Journal of Power Electronics

The Korean Institute of Power Electronics (전력전자학회)
권호 표지
DOI QR코드

DOI QR Code

Robust multi-objective transverse flux machine drive optimization considering torque ripple and manufacturing uncertainties

  • Yanbin Li (School of Electronic and Information, Zhongyuan University of Technology) ;
  • Heng Jia (School of Electronic and Information, Zhongyuan University of Technology) ;
  • Aijun Zhang (China Telecom Co., Ltd. Henan Branch) ;
  • Bing Xiao (China Telecom Co., Ltd. Henan Branch) ;
  • Yongsheng Zhu (School of Electronic and Information, Zhongyuan University of Technology) ;
  • Tingting Wei (School of Electronic and Information, Zhongyuan University of Technology)
  • Received : 2022.07.15
  • Accepted : 2022.12.25
  • Published : 2023.06.20
⟨ Previous Next ⟩

Abstract

This paper presents a multi-objective robust optimization method for a drive system consisting of a permanent magnet transverse flux machine with soft magnetic composite cores and a field-oriented controller. Unlike existing research work, the torque ripple is considered an optimization objective. Several machine uncertainties caused by manufacturing tolerances are investigated in the robust optimization model under the framework of the design for six-sigma. Since this is a system-level optimization problem, two approximation models are employed to decrease the computational cost. First, a Kriging model is used to approximate the steady-state electromagnetic performances of the motor, such as the output power and efficiency. Second, a Taylor series approximation is employed to estimate the dynamic performances of the control system, such as the speed overshoot and settling time. Furthermore, a sampling selection method is proposed to reduce the computational cost of the Monte Carlo analysis in robust optimization. To show the effectiveness of the proposed method, both deterministic and robust Pareto solutions are presented and discussed. It can be seen that the system-level multi-objective design optimization based on robust approach can produce optimal Pareto solutions with a high manufacturing quality for the whole drive system. This is valuable for the batch production of electrical drive systems.

Keywords

Acknowledgement

This work was supported by the National Natural Science Foundation of China (NSFC) under grant 61873292.

