The cost of decoupling trade and transport in the European entry-exit gas market with linear physics modeling

Böttger, Th.; Grimm, Veronika; Kleinert, Thomas; Schmidt, Martin

doi:10.1016/j.ejor.2021.06.034

Cited by 14 publications

(29 citation statements)

References 44 publications

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“…Similar to the studies in Robinius et al (2019); Labbé et al (2020) for tree-shaped and in Labbé et al (2021) for single-cycle networks, algorithms to solve the nonlinear subproblems of the characterizations presented in this paper can be beneficial. Finally, the analyses of the European gas market models studied in Böttger et al (2021); can be extended to take into account linearly modeled active elements by integrating the novel characterizations of feasible bookings presented in this paper.…”

Section: Discussionmentioning

confidence: 99%

A bilevel optimization approach to decide the feasibility of bookings in the European gas market

2021

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The European gas market is organized as a so-called entry-exit system with the main goal to decouple transport and trading. To this end, gas traders and the transmission system operator (TSO) sign so-called booking contracts that grant capacity rights to traders to inject or withdraw gas at certain nodes up to this capacity. On a day-ahead basis, traders then nominate the actual amount of gas within the previously booked capacities. By signing a booking contract, the TSO guarantees that all nominations within the booking bounds can be transported through the network. This results in a highly challenging mathematical problem. Using potential-based flows to model stationary gas physics, feasible bookings on passive networks, i.e., networks without controllable elements, have been characterized in the recent literature. In this paper, we consider networks with linearly modeled active elements such as compressors or control valves. Since these active elements allow the TSO to control the gas flow, the single-level approaches for passive networks from the literature are no longer applicable. We thus present a bilevel model to decide the feasibility of bookings in networks with active elements. While this model is well-defined for general active networks, we focus on the class of networks for which active elements do not lie on cycles. This assumption allows us to reformulate the original bilevel model such that the lower-level problem is linear for every given upper-level decision. Consequently, we derive several single-level reformulations for this case. Besides the classic Karush–Kuhn–Tucker reformulation, we obtain three problem-specific optimal-value-function reformulations. The latter also lead to novel characterizations of feasible bookings in networks with active elements that do not lie on cycles. We compare the performance of our methods by a case study based on data from the .

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Section: Discussionmentioning

confidence: 99%

A bilevel optimization approach to decide the feasibility of bookings in the European gas market

2021

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“…The model in [14] does not prescribe the physical model underlying the gas flow. For simplified linear flow models, this model can be solved on stylized small and passive (but cyclic) networks, i.e., networks without active elements such as compressor stations or (control) valves; see [2]. Unfortunately, the techniques exploited in [2] cannot be applied to nonlinear flow models.…”

Section: Introductionmentioning

confidence: 99%

“…For simplified linear flow models, this model can be solved on stylized small and passive (but cyclic) networks, i.e., networks without active elements such as compressor stations or (control) valves; see [2]. Unfortunately, the techniques exploited in [2] cannot be applied to nonlinear flow models. In this paper, we focus on solving the multilevel problem for a nonlinear flow model.…”

Section: Introductionmentioning

confidence: 99%

“…Our contribution is the following. We use the bilevel reformulation of the multilevel entry-exit gas market model presented in [14] and derive, as in [2], an exact single-level reformulation. In contrast to [2], we consider a nonlinear flow model of gas transport.…”

Section: Introductionmentioning

confidence: 99%

“…We use the bilevel reformulation of the multilevel entry-exit gas market model presented in [14] and derive, as in [2], an exact single-level reformulation. In contrast to [2], we consider a nonlinear flow model of gas transport. The obtained single-level reformulation is still computationally intractable since it contains infinitely many nonlinear adjustable robust constraints that model technical capacities.…”

Section: Introductionmentioning

confidence: 99%

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Global optimization for the multilevel European gas market system with nonlinear flow models on trees

2022

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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 multilevel 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 multilevel 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 multilevel entry-exit system can be solved for a real-world sized network and a nonlinear flow model.

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Outer approximation for global optimization of mixed-integer quadratic bilevel problems

2021

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Bilevel optimization problems have received a lot of attention in the last years and decades. Besides numerous theoretical developments there also evolved novel solution algorithms for mixed-integer linear bilevel problems and the most recent algorithms use branch-and-cut techniques from mixed-integer programming that are especially tailored for the bilevel context. In this paper, we consider MIQP-QP bilevel problems, i.e., models with a mixed-integer convex-quadratic upper level and a continuous convex-quadratic lower level. This setting allows for a strong-duality-based transformation of the lower level which yields, in general, an equivalent nonconvex single-level reformulation of the original bilevel problem. Under reasonable assumptions, we can derive both a multi- and a single-tree outer-approximation-based cutting-plane algorithm. We show finite termination and correctness of both methods and present extensive numerical results that illustrate the applicability of the approaches. It turns out that the proposed methods are capable of solving bilevel instances with several thousand variables and constraints and significantly outperform classical solution approaches.

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The cost of decoupling trade and transport in the European entry-exit gas market with linear physics modeling

Cited by 14 publications

References 44 publications

A bilevel optimization approach to decide the feasibility of bookings in the European gas market

A bilevel optimization approach to decide the feasibility of bookings in the European gas market

Global optimization for the multilevel European gas market system with nonlinear flow models on trees

Outer approximation for global optimization of mixed-integer quadratic bilevel problems

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