Accurate and efficient derivative-free three-phase power flow method for unbalanced distribution networks

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.

• Autores: Montoya, Oscar Danilo; Giraldo, Juan S.; Grisales-Noreña, Luis Fernando; Chamorro, Harold R.; Alvarado-Barrios, Lázaro
• Fecha de publicación: 2021
• Institución: Universidad Tecnológica de Bolívar
• Repositorio: Repositorio Institucional UTB
• Idioma: eng
• OAI Identifier: oai:repositorio.utb.edu.co:20.500.12585/10334
• Acceso en línea: https://hdl.handle.net/20.500.12585/10334
• Palabra clave: Banach fixed-point theorem; Three-phase power flow formulation; Upper-triangular representation; Recursive formulation; Genetic algorithm; Phase-balancing; LEMB
• Rights: openAccess
• License: http://creativecommons.org/licenses/by-nc/4.0/