Small Signal Stability Analysis Of Power System With Uncertain Parameters

There exist many stochastic disturbances in modern power systems, such as random power fluctuations which be induced by wind generation. The random factors will make the power system becomes complex random-certainty coupled system, and affect the stability of the power system. Studies on stability mechanism of systems under uncertainties affecting is important to ensure the safe operation of the power system. Based on several common deterministic models of power system, some random models and interval models are established, which are more realistic. Using the corresponding theory of stochastic differential equations, interval method and other knowledge, the stability theorems are proved, and the theorems are used in the stability analysis of actual power systems. Our work laid the foundation for the further research of random-certainty coupled power system. Include the following:The p-moment stability for a class of stochastic linear systems are researched. The sufficient conditions of stability are provided by using Ito isometry formula, Cr-inequality and other tools, and the obtained theorems promote the conclusions existing. Using the theorems in this paper, the stability of a wind power integrated system under small Gauss type random excitation is analyzed. Besides, the effectiveness of analysis is validated by numerical simulation and skewness kurtosis test.The stability of systems with interval parameters and stochastic systems with interval parameters are studied respectively. By Lyapunov method, matrix inequalities, interval system theory, random theory and so on, the interval stability theorem of the deterministic model and the main stability theorem of stochastic models is proved. The theorems show that the stability of the power system can be determined by ranges of system operating parameters. Based on the asynchronous wind turbine model, considering uncertain parameters in actual systems, the interval models of asynchronous wind turbine system were built. Taking an actual asynchronous wind turbine system as simulation example, the numerical simulation shows that our theorem is not only effective but also practical.The problem of delay-dependent asymptotic stability for linear system with interval time varying delay is investigated. Delay-dependent stability criteria of the system are got through constructing a new type of Lyapunov functional. The functional is constructed using delay decomposition method based on three points. In the process of the simplification on the derivative, the piecewise analysis method and a new convex combination technique are being repeated used. Taking single-machine infinite bus system as numerical examples, the analysis of numerical examples shows that using the proposed method the delay-dependent stability margin is larger than other methods, which means the delay-dependent stability criteria is effectiveness and less conservatism.