Stability Analysis of Load Frequency Control Systems with Sampling and Transmission Delay

To analyze the delay-dependent stability of a load frequency control (LFC) system with transmission delays, the continuous-time model with delay is usually adopted. However, practical LFC is actually a sampled-data system, where the power commands sent to generation units are updated every few seconds. It is therefore desirable to analyze the delay-dependent stability of LFC when sampling is introduced. This paper undertakes stability analysis of LFC with both sampling and transmission delay. The model of the LFC system is first modified to consider sampling and transmission delay separately. Based on Lyapunov stability theory and linear matrix inequalities, a new stability criterion for linear systems with both sampling and transmission delay is proposed using the Wirtinger-based integral inequality and its affine version. The proposed criterion is applicable for both time-invariant and time-varying transmission delays. Case studies are undertaken on both single-area and two-area LFC systems to verify the effectiveness and advantage of the proposed method.