Análisis y comparación de métodos multipunto Chebyshev–Halley para el cálculo del flujo de potencia en redes de corriente continua monopolares

Abstract

The increasing penetration of direct-current (DC) technologies in power transmission and distribution systems necessitates efficient and robust tools for steady-state analysis. This paper presents a comparative evaluation of the Chebyshev–Halley (CH) family of multipoint iterative methods against the classical Newton–Raphson (NR) method for power flow calculation in monopolar DC networks. Both methods were implemented in MATLAB and tested on four radial test systems of increasing complexity (10, 21, 33, and 69 nodes) under three distinct initialization scenarios: optimal (flat start), adverse (𝑉(0)=0.5 p.u.), and random (𝑉(0)∼𝒰[0.8,1.2] p.u.). Performance was assessed using key metrics including iteration count, CPU time, solution accuracy, and convergence failure rate. The results demonstrate that the cubic convergence of CH consistently reduces the number of iterations by one when compared to NR across all systems. However, this reduction does not translate into computational savings, as CH exhibits median CPU times 1.36 to 2.44 times higher than those of NR, given its higher cost per iteration, which involves solving two additional linear systems.