![]() 26 Index Terms-Cyber-physical power system, eigen-analysis, 27 order reduction, small signal stability, spectral discretization, time 28 delay, wide-area damping control, wide-area measurement system. ![]() Both theoretical 23 analyses and intensive tests on the 16-generator 68-bus test system 24 as well as a 516-bus and a 33028-bus real-life large power systems 25 verify the accuracy and efficiency of the presented method. Moreover, PEIGD is endowed with exactly the same accuracy 22 as EIGD in capturing critical oscillation modes. The computational burden of 19 PEIGD can be an order of magnitude less than that of EIGD 20 and nearly the same as eigen-analysis of a system without time 21 delay. In contrast to the 16 original EIGD method, the order of the resultant discretized matrix 17 of the infinitesimal generator is greatly reduced and close to the 18 number of actual state variables. Following the PSD idea, a partial and 13 explicit infinitesimal generator discretization (PEIGD) method is 14 presented for highly efficient eigen-analysis of large closed-loop 15 delayed cyber-physical power system (DCPPS). idea of partial spectral discretization (PSD) is proposed 11 in this paper where only the retarded state variables instead of all 12 system states are discretized. However, SDMs suffer from huge 8 dimension of the discretized matrices of spectral operators, which 9 is usually dozens of times of actual system states. The existing spectral discretization-based methods 5 (SDMs) are capable of accurately computing critical eigenvalues 6 of large power systems when time delays in wide-area damping 7 control loops are considered. 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. 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. Subsequently, the small signal stability of DCPPS can be readily and reliably determined. Third, critical electrome-chanical oscillation modes of DCPPS with the least damping ratios are captured with priority and an accelerated convergence rate by the implicitly restarted Arnoldi algorithm (IRA). Second, a rotation-and-multiplication preconditioning technique is presented to enhance the dispersion among eigenvalues of the solution operator's discretized matrix. The largest eigenvalues in moduli of the operator correspond to the ones of DCPPS with the largest real parts. ![]() Works with the version of Ghostscript shipped with MATLAB, if found, or with a user-specified. properties of solution operator are analyzed. The resulting PDF file will contain one page for each page defined in the postscript file, so a multi-page postscript file, like those generated by using the '-append' option of MATLAB's print command, can be used to generate a multi-page PDF file. 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. In eigen-analysis 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. ![]()
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