Journal
COMPUTATION
Volume 9, Issue 6, Pages -Publisher
MDPI
DOI: 10.3390/computation9060061
Keywords
banach fixed-point theorem; three-phase power flow formulation; upper-triangular representation; recursive formulation; genetic algorithm; phase-balancing
Categories
Funding
- Spanish Ministry of Economy and Competitiveness [DPI2016-75294-C2-2-R]
- Laboratorio de Simulacion Hardware-inthe-loop para Sistemas Ciberfisicos [TEC2016-80242-P]
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This research introduces a derivative-free numerical method based on an upper-triangular matrix to solve the power flow problem in three-phase unbalanced distribution networks, demonstrating its efficiency and computational advantages. The Banach fixed-point theorem is utilized to ensure the convergence of the method with Y-connected loads. Additionally, the application of the Chu-Beasley genetic algorithm and leader-follower optimization approach efficiently addresses phase balancing problems with optimal solutions and quick processing times.
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 Delta- 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.
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