Multi-Objective Design Optimization of a Tubular Permanent Magnet Linear Generator With 120° Phase Belt Toroidal Windings

Zuoguang Yan, Jikai Si, Zhongwen Li, Chun Gan, Yihua Hu

Research output: Contribution to journalArticlepeer-review


The utilization of 120° phase belt toroidal windings (120°-TWs) can bring power density improvement in a tubular permanent magnet linear generator (TPMLG). Unfortunately, the TPMLG with 120°-TWs (120°-TPMLG) usually involve multiple structural parameters, and the interaction or even conflict among those structural parameters would have strong impact on generator performances in the design optimization process. To alleviate this problem, a multi-objective design optimization method is proposed to conduct a multi-objectives optimization, which aims to obtain the high-power density and low-detent force. First, the comprehensive sensitivity analysis method, namely global sensitivity analysis, is adopted to evaluate the sensitivities of the structural parameters on the performances of the 120°-TPMLG. According to the evaluation results, the structural parameters are divided into three levels: non-sensitive level, mild-sensitive level, and strong-sensitive level. Then, to improve the whole design optimization efficiency, the direct-screening method, the surface method, and the genetic algorithm is implemented in the three levels, respectively. And the optimal structural parameters of the 120°-TPMLG are finally determined. To verify the feasibility of the 120°-TPMLG and the effectiveness of the proposed design optimization method, the performances of the optimal 120°-TPMLG are analyzed and compared with the initial one and the same dimensions TPMLG with traditional toroidal windings (T-TPMLG) in detail. It shows that the performances of the optimal 120°-TPMLG meet the design requirements. Moreover, the detent force is largely decreased and the power density is notably improved. The results prove that the proposed multi-objective design optimization method is available for the 120°-TPMLG.

Original languageEnglish
Pages (from-to)236-247
Number of pages12
JournalIEEE Journal of Emerging and Selected Topics in Power Electronics
Issue number1
Early online date24 Jun 2021
Publication statusPublished - Feb 2022

Bibliographical note

Funding Information:
This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant 51777060 and in part by the Major Special Project for Collaborative Innovation in Zhengzhou under Grant 20XTZX12023.

Publisher Copyright:
© 2013 IEEE.


  • 120° phase belt toroidal windings (120°-TWs)
  • comprehensive sensitivity analysis
  • detent force
  • multi-objective design optimization
  • power density
  • tubular permanent magnet linear generator (TPMLG)

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