Stochastic small disturbance stability analysis of nonlinear multi-machine system with Itô differential equation

The stochastic small disturbance stability is widely recognized as a major issue in the small signal stability of power system due to complex stochastic factors such as increasing large-scale renewable power grid integration, random fluctuations of electrical loads and so on. By the relevant theories of Itô differential equation, this paper proposes a new method to prove the mean stability and mean square stability of the power angle and the angular speed of the nonlinear multi-machine system under small Gauss random disturbances. In this approach, the stability criterion is derived from the system. Simulation results of 4-machine 11-bus system and the 16-machine 68-bus system using MATLAB demonstrate that the proposed method is able to analyze the stochastic small disturbance stability with high effectiveness and accuracy compared with the theoretical proof, and it is suitable for any nonlinear multi-machine system. Based on the application of stochastic differential equation, the influence of intensity and quantity of the random disturbances on the stability of the system is further analyzed.