Fluxo de potência multifásico probabilístico baseado em clustering e recuperações analíticas: uma nova ferramenta para análise de redes de distribuição desequilibradas ativas com incertezas

Abstract

This thesis presents as its primary focus the formulation of a new tool for simulating the Probabilistic Power Flow, specifically designed for Electric Power Distribution Systems, in a manner that captures their inherent characteristics. The method is called the Clustering and Analytical Recovery-Based Multiphase Probabilistic Power Flow. It involves the use of clustering techniques to reduce precomputed random variable samples, the execution of deterministic analyses that consider the multiphase modeling of the network to estimate the primary statistical moments of the output random variables, and, finally, the application of a technique called the Gram–Charlier Expansion to analytically recover the probability density functions of the variables of interest. The tool incorporates a new procedure for determining the optimal number of clusters, aimed at achieving high-precision results while maintaining a computationally feasible time for planning and operational applications. This is based on the construction of a curve involving intra-cluster and inter-cluster distances of the input data, identifying the optimal number of clusters for each specific application. To test its applicability, a range of scenarios were simulated in which variables must be treated as random within the Multiphase Power Flow context. The results demonstrate that the method: (i) is capable of addressing the multiphase formulation of the network, including multi-grounded systems with explicit modeling of neutral and ground conductors; (ii) delivers high precision, ensuring trustworthy results and providing superior accuracy compared with established methods in the literature; (iii) is efficient from a computational time perspective, yielding rapid solutions; (iv) is flexible, accommodating a broad range of conditions for the input random variables — including spatial and temporal correlations, Gaussian and nonGaussian variables, and the simulation of unbalanced distribution networks with uncertainty in both photovoltaic generation and load demand; and (v) is scalable, allowing for the simulation of large-scale problems with a high number of random variables, including specific guidelines for addressing the so-called “curse of dimensionality” that causes clustering algorithms to lose precision as the number of variables increases.