Structural properties of feasible bookings in the European entry–exit gas market system

Schewe, Lars; Schmidt, Martin; Thürauf, Johannes

doi:10.1007/s10288-019-00411-3

Cited by 9 publications

(19 citation statements)

References 42 publications

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“…With these auxiliary lemmas we can state the following convexity Theorem. The result is similar to Lemma 3.3 in [20]. But for that result, the authors only consider the conservation of mass (2), not the conservation of momentum (3).…”

Section: Martin Gugat Rüdiger Schultz and Michael Schustersupporting

confidence: 69%

“…The main difference of their model is, that they use a mixed-integer flow model for networks with compressor stations. However, our results about convexity and star-shapedness for networks with compressor stations are not stated in [20]. We will illustrate the difference of the results in the appropriate sections.…”

Section: Martin Gugat Rüdiger Schultz and Michael Schustermentioning

confidence: 90%

“…In a nutshell, we analyze the set of feasible loads in the mathematical model of gas transport, depending on the topology of the graph and on the pressure bounds at the nodes. In [20], the authors also analyze the structure of feasible sets in the context of gas transport, though in a different way. The main difference of their model is, that they use a mixed-integer flow model for networks with compressor stations.…”

Section: Martin Gugat Rüdiger Schultz and Michael Schustermentioning

confidence: 99%

“…But for that result, the authors only consider the conservation of mass (2), not the conservation of momentum (3). For the model considering both, conservation of mass and momentum, they only state, that the set of feasible loads in general is non-convex (see Lemma 4.1 in [20]). Proof.…”

Section: Martin Gugat Rüdiger Schultz and Michael Schustermentioning

confidence: 99%

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Convexity and starshapedness of feasible sets in stationary flow networks

Gugat¹,

Schultz²,

Schuster³

2020

Networks &Amp; Heterogeneous Media

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In this paper, we consider a stationary model for the flow through a network. The flow is determined by the values at the boundary nodes of the network. We call these values the loads of the network. In the applications, the feasible loads must satisfy some box constraints. We analyze the structure of the set of feasible loads. Our analysis is motivated by gas pipeline flows, where the box constraints are pressure bounds. We present sufficient conditions that imply that the feasible set is starshaped with respect to special points. Under stronger conditions, we prove the convexity of the set of feasible loads. All the results are given for passive networks with and without compressor stations. This analysis is motivated by the aim to use the spheric-radial decomposition for stochastic boundary data in this model. This paper can be used for simplifying the algorithmic use of the spheric-radial decomposition.

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Section: Martin Gugat Rüdiger Schultz and Michael Schustersupporting

confidence: 69%

Section: Martin Gugat Rüdiger Schultz and Michael Schustermentioning

confidence: 90%

Section: Martin Gugat Rüdiger Schultz and Michael Schustermentioning

confidence: 99%

Section: Martin Gugat Rüdiger Schultz and Michael Schustermentioning

confidence: 99%

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Convexity and starshapedness of feasible sets in stationary flow networks

Gugat¹,

Schultz²,

Schuster³

2020

Networks &Amp; Heterogeneous Media

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“…Structural properties like (non)convexity etc. of the sets of feasible nominations and bookings are established in [40]. Finally, an algorithm for solving the problem of robust discrete arc sizing is presented in [37].…”

Section: Introductionmentioning

confidence: 99%

Bookings in the European gas market: characterisation of feasibility and computational complexity results

Plein

Schmidt

2019

Optim Eng

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As a consequence of the liberalisation of the European gas market in the last decades, gas trading and transport have been decoupled. At the core of this decoupling are so-called bookings and nominations. Bookings are special capacity right contracts that guarantee that a specified amount of gas can be supplied or withdrawn at certain entry or exit nodes of the network. These supplies and withdrawals are nominated at the day-ahead. The special property of bookings then is that they need to be feasible, i.e., every nomination that complies with the given bookings can be transported. While checking the feasibility of a nomination can typically be done by solving a mixed-integer nonlinear feasibility problem, the verification of feasibility of a set of bookings is much harder. The reason is the robust nature of feasibility of bookingsnamely that for a set of bookings to be feasible, all compliant nominations, i.e., infinitely many, need to be checked for feasibility. In this paper, we consider the question of how to verify the feasibility of given bookings for a number of special cases. For our physics model we impose a steady-state potential-based flow model and disregard controllable network elements. For this case we derive a characterisation of feasible bookings, which is then used to show that the problem is in coNP for the general case but can be solved in polynomial time for linear potential-based flow models. Moreover, we present a dynamic programming approach for deciding the feasibility of a booking in tree-shaped networks even for nonlinear flow models. It turns out that the hardness of the problem mainly depends on the combination of the chosen physics model as well as the specific network structure under consideration. Thus, we give an overview over all settings for which the hardness of the problem is known and finally present a list of open problems.Date: June 5, 2019. 2010 Mathematics Subject Classification. 90B10, 90C30, 90C35, 90C39, 90C90.

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Deciding feasibility of a booking in the European gas market on a cycle is in P for the case of passive networks

2021

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We show that the feasibility of a booking in the European entry‐exit gas market can be decided in polynomial time on single‐cycle networks that are passive, i.e., do not contain controllable elements. The feasibility of a booking can be characterized by solving polynomially many nonlinear potential‐based flow models for computing so‐called potential‐difference maximizing load flow scenarios. We thus analyze the structure of these models and exploit both the cyclic graph structure as well as specific properties of potential‐based flows. This enables us to solve the decision variant of the nonlinear potential‐difference maximization by reducing it to a system of polynomials of constant dimension that is independent of the cycle's size. This system of fixed dimension can be handled with tools from real algebraic geometry to derive a polynomial‐time algorithm. The characterization in terms of potential‐difference maximizing load flow scenarios then leads to a polynomial‐time algorithm for deciding the feasibility of a booking. Our theoretical results extend the existing knowledge about the complexity of deciding the feasibility of bookings from trees to single‐cycle networks.

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Structural properties of feasible bookings in the European entry–exit gas market system

Cited by 9 publications

References 42 publications

Convexity and starshapedness of feasible sets in stationary flow networks

Convexity and starshapedness of feasible sets in stationary flow networks

Bookings in the European gas market: characterisation of feasibility and computational complexity results

Deciding feasibility of a booking in the European gas market on a cycle is in P for the case of passive networks

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