References

  1. Krings, A., Boglietti, A., Cavagnino, A., Sprague, S.: Soft magnetic material status and trends in electric machines. IEEE Trans. Ind. Electron. 64(3), 2405-2414 (2017) https://doi.org/10.1109/TIE.2016.2613844
  2. Kwon, Y.S., Kim, W.J.: Electromagnetic analysis and steady-state performance of double-sided flat linear motor using soft magnetic composite. IEEE Trans. Ind. Electron. 64(3), 2178-2187 (2017) https://doi.org/10.1109/TIE.2016.2619658
  3. Liu, C., Lei, G., Wang, T., Guo, Y., Wang, Y., Zhu, J.: Comparative study of small electrical machines with soft magnetic composite cores. IEEE Trans. Ind. Electron. 64(2), 1049-1060 (2017) https://doi.org/10.1109/TIE.2016.2583409
  4. Guo, Y., Zhu, J.G., Watterson, P.A., Wu, W.: Development of a PM transverse flux motor with soft magnetic composite core. IEEE Trans. Energy Convers. 21(2), 426-434 (2006) https://doi.org/10.1109/TEC.2005.860403
  5. Zhu, J.G., Guo, Y.G., Lin, Z.W., Li, Y.J., Huang, Y.K.: Development of PM transverse flux motors with soft magnetic composite cores. IEEE Trans. Magn. 47(10), 4376-4383 (2011) https://doi.org/10.1109/TMAG.2011.2157320
  6. Lei, G., Zhu, J., Guo, Y., Shao, K., Xu, W.: Multi-objective sequential design optimization of PM-SMC motors for six sigma quality manufacturing. IEEE Trans. Magn. 50(2), 717-720 (2014) https://doi.org/10.1109/TMAG.2013.2277598
  7. Schuller, D., Hohs, D., Schweizer, S., Goll, D., Schneider, G.: Tailoring the microstructure of soft magnetic composites for electric motor applications. IEEE Trans. Magn. 55(2), 1-4 (2019) https://doi.org/10.1109/TMAG.2018.2865660
  8. Sun, X., Wu, J., Lei, G., Guo, Y., Zhu, J.: Torque ripple reduction of SRM drive using improved direct torque control with sliding mode controller and observer. IEEE Trans. Ind. Electron. 68(10), 9334-9345 (2021) https://doi.org/10.1109/TIE.2020.3020026
  9. Nguyen, H.T., Jung, J.W.: Finite control set model predictive control to guarantee stability and robustness for surface-mounted PM synchronous motors. IEEE Trans. Ind. Electron. 65(11), 8510- 8519 (2018) https://doi.org/10.1109/TIE.2018.2814006
  10. Luo, Y., Liu, C.: Model predictive control for a six-phase PMSM motor with a reduced-dimension cost function. IEEE Trans. Ind. Electron. 67(2), 969-979 (2020) https://doi.org/10.1109/TIE.2019.2901636
  11. Sun, X., Li, T., Zhu, Z., Lei, G., Guo, Y., Zhu, J.: Speed sensorless model predictive current control based on finite position set for PMSHM drives. IEEE Trans. Transp. Electrif. 7(4), 2743-2752 (2021) https://doi.org/10.1109/TTE.2021.3081436
  12. Diao, K., Sun, X., Lei, G., Bramerdorfer, G., Guo, Y., Zhu, J.: System-level robust design optimization of a switched reluctance motor drive system considering multiple driving cycles. IEEE Trans. Energy Convers. 36(1), 348-357 (2021) https://doi.org/10.1109/TEC.2020.3009408
  13. Zhu, H., Xiao, X., Li, Y.: Torque ripple reduction of the torque predictive control scheme for permanent-magnet synchronous motors. IEEE Trans. Ind. Electron. 59(2), 871-877 (2012)
  14. Lei, G., Guo, Y.G., Zhu, J.G., Wang, T.S., Chen, X.M., Shao, K.R.: System level six sigma robust optimization of a drive system with PM transverse flux machine. IEEE Trans. Magn. 48(2), 923-926 (2012) https://doi.org/10.1109/TMAG.2011.2173795
  15. Lei, G., Wang, T., Guo, Y., Zhu, J., Wang, S.: System-level design optimization methods for electrical drive systems: Deterministic approach. IEEE Trans. Ind. Electron. 61(12), 6591-6602 (2014) https://doi.org/10.1109/TIE.2014.2321338
  16. Lei, G., Wang, T., Zhu, J., Guo, Y., Wang, S.: System-level design optimization method for electrical drive systems-Robust approach. IEEE Trans. Ind. Electron. 62(8), 4702-4713 (2015) https://doi.org/10.1109/TIE.2015.2404305
  17. Bramerdorfer, G., Tapia, J.A., Pyrhonen, J.J., Cavagnino, A.: Modern electrical machine design optimization: Techniques, trends, and best practices. IEEE Trans. Ind. Electron. 65(10), 7672-7684 (2018) https://doi.org/10.1109/TIE.2018.2801805
  18. Liu, Y., Wu, X., Zhang, X., Niu, S., Chan, W.L.: Coupled electromagnetic-thermal optimization of a separate-stator modular machine with biased flux. IEEE Trans. Magn. 55(6), 1-5 (2019) https://doi.org/10.1109/TMAG.2019.2905667
  19. Sun, X., Shi, Z., Lei, G., Guo, Y., Zhu, J.: Multi-objective design optimization of an IPMSM based on multilevel strategy. IEEE Trans. Ind. Electron. 68(1), 139-148 (2021) https://doi.org/10.1109/TIE.2020.2965463
  20. Wu, T., et al.: Multi-objective optimization of a tubular coreless LPMSM based on adaptive multi-objective black hole algorithm. IEEE Trans. Ind. Electron. 67(5), 3901-3910 (2020) https://doi.org/10.1109/TIE.2019.2916347
  21. Lei, G., Zhu, J., Guo, Y., Liu, C., Ma, B.: A review of design optimization methods for electrical machines. Energies 10(12), 1962 (2017)
  22. Song, J., Dong, F., Zhao, J., Wang, H., He, Z., Wang, L.: An efficient multi-objective design optimization method for a PMSLM based on an extreme learning machine. IEEE Trans. Ind. Electron. 66(2), 1001-1011 (2019) https://doi.org/10.1109/TIE.2018.2835413
  23. Zhu, X., Fan, D., Mo, L., Chen, Y., Quan, L.: Multi-objective optimization design of a double-rotor flux-switching permanent magnet machine considering multimode operation. IEEE Trans. Ind. Electron. 66(1), 641-653 (2019)
