Modeling of nine-phase interior permanent magnet machines (IPM) including harmonic effects

This paper presents the modeling of the nine-phase interior permanent magnet machine (IPM) with and without damper windings for the clear understanding of its advantages such as fault tolerant and torque ripple reduction. This includes the influence of the higher order magneto-motive force (MMF) harmonics of the stator windings and the buried magnets for the improvement of the torque capability of the machine through injection of corresponding stator harmonic currents. The inductances are determined using the concept of winding functions for exact computer simulation based calculation and using Fourier components of the stator windings and the magnet flux for achieving closed-form expressions for the fundamental, third, fifth and the seventh harmonic components. Further analysis of the q-d equations of the nine-phase machine also shows the presence of low impedance circuits which could be excited under fault conditions signaling the detrimental effects of fault conditions on the multi-phase machines which may be avoided/reduced when the machine is connected into various three-phase sets. Some inductances showing their existence in different harmonic representation as well as experimental waveforms have been included.