An analytical model for interior permanent-magnet synchronous machine with circumferential magnetization design

An analytical model for interior permanent-magnet synchronous machine is detailed using the equivalent d-q machine based on the determination of flux density waveforms in the different axes of the d-q frame. The main parameters of the Park model machine are analytically expressed. The expressions of electromotive force, d-, and q-axis synchronous inductances are derived considering the presence of leakage flux and stator teeth. Using the developed formulas, a design for a compressor application is deduced in order to obtain a reference for validating the analytical model. This is done making comparisons with a finite element model. Finally the analytical model is applied to an industrial machine in order to compare the estimated quantities to measurements.