Analytical Model of Modular Spoke-Type Permanent Magnet Machines for In-Wheel Traction Applications

Hengliang Zhang, Wei Hua, David Gerada, Zeyuan Xu, Chris Gerada

Research output: Journal PublicationArticlepeer-review

11 Citations (Scopus)


This article proposes an analytical model of modular spoke-type permanent magnet (MSTPM) machines based on air-gap field modulation (AFM) theory. Firstly, a fundamental AFM model of open-circuit MSTPM machines is introduced. The open-circuit air-gap field of MSTPM machines is determined by three fundamental elements including the primitive magnetizing magnetomotive force (MMF) produced by permanent magnet (PM), and two modulators which consist of stator and rotor permeance. The analytical MMF excited by PM (PM-MMF) can be calculated by using magnetic circuit method, while the stator and rotor permeance models are developed based on relative permeance (RP) method. Thereafter, a general model is proposed to calculate the open-circuit back electromotive force (EMF) of MSTPM machines. Further, the winding inductance model is established on the basis of equivalent magnetic circuit method and RP model. Finally, the machine performance is predicted by the analytical model, and verified by both finite element analysis (FEA) and experimental results.

Original languageEnglish
Article number9031315
Pages (from-to)1289-1300
Number of pages12
JournalIEEE Transactions on Energy Conversion
Issue number3
Publication statusPublished - Sept 2020


  • AC machines
  • Air-gap field modulation (AFM)
  • in-wheel traction
  • spoke-type PM machines

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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