Delay-dependent stability for load frequency control with constant and time-varying delays

Load frequency control (LFC) requires transmission of remote measurements to the control center and of control signals from the control center to the plant. Constant delays exist in the dedicated communication channel and an open communication network introduces time-varying delays. Those delays would degrade the dynamic performance of LFC and even cause instability. This paper investigates the delay-dependent stability of the LFC scheme by adopting a delay-dependent criterion and linear matrix inequalities (LMIs). The maximal delay time which allows a power system with a LFC scheme embedded to retain stable is defined as the delay margin for stability analysis. A proportional-integral (PI) controller using the area control error (ACE) as input signal is employed in the LFC scheme. Special attention is paid to the relationship between the gains of PI controller and the delay margin. Case studies are carried out based on one-area and two-area LFC schemes to demonstrate the effectiveness of the criterion. Both constant and time-varying delays are considered. Moreover, the accuracy of the criterion used is also verified by simulation studies.