Application of Three-Dimensional Electromagnetic Analysis Methods to Electrical Machinery and Devices

In Part I (Theory) of this two-part paper, the three-dimensional vector potential solutions for nonlinear magnetostatic problems and linear eddy current diffusion problems were presented. The field problems were modeled by the finite element method using prismatic triangular and quadrilateral isoparametric elements. The zero divergence condition on the vector potential was enforced by means of a penalty function formulation. The iron nonlinearity was handled by modeling the B-H characteristics by cubic spline fits; and the nonlinear equations were quasi-linearized by an N-R algorithm. The resulting set of linear equations were solved by a fast and efficient pre-conditioned conjugate gradient solution algorithm.