Quasi-Convex NoC Optimization in the Active Multiphase Probabilistic Power Flow

This article proposes a new method to optimize the number of clusters (NoC) in the active distance-based clustering multiphase probabilistic power flow (MPPF). The objective is to determine a NoC that highly accurately promotes output variables without overloading the computational time. The method is based on intracluster and intercluster distance evaluations to achieve a good partition. A quasi-convex curve is formed to select the optimal NoC, ensuring an excellent computational time to converge. Tests are carried out using K-means, and simulations are conducted using IEEE unbalanced test feeders. Different input random variables are tested, including correlated and noncorrelated variables, with and without renewable distributed generators. The results prove that the input conditions significantly affect the optimal NoC. Comparisons are made with Monte Carlo simulation to justify the proposed application, showing that the computational time reduction provided by the clustering algorithm reaches up to ∼99% . Since the optimal NoC increases dramatically with the size of the input database, guidelines are proposed to reduce the MPPF dimensionality for more effective probabilistic procedures.