Accurate and efficient derivative-free three-phase power flow method for unbalanced distribution networks
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Date
2021-05-27
Authors
Montoya, Oscar Danilo
Giraldo, Juan S.
Grisales-Noreña, Luis Fernando
Chamorro, Harold R.
Alvarado-Barrios, Lázaro
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Abstract
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.
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Citation
Montoya, O. D., Giraldo, J. S., Grisales, L. F., Chamorro, H. R., & Alvarado, L. (2021). Accurate and Efficient Derivative-Free Three-Phase Power Flow Method for Unbalanced Distribution Networks. Computation, 9(6), [61]. https://doi.org/10.3390/computation9060061