Efficient Eigen-Analysis for Large Delayed Cyber-Physical Power System Using Explicit Infinitesimal Generator Discretization

Time delays significantly compromise the performance of wide-area measurement and control system and thus may jeopardize the stability of cyber-physical power systems (CPPS). A delayed CPPS (DCPPS) has a transcendental characteristic equation, leading to an infinite number of eigenvalues basically unsolvable by traditional eigen-analysis methods. In this paper, an explicit infinitesimal generator discretization (EIGD) approach is presented to tackle the traditionally intractable problem. First, the delayed differential equation of DCPPS is transformed to an ordinary differential equation by using an operator called infinitesimal generator. The operator is then optimally discretized, resulting in a highly structured, sparse and explicit approximant matrix. By exploiting the sparsity of the matrix and that of system matrices, the rightmost eigenvalues of the original DCPPS can be accurately computed. The contributions of the EIGD approach lie in the following: 1) it forms a theoretical foundation for accurately obtaining the critical eigenvalues of a CPPS with multiple delays; 2) it constructs a highly structured approximant matrix that enables efficient eigen-analysis of a large DCPPS by making full use of sparsity techniques; and 3) it integrates the shift-invert transformation, Arnoldi algorithm, Newton correction and eigen-sensitivity to form a computational framework for the analysis of large DCPPS. The accuracy, efficiency and scalability of EIGD have been extensively studied and thoroughly validated on the two-area four-machine test system and a practical large transmission grid.