Validity of Finite Element Formulation and Solution of Three Dimensional Magnetostatic Problems in Electrical Devices with Applications to Transformers and Reactors

This paper shows that the three dimensional magnetostatic field formulation based on the magnetic vector potential curl curl equationi yields unique field solutions in the practical inhomogeneous, anisotropic case with a positive definite reluctivity tensor (laminated cores, etc.). It is also shown that this can be accomplished without the imposition of other constraints on the divergence of the vector potential, and still one obtains unique magnetic vector potential solutions. It will also be shown that in the finite element formulation, the stationary point of the energy functional is the minimum energy point.