An active multiphase probabilistic power flow based on a clustering approach

Abstract

Probabilistic methods for analyzing power systems have become more widespread, mainly due to the increase in load and generation uncertainties and the current need for planning problems that are sufficiently accurate to take appropriate actions. However, some characteristics need to be better investigated in the Distribution Systems (DS) analysis, such as the input random variables’ modeling using real databases and, mainly, the probabilistic treatment of unbalance and scalability studies. This paper proposes an active Multiphase Probabilistic Power Flow (MPPF) evaluation, considering real measurement databases to represent customer demand uncertainties. It is called Multiphase Probabilistic Power Flow Based on K-Means (MPPFKM), and it encompasses a mixture of a clustering technique and an analytical method. The K-Means algorithm divides the input database into a set of clusters that models the scenarios to be evaluated in the multiphase power flow problem, which considers the distribution network with its inherent unbalance. Subsequently, the output variables’ higher order statistical moments are calculated using the obtained responses for each cluster. Finally, their PDFs and CDFs are recovered using the Gram-Charlier Expansion analytical method. While the clustering algorithm allows working with real data, giving the proposed work greater proximity to real-world results, the analytical tool provides an accurate recovery of the probability functions, because it detects their distortions caused by the nature of the multiphase problem. Estimating the correct number of clusters is a key factor in obtaining the precision required by power systems engineers and achieving significant computational time reduction, especially for large-scale unbalanced systems. Simulations are carried out using several DS feeders to test the proposed method, which specifically addresses DS issues not yet well explored in the literature, such as probabilistic simulations under different unbalance situations, applications with single-phase DGs, and scalability studies are conducted using the IEEE 8500 test feeder. Comparisons are made with usual MPPF algorithms, including Monte Carlo Simulation (MCS) and Point Estimation Methods (PEM). Simulations using large-scale unbalanced systems proved that the output variables' probability functions might present distortions, becoming more challenging for other methods. Under this perspective, MPPFKM presents better exactness in the calculation of higher order statistical moments and, consequently, can estimate the PDFs of the MPPF output variables with great precision, which is crucial for statistical models that use actual input data.