Accuracy Improvement of the <scp>2S</scp>‐<scp>DIRK</scp> Method for <scp>EMT</scp> Simulations of Highly Nonlinear Circuits

Power electronics converters used for HVDC transmission, renewable‐energy interconnection, and system control now play an important role in power systems. Since power electronics converters control power by fast switching of semiconductor devices, the electromagnetic transient (EMT) simulations of power systems including such power electronics converters are crucial. In the past, the trapezoidal method was used for the numerical integration in the EMT simulation, and numerical or fictitious oscillation due to sudden changes of inductor currents and capacitor voltages was considered problematic. To cope with this problem, supplementary methods for the trapezoidal method and oscillation‐free integration methods were proposed. The two‐stage diagonally‐implicit Runge‐Kutta (2S‐DIRK) method, which is one of the oscillation‐free integration methods, does not generate numerical oscillations. But it sometimes produces numerical spikes when highly nonlinear elements are included in the circuit. Since semiconductor switching devices and diodes are highly nonlinear devices, eliminating the numerical spikes is important for EMT simulations including power electronics converters. In this paper, the spike phenomenon is first discussed, and then a method to eliminate the spikes is proposed. Finally, the proposed method is validated by numerical examples. © 2025 The Author(s). IEEJ Transactions on Electrical and Electronic Engineering published by Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.