Nonlinear Transient Finite Element Field Computation for Electrical Machines and Devices

This paper describes the procedure for analyzing nonlinear transient electromagnetic phenomena in electrical machines and devices with the finite element method. Two time integration methods are used which are based on (1) an implicit forward difference scheme and (2) the Crank-Nicholson method. The quasilinearization of the nonlinear matrix equation is handled by a simple chord iteration method in the former and the Newton-Raphson scheme in the latter. The associated variational expressions for the time-dependent diffusion equation are obtained in terms of energy-related functionals. The paper includes illustrative examples of application of the methods to one-and two-dimensional time-dependent eddy current problems in a conducting slab, a rotating machine under asynchronous operation, and a three- phase bus-bar enclosure.