Power-Equivalent Complex Permeability Model for Nonlinear and Hysteretic Materials in the Frequency Domain for Induction Heating Applications

Abstract

This article summarizes different levels of simplification for nonlinear and hysteretic <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$B$ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula> curves intended to be used in finite element modeling (FEM) simulations of induction heating processes. Models based on coenergy are first shown and compared to the idea of fitting an equivalent complex permeability from nonlinear time-transient 1-D simulated results. A simple algorithm based on the reworked diffusion equation system is presented in detail and allows obtaining a new power-equivalent model leading to nearly zero error on power density profiles in 1-D problems for both eddy current and hysteresis losses. The equivalent complex permeability obtained is then used as a property of a given material for time-harmonic (TH) simulations in 2-D and 3-D, leading to smaller errors on losses than coenergy-based models and a much smaller computational cost compared with time-transient simulations.