TY - JOUR
T1 - Accurate and Efficient Derivative-Free Three-Phase Power Flow Method for Unbalanced Distribution Networks
AU - Montoya, Oscar Danilo
AU - Giraldo, Juan S.
AU - Grisales, Luis Fernando
AU - Chamorro, Harold R.
AU - Alvarado, Lazaro
N1 - Funding Information:
This work was partially supported in part by the Laboratorio de Simulaci?n Hardware-in-the-loop para Sistemas Ciberf?sicos under Grant TEC2016-80242-P (AEI/FEDER), and in part by the Spanish Ministry of Economy and Competitiveness under Grant DPI2016-75294-C2-2-R.
Funding Information:
Funding: This work was partially supported in part by the Laboratorio de Simulación Hardware-in-the-loop para Sistemas Ciberfísicos under Grant TEC2016-80242-P (AEI/FEDER), and in part by the Spanish Ministry of Economy and Competitiveness under Grant DPI2016-75294-C2-2-R.
Funding Information:
Acknowledgments: This work was supported in part by the Centro de Investigación y Desarrollo Científico de la Universidad Distrital Francisco José de Caldas under grant 1643-12-2020 associated with the project: “Desarrollo de una metodología de optimización para la gestión óptima de recursos energéticos distribuidos en redes de distribución de energía eléctrica.” and in part by the Dirección de Investigaciones de la Universidad Tecnológica de Bolívar under grant PS2020002 associated with the project: “Ubicación óptima de bancos de capacitores de paso fijo en redes eléctricas de distribución para reducción de costos y pérdidas de energía: Aplicación de métodos exactos y metaheurísticos.”
Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.
PY - 2021/5/27
Y1 - 2021/5/27
N2 - 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
AB - 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
KW - Banach fixed-point theorem
KW - three-phase power flow
KW - upper triangular representation
KW - recursive formulation
KW - Genetic algorithm
KW - phase balancing
U2 - 10.3390/computation9060061
DO - 10.3390/computation9060061
M3 - Article
SN - 2079-3197
VL - 9
JO - Computation
JF - Computation
IS - 6
M1 - 61
ER -