Montoya, Oscar DaniloGiraldo, Juan S.Grisales-Noreña, Luis FernandoChamorro, Harold R.Alvarado-Barrios, Lázaro2021-07-292021-07-292021-05-272021-07-29Montoya, O. D., Giraldo, J. S., Grisales, L. F., Chamorro, H. R., & Alvarado, L. (2021). Accurate and Efficient Derivative-Free Three-Phase Power Flow Method for Unbalanced Distribution Networks. Computation, 9(6), [61]. https://doi.org/10.3390/computation9060061https://hdl.handle.net/20.500.12585/10334The 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.21 páginasRecurso en línea / Electrónicoapplication/pdfenghttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/article10.3390/computation9060061Banach fixed-point theoremThree-phase power flow formulationUpper-triangular representationRecursive formulationGenetic algorithmPhase-balancinginfo:eu-repo/semantics/openAccessAtribución-NoComercial 4.0 InternacionalUniversidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarLEMB