Existence of strong Lagrange duals to certain optimal power flows

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Abstract

In this paper, we consider the non-convex optimal power flow (OPF) problem. We apply the recently proposed continuous-time gradient dynamics approach to solve OPFs and study their convergence properties. This approach is appealing because it has a naturally distributed structure. We numerically show, for a three-bus OPF example, that the gradient dynamics locally converges to a saddle point (the primal dual optimum by definition) for the associated Lagrangian, whereas the semi-definite programming (SDP) dual approach yields a non-zero duality gap. This suggests that there are certain OPFs for which strong Lagrange duality holds, although their SDP duals fail to maintain a zero duality gap.

Original languageEnglish (US)
Title of host publication2014 22nd Mediterranean Conference on Control and Automation, MED 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages640-645
Number of pages6
ISBN (Electronic)9781479959006
DOIs
StatePublished - Nov 18 2014
Externally publishedYes
Event22nd Mediterranean Conference on Control and Automation, MED 2014 - Palermo, Italy
Duration: Jun 16 2014Jun 19 2014

Publication series

Name2014 22nd Mediterranean Conference on Control and Automation, MED 2014

Other

Other22nd Mediterranean Conference on Control and Automation, MED 2014
CountryItaly
CityPalermo
Period6/16/146/19/14

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