TY - GEN A1 - Hennings, Felix T1 - Benefits and Limitations of Simplified Transient Gas Flow Formulations N2 - Although intensively studied in recent years, the optimization of the transient (time-dependent) control of large real-world gas networks is still out of reach for current state-of-the-art approaches. For this reason, we present further simplifications of the commonly used model, which lead to a linear description of the gas flow on pipelines. In an empirical analysis of real-world data, we investigate the properties of the involved quantities and evaluate the errors made by our simplification. T3 - ZIB-Report - 17-39 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64570 SN - 1438-0064 ER - TY - CHAP A1 - Hennings, Felix T1 - Benefits and Limitations of Simplified Transient Gas Flow Formulations T2 - Operations Research Proceedings 2017 N2 - Although intensively studied in recent years, the optimization of the transient (time-dependent) control of large real-world gas networks is still out of reach for current state-of-the-art approaches. For this reason, we present further simplifications of the commonly used model, which lead to a linear description of the gas flow on pipelines. In an empirical analysis of real-world data, we investigate the properties of the involved quantities and evaluate the errors made by our simplification. Y1 - 2018 UR - https://link.springer.com/chapter/10.1007/978-3-319-89920-6_32 U6 - https://doi.org/10.1007/978-3-319-89920-6_32 VL - Operations Research Proceedings SP - 231 EP - 237 PB - Springer, Cham ER - TY - GEN A1 - Hennings, Felix T1 - Large-scale empirical study on the momentum equation's inertia term N2 - A common approach to reduce the Euler equations' complexity for the simulation and optimization of gas networks is to neglect small terms that contribute little to the overall equations. An example is the inertia term of the momentum equation since it is said to be of negligible size under real-world operating conditions. However, this justification has always only been based on experience or single sets of artificial data points. This study closes this gap by presenting a large-scale empirical evaluation of the absolute and relative size of the inertia term when operating a real-world gas network. Our data consists of three years of fine-granular state data of one of the largest gas networks in Europe, featuring over 6,000 pipes with a total length of over 10,000 km. We found that there are only 120 events in which a subnetwork consisting of multiple pipes has an inertia term of high significance for more than three minutes. On average, such an event occurs less often than once every ten days. Therefore, we conclude that the inertia term is indeed negligible for real-world transient gas network control problems. T3 - ZIB-Report - 21-08 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-81881 SN - 1438-0064 ER - TY - JOUR A1 - Hennings, Felix T1 - Large-scale empirical study on the momentum equation's inertia term JF - Journal of Natural Gas Science and Engineering N2 - A common approach to reduce the Euler equations' complexity for the simulation and optimization of gas networks is to neglect small terms that contribute little to the overall equations. An example is the inertia term of the momentum equation, which is said to be of negligible size under real-world operating conditions. However, this justification has always only been based on experience or single sets of artificial data points. This study closes this gap by presenting a large-scale empirical evaluation of the absolute and relative size of the inertia term when operating a real-world gas network. Our data consists of three years of fine-granular state data of one of the largest gas networks in Europe, featuring over 6,000 pipes with a total length of over 10,000 km. We found that there are only 120 events in which a subnetwork consisting of multiple pipes has an inertia term of high significance for more than three minutes. On average, such an event occurs less often than once every ten days. Therefore, we conclude that the inertia term is indeed negligible for real-world transient gas network control problems. Y1 - 2021 U6 - https://doi.org/10.1016/j.jngse.2021.104153 VL - 95 PB - Elsevier ER - TY - THES A1 - Hennings, Felix T1 - Modeling and solving real-world transient gas network transport problems using mathematical programming N2 - This thesis considers the transient gas network control optimization problem for on-shore pipeline-based transmission networks with numerous gas routing options. As input, the problem is given the network's topology, its initial state, and future demands at the boundaries of the network, which prescribe the gas flow exchange and potentially the pressure values. The task is to find a set of future control measures for all the active, i.e., controllable, elements in the network that minimizes a combination of different penalty functions. The problem is examined in the context of a decision support tool for gas network dispatchers. This