. Xia, B., M.-T. Pham, Y. Zhang, and C.-S. Koh, "A global optimization algorithm for electromagnetic devices by combining adaptive taylor kriging and particle swarm optimization," IEEE Trans. Magn., Vol. 49, No. 5, 2061-2064, 2013. Google Scholar

35. Sun, X., Z. Shi, G. Lei, Y. Guo, and J. Zhu, "Multi-objective design optimization of an IPMSM based on multilevel strategy," IEEE Trans. Ind. Electron., Vol. 68, No. 1, 139-148, Jan. 2021. Google Scholar

36. Sun, X., Z. Shi, and J. Zhu, "Multi-objective design optimization of an IPMSM for EVs based on fuzzy method and sequential taguchi method," IEEE Trans. Ind. Electron., Vol. 68, No. 11, 10592-10600, 2021. Google Scholar

37. Si, J., S. Zhao, H. Feng, R. Cao, and Y. Hu, "Multi-objective optimization of surface-mounted and interior permanent magnet synchronous motor based on Taguchi method and response surface method," Chin. J. Electr. Eng., Vol. 4, No. 1, 67-73, Mar. 2018. Google Scholar

38. Shi, Z. and X. Sun, "Robust design optimization of a five-phase PM hub motor for fault-tolerant operation based on taguchi method," IEEE Trans. Energy Convers., Vol. 35, No. 4, 9, 2020. Google Scholar

39. Croux, C. and C. Dehon, "Influence functions of the Spearman and Kendall correlation measures," Stat. Methods Appl., Vol. 19, No. 4, 497-515, Nov. 2010. Google Scholar

40. Lebensztajn, L., C. A. R. Marretto, M. C. Costa, and J.-L. Coulomb, "Kriging: A useful tool for electromagnetic device optimization," IEEE Trans. Magn., Vol. 40, No. 2, 1196-1199, Mar. 2004. Google Scholar

41. Deb, K., A. Pratap, S. Agarwal, and T. Meyarivan, "A fast and elitist multiobjective genetic algorithm: NSGA-II," IEEE Trans. Evol. Comput., Vol. 6, No. 2, 182-197, Apr. 2002. Google Scholar

42. Shi, Z., X. Sun, G. Lei, Z. Yang, Y. Guo, and J. Zhu, "Analysis and optimization of radial force of permanent-magnet synchronous hub motors," IEEE Trans. Magn., Vol. 56, No. 2, 1-4, 2020. Google Scholar

43. Sun, Q., W. Zhang, and Q. Wang, "Fundamental design and analysis of a novel bipolar transverse-flux motor with stator permanent-magnet excitation," Chin. J. Electr. Eng., Vol. 4, No. 1, 60-66, Mar. 2018. Google Scholar

Dr. Naxi Xu

Professor Xiaodong Sun

Dr. Ke Li

Dr. Ming Yao