Novel Structure-Exploiting Techniques Based Delay-Dependent Stability Analysis of Multi-Area LFC With Improved Numerical Tractability

Time-domain indirect methods based on Lyapunov stability theory and linear matrix inequality techniques (LMIs) have been applied for delay-dependent stability analysis of large-scale load frequency control (LFC) schemes. This paper aims to enhance the numerical tractability of large-scale LMIs by exploiting the special characteristics of the LFC loops. First, in the typical LFC model, only a few delayed states that are directly influenced by transmission delays are distinguished from other normal system states. Hence, an improved reconstruction model is formed, based on which the delay-dependent stability condition is established with the decreased order of the LMIs and decision variables. Then, to further improve the numerical tractability of the developed stability criterion, all weighting matrices required in the augmented Lyapunov functional are enforced to have structural restrictions by proposing an extended symmetry-exploiting technique. Case studies show that the method proposed in this paper significantly improves the calculation efficiency of stability criterion established for multi-area power systems at the cost of only a minor reduction in computational accuracy.