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Résolution de problèmes d’optimisation pour les réseaux de transport d’électricité de grande taille avec des méthodes de programmation semi-définie positive

Abstract : The Optimal Power Flow (OPF) is a famous power system optimization problem. It consistsin computing an optimal power generation dispatch for an alternating current transmissionnetwork that respects power flow equations and operational constraints. The OPF problemis highly nonconvex and there is still no efficient method to solve this problem to globaloptimality. Nevertheless, promising methods have been proposed recently. Most of them arebased on Semidefinite Programming (SDP) since semidefinite relaxations of OPF problemsare tight. However, the resolution of semidefinite relaxations is very costly, especially forlarge-scale networks. Therefore, all promising methods depend on large-scale SDP problemsbeing solved efficiently. The main objective of this research project is to decrease the resolutiontime of semidefinite relaxations of OPF problems to demonstrate that semidefiniterelaxations are still powerful to solve OPF problems, even for large-scale networks.To reach this objective, we first conceive programming tools to facilitate the implementationof the OPF problem and its variants. We then seek to speed up the resolution of the rankrelaxation for OPF problems thanks to clique decomposition techniques. We propose a newstrategy of clique merging which significantly improves the solving time for MATPOWERinstances. We finally propose a SDP-based Branch-and-Bound algorithm to solve severalReactive OPF problems that contain binary variables. Our algorithm computes the optimalsolution or at least a good feasible solution for all MATPOWER instances, including forlarge-scale networks. Moreover, it computes better solutions than a rounding heuristic andit is also more robust.Thus, we show in this thesis that it is possible to significantly speed up the resolution of therank relaxation of the OPF problem, which is the main SDP relaxation used to solve OPFproblems. We also demonstrate that semidefinite programming is a powerful tool to solveReactive Optimal Power Flow problems, even for networks with more than 6000 buses
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Submitted on : Friday, November 5, 2021 - 12:46:11 PM
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  • HAL Id : tel-03416774, version 1

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Julie Sliwak. Résolution de problèmes d’optimisation pour les réseaux de transport d’électricité de grande taille avec des méthodes de programmation semi-définie positive. Modélisation et simulation. Université Paris-Nord - Paris XIII; Ecole polytechnique (Montréal, Canada). Division du génie sanitaire, 2021. Français. ⟨NNT : 2021PA131013⟩. ⟨tel-03416774⟩

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