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

• Published in: Computation 2021, Vol.9 (6), p.61
• Main Authors: Montoya, Oscar Danilo, Giraldo, Juan S., Grisales-Noreña, Luis Fernando, Chamorro, Harold R., Alvarado-Barrios, Lazaro
• Format: Article
• Language: English
• Subjects: Algorithms; Applied and Computational Mathematics; banach fixed-point theorem; Efficiency; Electric power distribution; Energy conversion efficiency; Fixed points (mathematics); genetic algorithm; Genetic algorithms; Methods; Nodes; Numerical analysis; Numerical methods; Optimization; phase-balancing; Power; Power flow; Ratios; recursive formulation; Software; System effectiveness; three-phase power flow formulation; Tillämpad matematik och beräkningsmatematik; upper-triangular representation; Variables
• ISSN: 2079-3197; 2079-3197
• DOI: 10.3390/computation9060061

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.