MSFEM for the Eddy Current Problem in a Laminated Core Including Hysteresis

A multiscale finite-element method is extended to allow for materials with hysteresis. The method is developed for an eddy current problem, coupled with a network. As an example, a laminated toroidal transformer core is considered. Utilizing the symmetry of the domain, the problem can be rewritten as a 2-D one. The multiscale method shows good results compared to the reference solutions for both the nonlinear problem with magnetization curve and with the inclusion of hysteresis by the Preisach model while preserving its main advantages of drastically reducing the number of degrees of freedom by utilizing a coarse mesh that does not resolve each single iron sheet. Both the multiscale solution and the reference solution are compared to measurement data. It is demonstrated that the inclusion of hysteresis is necessary in order to achieve a good approximation of the measurement data, which is used to identify both the magnetization curve and the parameters for the Preisach model.