Title Accurate and efficient derivative-free three-phase power flow method for unbalanced distribution networks
Authors Montoya O.D. , Giraldo J.S. , Grisales-Noreña L.F. , Chamorro H.R. , ALVARADO BARRIOS, LÁZARO
External publication No
Means Computation
Scope Article
Nature Científica
SJR Quartile 2
Area International
Web https://www.scopus.com/inward/record.uri?eid=2-s2.0-85107848646&doi=10.3390%2fcomputation9060061&partnerID=40&md5=fa0bf93f1b496dbbb1a2d29f92ab8660
Publication date 01/01/2021
Scopus Id 2-s2.0-85107848646
DOI 10.3390/computation9060061
Abstract The power flow problem in three-phase unbalanced distribution networks is addressed in this research using a derivative-free numerical method based on the upper-triangular matrix. The upper-triangular matrix is obtained from the topological connection among nodes of the network (i.e., through a graph-based method). The main advantage of the proposed three-phase power flow method is the possibility of working with single-, two-, and three-phase loads, including ?-and Y-connections. The Banach fixed-point theorem for loads with Y-connection helps ensure the convergence of the upper-triangular power flow method based an impedance-like equivalent matrix. Numerical results in three-phase systems with 8, 25, and 37 nodes demonstrate the effectiveness and computational efficiency of the proposed three-phase power flow formulation compared to the classical three-phase backward/forward method and the implementation of the power flow problem in the DigSILENT software. Comparisons with the backward/forward method demonstrate that the proposed approach is 47.01%, 47.98%, and 36.96% faster in terms of processing times by employing the same number of iterations as when evaluated in the 8-, 25-, and 37-bus systems, respectively. An application of the Chu-Beasley genetic algorithm using a leader–follower optimization approach is applied to the phase-balancing problem utilizing the proposed power flow in the follower stage. Numerical results present optimal solutions with processing times lower than 5 s, which confirms its applicability in large-scale optimization problems employing embedding master–slave optimization structures. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
Keywords Banach fixed-point theorem; Genetic algorithm; Phase-balancing; Recursive formulation; Three-phase power flow formulation; Upper-triangular representation
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