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Certified and accurate SDP bounds for the ACOPF problem

Abstract : We propose a new method for improving the bound tightness of the popular semidefinite programming (SDP) relaxation for the ACOPF introduced in [1], [2]. First, we reformulate the ACOPF Lagrangian dual as an unconstrained concave maximization problem with a clique decomposition induced sparse structure. We prove that this new formulation has the same optimal value as the SDP relaxation. We then use the solution of the SDP relaxation as a starting point for a tailored structure-aware bundle method. This post-processing technique significantly improves the tightness of the SDP bounds computed by the state-of-the-art solver MOSEK, as shown by our computational experiments on large-scale instances from PGLib-OPF v21.07. For ten of the tested instances, our post-processing decreases by more than 50% the optimality gap obtained with MOSEK.
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https://hal.archives-ouvertes.fr/hal-03613385
Contributor : Antoine Oustry Connect in order to contact the contributor
Submitted on : Friday, March 18, 2022 - 2:12:53 PM
Last modification on : Saturday, March 26, 2022 - 3:21:43 AM
Long-term archiving on: : Sunday, June 19, 2022 - 6:59:57 PM

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  • HAL Id : hal-03613385, version 1

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Antoine Oustry, Claudia d'Ambrosio, Leo Liberti, Manuel Ruiz. Certified and accurate SDP bounds for the ACOPF problem. {date}. ⟨hal-03613385⟩

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