Calculation of Critical Oscillation Modes for Large Delayed Cyber-Physical Power System Using Pseudo-Spectral Discretization of Solution Operator

In eigenanalysis of large delayed cyber-physical power system (DCPPS), power engineers are interested in critical electromechanical oscillation modes with damping ratios less than a specified threshold. To efficiently compute these modes, a method based on pseudo-spectral discretization of the solution operator of DCPPS (SOD-PS) is presented in this paper. First, the unique spectral mapping properties of solution operator are analyzed. The largest eigenvalues in moduli of the operator correspond to the ones of DCPPS with the largest real parts. Second, a rotation-and-multiplication preconditioning technique is presented to enhance the dispersion among eigenvalues of the solution operator's discretized matrix. Third, critical electromechanical oscillation modes of DCPPS with the least damping ratios are captured with priority and an accelerated convergence rate by the implicitly restarted Arnoldi algorithm. Subsequently, the small signal stability of DCPPS can be readily and reliably determined. In SOD-PS, the unique property of Kronecker product and the inherent sparsity in augmented system matrices are fully exploited to guarantee efficiency and scalability. The accuracy and efficiency of the presented method are intensively studied and thoroughly validated on the 16-generator 68-bus test system and a real-life large transmission grid.