Abstract
To 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 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.
Highlights
Rapid transient simulations of gas flow in pipeline networks are essential for safe operations of gas networks as well as reliable delivery of denominations
To this end we evaluate customized model reduction techniques for an established class of gas network models
3 Model reduction for gas networks we summarize the principal approach behind all presented model reduction methods that are extended and tested in this work
Summary
Rapid transient simulations of gas flow in pipeline networks are essential for safe operations of gas networks as well as reliable delivery of denominations. This friction term is principal to the accuracy of the gas pipeline model [33, 61, 93, 107] In this model variant, a (globally) constant mean compressibility factor z0 := z(p0, T0) ∈ R is assumed [35, 62, 106, 111], as well as a constant gas state γ0 := RST0, whereas the temperature T0 and the specific gas constant RS are treated as parameters The following partial incidence matrices associating edges entering and leaving nodes respectively are defined similar to a Heaviside function: AR Based on this connectivity, certain conservation properties are enforced to maintain a network balance, and ensure physical relevance of the gas network model.
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