Calculation of extra copper losses with imposed current magnetodynamic formulations

To solve a magnetodynamics problem, two potential formulations can be used. In the case of the A - rho formulation, the voltage at the terminals of a conductor is naturally imposed, which is not the case for the current flowing through the conductor. On the contrary, for the T - Omega formulation, the current can be naturally prescribed, but not the voltage. In order to impose the complementary electric quantity in both formulations, a physics-based approach using a power balance is proposed. Both magnetodynamic formulations are presented by considering a domain made up of multiple conductors. These formulations are used to study the copper losses induced by the franging of the magnetic flux around a small air gap of an iron core coil. Theoretical results are compared with experimental results.