The Stability For Time-Delay Systems And Application In Power System

There are many uncertainties,such as the uncertainty of parameters,the interference of random terms and the variation of time delay,which all have a great impact on the stability of the system in power system.It is important and significant to study the stability mechanism of the system affected by uncertain factors and to ensure the safe operation of the power system.Stochastic model with small Gaussian excitation,interval time-varying delay model and uncertain stochastic time-delay model,which are more realistic and established based on several common deterministic models in the stability analysis of power system.The p-moment stability of the double machine infinite system under random disturbance is analyzed by using the stability methods and theory in power system,stochastic differential equations in mathematics and other knowledge.Then further on the interval time-varying delay system and uncertain stochastic time-delay systems are studied,corresponding stability criteria are presented and the stability theorems are proved.It mainly includes the following work:The p-moment stability problem of double machine infinite power systems with small random disturbance is verified.By modeling a double machine infinite system with Gaussian random small excitation,the p-moment stability for classical double machine infinite power systems with synchronous generators under Gaussian random small excitation is researched based on the definition of stochastic stability and the content of related stability theorem.Then the Euler-Maruyama(EM)method is used to simulate the stochastic response and the power angle curve under random excitation intensity is analyzed.With the relationship between the p-moment and expectation,variance,skewness and kurtosis,as well as the introduction of the origin moment and the central moment,the meaning and application of p-moment stability in power system are more clearly expressed.The stability for a class of linear systems with interval time-varying delay is studied.Using the stability theory of differential equation,a new Lyapunov functional is constructed.The delay-dependent stability criterion for system combining with the free weight matrix and integral inequality is obtained by means of the segmentation method of time delay and the idea of convex combination during the processing of the functional derivative.The numerical example and the Western Systems Coordinating Council(WSCC)three machine nine nodes power system are analyzed by MATLAB Linear Matrix Inequality Toolbox(LMI).The results show that the upper bound of admissible delay and the stability margin of time delay are larger and less conservative compared with the results of previous literature,which indicates the validity of the given stability theorem and provide a better basis for the control system.The stability for a class of uncertain stochastic nonlinear systems with time delay is analyzed.The stability theorem is proved by constructing the suitable Lyapunov functional,applying the knowledge of time-delay system,stochastic differential equation theory,LMI method and Ito's formula,handling boundary cross terms mainly with integral inequality and free weight matrix.Through the numerical simulation of single machine infinite and double machine infinite system in power system,the results show that the scope of delay upper bound or delay stability margin is bigger when given the lower time delay,which verify the effectiveness and superiority of the theorem.