Explicit Runge-Kutta Methods with an Extended Stability Region: Accuracy Analysis and Applicability for Dynamic Simulation of Large Power Systems

Abstract

An explicit Runge-Kutta (RK) method with an extended stability region (ESR) can be constructed based on an RK method with a stability function corresponding to the Taylor series for the exponential function. Such a method modifies the base method's stability region in order either to include (or exclude) some areas of the complex plane or to elongate the stability region along one of the axes. There exist other techniques of constructing RK-ESR methods. This paper discusses their applicability for dynamic simulation of large power systems. It is shown that these methods decrease the accuracy in some areas of the complex plane. In particular, the accuracy degradation relates to low-frequency and/or poorly damped modes; decreasing the time step size in order to improve the accuracy is less efficient. The RK-ESR methods should be considered highly specialized and, in general, are not applicable for dynamic simulation of large power systems.