Delay Dependent Stability Analysis of Load Frequency Control via Asymmetric Lyapunov-Krasovskii Functional

Time Delays are inevitable in the feedback loops of multi-area load frequency control (LFC), due to the deployment of an open communication network facilitating the transmission of signals from RTU to the control center, and from the center to the grid. Due to the existence of time delays in a communication network, the dynamic performance and stability of the LFC systems are adversely affected. It is necessary to incorporate the effect of time delay in the controller design. This paper focuses on the effects of constant time delays on the multi-area LFC system stability. The stability analysis of LFC subjected to time delays is investigated through the utilization of asymmetric Lyapunov-Krasovskii functional (LKF). Compared with symmetric LKF, asymmetric LKF provides relaxation on the condition that the matrix variables involved in LKF formulation need not be symmetric or positive definite, which provides less the conservativeness on the stability conditions. Further, to reduce the conservativeness, different tightly bounded integral inequalities are utilized in the derivation of stability conditions. By employing asymmetric LKF, two delay-dependent stability criteria are presented in the form of linear matrix inequalities (LMIs) for the systems under study such that an accurate delay margin can be obtained. The LFC system with one and two areas is taken into consideration with a PI controller to validate the efficacy of the proposed stability analysis. The PI controller gains are tuned by analyzing the relationship between PI controller gains and delay margin to balance the dynamic performance and the delay margin of the LFC system. Finally, simulation studies are conducted to validate the efficacy of the suggested methodology.