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Zero Duality Gap in Optimal Power Flow Problem

Lavaei, Javad and Low, Steven (2010) Zero Duality Gap in Optimal Power Flow Problem. California Institute of Technology , Pasadena, CA. (Submitted)

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The optimal power flow (OPF) problem is nonconvex and generally hard to solve. We provide a sufficient condition under which the OPF problem is equivalent to a convex problem and therefore is efficiently solvable. Specifically, we prove that the dual of OPF is a semidefinite program and our sufficient condition guarantees that the duality gap is zero and a globally optimal solution of OPF is recoverable from a dual optimal solution. This sufficient condition is satisfied by standard IEEE benchmark systems with 14, 30, 57, 118 and 300 buses after small resistance (10^(-5) per unit) is added to every transformer that originally assumes zero resistance. We justify why the condition might hold widely in practice from algebraic and geometric perspectives. The main underlying reason is that physical quantities such as resistance, capacitance and inductance, are all positive.

Item Type:Report or Paper (Technical Report)
Low, Steven0000-0001-6476-3048
Additional Information:The authors would like to gratefully acknowledge John C. Doyle for fruitful discussions on this topic.
Group:Control and Dynamical Systems Technical Reports
Subject Keywords:Power System; Optimal Power Flow; Convex Optimization; Linear Matrix Inequality; Polynomial-Time Algorithm
Record Number:CaltechCDSTR:2010.004
Persistent URL:
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work after proper citation.
ID Code:28140
Deposited By: Imported from CaltechCDSTR
Deposited On:22 Jul 2010
Last Modified:09 Mar 2020 13:19

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