Numerical integration methods in long-term dynamic calculations

This paper compares the Runge-Kutta, Adams-Bashforth, Adams-Molten, and Gear numerical integration methods with each other. These methods are abbreviated as R-K, A-B, A-M and Gear methods, respectively. They are applied first to analyze a simple linear system of the analytical solutions of which are known. Afterward, they are used for the analysis of power systems. In this study, the explicit methods (R-K and A-B methods) are combined with the alternate solution method, and the implicit methods (A-M and Gear methods) are combined with the simultaneous solution method. Since the Newton-Raphson method is used as the simultaneous solution method, it becomes difficult to set the initial values. This difficulty is overcome using the decoupled Jacobian matrix.