Open AccessConvergence analysis of the triangular-based power flow method for AC distribution grids
Author(s) -
Maria Camila Herrera,
Oscar Danilo Montoya,
Alexander Molina-Cabrera,
Luis Fernando Grisales-Noreña,
D. Ramı́rez
Publication year - 2022
Publication title -
international journal of power electronics and drive systems/international journal of electrical and computer engineering
Language(s) - English
Resource type - Journals
eISSN - 2722-2578
pISSN - 2722-256X
DOI - 10.11591/ijece.v12i1.pp41-49
Subject(s) - triangular matrix , iterative method , convergence (economics) , newton's method , gauss–seidel method , mathematics , matlab , matrix (chemical analysis) , mathematical analysis , computer science , topology (electrical circuits) , algorithm , combinatorics , physics , pure mathematics , materials science , nonlinear system , quantum mechanics , composite material , economics , invertible matrix , economic growth , operating system
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.