Eigenvalue Sensitivity and Eigenvalue Tracing of Power Systems With Inclusion of Time Delays

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.