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

Marcos Tostado-Véliz, Talal Alharbi, Hisham Alharbi, Salah Kamel and Francisco Jurado
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Marcos Tostado-Véliz: Department of Electrical Engineering, University of Jaén, 23700 Jaén, Spain
Talal Alharbi: Department of Electrical Engineering, College of Engineering, Qassim University, Buraydah 52571, Saudi Arabia
Hisham Alharbi: Department of Electrical Engineering, College of Engineering, Taif University, Taif 21974, Saudi Arabia
Salah Kamel: Department of Electrical Engineering, Faculty of Engineering, Aswan University, Aswan 81542, Egypt
Francisco Jurado: Department of Electrical Engineering, University of Jaén, 23700 Jaén, Spain

Mathematics, 2022, vol. 10, issue 8, 1-19

Abstract: 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.

Keywords: power-flow analysis; large-scale systems; continuous Newton’s method; Runge–Kutta formula; order of convergence; computational efficiency; numerical stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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