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 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.
Highlights
The European gas market is organized as a so-called entry-exit system
We exemplarily show the effects of modifying the economic data on the output of the four-level gas market model for the Greek gas network to shed some light on the sensitivity of the model and the solution approach
This paper provides optimization techniques that enable us to solve a multilevel model of the European entry-exit gas market system, see [14], with a nonlinear flow model for real-world sized and tree-shaped networks
Summary
The European gas market is organized as a so-called entry-exit system. This market structure was introduced as a result of the European gas market liberalization [7,8] with the main goal to decouple transport and trading of natural gas. From a mathematical point of view, the allocation of technical capacities leads to a highly challenging nonlinear adjustable robust problem, which is one of the major computational challenges of the entry-exit market organization. We will show how one can overcome these mathematical difficulties to analyze an entry-exit-system for a tree-shaped network with a nonlinear gas flow model. Since switching from a linear to a nonlinear flow model makes the computation of technical capacities much more challenging, we need to restrict ourselves to only considering tree-shaped networks. We assume that our gas flow model represents a stationary potential-based flow and that the network does not contain active elements such as compressor stations or control valves These assumptions allow us to consider the classic Weymouth equation for gas flows, which we formally introduce in Sect. We apply our findings to solve the entry-exit model for the real-world Greek gas network without active elements in Sect.
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