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

Chao Duan, Chuan Ke Zhang*, Lin Jiang, Wanliang Fang, Wei Yao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


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.

Original languageEnglish (US)
Article number7855826
Pages (from-to)4528-4540
Number of pages13
JournalIEEE Transactions on Power Systems
Issue number6
StatePublished - Nov 2017


  • Chordal sparsity
  • delay-dependent stability
  • linear matrix inequality
  • load frequency control
  • symmetry

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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