Purpose - This paper aims to introduce the decomposed harmonic balance finite element method (HBFEM) to decrease the memory requirement in large-scale computation of the DC-biasing magnetic field. Harmonic analysis of the flux density and flux distribution was carried out to investigate the DC biased problem in a laminated core model (LCM). Design/methodology/approach - Based on the DC bias test on a LCM, the decomposed HBFEM is applied to accurately calculate the DC-biasing magnetic field. External electric circuits are coupled with the magnetic field in the harmonic domain. The reluctivity matrix is decomposed and the block Gauss-Seidel algorithm solves each harmonic solution of magnetic field and exciting current sequentially. Findings - The calculated exciting currents and flux density are compared with that obtained from measurement and time domain finite element analysis, respectively, which demonstrates consistency. The DC bias leads to the significant saturation of the magnetic core and serious distortion of the exciting current. The flux density varies nonlinearly with DC bias excitation. Research limitations/implications - The harmonic balance method is only applicable in solving the steady state magnetic field. Future improvements in the method are necessary in order to manage the hysteresis effects in magnetic material. Originality/value - The proposed method to solve the DC biased problem significantly reduces the memory requirement compared to the conventional HBFEM. The decomposed harmonic balance equations are solved efficiently by the block Gauss-Seidel algorithm combined with the relaxation iterative scheme. An investigation on DC bias phenomena is carried out through the harmonic solution of the magnetic field. The decomposed HBFEM can also be applied to solve 3-D DC-biasing magnetic field and eddy current nonlinear problems in a practical power transformer.
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