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This dissertation studies two important problems in the field of biomass supply chain network. In the first part of the dissertation, we study the impact of different carbon regulatory policies such as carbon cap, carbon tax, carbon cap-and-trade and carbon offsetmechanism on the design and management of a biofuel supply chain network under both deterministic and stochastic settings. These mathematical models identify locations and production capacities for biocrude production plants by exploring the trade-offs that exist between transportations costs, facility investment costs and emissions. The model is solved using a modified L-shaped algorithm. We used the state of Mississippi as a testing ground for our model. A number of observations are made about the impact of each policy on the biofuel supply chain network. In the second part of the dissertation, we study the impact of intermodal hub disruption on a biofuel supply chain network. We present mathematical model that designs multimodal transportation network for a biofuel supply chain system, where intermodal hubs are subject to site-dependent probabilistic disruptions. The disruption probabilities of intermodal hubs are estimated by using a probabilistic model which is developed using real world data. We further extend this model to develop a mixed integer nonlinear program that allocates intermodal hub dynamically to cope with biomass supply fluctuations and to hedge against natural disasters. We developed a rolling horizon based Benders decomposition algorithm to solve this challenging NP-hard problem. Numerical experiments show that this proposed algorithm can solve large scale problem instances to a near optimal solution in a reasonable time. We applied the models to a case study using data from the southeast region of U.S. Finally, a number of managerial insights are drawn into the impact of intermodal-related risk on the supply chain performance.

This dissertation studies two important models in the field of the distributed generation technologies to provide resiliency to the electric power distribution system. In the first part of the dissertation, we study the impact of assessing a Combined Cooling Heating Power system (CCHP) on the optimization and management of an on-site energy system under stochastic settings. These mathematical models propose a scalable stochastic decision model for large-scale microgrid operation formulated as a two-stage stochastic linear programming model. The model is solved enhanced algorithm strategies for Benders decomposition are introduced to find an optimal solution for larger instances efficiently. Some observations are made with different capacities of the power grid, dynamic pricing mechanisms with various levels of uncertainty, and sizes of power generation units. In the second part of the dissertation, we study a mathematical model that designs a Microgrid (MG) that integrates conventional fuel based generating (FBG) units, renewable sources of energy, distributed energy storage (DES) units, and electricity demand response. Curtailment of renewable resources generation during the MG operation affects the long-term revenues expected and increases the greenhouses emission. Considering the variability of renewable resources, researchers should pay more attention to scalable stochastic models for MG for multiple nodes. This study bridges the research gap by developing a scalable chance-constrained two-stage stochastic program to ensure that a significant portion of the renewable resource power output at each operating hour will be utilized. Finally, some managerial insights are drawn into the operation performance of the Combined Cooling Heating Power and a Microgrid.

[pt] O crescente consumo de energia já se tornou uma preocupação mundial e atualmente mais de quarenta países estão envolvidos em pesquisas e programas para criar mecanismos para economizá-la. No presente trabalho é tratado o problema de Engenharia de Tráfego com base na energia (em inglês, energy-aware Traffic Engineering) aplicado ao backbone de uma rede IP que utiliza como protocolo de roteamento um SPF (Shortest Path First), como o OSPF (Open Shortest Path First), por exemplo. Na abordagem proposta são considerados os problemas de desligamento de nós (roteadores) e circuitos, para a economia de energia; e da garantia de um nível de máxima utilização dos circuitos, para assegurar os requisitos de QoS. Para a resolução do problema de otimização, em lugar de adotarem-se métodos heurísticos, propõe-se o tratamento direto por meio de decomposição de Benders, segmentando um problema complicado e de elevada carga computacional em vários menores cuja resolução é mais simples e cuja convergência é mais rápida. / [en] The growing energy consumption has already become a global concern and currently more than forty countries are involved in researches and programs in order to create mechanisms to save it. This work deals with the energy-aware Traffic Engineering problem applied to the backbone of an IP network in which the used routing protocol is a SPF (Shortest Path First) one, such as OSPF (Open Shortest Path First), for example. The proposed approach considers the problem of switching-off nodes (routers) and circuits, for energy saving; and it also considers the problem of ensuring a maximum utilization level by the circuits, towards to assure QoS requirements. In order to solve the optimization problem, rather than adopting heuristic methods, we propose the direct processing by means of Benders decomposition, crumbling a complicated and hard to solve problem into several smaller ones whose resolution is more simple and whose convergence is faster.

