Numerical integration by the 2-stage diagonally implicit Runge-Kutta method for electromagnetic transient simulations

Summary form only given. This paper proposes applying the 2-stage diagonally implicit Runge-Kutta (2S-DIRK) method of numerical integration to the calculation of electromagnetic transients (EMTs) in a power system. The accuracy and the numerical stability of 2S-DIRK are almost the same as those of the trapezoidal method, while 2S-DIRK does not produce sustained numerical oscillation due to a sudden change of an inductor current or a capacitor voltage unlike the trapezoidal method. Firstly, this paper reviews the 2S-DIRK integration scheme and derives the 2S-DIRK formulas of inductors and capacitors for both linear and nonlinear cases. Then, analytical comparisons of 2S-DIRK with the trapezoidal, backward Euler, and Gear-Shichman methods are carried out, and numerical examples which verify the analytical comparisons are shown. Finally, 2S-DIRK is compared with CDA (critical damping adjustment) implemented in EMTP (electro-magnetic transients program) for some simulation cases.