The Stability For Some Classes Of Uncertain Systems And Applications In Power System

In power system, due to effects from measurement error, model simplifying, external interference and time delay, some system parameters cannot be measured accurately, such as the uncertainty of wind power fluctuation and interval. In power market, factors including economy increasing, industrial structure and energy consumption structure, jointly come into a reason that makes the demand elasticity and the power demand uncertain. These uncertain factors influence the stability of power system and power market, so the research on their stability mechanism is essential to ensure the stable operation of power system.Combining the thought of randomness and interval, some stochastic and interval models are presented on a basis of the deterministic dynamic model put forward by Alvarado, which are more accurate and realistic. The theory of power system, economy and mathematics are adopted to analyze the stability of the corresponding models, including interval model, stochastic model and time-delay systems. These works are of great significance on the further research of random-certainty coupled power system. The main contributions are as follows.The interval model, stochastic model and interval stochastic model are established and their stability are analyzed. Pertaining to the random nature of demand sides and the range of demand elasticity with suppliers and consumers, using the theories of interval dynamical system, stochastic differential equation stability and stochastic process to give and prove the stability theorem of the corresponding model. The conclusions indicate that the demand elasticity stable interval can be calculated and the random excitation intensity does not impact the system stability. Some numerical examples are given to show the applicability and validity of the obtained results from a statistical perspective.A class of delay-dependent asymptotic stability for linear system with interval time-varying delay is considered. It is assumed that the time-varying delay belongs to an interval and no restrictions on its derivative. Adopting the approach of partitioning the delay interval into two segments of any length, a new type of appropriate Lyapunov-Krasovskii functional is constructed. Using improved integral equality and convex combination method on the derivative of the functional, several less conservative delay-dependent stability criteria are concluded. Numerical examples are presented to demonstrate the effectiveness of the proposed method.The problem of delay-dependent robust stability for uncertain stochastic systems with interval time-varying delay is investigated. In virtue of delay decomposition method of partitioning the delay interval into any two sub-intervals, a novel Lyapunov-Krasovskii functional is introduced without neglecting any useful terms. The new delay-dependent stability criteria, which are much less conservative than the results in existing literature, are proposed on the combination of some free weighting matrices, convex combination method, integral equality and linear matrix inequalities (LMIs) when processing the functional derivative. Taking classic numerical examples and the single machine infinite system as numerical examples, the numerical results show the effectiveness and validity of the proposed theoretical conclusions.