Structure-Exploiting Delay-Dependent Stability Analysis Applied to Power System Load Frequency Control

Linear matrix inequality (LMI) based delay-dependent stability analysis/synthesis methods have been applied to power system load frequency control (LFC) which has communication networks in its loops. However, the computational burden of solving large-scale LMIs poses a great challenge to the application of those methods to real-world power systems. This paper investigates the computational aspect of delay-dependent stability analysis (DDSA) of LFC. The basic idea is to improve the numerical tractability of DDSA by exploiting the chordal sparsity and symmetry of the graph related to LFC loops. The graph-theoretic analysis yields the structure restrictions of weighting matrices needed for the LMIs to inherit the chordal sparsity of the control loops. By enforcing those structure restrictions on weighting matrices, the positive semidefinite constraints in the LMIs can be decomposed into smaller ones, and the number of decision variables can be greatly reduced. Symmetry in LFC control loops is also exploited to reduce the number of decision variables. Numerical studies show the proposed structure-exploiting techniques significantly improves the numerical tractability of DDSA at the cost of the introduction of acceptable minor conservatism.