MathEnergy – Mathematical Key Technologies for Evolving Energy Grids

Clees, Tanja; Baldin, A. A.; Benner, Peter; Grundel, Sara; Klaassen, Bernhard; Küsters, Ferdinand; Marheineke, Nicole; Nikitina, Lialia; Nikitin, Igor; Pade, Jonas; Stahl, Nadine; Strohm, Christian; Tischendorf, Caren; Wirsen, Andreas

doi:10.1007/978-3-030-62732-4_11

Cited by 4 publications

(3 citation statements)

References 43 publications

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“…The time-varying input u v consists of a deterministic part u v D and a stochastic one u v S , where we particularly model u v S by an Ornstein-Uhlenbeck process with constant parameters κ v , μ v , σ v and a standard Wiener process W v t . The stochastic boundary data allows the incorporation of, e.g., market strategies or the concept of Power-to-Gas [4]. Certainly, also other boundary types can be considered, see e.g., [14].…”

Section: Hierarchical Gas Network Modelsmentioning

confidence: 99%

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Efficient state estimation for gas pipeline networks via low-rank approximations

Stahl¹,

Marheineke²

2022

ASIM SST 2022 Proceedings Langbeiträge

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In this paper we investigate the performance of projection-based low-rank approximations in Kalman filtering. For large-scale gas pipeline networks structurepreserving model order reduction has turned out to be an advantageous way to compute accurate solutions with much less computational effort. For state estimation we propose to combine these low-rank models with Kalman filtering and show the advantages of this procedure to established low-rank Kalman filters in terms of efficiency and quality of the estimate.

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Section: Hierarchical Gas Network Modelsmentioning

confidence: 99%

“…1. The pipe parameters are taken from [4]. For the linear model we use d e l = d e |q e av |/p e av , where p e av and q e av are the average pressure and mass flux on edge e of the stationary solution associated to the input…”

Section: Academic Diamond Networkunclassified

Efficient state estimation for gas pipeline networks via low-rank approximations

Stahl¹,

Marheineke²

2022

ASIM SST 2022 Proceedings Langbeiträge

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“…The swift numerical simulation of gas network twins by reduced order modeling is highly relevant, not only due to the transition towards renewables at the time of writing, which is underlined by the research projects MathEnergy 1 (Mathematical Key Technologies for Evolving Energy Grids) [23] that the authors are part of, and TRR154 2 (Mathematical Modelling, Simulation and Optimization using the Example of Gas Networks) [75], but also because of the intriguing numerical problem of model reduction for hyperbolic, nonlinear, coupled, parametric, multiscale partial differential-algebraic equation systems.…”

Section: Introductionmentioning

confidence: 99%

Model Order Reduction for Gas and Energy Networks

Himpe,

Grundel,

Benner

2020

Preprint

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To counter the volatile nature of renewable energy sources, gas networks take a vital role. But, to ensure fulfillment of contracts under these new circumstances, a vast number of possible scenarios, incorporating uncertain supply and demand, has to be simulated ahead of time. This many-query task can be accelerated by model order reduction, yet, large-scale, nonlinear, parametric, hyperbolic partial differential(-algebraic) equation systems, modeling gas transport, are a challenging application for model reduction algorithms. For this industrial application, we bring together the scientific computing topics of: mathematical modeling of gas transport networks, numerical simulation of hyperbolic partial differential equation, and model order reduction for nonlinear parametric systems. This research resulted in the morgen (Model Order Reduction for Gas and Energy Networks) software platform, which enables modular testing of various combinations of models, solvers, and model reduction methods. In this work we present the theoretical background on systemic modeling and structured, data-driven, system-theoretic model reduction for gas networks, as well as the implementation of morgen and associated numerical experiments testing model reduction adapted to gas network models.

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On Port-Hamiltonian Approximation of a Nonlinear Flow Problem on Networks

Liljegren-Sailer¹,

Marheineke²

2022

SIAM J. Sci. Comput.

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MathEnergy – Mathematical Key Technologies for Evolving Energy Grids

Cited by 4 publications

References 43 publications

Efficient state estimation for gas pipeline networks via low-rank approximations

Efficient state estimation for gas pipeline networks via low-rank approximations

Model Order Reduction for Gas and Energy Networks

On Port-Hamiltonian Approximation of a Nonlinear Flow Problem on Networks

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