Application of Runge-Kutta's Implicit Methods for Solving Stiff Non-linear Dif-ferential Equations of a Single-Phase Transformer Model in the No-load State - Bernard BARON; Joanna KOLAŃSKA-PŁUSKA; Andrzej WAINDOK; Tomasz KRASZEWSKI; Aleksandra KAWALA-STERNIUK (Communications of International Proceedings, 2021)
In this paper Runge-Kutta implicit methods for solving stiff nonlinear problems were compared. For the study purposes three different approximations were tested: Gauss-Legendre, Radau and Lobatto. In order to compare the methods, the inrush current under no-load state of a 1-phase transformer was calculated. The calculation results were compared with those obtained from Gear method. The original algorithms were overworked and used in the analysis. Additionally, a method for decreasing the calculation time by a proper choosing of the initial condition was proposed and tested. In chapter 4 and 6 times for Jacobian calculations and for solutions of stiff nonlinear PDE were compared. The shortest time was obtained for LobattoIIIC approximation and was more than double better compared to Gear method.
Keywords: stiff nonlinear ordinary differential equations; Runge-Kutta implicit methods; peripheral model of a single phase trans-former