On the problem of calculating steady state modes of electric power systems under conditions of interval data uncertainty

¹ Faculty of Mathematics and Informatics, Navoi State Pedagogical Institute, 210100, Navoi, Uzbekistan
² Department of Higher Mathematics and IT, Navoi State University of Mining and Technologies, 210100, Navoi, Uzbekistan

^* Corresponding author: alim-ibragimov@mail.ru

Abstract

Currently, there are several approaches for dealing with uncertain (inaccurate) data. The main ones are methods of probabilistic analysis, fuzzy set theory and interval analysis. In this paper, we consider the problem of calculating the parameters of steady-state modes of electric power systems with interval uncertainty of the initial data. The main reasons and the relevance of the use of interval methods for calculating the parameters of steady-state modes of networks of electrical systems are described. First, an interval calculation model is formulated, and then some interval iterative methods for solving nonlinear nodal equations of electrical networks are studied. Algorithms for the interval methods of Gauss-Seidel and Newton-Raphson are proposed for solving nonlinear nodal equations of steady state electrical networks. To demonstrate the level of efficiency of the developed algorithms, several test calculations were carried out with interval parameters formed through the middle and radius of the interval. The results of numerical calculations using these methods show that the Newton-Raphson method is superior to the Gauss-Seidel method in terms of the number of iterations and optimality (with a smaller width) of interval solutions.