Delay-Dependent Stability Criterion for Delayed Load Frequency Control Systems

In this paper, new results are presented for ascertaining delay-dependent stability of network controlled multiarea load frequency control (LFC) systems with time-invariant delay using Lyapunov-Krasovskii (LK) functional approach. In a networked control system, the feedback information (for effecting closed-loop control) is processed through a communication channel; as a result, time-delay appears in the feedback path. This delay adversely affects the performance of the closed-loop system and paves way to system instability. Delay-dependent stability analysis is carried out to compute the maximum value of the time-delay within which the system under consideration remains asymptotically stable in the sense of Lyapunov. In the presented stability analysis, to ascertain delay-dependent stability of the LFC system in a less conservative manner, an augmented LK functional is formulated, and the time-derivative of the functional is bounded without neglecting any useful terms using Wirtinger inequality. The presented stability criterion is tested on standard benchmark one-area and two-area LFC systems, and the obtained delay margins are compared with an existing result in literature. Simulation results are also presented to corroborate the effectiveness of the theoretical results.