Comparative application of the Crank-Nicolson and State-Space methods to the solution of nonlinear instantaneous eddy current and flux penetration problems in electrical machines

Two numerical methods are presented and compared for solution of nonlinear instantaneous electromagnetic diffusion problems. Finite differences are used for discretization of space. The Crank-Nicolson and improved State-Space methods are used for time. A magnetic vector potential (m.v.p.) formulation is used, which is effective in simplifying programming implementation to electrical machinery problems with complex contours. The methods are applied to a practical example of eddy currents, flux penetration and losses, and are found to yield results which are in excellent agreement with experimental test data. The results include a vivid display of the distortive effect of magnetic non-linearity on eddy current and flux density wave forms. The comparative suitability of both methods are evaluated in light of their characteristics and results.