Three-stage implicit integration for large time-step size electromagnetic transient simulation with shifted frequency-based modeling

Abstract

To improve the computational efficiency of electromagnetic transient (EMT) simulation, the shifted frequency (SF)-based EMT (SFEMT) simulation is proposed in the literature, and large time-step size can be adopted in the SFEMT simulation. In the existing SFEMT simulation, the trapezoidal (TR) method is used for numerical integration. Sustained oscillations will appear in the simulation due to the use of the TR method. To overcome this problem, this paper applies the three-stage singly diagonally implicit Runge–Kutta (3S-SDIRK) method to the numerical integration of SFEMT simulation. First, the SFEMT modeling is briefly reviewed, and the 3S-SDIRK method is introduced. Then, the numerical integration of SFEMT simulation using 3S-SDIRK is elaborated detailedly, and the merits of the 3S-SDIRK-based simulation are analyzed by comparing with the TR, 2S-DIRK and TR-BDF2-based simulations. Numerical results show that the SFEMT simulation using 3S-SDIRK for integration is free from numerical oscillation and is accurate and efficient.