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Time delays are inevitable in the power systems with wide-area control signals, which may compromise the control pe-rformance and thus jeopardize the stability of the power systems. To analyze the impacts of system parameters on critical oscillation modes of a time-delayed power system (TDPS), a new method for eigenvalue trajectory tracking of TDPS is proposed in this paper based on the continuation theory of invariant subspaces. When small changes are imposed on system parameters, such as parameters of wide-area damping controllers (WADCs) and time delays, the invariant subspaces are continuously predicted and corrected, followed by the eigenvalues and eigenvectors. In the process, the predictor and corrector are computed by solving linear equations sparsely and in blocks, which is highly scalable and computationally efficient for large-scale power system applications. The 16-generator 68-bus test system and two real-world power grids in China are used to test and demonstrate the proposed method. The results show that the proposed method can accurately and efficiently track eigenvalue trajectories for TDPS, especially for large-scale power grids. In addition, the sensitivities of eigenvalues and eigenvectors with respect to WADCs’ parameters and time delays are obtained as by-products of the approach. [ABSTRACT FROM AUTHOR]

The existing spectral discretization-based methods (SDMs) are capable of accurately computing critical eigenvalues of large power systems when time delays in wide-area damping control loops are considered. However, SDMs suffer from huge dimension of the discretized matrices of spectral operators, which is usually dozens of times of actual system states. To resolve the problem, an idea of partial spectral discretization (PSD) is proposed in this paper where only the retarded state variables instead of all system states are discretized. Following the PSD idea, a partial and explicit infinitesimal generator discretization (PEIGD) method is presented for highly efficient eigen-analysis of large closed-loop delayed cyber-physical power system (DCPPS). In contrast to the original EIGD method, the order of the resultant discretized matrix of the infinitesimal generator is greatly reduced and close to the number of actual state variables. The computational burden of PEIGD can be an order of magnitude less than that of EIGD and nearly the same as eigen-analysis of a system without time delay. Moreover, PEIGD is endowed with exactly the same accuracy as EIGD in capturing critical oscillation modes. Both theoretical analyses and intensive tests on the 16-generator 68-bus test system as well as a 516-bus and a 33028-bus real-life large power systems verify the accuracy and efficiency of the presented method. [ABSTRACT FROM AUTHOR]

Modeling and formulation of a delayed cyber-physical power system (DCPPS) are the basis of small-signal stability analysis and control synthesis of the system. First, a logic describing the interconnections between various systems of delayed differential algebraic equations (DDAEs) and delayed differential equations (DDEs) is established. It clearly shows the transformation of the most general DDAEs of the non-index-1 Hessenberg form to the widely used DDEs with finite terms of actual delays. Second, the DDAE model of the index-1 Hessenberg form is formulated in detail for DCPPS, which features in preserving the inherent sparsity in system's augmented state matrix. Exploiting the sparsity guarantees the scalability in stability analysis and controller design of a large DCPPS. Third, three delay merge properties are presented with complete proofs, which indicate that the feedback and control delays in one control loop can be treated as one single time delay. The properties facilitate modeling and formulating DCPPS. Last, numerical studies are carried out on a real-life large DCPPS with wide-area damping controllers embedded. Test results validate the correctness of the presented theoretical backgrounds. [ABSTRACT FROM AUTHOR]

This paper presents a nonsmooth optimization-based method to optimally tune wide-area damping controllers in large delayed cyber-physical power system (DCPPS). The objective is to maximize the damping ratios of the weakly damped interarea oscillation modes under multiple operating conditions. An eigenvalue-perturbation and receding-tracking method is then proposed to reliably trace the targeted interarea oscillation modes during the optimization process. The Broyden–Fletcher–Goldfarb–Shanno method combined with the gradient sampling technique is employed to efficiently solve the presented nonsmooth, nonconvex, and nonlinear eigenvalue optimization-based problem. The effectiveness of the proposed method is validated by the significantly improved damping of the interarea oscillation modes in the two-area four-machine test system and a real-life large DCPPS. [ABSTRACT FROM AUTHOR]

In this paper, solution operator discretization methods with linear multistep and implicit Runge–Kutta (SOD-LMS/IRK) are presented for efficient eigen-analysis of large delayed cyber-physical power system (DCPPS). First, the time integration-based discretization generates highly structured approximate matrices to the solution operator. Exploitation of the structure ensures low computational burden and high efficiency in solving the matrix-inversion-vector product involved in eigenvalue computation. Second, the implicitly restarted Arnoldi algorithm is employed to compute critical eigenvalue from the solution operator's discretized matrices. SOD-LMS/IRK are endowed with scalability in analyzing very large DCPPS by fully utilizing the inherent sparsity in the augmented system state matrices. The main contribution of the presented SOD-LMS/IRK is the improved efficiency and scalability of existing SOD-PS (pseudo-spectral collocation) and SOD-LMS/IRK. Numerical results on the 16-generator 68-bus test system, a 516-bus, and a 33028-bus real-life large transmission systems validate the effectiveness of the proposed SOD-LMS/IRK. [ABSTRACT FROM AUTHOR]

In eigenanalysis 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. 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. First, the unique spectral mapping properties of solution operator are analyzed. The largest eigenvalues in moduli of the operator correspond to the ones of DCPPS with the largest real parts. Second, a rotation-and-multiplication preconditioning technique is presented to enhance the dispersion among eigenvalues of the solution operator's discretized matrix. Third, critical electromechanical oscillation modes of DCPPS with the least damping ratios are captured with priority and an accelerated convergence rate by the implicitly restarted Arnoldi algorithm. Subsequently, the small signal stability of DCPPS can be readily and reliably determined. 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. 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. [ABSTRACT FROM PUBLISHER]

This letter presents a computationally efficient approach to implement the spectral discretization-based methods for eigenanalysis of large delayed cyber-physical power system by intensively exploiting the unique property of Kronecker product. Theoretical analyses and numerical tests demonstrate the novelty and effectiveness of the efficiently implemented explicit infinitesimal generator discretization method. [ABSTRACT FROM PUBLISHER]