Low-Frequency Stabilized Formulations of Darwin Model in Time-Domain Electromagnetic Finite-Element Method

The Darwin model for electromagnetic quasistatic (EMQS) field analysis is of particular interest for the analysis of power electronic devices, such as power transformers and wireless power transfer systems. This model is an approach that neglects the second derivative term in time of the displacement current and considers the electrostatic field. This approximation allows conventional techniques for magneto-quasistatic (MQS) field analysis, such as considering nonlinear magnetic material properties and coupled circuit analysis, to be appropriated, and capacitance effects to be included. Several methods have been proposed for frequency-domain (FD) analysis. This is because it is difficult to properly derive a formulation of time domain (TD) analysis. We have already proposed a potential formulation in FD analysis and succeeded in obtaining appropriate calculation results. In this study, we propose a TD analysis of the low-frequency stabilization formulation in the finite element method. The proposed formulation is based on the Coulomb-type gauge condition, which defines no additional variables and redundant variables to improve the convergence characteristics. In addition, the system matrix can be made symmetric for solving by general preconditioners with iterative solvers.