Efficient Simulation of DC–DC Switch-Mode Power Converters by Multirate Partial Differential Equations

In this paper, multirate partial differential equations (MPDEs) are used for the efficient simulation of problems with two-level pulsed excitations as they often occur in power electronics, e.g., dc-dc switch-mode converters. The differential equations describing the problem are reformulated as MPDEs, which are solved by a Galerkin approach and time discretization. For the solution expansion, two types of basis functions (BFs) are proposed, namely classical finite-element nodal BFs and the recently introduced excitation-specific pulsewidth modulation BFs. The new method is applied to the example of a buck converter. Convergence, accuracy of the solution, and computational efficiency of the method are numerically analyzed.