Index-Preserving Model Order Reduction for Differential-Algebraic Systems Arising in Gas Transport Networks

2019 ◽  
pp. 291-297
Author(s):  
Nicodemus Banagaaya ◽  
Peter Benner ◽  
Sara Grundel
Keyword(s):  
Model Order Reduction ◽  
Gas Transport ◽  
Order Reduction ◽  
Transport Networks ◽  
Model Order ◽  
Algebraic Systems

scholarly journals Model order reduction for gas and energy networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Christian Himpe ◽  
Sara Grundel ◽  
Peter Benner
Keyword(s):  
Model Reduction ◽  
Model Order Reduction ◽  
Gas Transport ◽  
Order Reduction ◽  
Partial Differential ◽  
Model Order ◽  
Vast Number ◽  
Gas Network ◽  
Gas Networks ◽  
Energy Networks

AbstractTo counter the volatile nature of renewable energy sources, gas networks take a vital role. But, to ensure fulfillment of contracts under these circumstances, a vast number of possible scenarios, incorporating uncertain supply and demand, has to be simulated ahead of time. This many-query gas network simulation task can be accelerated by model reduction, yet, large-scale, nonlinear, parametric, hyperbolic partial differential(-algebraic) equation systems, modeling natural gas transport, are a challenging application for model order 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 parametric model reduction for nonlinear systems. This research resulted in the (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 and associated numerical experiments testing model reduction adapted to gas network models.

scholarly journals Parametric Model Order Reduction for Gas Flow Models

2018 ◽  
Author(s):  
Christian Himpe ◽  
Peter Benner ◽  
Sara Grundel
Keyword(s):  
Model Order Reduction ◽  
Gas Flow ◽  
Gas Transport ◽  
Order Reduction ◽  
Parametric Model ◽  
Transport Infrastructure ◽  
Hyperbolic Model ◽  
Model Order ◽  
Variable Boundary ◽  
Parametric Model Order Reduction

Planning the dispatch of contracted gas denominations requires various simulations of the involved gas transport infrastructure. Furthermore, due to the growing interplay of traditional gas transport and fluctuating demands related to renewable energies, the number of necessary simulations vastly increases. Mathematically, a system of Euler equations, which are coupled according to the underlying gas network topology, embodies the associated nonlinear and hyperbolic model. Repeated simulation of large networks for varying supply and demand scenarios often necessitates model order reduction. Yet, beyond these variable boundary conditions, further attributes of the network may be uncertain or need to be kept variable throughout simulations, which motivates parametric model order reduction (pMOR).

THE NEW ALGORITHM OF SOLVING HARMONIC BALANCE EQUATIONS

2019 ◽  
Author(s):  
Vladimir Lantsov ◽  
A. Papulina
Keyword(s):  
Harmonic Balance ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Balance Equations ◽  
Model Order ◽  
Cad Systems ◽  
Computational Costs ◽  
Reduction Methods ◽  
Model Equations

The new algorithm of solving harmonic balance equations which used in electronic CAD systems is presented. The new algorithm is based on implementation to harmonic balance equations the ideas of model order reduction methods. This algorithm allows significantly reduce the size of memory for storing of model equations and reduce of computational costs.

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