Comparative analysis of various methods for modelling surface permanent magnet machines

K. Ramakrishnan, M. Curti, D. Zarko, G. Mastinu, J.J.H. Paulides, E.A. Lomonova

Research output: Contribution to journalArticleAcademicpeer-review

21 Citations (Scopus)
12 Downloads (Pure)


In this paper, six different modelling methods for permanent magnet (PM) electric machines are compared in terms of their computational complexity and accuracy. The methods are based primarily on conformal mapping, mode matching, and harmonic modelling. In the case of conformal mapping, slotted air gap of a complex machine geometry is transformed to a smooth slotless air gap where analytical expression for field solution is available. The solution in the canonical domain is then mapped back to the original slotted air gap domain. Mode matching or subdomain method, as it is called in different sources, is using a solution of Laplace’s equation to model the slotted air gap. In harmonic modelling, the machine cross section is divided into homogeneous regions that are represented using Fourier series and coupled with each other using boundary conditions. The boundary value problems in both the mode matching and harmonic models are solved to obtain the field solutions. The performance of the modelling methods are evaluated by comparing the global parameters such as cogging torque, electromagnetic torque, back-emf as well as the simulation time with the results of finite element transient analysis.
Original languageEnglish
Pages (from-to)540 - 547
Number of pages8
JournalIET Electric Power Applications
Issue number4
Publication statusPublished - 1 Apr 2017


  • Fourier series
  • Laplace equation
  • Laplace equations
  • air gaps
  • back-emf
  • boundary conditions
  • boundary value problems
  • boundary-value problems
  • cogging torque
  • complex machine geometry
  • computational accuracy
  • computational complexity
  • conformal mapping
  • electromagnetic torque
  • finite element analysis
  • finite element transient analysis
  • global parameters
  • harmonic analysis
  • harmonic modelling
  • machine cross-section
  • mode matching
  • performance evaluation
  • permanent magnet electric machine modelling methods
  • permanent magnet machines
  • slotted air gap
  • smooth slotless air gap
  • subdomain method


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