Iterative infinitesimal generator discretization-based method for eigen-analysis of large delayed cyber-physical power system

•The iterative IGD method is endowed with scalability for eigen-analysis of large DCPPS.•Blocks of infinitesimal generator's approximant are reformulated as Kronecker products.•The dominant block is factorized as sum of Kronecker products of system state matrices.•Sparsities in infinitesimal generator's approximant and system matrices are exploited.•Reformulation, preconditioning and IDR(s) ensure efficiency and scalability of IIGD.

To efficiently analyze the stability of large delayed cyber-physical power systems (DCPPS) incorporating wide-area damping controllers, an iterative infinitesimal generator discretization-based method (IIGD) for computing critical eigenvalues of the system is presented. IIGD contains three core techniques to guarantee efficiency and scalability. First, the sparsity of the infinitesimal generator's discretized matrix, which possesses identical spectrum to DCPPS, is explored by reformulating its blocks into Kronecker products. Especially, the dominant block is factorized as sum of Kronecker products of constant Lagrange vectors and system state matrices, which lays the basis of further utilizing the sparsities in the augmented state matrices of DCPPS. Second, the shift-invert preconditioning technique is applied to transform the required eigenvalues into those dominated in moduli. Third, the inverse iteration of the discretized matrix involved in sparse eigenvalue computation is iteratively achieved by utilizing the induced dimension reduction method (IDR(s)). Subsequently, the discretized matrix-vector product embedded in the method is efficiently implemented by exploiting the unique property of Kronecker product and the inherent sparsities in augmented system state matrices. The correctness, accuracy, efficiency and scalability of IIGD are extensively studied and thoroughly validated on the two-area four-machine test system and a real-life large transmission grid.