Convergence analysis of the triangular-based power ﬂow method for AC distribution grids - Maria Camila Herrera; Oscar Danilo Montoya; Alexander Molina-Cabrera; Luis Fernando Grisales-Noreña; Diego Armando Giral-Ramirez (Institute of Advanced Engineering and Science, 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.