Normalized Nonlinear Impedance Boundary Condition in Anhysteretic Magnetic Material for Eddy Current Problems

Numerical simulations of induction heating (IH) systems often assume that the properties of the induction load are linear. Thus, its electrical behavior is described by an equivalent impedance which exhibits frequency dispersion but remains independent of the excitation level. Although deriving such solutions is computationally complex, the use of the impedance boundary condition (IBC) provides high-quality results for linear media. This boundary condition replaces the effects of media with rapidly varying fields by a ratio between their tangential components at the surface. However, in typical induction loads, magnetic saturation of the material causes phenomena of dependence of the properties on the current level. The precise formulation of such an IBC can only be performed considering linear media. This article proposes calculating a nonlinear excitation level-dependent IBC numerically, considering the saturation dependence of the magnetic properties given by a Langevin function BH-loop. A normalized form of the nonlinear IBC will be obtained from the equation governing this type of behavior, thereby reducing the computational cost of the solution. The usefulness of the proposed nonlinear IBC will be validated by comparing it with results obtained from conventional time-domain simulations of a typical IH system.