Coupling of Compressible Euler Equations

Herty, Michaël; Müller, Siegfried; Sikstel, Aleksey

doi:10.1007/s10013-019-00353-7

Cited by 7 publications

(10 citation statements)

References 39 publications

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“…Therefore equation ( 10) is best understood not as a difference of two functions but as a sum of two very similar functions. Similar to [16], we show certain properties of the Lax curves that are used to define the new pressure laws. There will appear three propositions, which are numbered by A, B and C. These propositions present lists of conditions that are closely related.…”

Section: Well-posedness Of the Riemann Problem For The Isentropic Eul...mentioning

confidence: 96%

“…In this section, we focus on the coupling of the gas network to power grids. Following the ideas in [16,27], the coupling is done extending the already existing coupling conservation of fluxes (5) by a gas power plant. To model the power grid, we use the well-known powerflow equations [11], which describe real and reactive power nodewise.…”

Section: Coupling To Power Gridsmentioning

confidence: 99%

“…We focus on a junction with one incoming pipeline, one outgoing pipeline and an outlet that draws a set amount of flow ε, which is converted to electric power. The coupling condition is taken from [16] and reads…”

Section: Gas-to-power Couplingmentioning

confidence: 99%

“…Although the power network could also be modeled with full time-dependency [9], the high signal speed of electricity renders this unnecessary. Coupling of the networks happens at nodes common to both, where a gas-fired generator is placed such that it can convert gas to electricity, see [16,27]. The coupling is modeled by an equality constraint relating generated power to consumed gas flow.…”

Section: Introductionmentioning

confidence: 99%

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Modeling and simulation of gas networks coupled to power grids

2019

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In this paper, a mathematical framework for the coupling of gas networks to electric grids is presented to describe in particular the transition from gas to power. The dynamics of the gas flow are given by the isentropic Euler equations, while the power flow equations are used to model the power grid. We derive pressure laws for the gas flow that allow for the wellposedness of the coupling and a rigorous treatment of solutions. For simulation purposes, we apply appropriate numerical methods and show in a experimental study how gas-to-power might influence the dynamics of the gas and power network, respectively.

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Section: Well-posedness Of the Riemann Problem For The Isentropic Eul...mentioning

confidence: 96%

Section: Coupling To Power Gridsmentioning

confidence: 99%

Section: Gas-to-power Couplingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modeling and simulation of gas networks coupled to power grids

2019

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“…Except for a coupling in the gas-to-power setting [79] there is no control active at the first component of Ψ. The other components of Ψ may impose different physically desirable properties.…”

Section: Models For the Flow Through Verticesmentioning

confidence: 99%

Modeling, Control and Numerics of Gas Networks

Gugat¹,

Herty²

2020

Preprint

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In this article we survey recent progress on mathematical results on gas flow in pipe networks with a special focus on questions of control and stabilization. We briefly present the modeling of gas flow and coupling conditions for flow through vertices of a network. Our main focus is on gas models for spatially one-dimensional flow governed by hyperbolic balance laws. We survey results on classical solutions as well as weak solutions. We present results on well-posedness, controllability, feedback stabilization, the inclusion of uncertainty in the models and numerical methods.

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