An improved power system stability criterion with multiple time delays

Since there exist significant time delays in the data of phasor measurement unit (PMU) and wide-area measurement system (WAMS), to evaluate their impact is very important for power system online stability assessment and controller design in the wide-area environment. In this paper, we use Lyapunov stability theory and linear matrix inequality (LMI) method to analyze the impact of time delays on power system stability. An improved delay-dependent stability criterion for power system stability analysis with multiple time delays is presented. Based on Lyapunov-Krasovskii theory, a proper Lyapunov functional is firstly constructed. And, in deduction of its derivative function along the system trajectory, some necessary slack variables are introduced so as to reduce the method conservativeness. Then the derivative function is expressed as a set of linear matrix inequalities, which can be easily solved with LMI toolboxes in Matlab or Scilab. Finally, a typical two-dimension time-delayed system and WSCC 3-generator-9-bus system with two time delays are employed to validate the method effectiveness. It is revealed that the presented method is correct, effective and with less conservativeness. Work of this paper is helpful for power system stability assessment and control with considering time delays under wide-area environment.