Using Modal Participation to Improve Numerical Stability in Power System Simulations

This work presents a method for improving the numerical stability of the trapezoidal solver in discretized power system simulations. The approach identifies the appropriate physical locations in the system to apply optimized damping networks that mitigate spurious numerical oscillations. The identification procedure is based on the concept of state participation in the weak system modes. State participation is determined using the participation matrix, a concept borrowed from power system stability. The approach is tested on a standard benchmark system and the results are compared with the backward Euler method. Comparison shows that the trapezoidal method with the applied optimized damping is better able to capture high frequency transients while retaining acceptable numerical stability.