A LMI Based Approach to Power System Stability Analysis with Time Delay

Delay margin means the maximum delayed time that power system can sustain without losing its stability. Since, there exists significant time delay in the data of phasor measurement unit (PMU) and wide-area measurement system (WAMS), to evaluate system delay margin 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 evaluate power system delay margin. Lyapunov-Krasovskii criterion is firstly introduced to construct a suitable Lyapunov functional. Its derivative along the system trajectory is then expressed as a set of LMIs, which can be easily solved with LMI toolbox in Matlab or Scilab to obtain the system delay margin. In order to reduce conservativeness of the method, some slack variables are introduced in the derivation. Comparing with some existing numerical methods, such as eigenvalue based method, root clustering paradigm method, the presented method has a little conservativeness. However, it has much more flexibility and applicability in stability analysis to the time variant, nonlinear, switched and uncertain time delay systems. Finally, single-machine-infinite-bus (SMIB) system and WSCC 3-generator-9-bus system are employed to validate the effectiveness of the method.