Transmission Performance Analysis of Three-coil Wireless Power Transfer System with Relay Coils Based on Parity-Time Symmetric Principle

Based on the coupled mode theory, we analyzed the operational mechanism of the two-coil and three-coil parity-time symmetry (PT) wireless power transfer (WPT) systems. Initially, for the two-coil PT-WPT system, we solved for the eigenfrequencies of the system in the PT-symmetric state through mathematical derivation, elucidated the mechanism of the system automatically operating in the PT-symmetric state. We examined the stability of eigenfrequencies utilizing the Lyapunov stability theory. Subsequently, we extended the theory to the three-coil system containing relay coils and established a simplified model that neglects the internal resistance of the relay coils and cross-coupling between transmitter and receiver coils. Under this model, we deduced the eigenfrequencies of the system under different parameters, assessed their stability, and derived the expressions of output power and transmission efficiency, which guide the design and optimization of the system. Finally, based on the above theoretical analysis, we constructed a three-coil PT-WPT system model and carried out numerical simulation experiments using Simulink simulation software. The correctness of the theoretical model was verified by comparing the simulation results with theoretical values.