Calculation of the Eddy Current Losses in a Laminated Open-Type Transformer Core Based on the A→,T→−A→ Formulation

Losses due to eddy currents in an open-type transformer core are significantly reduced by the lamination of the transformer core. In order to further reduce the eddy current losses, the open-type core often has a multi-part structure, i.e., it is composed of several more slender cores. The complete homogenization of such a core is not possible when an A→,V−A→ formulation is used, where A and V represent the magnetic vector potential and electric scalar potential, respectively. On the other hand, an A→,T→−A→ formulation, where T represents the electric vector potential, enables the complete homogenization of the general open-type core, but the simulation converges poorly due to the large number of degrees of freedom. By eliminating the redundant degrees of freedom, the convergence rate is significantly improved, and is at least twice as good as the convergence rate of the simulation based on the A→,V−A→ formulation. In this paper, a method for the calculation of the eddy current losses in an open-type core based on the A→,T→−A→ formulation with the elimination of redundant degrees of freedom is presented. The method is validated by comparison with a brute force simulation based on the A→,V−A→ formulation, and the efficiency of the method is determined by comparison with the standard homogenization method based on the A→,V−A→ formulation.