The Stability Analysis And Application Research Of Stochastic Complex Power System

With the development of the national economy, the demand for electricity has been growing, the scale of power system has become bigger, and system structure has become more complex diversity. The randomness like the stochastic faults, the stochastic load fluctuations, the stochastic harmonic, makes the modern power system become a multidimensional complex nonlinear dynamic system with lots of stochastic perturbations, and the stability and security analysis of stochastic power system is becoming more important. However, the existing deterministic system analysis method can no longer meet the requirements of the stability analysis of stochastic system. Therefore, based on the full analysis of stochastic disturbance characteristics of power system, it has important value of theory and application to apply the thought and the method of stochastic system theory into power system, to establish a more accurate model of power system, and to analysis the stochastic stability of power system.As a cross field of probability theory and differential equations, stochastic differential algebraic equations can directly put the stochastic disturbance factors which describe the characteristics of stochastic disturbance into the dynamic equations of the system. In recent years, there have been a series of theories and research results in finance, mathematics, physics and other fields. But the application of stochastic differential algebraic equations in the field of power system stability analysis is still in the initial stage. This paper firstly analyzed and classified the various stochastic disturbances in power system, then combined with the theory of stochastic differential equation and its numerical solution, and aimed at the external stochastic excitation, a linear model of power system with stochastic perturbations was constructed. And the result that the linear power system is mean stable and mean square stable under stochastic small disturbance was proved, and the critical stability criterion of stochastic linear power system was given. Then based on the model of stochastic linear system and the theory of modeling nonlinear power system, a nonlinear model of power system with stochastic perturbations was constructed. There are two different conditions, considering the stochastic disturbance of each generator as one stochastic item and considering the stochastic disturbance factor of each generator as different stochastic terms. And the result that the nonlinear system is mean stable and mean square stable with stochastic disturbances in different conditions was proved. Finally, combined with stochastic differential algebraic equations and the characteristics of power system, a method of modeling power system into stochastic differential algebraic equations, containing all kinds of disturbance of state variables, algebraic variables and parameters was given. And the universal significance of the method was proved through simulation.Stochastic system theory can further explain the physical meaning of stochastic disturbances in the power system, make the expression form of power system model more clear and accurate, and provide an effective solution for the security and stability analysis of stochastic power system. It has a wide development prospect in the analysis of complex multi-machine power system.