Stability analysis of load frequency control for power systems with interval time-varying delays

Abstract

This study investigates the stability problem of load frequency control (LFC) for power systems with interval time-varying delays. The two categories of time delays, the lower bound being zero and non-zero, are considered. The systems can be described as time delay systems of load disturbances. First, an augmented Lyapunov–Krasovskii functional (LKF) is constructed. Some delay-dependent nonintegral terms and single integral terms are additionally introduced to make full use of the information on the system state variables and the time-varying delays. Second, to overcome the problem of nonlinear inequalities caused by the augmented LKF, the nonlinear inequalities are converted into linear matrix inequalities (LMIs) by applying the new negative definite inequality equivalence transformation lemma, which can be solved easily by the MATLAB LMI toolbox. A new stability criterion is presented by applying the Lyapunov stability theory. The stability criterion is less conservative than some existing literature studies, which further improves the stability margin for the power systems based on LFC. Finally, some numerical examples are given to show the effectiveness of the proposed method and the superiority of the results.