Mixed Integer Models for the Optimisation of Gas Networks in the Stationary Case

Through out the world the natural gas resources will be one of the most important sources of energy in the future. The development of optimised possibilities for the distribution of gas through a network of pipelines will be very important for an effective operation of a gas transmission network. The aim of this thesis is to formulate this problem as a suitable mathematical mixed integer problem and to find advanced solutions, using techniques of mixed integer programming. The main problem of the so called Transient Technical Optimisation (TTO) is to minimise the total supply costs of a gas transmission company that has to satisfy demands of different kinds. A gas network basically consists of a number of compressors and valves that are connected via pipes. The gas transmission companies dispatchers decide how to run the compressors and how to switch the valves cost-efficiently such that all demands of all customers are satisfied. The cost function mainly consists of the supply costs of driving the compressors. Note that the compressors consum a fraction of the gas transported through the pipelines. The costs imposed by consumed gas should be minimised. The gas transmission network has to satisfy several demands that are described by a minimal or maximal pressure requirement at a certain node or in a pipe. Also the consumers want to get gas of a certain volume and quality. Furthermore some physical constraints, like Kirchhoff's laws have to be modelled. There are also some combinatorial constraints, e.g. the different possibilities of switching the valves or compressor configurations. Note, that some of the constraints are nonlinear, like the pressure loss in a pipeline or the fuel-gas consumption of the compressors. In order to formulate TTO as a mixed integer program we approximate the nonlinear constraints by piecewise linear functions. Considering the experiences of other projects where mixed integer programs have been used, e.g. VLSI-Design or Telecommunications, we know that the problem can be solved by examination of the underlying polyhedra of such complex and high-dimensional mixed integer programs. We know from earlier test evaluations of smaller problems that it is not possible to solve real gas transmission problems with state-of-the-art general mixed integer programming solvers. One programming approach is the search of better valid (or even facet-defining) inequalities of the polyhedra for the use in a Branch-and-Cut Algorithm. We have developed a new class of valid inequalities that have been integrated in a general MIP solver algorithm. Summarising the results it was possible to develop a polynomial separation algorithm for a special class of polyhedra. The use of these cuts reduces the calculation time by a significant factor. A suitable branch-and-bound algorithm is also added. The cuts and the branching algorithms have been tested on several test-models of real gas-networks

Simulation of Piecewise Smooth Differential Algebraic Equations with Application to Gas Networks

Zuweilen wird gefördertes Erdgas als eine Brückentechnologie noch eine Weile erhalten bleiben, aber unsere Gasnetzinfrastruktur hat auch in einer Ära post-fossiler Brennstoffe eine Zukunft, um Klima-neutral erzeugtes Methan, Ammoniak oder Wasserstoff zu transportieren. Damit die Dispatcher der Zukunft, in einer sich fortwährend dynamisierenden Marktsituation, mit sich beständig wechselnden Kleinstanbietern, auch weiterhin einen sicheren Gasnetzbetrieb ermöglichen und garantieren können, werden sie auf moderne, schnelle Simulations- sowie performante Optimierungstechnologie angewiesen sein. Der Schlüssel dazu liegt in einem besseren Verständnis zur numerischen Behandlung nicht differenzierbarer Funktionen und diese Arbeit möchte einen Beitrag hierzu leisten. Wir werden stückweise differenzierbare Funktionen in sog. Abs-Normalen Form betrachten. Durch einen Prozess, der Abs-Linearisierung genannt wird, können wir stückweise lineare Approximationsmodelle erster Ordnung, mittels Techniken der algorithmischen Differentiation erzeugen. Jene Modelle können über Matrizen und Vektoren mittels gängiger Software-Bibliotheken der numerischen linearen Algebra auf Computersystemen ausgedrückt, gespeichert und behandelt werden. Über die Generalisierung der Formel von Faà di Bruno können auch Splinefunktionen höherer Ordnung generiert werden, was wiederum zu Annäherungsmodellen mit besserer Güte führt. Darauf aufbauend lassen sich gemischte Taylor-Kollokationsmethoden, darunter die mit Ordnung zwei konvergente generalisierte Trapezmethode, zur Integration von Gasnetzen, in Form von nicht glatten Algebro-Differentialgleichungssystemen, definieren. Numerische Experimente demonstrieren das Potential. Da solche implizite Integratoren auch nicht lineare und in unserem Falle zugleich auch stückweise differenzierbare Gleichungssysteme erzeugen, die es als Unterproblem zu lösen gilt, werden wir uns auch die stückweise differenzierbare, sowie die stückweise lineare Newtonmethode betrachten.As of yet natural gas will remain as a bridging technology, but our gas grid infrastructure does have a future in a post-fossil fuel era for the transportation of carbon-free produced methane, ammonia or hydrogen. In order for future dispatchers to continue to enable and guarantee safe gas network operations in a continuously changing market situation with constantly switching micro-suppliers, they will be dependent on modern, fast simulation as well as high-performant optimization technology. The key to such a technology resides in a better understanding of the numerical treatment of non-differentiable functions and this work aims to contribute here. We will consider piecewise differentiable functions in so-called abs-normal form. Through a process called abs-linearization, we can generate piecewise linear approximation models of order one, using techniques of algorithmic differentiation. Those models can be expressed, stored and treated numerically as matrices and vectors via common software libraries of numerical linear algebra. Generalizing the Faà di Bruno's formula yields higher order spline functions, which in turn leads to even higher order approximation models. Based on this, mixed Taylor-Collocation methods, including the generalized trapezoidal method converging with an order of two, can be defined for the integration of gas networks represented in terms of non-smooth system of differential algebraic equations. Numerical experiments will demonstrate the potential. Since those implicit integrators do generate non-linear and, in our case, piecewise differentiable systems of equations as sub-problems, it will be necessary to consider the piecewise differentiable, as well as the piecewise linear Newton method in advance

