Formulations and Finite Element Discretization for Solving 2D Eddy Current Problems

Planar steady state skin effect problems in current driven solid conductors and solid windings with several coils are studied for axisymmetric and plane geometries. The formulations involve a field equation and a current constraint equation for each solid conductor. The proposed formulations include eddy currents, source currents and displacement currents. The finite element discretization is shown to rely on the same basis functions and assembly matrices for the planar and axisymmetric case and any degree of interpolatory basis functions can be used. This results in a very efficient implementation. The formulation also can be used to model passive conductors where induced eddy currents reveil the proximity effect. Furthermore complex problems as electric motors with several windings, solid or stranded, can be handled. All physical quantities can be derived from a complex scalar magnetic vector potential.