A New Modeling Method for Multiple-Relay Wireless Power Transfer System Considering Cross-Coupling

The cross-coupling among coils makes it complex to analyze and understand the circuit characters of multiple-relay wireless power transfer (MR-WPT) systems. In order to describe and explain the interaction among cross-coupled coils, this article proposes a novel method named the transfer coefficient model (TCM), which is derived by the lower-diagonal-upper (LDU) factorization of the system's impedance matrix. This model can describe the interaction among cross-coupled coil loops and the composition of each coil current, with clear physical meanings and recursion forms for programming. As a result, the input and output characters of MR-WPT systems can be obtained and explained explicitly. This article presents the comprehensive and recursion form of TCM for an arbitrary number of coils, followed by the analysis of MR-WPT systems under various operation modes. A five-coil prototype is built to demonstrate the system characters obtained from the TCM. The experimental results coincide with the theoretical analysis, indicating that the TCM is an effective approach for analyzing MR-WPT systems.