On the convergence of decoupled optimal power flow methods

Xiaojiao Tong, Felix F. Wu, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)


This paper investigates the convergence of decoupled optimal power flow (DOPF) methods used in power systems. In order to make the analysis tractable, a rigorous mathematical reformation of DOPF is presented first to capture the essence of conventional heuristic decompositions. By using a nonlinear complementary problem (NCP) function, the Karush-Kuhn-Tucker (KKT) systems of OPF and its subproblems of DOPF are reformulated as a set of semismooth equations, respectively. The equivalent systems show that the sequence generated by DOPF methods is identical to the sequence generated by Gauss-Seidel methods with respect to nonsmooth equations. This observation motivates us to extend the classical Gauss-Seidel method to semismooth equations. Consequently, a so-called semismooth Gauss-Seidel method is presented, and its related topics such as algorithm and convergence are studied. Based on the new theory, a sufficient convergence condition for DOPF methods is derived. Numerical examples of well-known IEEE test systems are also presented to test and verify the convergence theorem.
Original languageEnglish
Pages (from-to)467-485
Number of pages19
JournalNumerical Functional Analysis and Optimization
Issue number3-4
Publication statusPublished - 1 Mar 2007
Externally publishedYes


  • Convergence
  • Decoupled OPF (DOPF)
  • Semismooth Gauss-Seidel method

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization


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