Existence of strong Lagrange duals to certain optimal power flows

Xu Ma; Nicola Elia

doi:10.1109/MED.2014.6961445

Existence of strong Lagrange duals to certain optimal power flows

Xu Ma, Nicola Elia

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

3 Scopus citations

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 language	English (US)
Title of host publication	2014 22nd Mediterranean Conference on Control and Automation, MED 2014
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	640-645
Number of pages	6
ISBN (Electronic)	9781479959006
DOIs	https://doi.org/10.1109/MED.2014.6961445
State	Published - Nov 18 2014
Externally published	Yes
Event	22nd Mediterranean Conference on Control and Automation, MED 2014 - Palermo, Italy Duration: Jun 16 2014 → Jun 19 2014

Publication series

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

Other

Other	22nd Mediterranean Conference on Control and Automation, MED 2014
Country/Territory	Italy
City	Palermo
Period	6/16/14 → 6/19/14

Bibliographical note

Publisher Copyright:
© 2014 IEEE.

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10.1109/MED.2014.6961445

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Existence of strong Lagrange duals to certain optimal power flows. / Ma, Xu; Elia, Nicola.
2014 22nd Mediterranean Conference on Control and Automation, MED 2014. Institute of Electrical and Electronics Engineers Inc., 2014. p. 640-645 6961445 (2014 22nd Mediterranean Conference on Control and Automation, MED 2014).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Ma, X & Elia, N 2014, Existence of strong Lagrange duals to certain optimal power flows. in 2014 22nd Mediterranean Conference on Control and Automation, MED 2014., 6961445, 2014 22nd Mediterranean Conference on Control and Automation, MED 2014, Institute of Electrical and Electronics Engineers Inc., pp. 640-645, 22nd Mediterranean Conference on Control and Automation, MED 2014, Palermo, Italy, 6/16/14. https://doi.org/10.1109/MED.2014.6961445

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AB - 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.

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Existence of strong Lagrange duals to certain optimal power flows

Abstract

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