Die Dissertationsschrift adressiert den Ausbau des Übertragungsnetzes in Deutschland für das Jahr 2030 und beantwortet damit die Frage nach den Einflüssen einer stärkeren Marktintegration der erneuerbaren Energien und die Wirkung dezentraler Speichersysteme auf den Netzausbau, welche in dieser Weise noch nicht analysiert wurden. Zusätzlich werden diesen Szenarien auch die Wirkung von zusätzlichen Einspeisekapazitäten aus erneuerbaren Energien bzw. einer reduzierten Last betrachtet. Schließlich werden die Effekte eines potenziellen Ausstieges aus der Stromerzeugung auf Braunkohlebasis in Gesamtdeutschland bzw. nur Teilen davon thematisiert. Bisherige Untersuchungen fokussierten u.a. die Wirkung von erneuerbaren Energien im Kontext des Ausbaus von europäischen Transportkapazitäten. Diese Analyse bewertet die Auswirkungen auf den Umfang des Netzausbaus mit Auflösung auf einzelnen Trassen, die Integration der erneuerbaren Energien mit hoher regionaler Auflösung und die Systemkosten als Indikator der volkswirtschaftlichen Bewertung. Der in der Arbeit entwickelte Ansatz zur mathematischen Lösung des Optimierungsproblems basiert auf der Weiterentwicklung des Benders-Dekompositionsansatzes. Im Ergebnis zeigt sich, dass eine stärkere Flexibilisierung der Einspeisung den Netzausbaubedarf senken kann. Auch dezentrale Speicher tragen dazu bei, wobei diese Option mit hohen Investitionen einhergeht. Der Zuwachs an Erzeugung aus erneuerbaren Energien führt zu mehr Netzausbau, während eine Reduktion der elektrischen Last diesen Anstieg abmildern kann. Bei der abschließenden Analyse der Wirkung des Braunkohleausstiegs wird der deutlich erhöhte Bedarf an weiteren Übertragungskapazitäten in Deutschland aufgedeckt, während ein auf Ostdeutschland begrenzter Ausstieg eine geringe Reduzierung ermöglicht.:1 Einleitung 1.1 Analyse der Ausgangslage 1.2 Zielstellung und Lösungsweg 1.3 Zusammenfassung 2 Grundlagen zum deutschen Elektroenergiesystem 2.1 Derzeitige Entwicklungen im deutschen Elektroenergiesystem und Strommarkt 2.2 Derzeitiges Marktdesign und der Einfluss der erneuerbaren Energien auf die Preisbildung 2.3 Einfluss der erneuerbaren Energien auf die Residuallast 2.4 Rolle der Übertragungsnetzbetreiber 2.5 Maßnahmen zur Behebung von Netzengpässen 2.6 Grundlagen zur Abregelung von erneuerbaren Energien 2.7 Planungsverfahren des Netzausbaus 3 Überblick und Klassifizierung von Analysen auf der Basis von Übertragungsnetzmodellen 3.1 Grundlagen zu Modellen in der Energiewirtschaft 3.2 Wirkung von Flexibilitätsmaßnahmen auf den Netzausbau 3.3 Wirkung von Veränderungen des regulatorischen Rahmens auf den Netzausbau 3.4 Ausprägungen des europäischen und deutschen Übertragungsnetzes in Zukunft 3.5 Methodische Ansätze zum Ermitteln bzw. Bewerten des Netzausbaus 3.6 Zusammenfassung zentraler Aspekte der Analyse und Modellierung des Netzausbaus in der Literatur 4 Formulierung des Übertragungsnetzausbaus im Stromnetzmodell ELMOD 4.1 Anforderungen an das Übertragungsnetzmodell 4.2 Vereinfachte Lastflussmodellierung 4.3 Ausgangsmodell für die Ermittlung des optimalen Übertragungsnetzes 4.4 Anwendung des NOVA-Prinzips im Stromnetzmodell ELMOD 4.5 Investitionen in das Übertragungsnetz 4.6 Modellierung der dezentralen Speicher 4.7 Zusammenfassung der Modellformulierung 5 Dekompositionsmethoden zum effizienten Lösen des Netzausbauproblems 5.1 Mathematische Analyse des Netzausbauproblems 5.2 Verfahren zur Lösung von Optimierungsproblemen 5.3 Anwendung der Benders-Dekomposition für die Berechnung des Netzausbaues 5.4 Anwendung des Karush-Kuhn-Tucker-Systems 6 Definition der Szenarien für die modellgestützte Untersuchung des Übertragungsnetzausbaus 6.1 Grundlagen zur Szenarientechnik 6.2 Begründung für die Nutzung eines deterministischen Optimierungsmodells 6.3 Bestimmung der Prämissen und Deskriptoren 6.4 Szenarienzusammenstellung 6.5 Referenzszenario als wahrscheinlichste Entwicklung des Energiesystems 6.6 Integrationsregime für fluktuierende erneuerbare Energien 6.7 Szenarien zur Reduktion des Netzausbaus durch dezentrale Energiespeicher 6.8 Wirkung eines weiteren EE-Ausbaus und Lastreduzierungen auf den Netzausbau 6.9 Einfluss eines Braunkohleausstiegs auf den Netzausbau 6.10 Aufbereitung übergreifender Eingangsdaten für die Modellierung 6.11 Methodik der Kalibrierung 6.12 Ergebnisse der Kalibrierung 6.13 Zusammenfassung und Überblick 7 Ergebnisse der modellgestützten Analyse 7.1 Ergebnisse des Referenzszenarios 7.2 Analyse verschiedener Integrationsmechanischmen von erneuerbaren Energien auf den Netzausbau 7.3 Auswirkungen von dezentralen Speichersysteme auf den Ausbau des Übertragungsnetzes in Deutschland 7.4 Analyse ausgewählter Komponenten der energiepolitischen Ziele 7.5 Auswirkungen verschiedener Braunkohleausstiegsszenarien in Deutschland