MULTI-MODAL BEHAVIOR AND CLUSTERING IN DYNAMICAL SYSTEM WITH APPLICATIONS TO WIND FARMS

he objective of this research is to develop a comprehensive model identification approach for complex multi-modal systems based on spectral theory for nonreversible Markov process that entails (i)model reduction techniques for a nonreversible Markov chain, (ii) the identification of the modal dynamics, and (iii) modeling and identification of local dynamics. This dissertation addresses the theoretical approach, algorithmic development, computational efficiency and numerical examples of the developed techniques.The dissertation then presents a novel methodology for clustering wind turbines of a wind farm into different groups. The method includes creation of a Markov transition matrix given the power output of each turbine, spectral analysis of the transition matrix and identification approach of each group. An application of the method is provided based on real data of a wind farms consisting of 25 turbines and 79 turbines, respectively. The application shows that those distinct wind farm groups with different dynamic output characteristics can be identified and the turbines in each group can also be determined