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This letter proposes an efficient method for com-puting the delay-margins of large-scale power systems with single constant delay. The method computes the margin by identifying the minimal delay under which some eigenvalues are about to cross the imaginary axis from the left to the right half complex plane. Based on the Rekasius substitution, a new characterization for the crossing points is developed, followed by a method for determining the delay margins. The method only involves eigen-value decomposition on a low-order matrix whose dimension is independent of the system scale. Further leveraging the sparsity of power systems makes it computationally very attractive for practical large-scale system applications. [ABSTRACT FROM AUTHOR]

This paper proposes a new discretization model for computing the rightmost eigenvalues, i.e., the dominant modes, of the power system with inclusion of time delays. At first, a general model of the time-delay power system is introduced. This model can be adopted for analysis of both retarded and neutral-type time-delay systems. Then, based on the general model, a discretization method for computing the rightmost eigenvalues is developed. In the method, only the retarded variables are required to be discretized. As a result, the order of the proposed model is far less than the order of existing models for solving eigenvalues of time-delay power systems. Meanwhile, the sparsity of the original power system model is passed down to the discretized model. The proposed model is tested on 5 power systems, from 4 machines to 562 machines, to show its effectiveness and efficiency. [ABSTRACT FROM AUTHOR]

As the operational conditions of power systems change, the operating point (i.e., the equilibrium point) may approach the small-signal security boundary. Given the current operating condition as well as the load and generation variations, it is meaningful to compute the small-signal security margin (SSSM). In this paper, an effective method that consists of three stages to compute the SSSM is proposed and examined. In the first stage, which is an estimation stage, the critical mode crossing the damping ratio line is estimated. The SSSM is then computed by a test function or by a direct method in the second stage, which is a correction stage. The computational results are then verified in the third stage, which is a verification stage. Numerical results on a 10-machine and a 160-machine system (with the state variables being 1600) show that the proposed three-stage method is efficient and promising. [ABSTRACT FROM AUTHOR]

As time delays of some remote signals cannot be ignored, the power system model must be represented as time-delay differential and algebraic equations. For this case, we can analyze the local dynamical characteristic of the system by calculating the eigenvalues of the related linearized system. In this paper, we present some practical tools to evaluate the impact of the delays on system modes. First, we derive an analytical method for computing the eigenvalue sensitivity. A Newton method for computing the exact eigenvalues of the time-delay system is then proposed, followed by an eigenvalue tracing method to obtain the eigenvalue trajectory when the delay varies. To realize the methods, a general linearized model and the generalized eigenvalue problem formulation are adopted. The proposed methods are applied to analyze the oscillation modes of two power systems with wide-area controllers. [ABSTRACT FROM AUTHOR]

As power system operation conditions vary, the system may move into critical operating conditions with oscillatory behaviors. In this paper, a generation rescheduling method is proposed for damping critical modes so that oscillations can be suppressed. This proposed method calculates the analytical eigenvalue sensitivity to identify the most effective generators for rescheduling to enhance the damping of the critical mode, thereby suppressing the oscillations. The eigenvalue sensitivity calculation is based on the structure-preserving network representation and the generalized eigenvalue problem. Numerical evaluation of the proposed method is performed with a focus on mode shape and participation factor analysis. The results show that the proposed method is effective in controlling power system oscillations via generation rescheduling. [ABSTRACT FROM PUBLISHER]

This paper describes inexact two-sided Jacobi- Davidson (ITSJD) method to compute the critical (least damping ratio) eigenvalues and corresponding left and right eigenvectors of power systems. Using approximation correction vectors to expand search spaces of two-sided Jacobi-Davidson method leads to ITSJD, which is used to compute eigenvalues closest to the target. Only one LU factorization is needed in whole iteration to improve the computing efficiency. The critical eigenvalues are mapped to extreme eigenvalues of Cayley transformation matrix which can be calculated by using ITSJD. The proposed method has been tested on systems with orders of 493, 1461, and 3781. The results show that ITSJD is effective and able to compute the critical eigenvalues and eigenvectors. [ABSTRACT FROM PUBLISHER]

The dominant modes of the system can be described by the critical eigenvalues, which reflect the stability and stability margin. This paper proposes a dominant mode identification (DMI) method to assess the stability of the grey-box grid-tied converter. First, the analytical relationship between the eigenvalues and the transfer function is clarified based on the small-signal model. Furthermore, the critical eigenvalues are estimated by the system's transfer function. On this basis, the discrete transfer function of the grey-box grid-tied converter is constructed utilizing the frequency sweeping technique. Finally, the critical eigenvalues are determined using the measured data based on the customized particle swarm optimization algorithm. The method can apply to different grid connection scenarios of converter-based components and is easy to implement. The DMI method can not only assess the stability margin of grey-box grid-tied converters in operation, but also predict the stability of black-box converters after being connected to the grid in the planning stage. • The relationship between the frequency responses and the eigenvalues is clarified. • The stability is analyzed according to the dominant mode of the system. • The method can pre-analyze the stability of the black-box converter. • The PSO algorithm for identifying dominant modes is easy to implement. [ABSTRACT FROM AUTHOR]