auf den Ausbau des Übertragungsnetzes 7.6 Übergreifende Analyse der einflussstärksten Gestaltungsoptionen 8 Sensitivitätsanalyse zu ausgewählten szenarioübergreifenden Parametern 8.1 Definition der Sensitivitäten 8.2 Effekte auf die Jahreserzeugungen 8.3 Effekt der Sensitivitäten auf die Treibhausgasemissionen 8.4 Effekt der Sensitivitäten auf die Integration von erneuerbaren Energien 8.5 Effekt der Sensitivitäten auf den Netzausbau 8.6 Effekt der Sensitivitäten auf die Systemkosten 8.7 Fazit zur Sensitivitierung ausgewählter Eingangsgrößen 9 Zusammenfassungen und Ausblick 9.1 Zusammenfassung der Modellentwicklung und Lösung des Optimierungsmodells 9.2 Zusammenfassung der Modellergebnisse 9.3 Beantwortung der aufgestellten Forschungsfragen als Fazit 9.4 Ausblick auf weiterführende Analysen 10 Literaturverzeichnis A Anhang A.1 Einführung in die Benders-Dekomposition A.2 Nichtlineare, kontinuierliche Optimierung A.3 Grundlagen der Karush-Kuhn-Tucker-Theorie A.4 Anhang zur Analyse der Wirkung von dezentralen Speichern auf den Ausbau des Übertragungsnetzes A.5 Anhang zur Analyse der Wirkung der Komponenten der abgeleiteten energiepolitischen Ziele auf den Ausbau des Übertragungsnetzes

Yes / This paper presents a robust framework for active and reactive power management in distribution networks using electric vehicles (EVs). The method simultaneously minimizes the energy cost and the voltage deviation subject to network and EVs constraints. The uncertainties related to active and reactive loads, required energy to charge EV batteries, charge rate of batteries and charger capacity of EVs are modeled using deterministic uncertainty sets. Firstly, based on duality theory, the max min form of the model is converted to a max form. Secondly, Benders decomposition is employed to solve the problem. The effectiveness of the proposed method is demonstrated with a 33-bus distribution network.

In the past few years a new class of layered piezoceramic and piezoceramic-composite actuators, known as RAINBOW and GRAPHBOW, respectively, that are capable of achieving 100 times greater out-of-plane displacements than previously available has been developed. Prior to the development of RAINBOW and GRAPHBOW, large stacks of piezoelectric actuators, requiring complicated electronic drive circuits, were necessary to achieve the displacement now possible through the use of a single RAINBOW actuator. The major issues with both RAINBOW and GRAPHBOW are the prediction of their room-temperature shapes after processing, and their deformation response under application of electric field. In this research, a methodology for predicting the manufactured shapes of rectangular and disk-style RAINBOW and GRAPHBOW is developed. All of the predictive analyses developed are based on finding approximate displacement responses that minimize the total potential energy of the devices through the use of variational methods and the Rayleigh-Ritz technique. These analyses are based on classical layered plate theory and assumed the various layers exhibited linear elastic, temperature-independent behavior. Geometric nonlinearities are important and are included in the strain-displacement relations. Stability of the predicted shapes is determined by examining the second variation of the total potential energy. These models are easily modified to account for the deformations induced by actuation of the piezoceramic. The results indicate that for a given set of material properties, rectangular RAINBOW can have critical values of sidelength-to-thickness ratio (Lx/H or Ly/H) below which RAINBOW exhibits unique, or single-valued, spherical or domed shapes when cooled from the processing temperature to room temperature. For values of sidelength-to-thickness ratio greater than the critical value, RAINBOW exhibits multiple room-temperature shapes. Two of the shapes are stable and are, in general, near-cylindrical. The third shape is spherical and is unstable. Similarly, disk-style RAINBOW can have critical values of radius-to-thickness ratios (R/H) below which RAINBOW exhibits axisymmetric room-temperature shapes. For values of R/H greater than the critical value, disk-style RAINBOW exhibits two stable near-cylindrical shapes and one unstable axisymmetric shape. Moreover, it is found that for the set of material properties used in this study, the optimal reduced layer thickness would be at 55%, since the maximum change in curvature is achieved under the application of an electric field, while the relationship between the change in curvatures and the electric field is kept very close to being linear. In general, good agreement is found for comparisons between the predicted and manufactured shapes of RAINBOW. A multi-step thermoelastic analysis is developed to model the addition