results in detailed models featuring a diverse set of constraints, large and challenging real-world instances, and demanding time limit requirements. All these factors further complicate the problem, which is already difficult to solve in theory due to the inherent combination of non-linear and combinatorial aspects. Our contributions concern different steps of the process of solving the problem. Regarding the model formulation, we investigate the validity of two common approximations of the gas flow description in transport pipes: neglecting the inertia term and assuming a friction term that linearly depends on the gas flow and the pressure. For both, we examine if they can be applied under real-world conditions by evaluating a large amount of historical state data of the network of our project partner, the gas network operator Open Grid Europe. While we can confirm that it is reasonable to ignore the influence of the inertia term, the friction term linearization leads to significant errors and, as a consequence, cannot be used for describing the general gas flow behavior in transport pipes. As another topic of this thesis, we introduce the target value concept as a more realistic approach to express control actions of dispatchers regarding regulators and compressor stations. Here, we derive the mechanisms defined for target values based on the gas flow principles in pipes and develop a mixed-integer programming model capturing their behavior. The accuracy of this model is demonstrated in comparison to a target-value-based industry-standard simulator. Furthermore, we present two heuristics for the transient gas network control optimization problem featuring target values that are based on approximative models for the target-value-based control and determine the final decisions in a post-processing step. To compare the performance of the two heuristics with the approach of directly solving the corresponding model, we evaluate them on a set of artificially created test instances. Finally, we develop problem-specific algorithms for two variants of the described problem. One considers the control optimization for a single network station, which represents a local operation site featuring a large number of active elements. The used transient model is very detailed and includes a sophisticated representation of the compressor stations. Based on the shortness of the pipes in the station, the corresponding algorithm finds valid solutions by solving a series of stationary model variants as well as a transient rolling horizon approach. As the second variant, we consider the problem on the entire network but assume an approximative model representing the control capabilities of network stations. Aside from a new description of the compression capabilities, we introduce an algorithm that uses a combination of sequential mixed-integer programming, two heuristics based on reduced time horizons, and a specialized dynamic branch-and-bound node limit to determine promising values for the binary variables of the model. Complete solutions for the problem are obtained by fixing the binary values and solving the remaining non-linear program. Both algorithms are investigated in extensive empirical studies based on real-world instances of the corresponding model variants. N2 - Diese Arbeit behandelt das Optimierungsproblem der transienten Gasnetzwerksteuerung von Fernleitungsnetzen auf dem Festland mit einer großen Anzahl möglicher Gastransportrouten. Die Eingabedaten bestehen aus der Netzwerktopologie, dem Anfangszustand des Netzes und zukünftigen Vorgaben an den Randknoten des Netzes, welche den Gaseinfluss und Gasausfluss sowie eine potenzielle Vorgabe von Druckwerten umfassen. Gegeben diese Daten besteht die Aufgabe besteht darin, eine Menge an zukünftigen Steuerungsentscheidungen für alle aktiven, also steuerbaren, Elemente des Netzes zu finden, sodass eine Kombination von Straffunktionen minimiert wird. Das Problem wird in dieser Arbeit im Rahmen der Erstellung eines entscheidungsunterstützenden Systems für Dispatcher betrachtet, welche das Gasnetz steuern. Dies resultiert in einer detaillierten Modellierung mit einer Vielzahl von Nebenbedingungen, großen und herausfordernden realistischen Instanzen sowie anspruchsvollen Vorgaben zur maximalen Laufzeit. Diese Eigenschaften erhöhen die Komplexität des Problems, welches bereits in der Theorie auf Grund der inhärenten Kombination von nichtlinearen und kombinatorischen Aspekten schwierig zu lösen ist. Die Beiträge dieser Arbeit betreffen verschiedene Schritte des Prozesses zur Lösung des Problems. Bezüglich der Modellformulierung werden zwei übliche Approximationen der Gasflussbeschreibung in Fernleitungsrohren auf Validität überprüft: die Vernachlässigung des Trägheitsterms und die Annahme einer linearisierten Beschreibung des Reibungsterms. Für beide Approximationen wird untersucht, ob sie für reale Gasflussbedingungen zulässig sind. Dazu wird eine große Anzahl historischer Netzzustandsdaten des Gasnetzbetreibers Open Grid Europe ausgewertet. Während