Flux penetration and losses in solid nonlinear ferromagnetics using state space techniques applied to electrical machines

A state space model is developed in terms of magnetic vector potential (M.V.P.),\bar{A}, for the calculation of instantaneous values of eddy currents, flux penetration, and losses in nonlinear solid ferromagnetics. Finite differences in space and sampled data techniques in time are used to obtain the solutions. This formulation is very effective in simplifying the computer programming implementation to electrical machinery problems, which contain a mixture of regions of air-gaps and conductors. An application of this technique to a solid steel damper bar in a salient-pole synchronous machine of the type used in hydroelectric pumped-storage stations is presented. Resulting damper bar losses, due to sinusoidal excitation are given and found to be in good agreement with experimental test data. Also, instantaneous flux density and current density wave forms are given for various depths into the bar with vivid display of the effects of nonlinearity. Equivalent bar resistances and reactances determined by the present method are compared with corresponding results obtained by earlier techniques. Favorable comparison is achieved.