DC-Biased Homogenized Harmonic Balance Finite Element Method

2025-12-07

AI Summary

Accurate and efficient modeling of eddy current fields in three-dimensional laminated structures under DC-biased excitation and ferromagnetic saturation remains challenging. Method: This paper proposes an extended homogenized harmonic balance finite element method (HB-FEM), integrating frequency-domain homogenization with the harmonic balance technique and incorporating a lookup-table approach based on 1D finite element simulations to precisely capture DC-bias-dependent nonlinear permeability and frequency-dependent skin depth. Contribution/Results: The method enables high-fidelity homogenized representation of saturation effects using coarse meshes. Within 50 Hz–10 kHz, it achieves prediction errors <10% for both eddy current losses and magnetic energy, reduces degrees of freedom by ~90% (i.e., one-and-a-half orders of magnitude), and cuts simulation time from two days to 90 minutes—substantially enhancing both accuracy and efficiency for nonlinear, high-frequency electromagnetic field analysis.

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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.

Problem

• Extends homogenized harmonic balance FE method to handle DC-biased excitation signals.
• Adapts homogenization technique to account for ferromagnetic saturation effects in laminations.
• Reduces simulation time significantly while maintaining accuracy in eddy-current loss calculations.

Innovation

• Homogenization technique adapted for DC bias
• Look-up table from 1-D simulation for reluctivity
• Coarse mesh reduces simulation time significantly