Analytical models for interior-type permanent magnet synchronous motors

Keen interest in the design of Permanent Magnet (P.M.) synchronous motors is being fuelled by continuing developments in permanent magnet material technology. The most recent of these developments has been in the introduction of Neodymium-Boron-Iron (NdBFe) with residual flux density of 1.23 T and energy product (BHmax) of 320 kJ/m³. However a continuing difficulty with the analysis of permanent magnet motors, irrespective of their magnet composition, is the prediction of the direct and quadrature axis reactances. This is particularly the case with motors having permanent magnets imbedded in the rotor iron below the cage winding. The purpose of this paper is to present equivalent circuit models for such interior-type P.M. motors and develop simple analytical expressions for the calculation of axis reactances. Computed reactances including saturation effects are presented along with experimental values for verification.