Exploitation of independent stator and rotor geometrical periodicities in electrical machines using the Schur complement

Abstract

In this paper we present a-priori model reduction technique that enables to take full advantage of the periodicity existing in the stator and rotor geometrical structures of electrical machines in order to reduce the computational time. Firstly, a change of basis is performed by applying two distinct discrete Fourier transformations on the stator and rotor periodic structures independently. Secondly, the Schur complement is introduced in the new spectral basis, to allow a parallel solving of the resulting block-diagonal matrix systems. Moreover, the using of a matrix-free Krylov method based on the conjugate gradient solver has verified an efficient solving of the equation system associated to the stator-rotor interface. Furthermore, in the peculiar case of balanced supply conditions, a model order reduction can be carried out by considering only the dominant discrete Fourier transform components. This model reduction approach is applied on a buried permanent magnet machine and has successfully shown its efficiency under balanced and unbalanced conditions.