K-means Clustering Method for Ultra-High Frequency Partial Discharge in Gas-insulated Metal-Enclosed Switchgear Based on the Elbow Method and Pearson Correlation Coefficient

Gas-insulated metal-enclosed switchgear (GIS) is widely used in power systems, and it may have insulation defects that can lead to serious accidents. Partial discharge (PD) monitoring of GIS is an efficient way to detect insulation defects. The K-means clustering method is often applied in PD monitoring, where the determination of the total number of clusters $\boldsymbol{k}$ significantly affects the clustering results. However, the selection of $\boldsymbol{k}$ often relies on experience, and there is less research focusing on the determination of the optimal number of clusters for K-means clustering. Therefore, to achieve better clustering effects, this article proposes a K-means clustering method by determining the optimal number of clusters based on the elbow method and Pearson correlation coefficient for GIS ultra-high frequency (UHF) partial discharge. For UHF partial discharge data of free metal particle defect, sharp point defect, and floating potential defect, the relationship curve of within cluster sum of square ($W C S S$) with respect to the number of clusters k was calculated. Based on the elbow method and Pearson correlation coefficient, the inflection point of the curve was determined based on the principle that the curve began to linearly decrease, thus determining the optimal number of clusters and performing K means clustering. The results show that the K-means clustering effect with the number of clusters determined by this method is good, and the classification accuracy for three typical GIS insulation defects is high. The total number of clusters determined by this method can be considered the optimal number of clusters, and this method can provide reference and guidance for the operation and maintenance of GIS.