Exact Modeling and Multi-Objective Optimization of Vernier Machines

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

3 Scopus Citations
View graph of relations


Original languageEnglish
Pages (from-to)11740-11751
Journal / PublicationIEEE Transactions on Industrial Electronics
Issue number12
Online published21 Dec 2020
Publication statusPublished - Dec 2021


This paper presents a high-fidelity analytical solution and a fast integrated optimization method for vernier machines. Firstly, a harmonic modeling method (HMM) is adopted to obtain the magnetic field distribution of vernier machines. Particularly, the stator teeth of vernier machines are divided into several blocks to take account of the local magnetic saturation of soft-magnetic material. Then, the electromagnetic parameters, such as the average torque, torque ripple and efficiency, can be calculated via the analytical model. Next, the proposed harmonic model is combined with the non-dominated sorting genetic algorithm II (NSGA-II) to determine a multi-objective optimal design for the studied vernier machine. This integrated optimization method can save computation time, because the data interaction process between the finite element analysis (FEA) software and the optimization software is eliminated. Finally, the performances of the optimal case are verified by both FEA and experiments with the prototype.

Research Area(s)

  • Analytical models, Fourier series, Harmonic analysis, Harmonic modeling method, Hidden Markov models, integrated optimization, Magnetic fields, magnetic saturation, permanent magnet machine, Permeability, Saturation magnetization, vernier machine