Generalized Primitive Stamps for Nonlinear Circuit-Field Coupling in the Transient Case

The simultaneous solution of circuit and field equations is often required in the analysis of magnetic devices. Although schemes for the solution of this coupled problem have been proposed, the existing formulations are usually tied to specific time discretization or nonlinear iteration expressions and therefore lack generality. In this paper, a highly systematized approach is proposed for strong circuit-field coupling in a transient finite element context, by identifying primitive stamps for field elements, circuit elements, and circuit-field couplings. The filamentary and solid conductors of the field model are the key elements for systematic interconnection using generalized stamps and modified nodal analysis. As a result, the coupling equations are treated just as any other circuit element, simplifying the implementation and providing a unified framework for circuit-field analysis. Both circuit and field stamps are independent of the time discretization and nonlinear solving procedure. With the proposed scheme, the finite element equations can be linked to circuits of arbitrary topology. The theory is developed for the axisymmetric and Cartesian 2-D cases and several examples are then solved to show the effectiveness of our new approach. Solutions are compared with those produced by well-known and validated commercial software packages which implement different, proprietary, and/or undisclosed circuit-field coupling methods.