bestätigt werden kann, dass eine Vernachlässigung des Trägheitsterms unter Realbedingungen angemessen ist, führt die Linearisierung des Reibungsterms zu signifikanten Fehlern und kann daher nicht für die allgemeine Beschreibung des Gasflusses in Fernleitungsrohren verwendet werden. In einem weiteren Teil dieser Arbeit wird das Konzept der Sollwerte eingeführt. Mit diesen ist eine realistischere Beschreibung der Steuerungsbefehle möglich, welche den Dispatchern für Regler und Verdichterstationen zur Verfügung stehen. Der Sollwertmechanismus wird basierend auf den Gasflussprinzipien in Rohrleitungen hergeleitet, um anschließend ein gemischt-ganzzahliges Programm zu entwickeln, welches das entsprechende Verhalten erzeugt. Die Präzision dieses Modells wird durch einen Vergleich mit einem Simulator von Industriestandard sichergestellt, welcher auf Sollwerten basiert. Außerdem werden zwei Heuristiken für das Optimierungsproblem der transienten Gasnetzwerksteuerung mit Sollwertmodellierung vorgestellt. Diese basieren auf approximativen Modellen für die Sollwertsteuerung und ermitteln die letztendlichen Steuerungsentscheidungen in einer nachgelagerten Routine. Basierend auf künstlich erzeugten Testinstanzen werden die Heuristiken schließlich mit dem direkten Lösen des entsprechenden Modells verglichen. Zudem werden in dieser Arbeit problemspezifische Algorithmen für zwei Varianten des beschriebenen Optimierungsproblems entwickelt. Die erste Variante betrachtet das Gasnetzwerksteuerungsproblem beschränkt auf eine einzelne Netzstation, die lokale Betriebsstellen darstellen und über eine Vielzahl an aktiven Steuerungselementen verfügen. Das entsprechende transiente Modell ist sehr detailliert und beinhaltet eine differenzierte Beschreibung der Verdichterstationen. Der problemspezifische Algorithmus basiert auf der Kürze der Rohre innerhalb der Station und findet zulässige Lösungen durch das Lösen von stationären Varianten des Modells sowie der Nutzung eines transienten Rolling-Horizon Ansatzes. In der zweiten Problemvariante wird das gesamte Gasnetz betrachtet, wobei eine vereinfachte Modellierung der Steuerungsmöglichkeiten innerhalb von Netzstationen angenommen wird. Neben einer neuen Beschreibung der Verdichtungsmöglichkeiten einer Station wird ebenfalls ein problemspezifischer Algorithmus entwickelt. Dieser erstellt aussichtsreiche Werte für die Binärvariablen und nutzt dafür eine Kombination aus sequenzieller gemischt-ganzzahliger Programmierung, zwei auf verkürzten Zeithorizonten basierenden Heuristiken und eine spezialisierte dynamische Obergrenze für die Anzahl der Branch-and-Bound-Knoten. Diese Teillösungen werden durch eine Fixierung der binären Variablen und das anschließende Lösen des restlichen nichtlinearen Programms komplettiert. Die Güte beider Algorithmen wird in umfangreichen empirischen Experimenten untersucht, welche reale Instanzen der jeweiligen Problemvarianten betrachten. Y1 - 2023 ER - TY - GEN A1 - Hennings, Felix A1 - Anderson, Lovis A1 - Hoppmann, Kai A1 - Turner, Mark A1 - Koch, Thorsten T1 - Controlling transient gas flow in real-world pipeline intersection areas N2 - Compressor stations are the heart of every high-pressure gas transport network. Located at intersection areas of the network they are contained in huge complex plants, where they are in combination with valves and regulators responsible for routing and pushing the gas through the network. Due to their complexity and lack of data compressor stations are usually dealt with in the scientific literature in a highly simplified and idealized manner. As part of an ongoing project with one of Germany's largest Transmission System Operators to develop a decision support system for their dispatching center, we investigated how to automatize control of compressor stations. Each station has to be in a particular configuration, leading in combination with the other nearby elements to a discrete set of up to 2000 possible feasible operation modes in the intersection area. Since the desired performance of the station changes over time, the configuration of the station has to adapt. Our goal is to minimize the necessary changes in the overall operation modes and related elements over time, while fulfilling a preset performance envelope or demand scenario. This article describes the chosen model and the implemented mixed integer programming based algorithms to tackle this challenge. By presenting extensive computational results on real world data we demonstrate the performance of our approach. T3 - ZIB-Report - 19-24 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73645 SN - 1438-0064 ER - TY - JOUR A1 - Hennings, Felix A1 - Anderson, Lovis A1 - Hoppmann-Baum, Kai A1 - Turner, Mark A1 - Koch, Thorsten T1 - Controlling transient gas flow in real-world pipeline intersection areas JF - Optimization and Engineering N2 - Compressor stations are the heart of every high-pressure gas transport network. Located at intersection areas of the network they are contained in huge complex plants, where they are in combination