Many fault-related data are generated in the intelligent operation of power equipment, and analyzing these data can help understand the operating condition of the equipment. This paper studied the clustering analysis methods and introduced K-means, kernel C-means (KCM), and fuzzy kernel C-means (FKCM) methods. The gray wolf optimization (GWO) algorithm was used to optimize the initial clustering center and kernel parameters of the FKCM algorithm to obtain the GWO-FKCM algorithm. Experiments were conducted taking transformer data as an example. It was found that the GWO-FKCM algorithm obtained the optimal clustering results at the 763rd iteration, and its accuracy rates for different fault types were all above 90%, with an average value of 92.92%, which was higher than the other clustering analysis methods. The results prove the reliability of the GWO-FKCM algorithm for equipment fault data analysis. This algorithm can be promoted and applied in actual power equipment.