On the Convergence of Decoupled Optimal Power Flow Methods |
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| Authors: | Xiaojiao Tong Felix F Wu Liqun Qi |
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| Institution: | 1. College of Mathematics and Computing Science, Changsha University of Science and Technology , Changsha, China tongxj@csust.edu.cn;3. Department of Electrical and Electronic Engineering , The University of Hong Kong , Hong Kong, China;4. Department of Mathematics , City University of Hong Kong, Kowloon Tong , Kowloon, Hong Kong, China |
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| 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. |
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| Keywords: | Convergence Decoupled OPF (DOPF) Semismooth Gauss–Seidel method |
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