Frequency‐domain homogenization for periodic electromagnetic structure

Abstract

PurposeThe purpose of this paper is to propose a general approach for the frequency‐domain homogenization of electromagnetic periodic structures. The method allows calculating macroscopic equivalent properties including local effects. It is based on the equivalence of active and reactive electromagnetic powers on an elementary cell. This work is applied to the modelling of eddy current losses in windings, by the use of the finite element method in 2D and 3D.Design/methodology/approachThe approach is based on an homogenization technique, allowing describing local properties (permeability and conductivity) and local effects (eddy currents) of periodical structures, through macroscopic homogenized behaviour laws.FindingsIt was found that the presence of local loops of eddy currents at the local scale implies that the average values of the electric and magnetic field are different from the macroscopic fields. This implies some precautions to implement the homogenization. Furthermore, the question of the coupling of the macroscopic laws has been clarified.Research limitations/implicationsThe proposed method is limited to the frequency domain. Some additional work is necessary to extend the researches in the time domain.Practical implicationsThe proposed methodology is applied for determining losses in coils with the finite element method. The major interest of the method is that it allows taking into account local effects (losses in particular), with a reduced computational time.Originality/valueThe method proposed in this paper is general and clarifies the principle of homogenization in the case of periodical structure in presence of local eddy currents (local loops of current).