Time Integration-Based IGD Methods for Eigen-Analysis of Large Delayed Cyber-Physical Power System

Two spectral discretization methods based on linear multistep and implicit Runge-Kutta discretization of infinitesimal generator (IGD-LMS/IRK) are presented in this paper for eigen-analysis of large delayed cyber-physical power system (DCPPS) with large time delays. First, the whole delay interval is partitioned into several sub-intervals by time delays in the system. The piecewise partitioning allows the avoidance of interpolations in evaluating system states at the delay points. Second, two time integration methods, i.e., LMS and IRK, are utilized to discretize infinitesimal generator on each sub-interval, resulting in highly structured and sparse discretization matrices. Third, IGD-LMS/IRK are efficiently implemented to compute the system's electromechanical oscillation modes. The shift-invert preconditioning technique is used and the sparsity in augmented system state matrices is exploited to guarantee the efficiency and scalability of IGD-LMS/IRK in dealing with large DCPPS. Numerical results on the two-area four-machine test system and a real-life large transmission grid validate the improved efficiency and accuracy of the proposed methods in analyzing DCPPS with large time delays.