A novel method for the solution of a finite element-circuit coupled equation using an reduced equivalent equation

The Finite Element Method (FEM) has been extensively used to solve the field equations of electric machines or devices. It is possible to reduce the complexity of the method considering plane symmetry on the behavior of the magnetic field. Nevertheless, this simplification does not include the side effects of the magnetic field. It is possible to couple into the FEM field equation, a voltage-current circuit equation which includes resistances or inductances that allow a better modeling of the field side effects. Thus, a FEM-circuit coupled equation is obtained. In this paper, a novel method is proposed to solve a FEM-circuit coupled equation, and a field FEM equation in which its forcing function is known. The method consists on obtaining an reduced equivalent equation, using a nodal reordering of the field FEM equation and performing some matrix operations. The equivalent equation can be solved in the frequency domain and in the time domain.