The stability of synchronized state is essential for the stable operation and control of power network. This paper focuses on the multiplex oscillatory power network model, and then analyzes the stability of multiplex power network being comprised of Kuramoto oscillators. In specific, we infer the analytical important conditions for synchronous stability in a multiplex oscillatory power network. Furthermore, the adaptive controller is designed to achieve the frequency synchronization for multiplex power network. Combining analytical considerations with numerical simulations on small scale multiplex network, we address the synchronous stability and adaptive control in multiplex power network. In addition, we investigate synchronous cost of oscillatory power network via phase difference. It can be found that the synchronous cost of power network varies with different stable states. Therefore, our results can provide an innovative guide for adaptive control in conjunction with topology for stable operation.

同步状态的稳定性对于电网的稳定运行和控制至关重要。本文重点研究了多重振荡电网模型，然后分析了由仓本振荡器组成的多重电网的稳定性。具体而言，我们推断了多路振荡电力网络中同步稳定性的分析重要条件。此外，自适应控制器旨在实现多路电网的频率同步。将分析考虑与小规模多路网络的数值模拟相结合，我们解决了多路电网中的同步稳定性和自适应控制问题。此外，我们通过相位差研究了振荡电网的同步成本。可以发现，电网的同步成本随不同的稳定状态而变化。因此，我们的结果可以为自适应控制与拓扑相结合以实现稳定运行提供创新指导。