Homogenization of the Eddy Current Problem in 2D

Abstract—Homogenization represents a promising method to simulate eddy current losses in laminated iron cores efficiently. First, multi-scale homogenization is demonstrated by a multi-scale approach in the context of an electrostatic problem. Then, multi-scale homogenization is extended to the eddy current problem. Two multi-scale approaches for the magnetic vector potential have been derived to simulate the eddy current losses of a laminated iron core in 2D efficiently and accurately. A rather coarse finite element grid suffices to approximate the homogenized solution of laminated media accurately. A representative numerical example for the electrostatic problem and one for the eddy current problem are presented to demonstrate the validity of multi-scale homogenization, the accuracy of the homogenized solution and to compare the computational costs. Index Terms—Eddy current losses, finite element method, lamination, multi-scale homogenization. I