Cluster analysis of wind turbines of large wind farm

Understanding the dynamics of the power output of a wind farm is important to the integration of large scale wind energy into the power system. In a large complex dynamic engineering system, such as a wind farm, clustering is an effective way to reduce the model complexity and improve the understanding of its local dynamics. The paper proposes a novel methodology to cluster wind turbines of a wind farm into different groups based on a particular distance measure. We first build a weighted graph to represent the complex relationships between power output of wind turbines. The graph is used to construct a Markov Chain and estimate the likelihood of any two wind turbines belong to the same cluster. We analyze the spectral properties of the Markov chain to identify the number of clusters. With the proposed method, the elements of each cluster can be identified in the feature space. Theoretical study showed that the proposed methodology simplifies the model of the dynamics of power output of wind farm without compromising the overall dynamic characteristics of the original system asymptotically. This paper also presents the results of clustering of 25 wind turbines located in three distinct locations of a wind farm with the proposed methodology based on the real power outputs for illustration and verification purpose. Then the results of a comprehensive study of all turbines of the wind farm are also included. We show that the method effectively cluster the wind turbines into three groups. The methodology is very useful for simplification of controller design, operation and forecast of wind generation.