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Article

Accurate and Efficient Derivative-Free Three-Phase Power Flow Method for Unbalanced Distribution Networks

1
Facultad de Ingeniería, Universidad Distrital Francisco José de Caldas, Bogotá D.C. 11021, Colombia
2
Laboratorio Inteligente de Energía, Universidad Tecnológica de Bolívar, Cartagena 131001, Colombia
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Electrical Engineering, Mathematics and Computer Science—MOR Group, University of Twente, 7522 NB Enschede, The Netherlands
4
Grupo GIIEN, Facultad de Ingeniería, Institución Universitaria Pascual Bravo, Campus Robledo, Medellín 050036, Colombia
5
Department of Electrical Engineering at KTH, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
6
Department of Engineering, Universidad Loyola Andalucía, 41704 Sevilla, Spain
*
Authors to whom correspondence should be addressed.
Academic Editors: George Tsakalidis and Kostas Vergidis
Received: 27 April 2021 / Revised: 14 May 2021 / Accepted: 24 May 2021 / Published: 27 May 2021
(This article belongs to the Special Issue Recent Advances in Process Modeling and Optimisation)
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 Δ- 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. View Full-Text
Keywords: banach fixed-point theorem; three-phase power flow formulation; upper-triangular representation; recursive formulation; genetic algorithm; phase-balancing banach fixed-point theorem; three-phase power flow formulation; upper-triangular representation; recursive formulation; genetic algorithm; phase-balancing
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MDPI and ACS Style

Montoya, O.D.; Giraldo, J.S.; Grisales-Noreña, L.F.; Chamorro, H.R.; Alvarado-Barrios, L. Accurate and Efficient Derivative-Free Three-Phase Power Flow Method for Unbalanced Distribution Networks. Computation 2021, 9, 61. https://0-doi-org.brum.beds.ac.uk/10.3390/computation9060061

AMA Style

Montoya OD, Giraldo JS, Grisales-Noreña LF, Chamorro HR, Alvarado-Barrios L. Accurate and Efficient Derivative-Free Three-Phase Power Flow Method for Unbalanced Distribution Networks. Computation. 2021; 9(6):61. https://0-doi-org.brum.beds.ac.uk/10.3390/computation9060061

Chicago/Turabian Style

Montoya, Oscar D., Juan S. Giraldo, Luis F. Grisales-Noreña, Harold R. Chamorro, and Lazaro Alvarado-Barrios. 2021. "Accurate and Efficient Derivative-Free Three-Phase Power Flow Method for Unbalanced Distribution Networks" Computation 9, no. 6: 61. https://0-doi-org.brum.beds.ac.uk/10.3390/computation9060061

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