Analytical Determination of Capacitance and Conductance Coupling Matrices for Assisting the Design of Capacitively Coupled Planar Power Conversion Apparatuses

The emergence of higher performance capacitively coupled power conversion systems, for example, electrostatic rotating machines and capacitive power transfer, prompts the need for tools to assist the design and optimization process. Finite-element analysis (FEA) has been the default method to analyze these systems, due to the complexity of solving the electrostatic field in a multipotential-multimaterial structure. However, the variational and discretized nature of FEA introduces a bottleneck in the speed of the optimization process. This article presents an analytical approach that is capable of solving problems with nonzero electrode thickness and multiple materials, to evaluate the capacitance coupling matrix in planar power conversion apparatuses as an alternative to FEA. The duality between the electric displacement and the current fields allows this method to easily compute the conductance matrix as well, yielding effective loss models. When benchmarked against FEA for a synchronous electrostatic machine, this proposed analytical solution shows less than 2% relative error and takes merely 1 s to complete the computation for each set of design parameters, whereas the FEA takes 9 h.