Two‐dimensional harmonic balance finite element modelling of electrical machines taking motion into account

An original and easy‐to‐implement method to take into account movement (motion) in the 2D harmonic balance finite element modelling of electrical machines is presented. The global harmonic balance system of algebraic equations is derived by applying the Galerkin approach to both the space and time discretisation. The harmonic basis functions, i.e. a cosine and a sine function for each nonzero frequency and a constant function 1 for the DC component, are used for approximating the periodic time variation as well as for weighing the time domain equations in the fundamental period. In practice, this requires some elementary manipulations of the moving band stiffness matrix. Magnetic saturation and electrical circuit coupling are considered in the analysis as well. As an application example, the noload operation of a permanent‐magnet machine is considered. The voltage and induction waveforms obtained with the proposed harmonic balance method are shown to converge well to those obtained with time stepping.