Stability criterion of load frequency control with multiple time-varying delays: A delays-dependent region partitioning approach

In this paper, considering the delay information of each area in the multi-area load frequency control (LFC) system with multiple time-varying delays, an augmented reciprocally convex approach and the Lyapunov theory is proposed for analyzing their delays-dependent stability. For the delay information about all N areas, the delay interval [−h, 0] is divided into 2 N subintervals by using a region partitioning approach, and then the previous LFC system model will be reconstructed. For this reconstructed model, the cross-convex method and the Wirtingerbased integral inequality are applied to the terms generated by the region partitioning approach, such that the stability criterion of multi-area LFC system with multiple time-varying delays can be attained. Meanwhile, comparing with the existing methods, the proposed method is less computation and less conservative. Three cases of the traditional two-area, deregulated two-area and the traditional three-area LFC systems are considered to verify the validity of the proposed stability criterion.