Convergence Analysis for Delay Dependent LFC Scheme for Power Systems Networks Over Open Communication Networks with Disturbances

This paper presents a delay-dependent convergence criterion for load frequency control (LFC) for smart power grid networks with the presence of disturbances and time-varying delays. The LFC scheme comprises delayed remote measurement and control signals with local state feedback signals. The convergence criteria are developed by using Lyapunov-Krasovskii functional for both symmetrical and asymmetrical time-varying delays associated with remote measurement and control channel. First, the analysis shows that all the power system states are bounded and asymptotically stable without the presence of disturbances. Then, the convergence analysis proves that all the power systems states are bounded and their bounds guarantee the convergence property of the
$H_{\infty}$
control with the presence of bounded disturbances. These convergence properties are achieved by using well know Linear Matrix Inequalities (LMIs). Compared with the existing design, the proposed analysis uses both symmetrical and asymmetrical time-varying delays in the measurement channel from RTU to the control center and in the control channel from the control center to the power generation unit. In contrast with reported designs, the proposed design and analysis uses the disturbances associated with the closed loop systems appearing from modeling errors and other external load disturbances and faults.