Finite element modeling of magnetic field in electrical machines: Scalar or vector potential formulation part I: Comparative description of methods

The scalar and vector potential formulations for electromagnetic fields calculation using finite element (FE) methods are discussed. Attention is paid to the application of these formulations in the 3D analysis of magnetic field in electrical machines. The nodal FEs for scalar potentials and the edge FEs for vector potentials are considered. The equivalent magnetic network models related to both formulations are described. The FE equations for the scalar potential represent nodal equations of the magnetic network with branches associated with element edges. The edge element equations for the vector potential are equivalent to the loop equations of the network with nodes in element centers. Finally the methods of winding description in the finite element space and the methods of calculation of magnetic flux linkage are discussed.