Chaos and Markov Based Approaches to Time Series Modeling of Power System Elements

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This project relates to research in advanced concepts in power system load and component modeling. The proposed project encompasses two distinct approaches to the modeling of irregularly time varying power system loads and elements to capture information from measurements (time series recorded data) so that those elements can be modeled accurately. The goal is to develop models directly from operating system data, thereby permitting continuously updated models without specialized tests and disruptive operating conditions. The models shall be used in control system design and for accurate dynamic simulations.The first modeling approach is based chaotic dynamics. The objective is to design a system of local linear approximations to the dynamics of a chaotic process that can be updated in real time as more observations become available or when the underlying process is subject to a slow drift. The second modeling approach is based on the concept of random iterations. It is a statistical approach that can work well when noise, approximation errors, or rapid time variability of system parameters make the first approach unreliable. Random iterations are well suited to explain chaotic series exhibiting statistical regularity in terms of stability of time averages. They can be used to make predictions about average future behavior with specified levels of accuracy and confidence and make predictions based on large data sets more feasible.An educational component of the proposed work is the development of Web-based resources for interdisciplinary graduate courses involving applications of nonlinear dynamics and statistics to contemporary engineering problems.