Comparative analysis of various methods for modelling surface permanent magnet machines

In this study, six different modelling methods for permanent magnet 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.