A Power-Balanced Time-Stepping Finite Element Method for Transient Magnetic Field Computation

Conventional transient finite-element methods (FEM) of magnetic field and electric circuit coupled problems often result in unbalanced power computation. In the worst case, the output power may be even miscomputed to be larger than the input power which violates all fundamental laws of physics. Eddy-current loss computation in laminated iron cores is usually carried out in a postprocessing algorithm, and thus the effect of eddy-current on both the system equations and other physical quantities cannot be included conveniently. This paper studies the power-balanced computation in FEM from two important aspects, which are, namely, the time integration algorithms and the inclusion of eddy-current loss in laminated iron cores of the system equations. A novel approach is presented, which retains the power balance property (i.e., all power, including the losses, are considered and balanced in both input and output) in the time integration process, to include the eddy-current loss effect in the FEM system equations. It also insures the solution is stable. Consequently, the input power, losses, and output power of the electromagnetic systems are balanced, and the accuracy of the solutions, especially the efficiency, is guaranteed. A numerical experiment is carried out on a laminated transformer to verify the accuracy of the proposed method.