Supplementary techniques for 2S-DIRK-based EMT simulations

• The trapezoidal method produces “fictitious” numerical oscillation in EMT simulations of power systems.
• The 2S-DIRK method which is inherently oscillation free has been successfully applied to EMT simulations.
• To bring out full accuracy of the 2S-DIRK method, supplementary numerical techniques are proposed in this paper.
• This paper illustrates these techniques with numerical examples.

Electromagnetic transient (EMT) simulations are now often used for system studies including power electronics converters which control voltages and currents using switching devices. The trapezoidal method, used in Electro-Magnetic Transients Program (EMTP) for numerical integration, produces “fictitious” sustained numerical oscillation, when an inductor current or a capacitor voltage is suddenly changed especially by switching. To cope with this problem, the research group of the authors has proposed applying the two-stage diagonally implicit Runge–Kutta (2S-DIRK) method which is an inherently “oscillation-free” numerical integration method. In order to bring out full accuracy of the 2S-DIRK method, supplementary numerical techniques are required for the representation of voltage sources, current sources and switches. This paper illustrates these techniques with numerical examples.