DC-Biased Homogenized Harmonic Balance Finite Element Method

TL;DR

This paper extends the homogenized harmonic balance finite element method to include dc bias in ferromagnetic materials, significantly reducing simulation time while maintaining accuracy in nonlinear eddy-current simulations.

Contribution

The authors adapt the homogenization technique to account for dc bias and ferromagnetic saturation, enabling efficient simulations of laminated devices with improved accuracy.

Findings

Relative errors below 10% for moderate saturation

Simulation time reduced from 2 days to 90 minutes

Effective at frequencies between 50 Hz and 10 kHz

Abstract

The homogenized harmonic balance finite element (FE) method enables efficient nonlinear eddy-current simulations of 3-D devices with lamination stacks by combining the harmonic balance method with a frequency-domain-based homogenization technique. This approach avoids expensive time stepping of the eddy-current field problem and allows the use of a relatively coarse FE mesh that does not resolve the individual laminates. In this paper, we extend the method to handle excitation signals with a dc bias. To achieve this, we adapt the original homogenization technique to better account for ferromagnetic saturation. The resulting formula for the homogenized reluctivity is evaluated using a look-up table computed from a 1-D FE simulation of a lamination and containing the average magnetic flux density in the lamination and the corresponding skin depth. We compare the results of the proposed method to those from a fine-mesh transient reference simulation. The tests cover different levels of ferromagnetic saturation and frequencies between 50 Hz and 10 kHz. For moderate ferromagnetic saturation, the method gives a good approximation of the eddy-current losses and the magnetic energy, with relative errors below 10%, while reducing the required number of degrees of freedom at 10 kHz by 1.5 orders of magnitude. This results in a reduction in simulation time from 2 days on a contemporary server to 90 minutes on a standard workstation.