A PCA-Based Consistency and Sensitivity Approach for Assessing Linkage Methods in Voltage Sag Studies

In the light of Brazilian energy regulatory context, cluster strategies are required to classify groups of substations for voltage sag purposes. Tuning cluster algorithms is not a trivial task, due to the fact that these methods are sensitive to small errors. Therefore, this study proposes a new methodology based on principal components analysis (PCA), attribute agreement and analysis of covariance to verify the level of consistency and sensitivity of the linkage methods in the cluster formation for voltage sag studies. In order to prove this methodology, real data from power quality indices of distribution substations are used. Four distinct scenarios with disturbances are evaluated. PCA is applied for dimensionality reduction of the data. Then, grouping is performed for eight different linkage methods and agreement analysis is applied. Ward method was the only one that presented 100% consistency in all scenarios, considered as the most robust method whereas k-means showed consistency of 94.11%, with inversion of the clusters. However, when evaluating their groupings, it was found that k-means was unable to adequately separate the groups for this dataset. Finally, the proposed methodology is adequate for choose cluster methods for extensive data and it can be extended to applications in different areas.