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Highlights • Matrix perturbation theory is applied to stability analysis and control of DCPPS. • A perturbation-based eigenvalue tracking method is offered to track targeted modes. • It is a building block for optimally tuning WADCs to damp interarea oscillations. • Delay approximation effect on SOD-based eigenvalue method's accuracy is analyzed. • Identified key factors guide to select suitable parameters to precondition DCPPS. Abstract In this paper, the matrix perturbation theory is introduced to delayed cyber-physical power system (DCPPS) for analyzing the variations of eigenvalues and eigenvectors when small changes are imposed on system parameters and time delays. On one hand, a perturbation-based eigenvalue tracking method is presented to reliably track the targeted interarea oscillation modes so that wide-area damping controllers (WADCs) can be optimally designed to damp them. On the other hand, key factors affecting the accuracy of the solution operator discretization (SOD)-based eigenvalue computation methods for DCPPS are identified by matrix perturbation analysis, which provide a guidance for selecting suitable parameters to precondition the DCPPS. The study results on the 16-generator 68-bus test system validate the effectiveness of the two applications of matrix perturbation theory. [ABSTRACT FROM AUTHOR]

• The idea of partial spectral discretization is applied to the SOD-PS method. • Only the retarded system states are discretized, leading to the PSOD-PS method. • The PSOD-PS method can largely improve the availability and efficiency of SOD-PS. • Two implementation ways of rotation-multiplication preconditioning are derived. To analyze the small signal stability of large-scale time-delay power systems (TDPSs), critical oscillation modes are required to be reliably computed. The solution operator discretization with pseudo-spectral collocation (SOD-PS)-based method has been proposed to indirectly calculate critical eigenvalues from the solution operator's discretization matrix. However, dimension of the discretization matrix is dozens of times the number of system state variables, and thus limits the efficiency of SOD-PS. To resolve this, SOD-PS is evolved into partial SOD-PS (PSOD-PS) in this paper by applying the idea of partial spectral discretization (PSD). Specifically, only the discretization of retarded states is reserved instead of discretizing all system states in delay interval. The resultant partial discretization matrix exhibits very low order, which is close to the number of system state variables. In addition, the rotation-and-multiplication preconditioning technique is studied to efficiently capture oscillation modes with damping ratios less than the given threshold. Specifically, the preconditioning technique is implemented by two ways and their consistency is derived in detail. Both theoretical analyses and intensive tests on the 16-machine 68-bus test system, a real-life 516-bus provincial transmission system of China and the 33028-bus ultra-high-voltage (UHV) interconnected system of China verify the accuracy and efficiency of the presented PSOD-PS. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]