Application of gray relational analysis to k-means clustering for dynamic equivalent modeling of wind farm

Considering the characteristics of dynamic gray correlation among operational conditions of wind turbines, an innovative clustering method for dynamic equivalent modeling of wind farms (WFs) based on the dynamic gray cluster algorithm is proposed. The proposed method is used to determine the number and composition of equivalent wind turbine (WT) groups that can be used to represent a WF. Based on an analysis of auto-correlation coefficients among the various monitoring items of a supervisory control and data acquisition (SCADA) system for a WT, the time span of clustering samples is determined. Then, a correlation matrix of the clustering samples is constructed by using the dynamic gray relational analysis method. Finally, WTs are divided into groups by analyzing the abovementioned correlation matrix by using the k-means clustering algorithm, and WTs belonging to the same group are considered equivalent to one turbine to realize dynamic equivalent modeling of WFs. The method is demonstrated on a WF comprising 22 WTs connected to an IEEE 39 bus test system. Dynamic responses of the proposed model for the WF are compared against the response of the detailed model and other models for various scenarios. The comparison results show that the proposed dynamic equivalent model can describe the dynamic response characteristics of a WF with accuracy similar to that of the detailed model, and the proposed model is simpler and has lower computational complexity.