Cluster analysis of wind turbines of large wind farm with diffusion distance

Understanding the dynamics of power output of a wind farm is important for integration of large-scale wind energy. In a large complex dynamic system, such as a wind farm, clustering is a way to reduce the model complexity and improve the understanding of the model dynamics. This study presents a methodology for clustering wind turbines of a wind farm into different groups. A weighted graph is firstly designed to represent the complex relationships between the power outputs of wind turbines. Such graph is used to construct a Markov chain for estimation of the likelihood of wind turbines belonging to the same cluster. The spectral properties of the constructed Markov chain are analyzed to identify the number of clusters, so the elements of each cluster can be identified in a feature space. Theoretical study shows that the proposed methodology can simplify the dynamic model of power output of wind farm without compromising the overall dynamic characteristics of the original system asymptotically. The methodology of clustering is demonstrated and tested based on observations of power output of wind turbines in an actual wind farm. The methodology can be used to simplify controller design, and operation and forecast of wind farm output.