Analysis of synchronous stability and control of multiplex oscillatory power network

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.