Detection And Prediction Of Chaos In Time Series And Their Applications In Power Systems

Two kinds of purpose of the chaos study in power systems are, firstly to prevent or remove the undesired chaos, secondly to utilize the existing chaos objectively. Two kinds of mathematical tools for chaos study are the mathematical equations of power systems and the time series sampled from the real power systems.The detection and prediction of chaos in time series of power systems are studied in this dissertation. Some methods of chaos detection and prediction are improved, and are used to power systems. Then the following results are gotten.In the fields of power system stability. Chaos and instabilities caused by unstable limit sets can be detected real-timely by the techniques of estimating the largest window Lyapunov exponent (1 combining the matrix eigenvalues shifting techniques. In addition, it is proved that there is no chaos in the classic equations of transient processes.In the short term load forecasting. The given time series are the 24h load records of a northern area in China. The series are thought as "double periods + chaos" after the analyses of their power spectra, (1 and correlative dimensions. The short term load forecasting precision comes from the forecasting errors of chaotic component, since there is no error directly resulted from the forecasting of double periodical component. The predictable time, which is estimated by observing the "overlapping phenomena" in the time delay space trajectories of chaotic component, is approximately 3 days. "Double periods + chaos" method can be also used to forecast the short term loads successfully. A large amount of simulations provide basic materials for optimizing the forecasting of chaotic component. The causes of chaos of load records are also discussed. It is found that a stochastic process with memory is the fundamental cause of the load chaos. A minor important cause is the chaotic weather.From the viewpoints of nonlinear dynamical studies, three contributions are made. (1) It is primarily found that chaotic characteristics can occur in "autoregressive stochastic processes AR(n)". (2) In a lower dimension chaoticsystem, the sum of all its positive (1 can be approximately estimated by observing the "overlapping phenomena" in the time delay space trajectories. (3) The behavior types of time series can be changed using the matrix eigenvalue shifting techniques...