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High-Order Parity-Time Symmetric Model for Stable Three-Coil Wireless Power Transfer

A noteworthy challenge in actual wireless power transfer (WPT) applications is to achieve stable power transfer efficiency at varying distances. It was recently proposed and demonstrated that maximum transferred efficiency was ensured when a two-coil WPT system was always tuned at the purely real eigenfrequency. However, this condition prevents optimal operation with a fixed operating frequency. To address the issue, we introduce the concept of high-order (higher than second-order) parity-time (PT) symmetry to bypass this difficulty and construct straightforward physical pictures to obtain the mechanism of stable and efficient power transfer in a three-coil WPT system. Before the PT phase transition, there is a coupling-independent entirely real eigenfrequency, despite three branched eigenmodes existing. It means that this WPT system, with high-order PT symmetry, could be highly efficient without frequency tracking at varying distances. Additionally, the nonideal high-order PT model, with asymmetric coupling for practical WPT applications, is discussed. It is demonstrated experimentally that the efficient stability of the high-order WPT system is significantly superior to that of the second-order system at a fixed frequency, which can be explained by the fact that the eigenfrequency of the nonideal high-order model used is less sensitive to the coupling strength than that of the second-order model. Furthermore, the idle power loss of this WPT system is less than that of the other at the resonant frequency (in an idle state without receiver terminals), reducing power consumption at the transmitters and benefiting wireless charging intermittently. As an example, the high-order PT symmetric model is applied to the WPT system with miniaturized receivers, showing stable transfer efficiency with a wide range of axial transfer distances and lateral misalignment. Our work provides an alternative application for the study of high-order PT physics in designing a properly multiple-coil WPT system in the long term.