The trapezoidal method faces numerical oscillation problems in electromagnetic transients (EMT) simulation of nonlinear circuits. Although the 2-stage diagonally implicit Runge-Kutta method (2S-DIRK) is L-stable and does not produce numerical oscillations

it has the problems of numerical spikes and difficulty in handling switching events. To address these problems

this paper proposes a modified 2S-DIRK (M2S-DIRK) numerical integration method. The paper first analyzes the numerical integration process of 2S-DIRK and explains the causes of numerical spikes. Then

the numerical integration formulas and companion model of M2S-DIRK are given

along with the design of an event location algorithm and a variable step-size scheme. Finally

the correctness and effectiveness of M2S-DIRK are verified by simulation examples. The simulation results show that the M2S-DIRK method inherits the L-stability of 2S-DIRK

fundamentally solves the numerical oscillation problem

effectively avoids numerical spikes

and can flexibly and accurately handle switching events. Compared with algorithms such as zero-crossing interpolation

critical damping adjustment

and characteristic compensation method

the M2S-DIRK method is simpler and has higher numerical stability

and is suitable for EMT simulation of nonlinear circuits.