Evaluation of the Influence of the Load Resistance on Power and Efficiency in the Square and Circular Periodic WPT Systems

We are currently seeing an increasing number of devices that support wireless power transfer (WPT) technology. In order to avoid early prototyping and carry out a series of experimental analyses, it was possible to use numerical methods at the design stage to estimate the potential power transfer and efficiency of the system. The purpose of this study is to present a method of analysis for a periodic wireless power transfer system, using periodically arranged planar coils with field and circuit models. A three-dimensional numerical model of a multi-segment charging system with periodic boundary conditions was solved with the finite element method (FEM). An equivalent circuit model of the periodic WPT system was proposed, and the required lumped parameters were obtained using analytical formulas. Mathematical formulas were supplemented with the analysis of several geometric variants, taking into account different sizes of transmitting and receiving coils, as well as different numbers of turns. Both proposed methods of analysis allowed for the determination of load resistance values at which the variants of WPT systems considered in the research had maximum efficiency. The ranges of load resistance values in which the efficiency of the system exceeded 50% were indicated. The results obtained are very helpful in the proper selection of the load resistance, without the need for multiple tests and their resulting multiple measurements. The results also showed that the proposed circuit model was able to achieve similar accuracy as the numerical model, and the complexity of the model and analysis was significantly reduced. The obtained results will allow the design of WPT systems with appropriate selections of load resistance to achieve maximum efficiency.