Acoustic scattering in a small centrifugal compressor based on the use of linearized equations in a rotating frame

Numerical solutions of acoustic wave scattering are often used to describe sound propagation through complex geometries. For cases with flow, various forms of the convected equation have been used. A better alternative that includes vortex-sound interaction is instead to use the linearized and harmonic forms of the unsteady fluid flow governing equations. In this paper, a formulation of the linearized equations that include rotational effects, in an acoustic computation using a rotating frame of reference in a stationary geometry, is presented. We demonstrate that rotational effects can be important, e.g., when computing the transmission loss through high-speed compressors. The implementation of the proposed addition to the existing schemes is both simple and numerically inexpensive. The results are expected to have an impact on the research and development related to noise control of high-performance turbo-machinery, e.g., used in automotive or aviation applications at operating conditions that can be represented by steady background flows

Bilevel Optimization Approaches to Decide the Feasibility of Bookings in the European Gas Market

The European gas market is organized as a so-called entry-exit system with the main goal to decouple transport and trading. To this end, gas traders and the transmission system operator (TSO) sign so-called booking contracts that grant capacity rights to traders to inject or withdraw gas at certain nodes up to this capacity. On a day-ahead basis, traders then nominate the actual amount of gas within the previously booked capacities. By signing a booking contract, the TSO guarantees that all nominations within the booking bounds can be transported through the network. This results in a highly challenging mathematical problem. Using potential-based flows to model stationary gas physics, feasible bookings on passive networks, i.e., networks without controllable elements, have been characterized in the recent literature. In this paper, we consider networks with linearly modeled active elements such as compressors and control valves that do not lie on cycles of the network. Since these active elements allow the TSO to control the gas flow, the single-level approaches from the literature are no longer applicable. We thus present a bilevel approach to decide the feasibility of bookings in networks with active elements. Besides the classical Karush-Kuhn-Tucker reformulation, we obtain three problem-specific optimal-value-function reformulations, which also lead to novel characterizations of feasible bookings in active networks. We compare the performance of our methods by a case study based on data from the GasLib

Optimization of Critical Infrastructure with Fluids

Many of the world's most critical infrastructure systems control the motion of fluids. Despite their importance, the design, operation, and restoration of these infrastructures are sometimes carried out suboptimally. One reason for this is the intractability of optimization problems involving fluids, which are often constrained by partial differential equations or nonconvex physics. To address these challenges, this dissertation focuses on developing new mathematical programming and algorithmic techniques for optimization problems involving difficult nonlinear constraints that model a fluid's behavior. These new contributions bring many important problems within the realm of tractability. The first focus of this dissertation is on surface water systems. Specifically, we introduce the Optimal Flood Mitigation Problem, which optimizes the positioning of structural measures to protect critical assets with respect to a predefined flood scenario. Two solution approaches are then developed. The first leverages mathematical programming but does not tractably scale to realistic scenarios. The second uses a physics-inspired metaheuristic, which is found to compute good quality solutions for realistic scenarios. The second focus is on potable water distribution systems. Two foundational problems are considered. The first is the optimal water network design problem, for which we derive a novel convex reformulation, then develop an algorithm found to be more effective than the current state of the art on select instances. The second is the optimal pump scheduling (or Optimal Water Flow) problem, for which we develop a mathematical programming relaxation and various algorithmic techniques to improve convergence. The final focus is on natural gas pipeline systems. Two novel problems are considered. The first is the Maximal Load Delivery (MLD) problem for gas pipelines, which aims at finding a feasible steady-state operating point that maximizes load delivery for a severely damaged gas network. The second is the joint gas-power MLD problem, which couples damaged gas and power networks at gas-fired generators. In both problems, convex relaxations of nonconvex dynamical constraints are developed to increase tractability.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169849/1/tasseff_1.pd

