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.
- Decoupled OPF (DOPF)
- Semismooth Gauss-Seidel method
ASJC Scopus subject areas
- Applied Mathematics
- Control and Optimization