Chapter 2: Physical and technical fundamentals of gas networks

Fügenschuh, Armin; Geißler, Björn; Gollmer, Ralf; Morsi, Antonio; Rövekamp, Jessica; Schmidt, Martin; Spreckelsen, Klaus; Steinbach, Marc C.; Pfetsch, Marc E.

doi:10.1137/1.9781611973693.ch2

Cited by 51 publications

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“…The relation between mass flows and gas pressure squares at gas pipes a = ( u , v ) ∈ A L is typically approximated by pressure loss functions of the type

π_{u} - π_{v} = β_{a} ψ (x_{a}), ψ (x_{a}) = ∣ x_{a} ∣ x_{a} .

The arc‐specific constant β a is positive and depends on technical parameters of the pipe like its diameter, its length, or the roughness of its inner wall, and so on. For more details on modeling stationary gas flow in pipeline networks see the chapter Fügenschuh et al of the book Koch et al and the references therein. Note that assumes a constant elevation of the network.…”

Section: Basic Modelmentioning

confidence: 99%

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Algorithmic results for potential‐based flows: Easy and hard cases

et al. 2018

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Potential‐based flows are an extension of classical network flows in which the flow on an arc is determined by the difference of the potentials of its incident nodes. Such flows are unique and arise, for example, in energy networks. Two important algorithmic problems are to determine whether there exists a feasible flow and to maximize the flow between two designated nodes. We show that these problems can be solved for the single source and sink case by reducing the network to a single arc. However, if we additionally consider switches that allow to force the flow to 0 and decouple the potentials, these problems are NP‐hard. Nevertheless, for particular series‐parallel networks, one can use algorithms for the subset sum problem. Moreover, applying network presolving based on generalized series‐parallel structures allows to significantly reduce the size of realistic energy networks.

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“…The relation between mass flows and gas pressure squares at gas pipes a = ( u , v ) ∈ A L is typically approximated by pressure loss functions of the type

π_{u} - π_{v} = β_{a} ψ (x_{a}), ψ (x_{a}) = ∣ x_{a} ∣ x_{a} .

Section: Basic Modelmentioning

confidence: 99%

“…The arc-specific constant a is positive and depends on technical parameters of the pipe like its diameter, its length, or the roughness of its inner wall, and so on. For more details on modeling stationary gas flow in pipeline networks see the chapter Fügenschuh et al [16] of the book Koch et al [24] and the references therein.…”

Section: Potential-based Flowsmentioning

confidence: 99%

Algorithmic results for potential‐based flows: Easy and hard cases

et al. 2018

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“…For biquadratic functions f A (x, y), we have f A (x, y) = x Ay with A ∈ R 3×3 , x = (1, x, x 2 ) , and y = (1, y, y 2 ) . More details about the technical and physical background as well as on the mathematical modeling can be found in [4] or [22].…”

Section: The Cs Filementioning

confidence: 99%

“…For exemplary XML specifications, see Figure 18. For further details on modeling drives, we refer the reader to [4,21,29].…”

Section: The Cs Filementioning

confidence: 99%

GasLib—A Library of Gas Network Instances

Schmidt

Aßmann

Burlacu

et al. 2017

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Abstract:The development of mathematical simulation and optimization models and algorithms for solving gas transport problems is an active field of research. In order to test and compare these models and algorithms, gas network instances together with demand data are needed. The goal of GasLib is to provide a set of publicly available gas network instances that can be used by researchers in the field of gas transport. The advantages are that researchers save time by using these instances and that different models and algorithms can be compared on the same specified test sets. The library instances are encoded in an XML (extensible markup language) format. In this paper, we explain this format and present the instances that are available in the library.Data Set: http://gaslib.zib.de Data Set License: CC BY 3.0 Keywords: gas transport; networks; problem instances; mixed-integer nonlinear optimization; GasLib MSC: 90-08; 90C90; 90B10 SummaryThe mathematical simulation and optimization of gas transport through pipeline systems is an important field of research with a large practical impact. Over the last decades, many different mathematical models on different levels of accuracy for different components of gas networks have been developed. On the basis of these models, several simulation and optimization algorithms have been proposed. We refer to [1][2][3] and the references therein for more information. With GasLib, we provide a set of network instances that can be used to test and compare such models and the algorithms for solving them.

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“…Each arc represents either an active or a passive network element as described below. More details can be found in Fügenschuh et al (2014).…”

Section: Topology Optimization Of Gas Transport Networkmentioning

confidence: 99%

Valid inequalities for the topology optimization problem in gas network design

2015

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One quarter of Europe's energy demand is provided by natural gas distributed through a vast pipeline network covering the whole of Europe. At a cost of 1 million Euro per km extending the European pipeline network is already a multi-billion Euro business. Therefore, automatic planning tools that support the decision process are desired. Unfortunately, current mathematical methods are not capable of solving the arising network design problems due to their size and complexity. In this article, we will show how to apply optimization methods that can converge to a proven global optimal solution. By introducing a new class of valid inequalities that improve the relaxation of our mixed-integer nonlinear programming model, we are able to speed up the necessary computations substantially.

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Chapter 2: Physical and technical fundamentals of gas networks

Cited by 51 publications

References 0 publications

Algorithmic results for potential‐based flows: Easy and hard cases

Algorithmic results for potential‐based flows: Easy and hard cases

GasLib—A Library of Gas Network Instances

Valid inequalities for the topology optimization problem in gas network design

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