Development of an Installation to Emulate Altitude, Ambient Temperature, and Ambient Humidity on Thermal Engines. Application to the Study of the Impact over E6 Engine Performance

[ES] Las normativas cada vez más restrictivas sobre las emisiones contaminantes de los vehículos de motor impuestas por la Unión Europea han obligado a los fabricantes de equipos originales (OEM) a proporcionar a los centros de investigación herramientas e instalaciones que pueden reproducir de forma precisa y repetida diferentes condiciones atmosféricas durante las primeras etapas del desarrollo del motor. En la actualidad la legislación europea incluye pruebas de emisiones reales en conducción (RDE) en diferentes condiciones atmosféricas, con altitudes de hasta 1300 metros sobre el nivel del mar y temperaturas que alcanzan los -7 ºC. Esto se ha hecho típicamente utilizando cámaras climáticas y altimétricas que permiten la reproducción de las condiciones atmosféricas en toda la celda de prueba, y más recientemente conectando a motor simuladores de altitud acoplados con unidades de tratamiento de aire (AHU). En esta Tesis Doctoral, se presenta la mejora del simulador de altitud comercializado por la empresa HORIBA denominado MEDAS, utilizando procedimientos tanto inductivos como deductivos, con el objetivo de ampliar el rango de prestaciones de la instalación, así como mejorar la precisión del control de la presión del aire comburente y reducir el consumo energético global. Además, durante esta fase, se lleva a cabo el desarrollo de un modelo 1D del simulador de altitud, con el que es posible obtener resultados precisos sobre el desempeño de la instalación para diferentes condiciones de contorno, como puede ser el punto operativo del motor, la presión de la sala o la temperatura del agua de refrigeración. A continuación, se han desarrollado dos nuevos equipos: el Módulo de Temperatura del MEDAS (MTM) y el Módulo de Humedad del MEDAS (MHM); mejorando las estrategias de control y algunos componentes clave (por ejemplo, la columna de agua de burbujas) para controlar con precisión la temperatura y la humedad del aire de combustión. Estos dos junto con el MEDAS crean un simulador de atmósfera completo, que permite el control independiente de las tres variables psicrométricas del aire de combustión del motor: presión, temperatura y humedad. Por último, el simulador de atmósfera desarrollado se utiliza para estudiar el efecto que las tres variables psicométricas del aire ambiente tienen sobre el rendimiento y las emisiones contaminantes de un motor Diesel Euro 6 turboalimentado, demostrando el gran efecto que tiene la humedad ambiental sobre las emisiones contaminantes de los motores Diesel y la necesidad de considerar este parámetro en las estrategias de calibración. Algunos resultados obtenidos podrían ser la reducción de potencia que el motor sufre al operar en condiciones de altitud, los cambios que la temperatura ambiente causa en el punto de operación del turbo grupo o como las emisiones de NOx se reducen cuando la humedad ambiente aumenta.[CA] Les normatives cada vegada més restrictives sobre les emissions contaminants dels vehicles de motor imposades per la Unió Europea han obligat als fabricants d'equips originals (OEM) a proporcionar als centres d'investigació eines i instal·lacions que poden reproduir de manera precisa i repetida diferents condicions atmosfèriques durant les primeres etapes del desenvolupament del motor. En l'actualitat la legislació europea inclou proves d'emissions reals en conducció (RDE) en diferents condicions atmosfèriques, amb altituds de fins a 1300 metres sobre el nivell de la mar i temperatures que aconsegueixen els -7 °C. Això s'ha fet típicament utilitzant cambres climàtiques i altimètriques que permeten la reproducció de les condicions atmosfèriques en tota la cel·la de prova, i més recentment connectant a motor simuladors d'altitud acoblats amb unitats de tractament d'aire (AHU). En aquesta Tesi Doctoral, es presenta la millora del simulador d'altitud comercialitzat per l'empresa HORIBA denominat MEDAS, utilitzant procediments tant inductius com deductius, amb l'objectiu d'ampliar el rang de prestacions de la instal·lació així com millorar la precisió del control de pressió de l'aire de combustió i reduir el consum energètic global. A més, durant aquesta fase, es du a terme el desenvolupament d'un model 1D del simulador d'altitud, amb el qual és possible obtindre resultats precisos sobre l'acompliment de la instal·lació per a diferents condicions de contorn, com pot ser el punt d'operació del motor, l'altitud d'instal·lació o la temperatura de l'aigua de refrigeració. A continuació, s'han desenvolupat dos nous equips: el Mòdul de Temperatura del MEDAS (MTM) i el Mòdul d'Humitat del MEDAS (MHM); millorant les estratègies de control i alguns components clau (per exemple, la columna d'aigua de bambolles) per a controlar amb precisió la temperatura i la humitat de l'aire de combustió. Aquests dos juntament amb el MEDAS creen un