Enhancement of discriminatory power by ellipsoidal functions for substation clustering in voltage sag studies

Herein, an innovative methodology is proposed to improve the discriminatory power in the estimation of voltage sag patterns and substation groupings attributed to the power quality distribution. Regulation for the Brazilian energy context was considered for the analysis of real data. For this, factor analysis with varimax rotation was applied, which favors the explanation of latent variables. On the basis of these considerations, substation clusters were formed according to the level of similarity of the voltage sag based on the Ward's method. After that, the ellipses of confidence for the clusters were proposed and it was possible to estimate clusters for voltage sag regulatory purposes at three levels: low, medium, and high numbers of events. To prove the efficiency of this approach, the design of the experiments considered different multivariate configurations, linkage methods, and analysis. Then, simultaneous optimization was performed to verify the optimal parameterization that reduced the variance in the clustering estimation. The method was applied in different scenarios to verify the robustness for estimating cluster patterns. The method promoted better discriminatory power for the ellipsoidal functions to estimate the voltage sag patterns and substation groupings, providing results that are more reliable, precise, and stable.