Convergence analysis of the triangular-based power flow method for AC distribution grids

Maria Camila Herrera (Universidad Distrital Francisco José de Caldas)
Oscar Danilo Montoya (Universidad Distrital Francisco José de Caldas)
Alexander Molina-Cabrera (Universidad Tecnológica de Pereira)
Luis Fernando Grisales-Noreña (Instituto Tecnológico Metropolitano)
Diego Armando Giral-Ramirez (Universidad Distrital Francisco José de Caldas)

International Journal of Electrical and Computer Engineering
Vol 12, No 1: February 2022

This paper addresses the convergence analysis of the triangular-based power flow (PF) method in alternating current radial distribution networks. The PF formulation is made via upper-triangular matrices, which enables finding a general iterative PF formula that does not require admittance matrix calculations. The convergence analysis of this iterative formula is carried out by applying the Banach fixed-point theorem (BFPT), which allows demonstrating that under an adequate voltage profile the triangular-based PF always converges. Numerical validations are made, on the well-known 33 and 69 distribution networks test systems. Gauss-seidel, newton-raphson, and backward/forward PF methods are considered for the sake of comparison. All the simulations are carried out in MATLAB software.