No abstract

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.

Air gap field solution for an outer rotor permanent magnet (PM) machine is derived based on numerical Schwarz-Christoffel (SC) transformation of a single slot geometry and analytical solution of a point wire field in the rectangular canonical domain. This approach takes into account geometrical distortions of PM edges and field evaluation points located along the air gap centre, which occur due to conformal mapping of the slotted air gap into a slotless domain and impair the accuracy of the existing analytical field solutions using SC transformation and complex relative air gap permeance. The increased accuracy of the improved solution is confirmed by comparing the air gap flux density waveforms produced by the PMs and armature winding, cogging torque, and total torque with the results of time-stepping transient finite element simulation.

No abstract

In this paper, four different modelling techniques for permanent magnet (PM) machines are compared for their accuracy and computational complexity. The considered techniques are primarily based on conformal mapping and harmonic modelling. In conformal mapping, the slotted air gap is mapped into a simpler canonical shape, where the field solution is calculated and then mapped back to the original domain. In harmonic modelling, the regions of the machine cross section are represented as Fourier series and coupled with each other by means of boundary conditions. The field solution is obtained by solving the boundary value problem. In order to quantify the accuracy of the field solutions, global parameters such as cogging torque and flux linkage are computed. The effectiveness of the modelling techniques are evaluated by comparing the global parameters and the simulation time with finite element analysis (FEA) results.