  24. Zhu, X., Xiang, Z., Quan, L., Chen, Y., Mo, L.: Multimode optimization research on a multiport magnetic planetary gear permanent magnet machine for hybrid electric vehicles. IEEE Trans. Ind. Electron. 65(11), 9035-9046 (2018) https://doi.org/10.1109/TIE.2018.2813966
  25. Lei, G., Bramerdorfer, G., Liu, C., Guo, Y., Zhu, J.: Robust design optimization of electrical machines: a comparative study and space reduction strategy. IEEE Trans. Energy Convers. 36(1), 300-313 (2021) https://doi.org/10.1109/TEC.2020.2999482
  26. Bramerdorfer, G., Lei, G., Cavagnino, A., Zhang, Y., Sykulski, J., Lowther, D.A.: More robust and reliable optimized energy conversion facilitated through electric machines, power electronics and drives, and their control: State-of-the-art and trends. IEEE Trans. Energy Convers. 35(4), 1997-2012 (2020) https://doi.org/10.1109/TEC.2020.3013190
  27. Lei, G., Guo, Y.G., Zhu, J.G., Chen, X.M., Xu, W., Shao, K.R.: Sequential subspace optimization method for electromagnetic devices design with orthogonal design technique. IEEE Trans. Magn. 48(2), 479-482 (2012) https://doi.org/10.1109/TMAG.2011.2173921
  28. Lei, G., Liu, C., Zhu, J., Guo, Y.: Techniques for multilevel design optimization of permanent magnet motors. IEEE Trans. Energy Convers. 30(4), 1574-1584 (2015)
  29. Shukla, S., Sreejeth, M., Singh, M.: Minimization of ripples in stator current and torque of PMSM drive using advanced predictive current controller based on deadbeat control theory. J. Power Electron. 21(1), 142-152 (2021) https://doi.org/10.1007/s43236-020-00151-2
  30. Suryakant, S.M., Singh, M., Seth, A.K.: Minimization of torque ripples in PMSM drive using PI- resonant controller-based model predictive control. Electr. Eng. (2022). https://doi.org/10.1007/s00202-022-01660-y
  31. Kim, K.C.: A novel method for minimization of cogging torque and torque ripple for interior permanent magnet synchronous motor. IEEE Trans. Magn. 50(2), 793-796 (2014) https://doi.org/10.1109/TMAG.2013.2285234
  32. Jang, S.M., Park, H.I., Choi, J.Y., Ko, K.J., Lee, S.H.: Magnet pole shape design of permanent magnet machine for minimization of torque ripple based on electromagnetic field theory. IEEE Trans. Magn. 47(10), 3586-3589 (2011) https://doi.org/10.1109/TMAG.2011.2151846
  33. Wu, H., Depernet, D., Lanfranchi, V., Benkara, K.E.K., Rasid, M.A.H.: A novel and simple torque ripple minimization method of synchronous reluctance machine based on torque function method. IEEE Trans. Ind. Electron. 68(1), 92-102 (2021) https://doi.org/10.1109/TIE.2019.2962490
  34. Beltran-Pulido, A., Aliprantis, D., Bilionis, I., Munoz, A.R., Leonardi, F., Avery, S.M.: Uncertainty quantification and sensitivity analysis in a nonlinear finite-element model of a permanent magnet synchronous machine. IEEE Trans. Energy Convers. 35(4), 2152-2161 (2020) https://doi.org/10.1109/TEC.2020.3001914
  35. Bramerdorfer, G.: Quantifying the impact of tolerance-affected parameters on the performance of permanent magnet synchronous machines. IEEE Trans. Energy Convers. 35(4), 2170-2180 (2020) https://doi.org/10.1109/TEC.2020.2997391
  36. Kolb, J., Hameyer, K.: Sensitivity analysis of manufacturing tolerances in permanent magnet synchronous machines with stator segmentation. IEEE Trans. Energy Convers. 35(4), 2210-2221 (2020) https://doi.org/10.1109/TEC.2020.3017279
  37. Dong, F., Zhao, J., Song, J., Feng, Y., He, Z.: Optimal design of permanent magnet linear synchronous motors at multispeed based on particle swarm optimization combined with SN ratio method. IEEE Trans. Energy Convers. 33(4), 1943-1954 (2018) https://doi.org/10.1109/TEC.2018.2841421
  38. Lei, G., Bramerdorfer, G., Ma, B., Guo, Y., Zhu, J.: Robust design optimization of electrical machines: Multi-objective approach. IEEE Trans. Energy Convers. 36(1), 390-401 (2021) https://doi.org/10.1109/TEC.2020.3003050
  39. Orosz, T., et al.: Robust design optimization and emerging technologies for electrical machines: Challenges and open problems. Appl. Sci. 10(19), 6653 (2020)
  40. Ren, Z., Ma, J., Qi, Y., Zhang, D., Koh, C.S.: Managing uncertainties of permanent magnet synchronous machine by adaptive kriging assisted weight index Monte Carlo simulation method. IEEE Trans. Energy Convers. 35(4), 2162-2169 (2020) https://doi.org/10.1109/TEC.2020.3009249
  41. Xu, L., Wu, W., Zhao, W., Liu, G., Niu, S.: Robust design and optimization for a permanent magnet vernier machine with hybrid stator. IEEE Trans. Energy Convers. 35(4), 2086-2094 (2020) https://doi.org/10.1109/TEC.2020.3011925
  42. Kim, S., Lee, S.G., Kim, J.M., Lee, T.H., Lim, M.S.: Robust design optimization of surface-mounted permanent magnet synchronous motor using uncertainty characterization by bootstrap method. IEEE Trans. Energy Convers. 35(4), 2056-2065 (2020) https://doi.org/10.1109/TEC.2020.3004342
  43. Koch, P.N., Yang, R.J., Gu, L.: Design for six sigma through robust optimization. Struct. Multidiscip. Optim. 26(3-4), 235-248 (2004) https://doi.org/10.1007/s00158-003-0337-0
  44. Yang, Y., Bianchi, N., Bacco, G., Zhang, S., Zhang, C.: Methods to reduce the computational burden of robust optimization for permanent magnet motors. IEEE Trans. Energy Convers. 35(4), 2116-2128 (2020) https://doi.org/10.1109/TEC.2020.3016067
  45. Li, Y., Lei, G., Bramerdorfer, G., Peng, S., Sun, X., Zhu, J.: Machine learning for design optimization of electromagnetic devices: Recent developments and future directions. Appl. Sci. 11(4), 1627 (2021)