Stability Analysis of Two-Area LFC Power Systems With Two Additive Interval Time-Varying Delays

Abstract

In this paper, the stability problem of load frequency control (LFC) based power systems with two additive interval time-varying delays is studied. Firstly, considering the time delays of transmission from control center to regulator and sensor to control center, the mathematical model of two-area LFC power system based on proportional integral control is established. Secondly, under the condition that the lower bounds of interval time-varying delays are non-zero, an augmented Lyaounov-Krasovskii functional (LKF) is constructed, and a new delay-dependent stability criterion is derived. Since the extension of LKF introduces the nonlinear term of time-varying delay square, a new negative definite integral inequality transformation lemma is used to transform the nonlinear matrix inequality in the stability criterion into linear matrix inequality (LMI) equally-without introducing additional conservatism. Finally, the maximum stability margin of the LFC power systems is obtained by using MATLAB LMI-toolbox, and simulation results based on Simulink-toolbox show the effectiveness of the stability criterion.