Thierry Van Craenenbroeck

Implementation of the harmonic balance FEM method for large-scale saturated electromagnetic devices

The Harmonic Balance Finite Element Method (HBFEM) is an alternative for time-consuming transient analysis if only the steady-state solution is of interest. However, when used for realistic large-scale problems, such as simulation of the current redistribution in saturable transformers subject to a large spectrum of harmonic currents and voltages, practical implementation aspects have to be considered. An alternative derivation of the method in the complex frequency domain, leading to a block decomposition, is presented. Its implementation as a Gauss-Seidel iteration or a Jacobi-method, allowing a parallel algorithm, is discussed. A method to perform adaptive relaxation of the non-linear algorithm is presented. Effects associated with the representation of the material characteristic are studied. The computational effort in the outer non-linear iteration loop is minimised using FFT-algorithms, allowing to use adaptive relaxation methods to stabilise the overall procedure.