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.

中文翻译：

---

稳定三线圈无线功率传输的高阶奇偶时间对称模型

实际无线功率传输（WPT）应用中的一个值得注意的挑战是在不同距离上实现稳定的功率传输效率。最近有人提出并证明，当始终以纯真实本征频率调整两线圈WPT系统时，可以确保最大的传输效率。但是，这种情况会阻止以固定的工作频率进行最佳操作。为解决此问题，我们引入了高阶（高于二阶）奇偶时间（PT）对称性的概念来绕过此难题，并构造简单的物理图像，以在三级结构中获得稳定有效的功率传输机制。线圈WPT系统。PT之前尽管存在三个分支本征模式，但在相变过程中，仍存在一个独立于耦合的完全本征频率。这意味着，这种具有高阶PT对称性的WPT系统可以高效运行，而无需在不同距离进行频率跟踪。此外，非理想的高阶PT讨论了用于WPT实际应用的非对称耦合模型。实验证明，在固定频率下，高阶WPT系统的效率稳定性明显优于二阶系统，这可以通过以下事实来解释：所用非理想高阶模型的本征频率为对耦合强度的敏感性不如二阶模型。此外，该WPT系统的空闲功率损耗在谐振频率下（在没有接收器终端的空闲状态下）比其他WPT系统的功率损耗小，从而减少了发射器的功耗，并间歇性地受益于无线充电。例如，高阶PT对称模型应用于带有小型接收器的WPT系统，显示出稳定的传输效率，并且具有宽范围的轴向传输距离和横向未对准。从长远来看，我们的工作为高阶PT物理研究提供了另一种应用，可用于设计适当的多线圈WPT系统。