Finite element modeling of magnetic field in electrical machines: Scalar or vector potential formulation part II: Comparison of results for test problems

The paper discusses the method of solving the finite element (FE) equations that describe the magnetic field distribution for scalar and vector potential formulations. The 3D field problems have been analyzed. The nodal FEs for a scalar potential and the edge elements (EE) for a vector potential are considered. The FE equations have been described using the language of circuit theory. For selected test problems comparisons are made between the results of scalar and vector potential applications. Forces in systems containing permanent magnets and torques in permanent magnet machines are calculated and compared using both formulations. In the calculations, the methods with a non-unique description of branch sources in the scalar potential formulation and a non-unique solution of edge element equations for the vector potential formulation have been applied.