simulador d'atmosfera complet, que permet el control independent de les tres variables psicromètriques de l'aire de combustió del motor: pressió, temperatura i humitat. Finalment, el simulador d'atmosfera desenvolupat s'utilitza per a estudiar l'efecte que les tres variables psicomètriques de l'aire ambient tenen sobre el rendiment i les emissions contaminants d'un motor Dièsel Euro 6 *turboalimentado, demostrant el gran efecte que té la humitat ambiental sobre les emissions contaminants dels motors Dièsel i la necessitat de considerar aquest paràmetre en les estratègies de calibratge. Alguns resultats obtinguts podrien ser la reducció de potència que el motor pateix en operar en condicions d'altitud, els canvis que la temperatura ambient causa en el punt d'operació del turbo grup o com les emissions de NOx es redueixen quan la humitat ambiente augmenta.[EN] Increasingly restrictive regulations on pollutant emissions for motor vehicles imposed by the European Union have forced original equipment manufacturers (OEMs) to provide research centers with tools and facilities that can accurately and repeatedly reproduce different atmospheric conditions during the early stages of engine development. Nowadays, the European legislation includes real driving emissions (RDE) tests at different atmospheric conditions, with altitudes up to 1300 meters above sea level and temperatures reaching -7 ºC. This has been done typically using altimetric and climatic chambers, which allow the reproduction of the atmospheric conditions in the whole test cell. More recently, connecting to the engine altitude simulators coupled with air handling units (AHU). In this Ph.D. Thesis, the improvement of the altitude simulator commercialized by the company HORIBA called MEDAS, carried out by inductive and deductive procedures, is presented to extend the installation's performance range, improve the combustion air pressure control accuracy, and reduce the installation global energy consumption. Furthermore, during this phase, the development of a 1D model of the altitude simulator is carried out, with which it is possible to obtain accurate results about the performance of the installation for different boundary conditions such as the engine operation point, the room pressure, or the cooling water temperature. Following, two new pieces of equipment have been developed: MEDAS Temperature Module (MTM) and MEDAS Humidity Module (MHM), improving the control strategies and some key components (i.e., the bubbles water-column) to increase the accuracy of the combustion air temperature and humidity control. Together with the MEDAS, these two create a complete atmosphere simulator, which allows the independent control of the three psychrometric variables of the engine combustion air: pressure, temperature, and humidity. Lastly, the atmosphere simulator developed is used to study the effect that the three psychometric variables of the ambient air have on the performance and the pollutant emissions of a Euro 6 turbocharged diesel engine, proving the significant effect that the ambient humidity has on the diesel engines pollutant emissions and the necessity of considering this parameter in the calibration strategies. Some results could be the reduction in power that the engine suffers when operating in altitude conditions, the changes that the ambient temperature causes at the turbocharger operative point, or the decrease in NOx emissions that happen when the ambient humidity increases.Tabet Aleixandre, R. (2022). Development of an Installation to Emulate Altitude, Ambient Temperature, and Ambient Humidity on Thermal Engines. Application to the Study of the Impact over E6 Engine Performance [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/183753TESI

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

14th International Conference on Turbochargers and Turbocharging

14th International Conference on Turbochargers and Turbocharging addresses current and novel turbocharging system choices and components with a renewed emphasis to address the challenges posed by emission regulations and market trends. The contributions focus on the development of air management solutions and waste heat recovery ideas to support thermal propulsion systems leading to high thermal efficiency and low exhaust emissions. These can be in the form of internal combustion engines or other propulsion technologies (eg. Fuel cell) in both direct drive and hybridised configuration. 14th International Conference on Turbochargers and Turbocharging also provides a particular focus on turbochargers, superchargers, waste heat recovery turbines and related air managements components in both electrical and mechanical forms

Aeronautical engineering: A continuing bibliography with indexes (supplement 249)

This bibliography lists 637 reports, articles, and other documents introduced into the NASA scientific and technical information system in November, 1988. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics