Resonant Analysis of Magnetic Coupling Wireless Power Transfer Systems

For a general multi-coil magnetic coupling wireless power transfer (MC-WPT) system with different coil properties and non-negligible cross couplings, there is no analytical solution that connects the resonant frequencies of the system to its electric parameters. Establishing such a generalized analytical solution not only permits quantitative analysis of resonant points but also provides a generic platform for the physical interpretation of resonance. For this purpose, a novel modeling and analysis method of integrating time domain and frequency domain is proposed in this paper, with that all possible resonant points of arbitrary coil MC-WPT systems can be quickly and accurately determined. First, an accurate state-space model of a general MC-WPT system with arbitrary number of transmitters, repeaters, and receivers is established and the analytical current response on each circuit is derived. Then, several key system concepts about resonance are elucidated, based on which the generalized analytical expressions of resonant points of MC-WPT systems, including resonant frequencies and corresponding powers and efficiencies, are derived. Furthermore, the physical interpretation along with the mathematic relationships of several key easy-confusing concepts are deduced, which provides a systematic theoretical criteria for the selection of operating frequency to achieve the resonant states for MC-WPT systems.