A partial solution operator discretization-based method for small signal stability analysis of time-delay power systems

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 (SODPS)-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.