Solving realistic large-scale ill-conditioned power flow cases based on combination of numerical solvers

With the increasing electricity consumption and difficulty in upgrading existing infrastructures, ill-conditioned power flow (PF) cases are becoming more frequent nowadays. In this context, classical robust solvers may be unsuitable for realistic networks, which typically encompass thousands of buses, because of their high computational burden or low convergence rate. This article tackles this issue by proposing a novel PF solver, which presents acceptable robustness and efficiency in solving large-scale ill-conditioned systems. The proposed algorithm collects the advantage of various numerical solvers, which by separate present different weaknesses, but actuating in coordination their strengths can be jointly exploited. More precisely, the robust Forward-Euler and Trapezoidal rules are combined with the efficient Darvishi cubic technique. Thereby, an original predictor-corrector algorithm is developed to effectively coordinate the different numerical algorithms involved, obtaining a robust but efficient yet solution procedure. Various large-scale ill-conditioned benchmark systems are studied under different stressing conditions. The results obtained with the developed technique are promising, outperforming other robust and standard PF solvers.