Finite-Element Homogenization of Laminated Iron Cores With Inclusion of Net Circulating Currents Due to Imperfect Insulation

This paper deals with the time-domain homogenization of laminated cores in 2-D or 3-D finite-element (FE) models of electromagnetic devices, allowing for net circulating current in the laminations (e.g., due to imperfect or damaged insulation). The homogenization is based on the expansion of the induction throughout the lamination thickness using a set of orthogonal polynomial basis functions (BFs), in conjunction with the magnetic vector potential formulation. These BFs allow for net flux, net current, and skin effect in the laminations; by choosing the number of BFs, one can compromise between accuracy and computational cost. The approach is validated through a linear 2-D test case with in-plane imposed and induced current density. A brute-force model, in which all laminations are finely meshed, produces the reference solution. The extension to nonlinear 3-D problems is expected to be straightforward.

I. Introduction

When modeling electromagnetic devices comprising laminated iron cores by means of the finite-element (FE) method, it may be essential that the induced eddy currents, the associated losses, and the ensuing skin effect in the laminations are directly considered in the resolution, and not just in the post-processing stage. For real-life applications, it is mostly prohibitive to model and discretize each lamination separately. Dedicated numerical techniques are therefore of great practical interest.