Stochastic Stability Analysis of the Power Systems Based on Lyapunov Function

Abstract

With the development of new energy power systems, and the penetration of storage equipments and rechargeable equipments, it is imperative to study the stochastic stability of power systems. To determine the stability of the power systems, Lyapunov function played an important role. However, for nonlinear systems, there is no general method to construct Lyapunov functions, and the direct method gives sufficient conditions for the system, which makes it difficult to judge the stability of the system. In addition, if the Lyapunov function of the system exists, the Lyapunov function is generally not unique. In this paper, the equivalent stochastic model of two-machine power systems based on EEAC theory is taken as an example. The separable variable method is proposed to construct the Lyapunov function and then the weak stochastic asymptotic stability of the system is proved. The method is compared with the traditional Lyapunov first method to analyze the stochastic stability of the system. Finally, the case study is given and the stochastic response of the system is verified by simulation.