On Optimal Settings for a Family of Runge-Kutta-Based Power-Flow Solvers Suitable for Large-Scale Ill-Conditioned Cases

Growing demand, interconnection of multiple systems, and difficulty in upgrading existing infrastructures are limiting the capabilities of conventional computational tools employed in power system analysis. Recent studies manifest the importance of efficiently solving well- and ill-conditioned Power-Flow cases in a modern power-system paradigm. While the well-conditioned cases are easily solvable using standard methods, the ill-conditioned ones suppose a challenge for such solvers. In this regard, methods based on the Continuous Newton's principle have demonstrated their ability to address ill-conditioned cases with acceptable efficiency. This paper demonstrates that the approaches proposed so far do not extract the best numerical properties of such solvers. To fill this gap, an optimization framework is proposed by which the parameters involved in the two-stage Runge-Kutta-based solvers are appropriately set, so that the stability and convergence order of the numerical mapping are maximized. By using the developed optimization technique, three solvers with quadratic, cubic, and 4th order of convergence are developed. The new proposals are tested on a variety of large-scale ill-conditioned cases. Results obtained were promising, outperforming other conventional and robust approaches.