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Global Optimization for the Multilevel European Gas Market System with Nonlinear Flow Models on Trees

Lars Schewe(lars.schewe***at***ed.ac.uk)
Martin Schmidt(martin.schmidt***at***uni-trier.de)
Johannes Thürauf(johannes.thuerauf***at***fau.de)

Abstract: The European gas market is implemented as an entry-exit system, which aims to decouple transport and trading of gas. It has been modeled in the literature as a four-level problem, which contains a nonlinear flow model of gas physics. Besides the multilevel structure and the nonlinear flow model, the computation of so-called technical capacities is another major challenge. These lead to nonlinear adjustable robust constraints that are computationally intractable in general. We provide techniques to equivalently reformulate these nonlinear adjustable constraints as finitely many convex constraints including integer variables in the case that the underlying network is tree-shaped. We further derive additional combinatorial constraints that significantly speed up the solution process. Using our results, we can recast the four-level model as a single-level nonconvex mixed-integer nonlinear problem, which we then solve on a real-world network, namely the Greek gas network, to global optimality. Overall, this is the first time that the considered four-level entry-exit system can be solved for a real-word sized network and a nonlinear flow model.

Keywords: European Entry-Exit Gas Market, Multilevel Optimization, Robust Optimization, Mixed-Integer Nonlinear Optimization, Nonlinear Flows

Category 1: Global Optimization

Category 2: Robust Optimization

Category 3: Applications -- OR and Management Sciences


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Entry Submitted: 08/21/2020
Entry Accepted: 08/21/2020
Entry Last Modified: 08/21/2020

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