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.|
|Number of pages||6|
|State||Published - Nov 18 2014|
|Event||22nd Mediterranean Conference on Control and Automation, MED 2014 - Palermo, Italy|
Duration: Jun 16 2014 → Jun 19 2014
|Name||2014 22nd Mediterranean Conference on Control and Automation, MED 2014|
|Other||22nd Mediterranean Conference on Control and Automation, MED 2014|
|Period||6/16/14 → 6/19/14|
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© 2014 IEEE.