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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
Keywords Finite element method, Electrical machines, Harmonics, Magnetic devices
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