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With this overview we want to provide a compilation of different models for the description of gas flow in networks in order to facilitate the introduction to the topic. Special attention is paid to the hierarchical structure inherent to the modeling, and the detailed description of individual components such as valves and compressors. Also included are network model classes based on purely algebraic relations, and energy-based port-Hamiltonian models. A short overview of basic numerical methods and concepts for the treatment of hyperbolic balance equations is also given. We do not claim completeness and refer in many places to the existing literature.
The idea of a model catalog came to us in the context of the application for the CRC/Transregio 154 ``Mathematical modeling, simulation and optimization using the example of gas networks''. The present
English translation is an extension from
[P. Domschke, B. Hiller, J. Lang, and C. Tischendorf. Modellierung von Gasnetzwerken: Eine Übersicht. Preprint, TRR 154, 2017]. At this point we would like to thank the DFG for its support.
Gas Network Benchmark Models
(2017)
The simulation of gas transportation networks becomes increasingly more important as its use-cases broaden to more complex applications. Classically, the purpose of the gas network was the transportation of predominantly natural gas from a supplier to the consumer for long-term scheduled volumes. With the rise of renewable energy sources, gas-fired power plants are often chosen to compensate for the fluctuating nature of the renewables, due to their on-demand power generation capability. Such an only short-term plannable supply and demand setting requires sophisticated simulations of the gas network prior to the dispatch to ensure the supply of all customers for a range of possible scenarios and to prevent damages to the gas network. In this work we describe the modeling of gas networks and present benchmark systems to test implementations and compare new or extended models.
One challenge for the simulation and optimization of real gas pipe networks is the treatment of compressors. Their behavior is usually described by characteristic diagrams reflecting the connection of the volumetric flow and the enthalpy change or shaft torque. Such models are commonly used for an optimal control of compressors and compressor stations [4, 7] using stationary models for the gas flow through the pipes. For transient simulations of gas networks, simplified compressor models have been studied in [1–3]. Here, we present a transient simulation of gas pipe networks with characteristic diagram models of compressors using a stable network formulation as (partial) differential-algebraic system.
Mit dieser Übersicht wollen wir eine Zusammenstellung von unterschiedlichen Modellen zur Beschreibung des Gasflusses in Netzwerken bereitstellen, um den Einstieg in das Thema zu erleichtern. Besonderes Augenmerk wird dabei auf die der Modellierung inneliegende hierarchische Struktur und die detaillierte Beschreibung einzelner Bauteile wie Ventile und Kompressoren
gelegt. Daneben finden sich ebenfalls Netzmodellklassen, die auf rein algebraische Relationen aufbauen. Am Ende geben wir einen kurzen Überblick über grundlegende numerische Verfahren und Konzepte zur Behandlung von hyperbolischen Bilanzgleichungen. Wir erheben keinen Anspruch auf Vollständigkeit und verweisen an vielen Stellen auf die bestehende Literatur.
Die Idee eines Modellkataloges ist uns im Rahmen der Antragstellung zum SFB/Transregio 154 „Mathematische Modellierung, Simulation und Optimierung am Beispiel von Gasnetzwerken“ gekommen. Wir möchten an dieser Stelle die Förderung durch die DFG dankend erwähnen.
Im Mai 2014 wurde seitens der DFG der Transregio
154 Mathematische Modellierung, Simulation und
Optimierung am Beispiel von Gasnetzwerken bewilligt.
Die Forschungsarbeiten an den beteiligten Standorten,
der Friedrich-Alexander-Universität Erlangen-Nürnberg
(Sprecheruniversität; Sprecher: Alexander Martin), der
Technischen Universität Darmstadt (stellvertretender
Sprecher: Jens Lang), der Technischen Universität Berlin,
der Humboldt Universität (stellvertretende Sprecherin:
Caren Tischendorf) sowie den Partnerinstitutionen
Weierstraß-Institut (Berlin), Konrad-Zuse-Zentrum (Berlin)
und Universität Duisburg-Essen haben im Oktober
2014 begonnen.
This paper studies the numerical simulation of gas networks with regulating elements using differential algebraic equations (DAEs) in combination with least-squares collocation. In contrast to classical collocation methods, more collocation points than degrees of freedom for the collocation polynomials are used. Recently, it has been shown that such a least-squares collocation has a regularizing effect for DAEs, in particular for DAEs with higher index. In each time step of the numerical integration, one has to solve a system of nonlinear equations that is nonsmooth due to the regulating elements in the gas networks. We consider four solvers one of which explicitly exploits the inherent nonsmooth nature. Numerical results are given for three different test cases with increasing complexity illustrating the feasibility of the proposed approach to approximate a solution of the DAE and the advantageous performance of the nonsmooth solver that is based on the concept of abs-linearization.