On-Load Analysis of Saturated Surface Permanent Magnet Machines Using Conformal Mapping and Magnetic Equivalent Circuits

Abstract

This paper presents an iterative method based on conformal mapping and magnetic equivalent circuits for on-load analysis of saturated surface permanent magnet machines with integer slot and fractional slot windings. Magnetic saturation is taken into account by defining additional point wires in the stator slots and interpolar region between the magnets. The added point wires create magnetomotive force equal to the magnetic voltage drops across iron core flux tubes that are calculated using magnetic equivalent circuit. An improved stator tooth model has been introduced that enables more accurate field calculations for tooth geometries with highly saturated tooth tips. The model also takes into account variation of permanent magnet magnetization due to external magnetic field. The proposed method has been implemented on a saturated 12 slot, 10 pole surface permanent magnet machine with nonoverlapping concentrated winding and shows a very good agreement with finite element calculations in terms of flux density, back electromotive force, and torque waveforms as well as $d$ - and $q$ -axis inductances, cross-saturation inductance, and permanent magnet flux linkage in both axes.