Dual stepsize explicit numerical integration method and applications

Abstract

Numerical integration, or time domain simulation, is an important tool to study dynamical systems. Many dynamical systems are stiff, for instance, electric power systems consist of a variety of components with greatly different time scales. Although explicit integration methods are computationally efficient, they are not commonly used for studying stiff systems, because these methods may have numerical instability problems. In this paper, an explicit numerical integration method with dual stepsizes is proposed for analyzing stiff systems. The algorithm uses a small and a large stepsize to integrate different system components. Under the proposed decomposition, we demonstrate the numerical property and prove that dual stepsize integration is guaranteed to converge for all linear test systems in absolute stability. Thus, the method has both advantages: numerical stability and computational efficiency. The properties of the proposed method are illustrated through a mathematical example and two power system examples.