Zero Duality Gap in Optimal Power Flow Problem

The optimal power flow (OPF) problem is nonconvex and generally hard to solve. In this paper, we propose a semidefinite programming (SDP) optimization, which is the dual of an equivalent form of the OPF problem. A global optimum solution to the OPF problem can be retrieved from a solution of this co...

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Bibliographic Details
Published in:IEEE transactions on power systems Vol. 27; no. 1; pp. 92 - 107
Main Authors: Lavaei, Javad, Low, S. H.
Format: Journal Article
Language:English
Published: IEEE 01.02.2012
Subjects:
Convex optimization
Integrated circuit modeling
Linear matrix inequalities
linear matrix inequality
optimal power flow
Optimization
polynomial-time algorithm
Polynomials
power system
Power systems
Programming
Symmetric matrices
ISSN:0885-8950, 1558-0679
Online Access:Get full text
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Summary:The optimal power flow (OPF) problem is nonconvex and generally hard to solve. In this paper, we propose a semidefinite programming (SDP) optimization, which is the dual of an equivalent form of the OPF problem. A global optimum solution to the OPF problem can be retrieved from a solution of this convex dual problem whenever the duality gap is zero. A necessary and sufficient condition is provided in this paper to guarantee the existence of no duality gap for the OPF problem. This condition is satisfied by the standard IEEE benchmark systems with 14, 30, 57, 118, and 300 buses as well as several randomly generated systems. Since this condition is hard to study, a sufficient zero-duality-gap condition is also derived. This sufficient condition holds for IEEE systems after small resistance (10 -5 per unit) is added to every transformer that originally assumes zero resistance. We investigate this sufficient condition and justify that it holds widely in practice. The main underlying reason for the successful convexification of the OPF problem can be traced back to the modeling of transformers and transmission lines as well as the non-negativity of physical quantities such as resistance and inductance.
ISSN:0885-8950
1558-0679
DOI:10.1109/TPWRS.2011.2160974