with valves and regulators responsible for routing and pushing the gas through the network. Due to their complexity and lack of data compressor stations are usually dealt with in the scientific literature in a highly simplified and idealized manner. As part of an ongoing project with one of Germany's largest Transmission System Operators to develop a decision support system for their dispatching center, we investigated how to automatize control of compressor stations. Each station has to be in a particular configuration, leading in combination with the other nearby elements to a discrete set of up to 2000 possible feasible operation modes in the intersection area. Since the desired performance of the station changes over time, the configuration of the station has to adapt. Our goal is to minimize the necessary changes in the overall operation modes and related elements over time, while fulfilling a preset performance envelope or demand scenario. This article describes the chosen model and the implemented mixed integer programming based algorithms to tackle this challenge. By presenting extensive computational results on real world data we demonstrate the performance of our approach. Y1 - 2021 U6 - https://doi.org/https://doi.org/10.1007/s11081-020-09559-y VL - 22 SP - 687 EP - 734 PB - Springer Nature ET - 2 ER - TY - GEN A1 - Hennings, Felix A1 - Hoppmann-Baum, Kai A1 - Zittel, Janina T1 - Optimizing transient gas network control for challenging real-world instances using MIP-based heuristics N2 - Optimizing the transient control of gas networks is a highly challenging task. The corresponding model incorporates the combinatorial complexity of determining the settings for the many active elements as well as the non-linear and non-convex nature of the physical and technical principles of gas transport. In this paper, we present the latest improvements of our ongoing work to solve this problem for real-world, large-scale problem instances: By adjusting our mixed-integer non-linear programming model regarding the gas compression capabilities in the network, we reflect the technical limits of the underlying units more accurately while maintaining a similar overall model size. In addition, we introduce a new algorithmic approach that is based on splitting the complexity of the problem by first finding assignments for discrete variables and then determining the continuous variables as locally optimal solution of the corresponding non-linear program. For the first task, we design multiple different heuristics based on concepts for general time-expanded optimization problems that find solutions by solving a sequence of sub-problems defined on reduced time horizons. To demonstrate the competitiveness of our approach, we test our algorithm on particularly challenging historic demand scenarios. The results show that high-quality solutions are obtained reliably within short solving times, making the algorithm well-suited to be applied at the core of time-critical industrial applications. T3 - ZIB-Report - 22-08 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-86842 SN - 1438-0064 ER - TY - JOUR A1 - Hennings, Felix A1 - Hoppmann-Baum, Kai A1 - Zittel, Janina T1 - Optimizing transient gas network control for challenging real-world instances using MIP-based heuristics JF - Open Journal of Mathematical Optimization Y1 - 2024 ER - TY - GEN A1 - Hennings, Felix A1 - Petkovic, Milena A1 - Streubel, Tom T1 - On the Numerical Treatment of Interlaced Target Values - Modeling, Optimization and Simulation of Regulating Valves in Gas Networks N2 - Due to the current and foreseeable shifts in energy production, the trading and transport operations of gas will become more dynamic, volatile, and hence also less predictable. Therefore, computer-aided support in terms of rapid simulation and control optimization will further broaden its importance for gas network dispatching. In this paper, we aim to contribute and openly publish two new mathematical models for regulators, also referred to as control valves, which together with compressors make up the most complex and involved types of active elements in gas network infrastructures. They provide full direct control over gas networks but are in turn controlled via target values, also known as set-point values, themselves. Our models incorporate up to six dynamical target values to define desired transient states for the elements' local vicinity within the network. That is, each pair of every two target values defines a bounding box for the inlet pressure, outlet pressure as well as the passing mass flow of gas. In the proposed models, those target values are prioritized differently and are constantly in competition with each other, which can only be resolved dynamically at run-time of either a simulation or optimization process. Besides careful derivation, we compare simulation and optimization results with predictions of the commercial simulation tool SIMONE. T3 - ZIB-Report - 21-32 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-85359 SN - 1438-0064 ER -