Abstract
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 language | English |
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Pages (from-to) | 467-485 |
Number of pages | 19 |
Journal | Numerical Functional Analysis and Optimization |
Volume | 28 |
Issue number | 3-4 |
DOIs | |
Publication status | Published - 1 Mar 2007 |
Externally published | Yes |
Keywords
- Convergence
- Decoupled OPF (DOPF)
- Semismooth Gauss-Seidel method
ASJC Scopus subject areas
- Applied Mathematics
- Control and Optimization