Harmonic-Balanced Finite Element Method and Its Application

Abstract

This chapter mainly introduces the harmonic-balanced finite element method (HBFEM) and its application in electrical engineering. Different from the traditional frequency domain method, the HBFEM is able to compute the nonlinear magnetic field with electrical equipments with significant saturation. Compared with the time-stepping method, transient process can be avoided in HBFEM to reduce the computational time. Furthermore, the hybrid with the fixed-point technique realizes the decomposition of harmonic solutions, which greatly improves the efficiency of numerical computation in the frequency domain. The HBFEM is employed to compute the nonlinear electromagnetic field under DC bias condition and to investigate the force characteristic in a gapped reactor core model under harmonic magnetization. Actually the principle of harmonic-balanced method is applicable to steady-state thermal problems, and it is predicted to have further contribution on loss modeling and thermal analysis of power transformers.