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Time delays are inevitable in load frequency control (LFC) of the power system, especially in a deregulated system where open communication networks are more favorable than the dedicated ones. However, extensive delays may affect the stability of a system. In this paper, an exact frequency-domain method for calculating the delay margin of LFC systems is presented, which is likely to be used to assess a system's stability caused by time-delays and guide the controller design. Firstly, a dynamic model of load frequency control systems is established, described by delay differential and algebraic equations (DDAEs). The Rekasius substitution is then employed to eliminate the transcendental terms in the characteristic equation without making any approximation. Afterward, an eigenvalue perturbation theory is introduced to transform the problem of calculating the delay margin into solving a series of one-dimensional nonlinear equations. Since only equivalent transforms are involved in the whole process, the delay margins obtained by the proposed method are exact. Finally, a two-area and a three-area deregulated LFC systems are applied to verify the correctness and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This letter proposes a method for calculating the sensitivity of delay margin with respect to system parameters. According to the property that the delay margin is achieved when the rightmost eigenvalues of the close-loop system locate exactly on the imaginary axis, a characteristic equation with inclusion of the delay margin is established. By differentiating the characteristic equation and further introducing normalization condition for the eigenvector, the sensitivity of the delay margin with respect to any given parameters can be obtained by solving a set of sparse linear equations. Due to the general differential and algebraic equation used in the derivation, the proposed delay margin sensitivity analysis method applies to various power system models and control problems. [ABSTRACT FROM AUTHOR]

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]