High detail stationary optimization models for gas networks: validation and results

Schmidt, Martin; Steinbach, Marc C.; Willert, Bernhard M.

doi:10.1007/s11081-015-9300-3

Cited by 41 publications

(31 citation statements)

References 9 publications

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“…The edges represent pipes or other network elements such as valves, control valves, heaters, or compressors. Gas flow through a single pipe of length L with diameter A is described by the Euler equations, a set of partial differential equations [9,10,18]. The first equation is the continuity equation…”

Section: Euler Equations For Pipesmentioning

confidence: 99%

“…is necessary to describe the state of a real compressible gas for a given set of values for temperature T , density ρ, and pressure p. The first law of thermodynamics must be taken into account to describe any heat transfer process. A solution to this system of equations can be found analytically if we assume a stationary and isothermal gas flow [18]. Analogously to Kirchhoff's law, the mass must be conserved at junctions where several pipes are connected.…”

Section: Euler Equations For Pipesmentioning

confidence: 99%

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Simplex Stochastic Collocation for Piecewise Smooth Functions With Kinks

Fuchs

Garcke

2020

Int. J. UncertaintyQuantification

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Most approximation methods in high dimensions exploit smoothness of the function being approximated. These methods provide poor convergence results for non-smooth functions with kinks. For example, such kinks can arise in the uncertainty quantification of quantities of interest for gas networks. This is due to the regulation of the gas flow, pressure, or temperature. But, one can exploit that for each sample in the parameter space it is known if a regulator was active or not, which can be obtained from the result of the corresponding numerical solution. This information can be exploited in a stochastic collocation method. We approximate the function separately on each smooth region by polynomial interpolation and obtain an approximation to the kink. Note that we do not need information about the exact location of kinks, but only an indicator assigning each sample point to its smooth region. We obtain a global order of convergence of (p + 1)/d, where p is the degree of the employed polynomials and d the dimension of the parameter space.

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Section: Euler Equations For Pipesmentioning

confidence: 99%

Section: Euler Equations For Pipesmentioning

confidence: 99%

Simplex Stochastic Collocation for Piecewise Smooth Functions With Kinks

Fuchs

Garcke

2020

Int. J. UncertaintyQuantification

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“…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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“…If the boundary conditions are infeasible, it may be useful to add slack variables to a certain set of constraints and minimize the total infeasibility, measured by a suitable norm of the vector of slack variables. The reader interested in problem-specific slack variable formulations for gas network planning is referred to Schmidt et al (2015a).…”

Section: Objective Functionmentioning

confidence: 99%

Computational optimization of gas compressor stations: MINLP models versus continuous reformulations

et al. 2016

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When considering cost-optimal operation of gas transport networks, compressor stations play the most important role. Proper modeling of these stations leads to nonconvex mixed-integer nonlinear optimization problems. In this article, we give an isothermal and stationary description of compressor stations, state MINLP and GDP models for operating a single station, and discuss several continuous reformulations of the problem. The applicability and relevance of different model formulations, especially of those without discrete variables, is demonstrated by a computational study on both academic examples and real-world instances. In addition, we provide preliminary computational results for an entire network.

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High detail stationary optimization models for gas networks: validation and results

Cited by 41 publications

References 9 publications

Simplex Stochastic Collocation for Piecewise Smooth Functions With Kinks

Simplex Stochastic Collocation for Piecewise Smooth Functions With Kinks

GasLib—A Library of Gas Network Instances

Computational optimization of gas compressor stations: MINLP models versus continuous reformulations

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