3-D analyses of electromagnetic field including conductors connected with voltage sources

Three novel calculation methods for voltage-source problems with conductors, considering current distributions in conductors, have been developed using the finite element method and the A-φ formulation. The first is a dividing method for conductors. Equations for circuits including divided conductors are solved with Maxwell´s equations. The second performs two sequential procedures: (1) current distributions are solved by putting electrical potentials on boundaries of conductors using Poisson´s equation: and (2) eddy currents are solved by Maxwell´s equations with the solutions of (1). The sum of both currents is the real distributions in conductors. The third is a direct method to put electric potentials as the scalar potential on the boundaries. These methods are applied to two models. The inductances were also measured, and the experimental results have shown good agreement with the calculations