of the fiber-reinforced composite layer to RAINBOW to make GRAPHBOW. Results obtained for rectangular RAINBOW indicate that if the bifurcation temperature in the temperature-curvature relation is lower than the composite cure temperature, then a unique stable GRAPHBOW shape can be obtained. If the RAINBOW bifurcation temperature is above the composite cure temperature, multiple room-temperature GRAPHBOW shapes are obtained and saddle-node bifurcations can be encountered during the cooling to room temperature of [0°/RAINBOW], [RAINBOW/0o], and [0o2/RAINBOW]. Rectangular [RAINBOW/0o/90o] seems to be less likely to encounter saddle-node bifurcations. Furthermore, the unstable spherical RAINBOW configuration is converted to a stable near-cylindrical configuration. For the case considered of disk-style GRAPHBOW, three stable room-temperature shapes are obtained and the unstable axisymmetric RAINBOW configuration is also converted to a stable near-cylindrical configuration. For both rectangular and disk-style GRAPHBOW, the relationship between the major curvature and the electric field is shown to be very close to being linear. This characteristic would aid any dynamic analysis of RAINBOW or GRAPHBOW. / Ph. D.

[pt] Esta tese de doutorado é composta de dois artigos científicos com contribuições na área de Smart Grid. Além disso, a tese também contribui para o desenvolvimento de soluções computacionais eficientes para problemas de programação linear mista e inteira. Outra importante contribuição é o desenvolvimento de método de decomposição benders com segundo estágio inteiro e não convexo aplicado ao problema de Transmission Switching. O primeiro artigo científico mostra os benefícios com o advento de uma rede inteligente e o aumento da capacidade do operador do sistema de energia elétrica em tomar ações corretivas em face de ocorrências de contingências. O artigo também analisa consequências práticas na capacidade de self-healing da rede pós-contingência. Em nosso contexto, uma rede self-healing é uma rede com total flexibilidade para ajustar a geração e as linhas de transmissão antes e depois da ocorrência de alguma contingência. Resultados numéricos mostram significantes reduções no corte de carga para cada contingência e no total. Foi considerado um único período que representa a demanda de pico do sistema, comparou-se o novo método com os utilizados em publicações anteriores. O segundo artigo contribui também para a aplicação da tecnologia de Smart Grid, em particular a teoria de Transmission Switching. De fato, desenvolvemos uma estratégia de solução para lidar com a complexibilidade NP-Hard criada pelas variáveis de transmission switching e unit commitment do problema de otimização. Foi desenvolvida uma solução algorítmica baseada na teoria dos grafos. Estudou-se a estrutura topológica desses problemas. Além disso, a maior contribuição foi o desenvolvimento de um novo método de decomposição de benders aplicado para o problema de transmission switching com o segundo estágio inteiro e não convexo. Para lidar com este problema de não convexidade, foi desenvolvido um método de convexificação sequencial, implícito a decomposição de benders. / [en] This PhD Thesis is composed by two papers with contributions on operations research applied to smart grid theory. The first paper highlights the economic and security benefits of an enhanced system operation with the advent of a smart grid technology by introducing a novel model, which is a joint energy and reserve scheduling that incorporates the network capability to switch transmission lines as a corrective action to enhance the system capability to circumvent contingency events. The main goal is to reduce operating costs and electric power outages, by adjusting the network connectivity when a contingency occurs. In such a framework, results show that, with a limited number of corrective switches, the system operator is able to circumvent a wider range of contingencies, while resulting in lower operational costs and reserve levels. In our context, a grid that is capable to adjust its generation and also its topology through post-contingency line switching is called a self-healing grid, and its importance in network security and operating costs is demonstrated in this work. The graph structure is explored in the algorithmic solution of the post-contingency transmission switching problem. Numerical results demonstrate a significant reduction in total load shedding and operating cost. It has been also illustrated an expressive improvement in terms of security and operating cost, in comparison to the transmission switching models previously published. The second paper is an application of a modified Benders decomposition to the post-contingency transmission switching problem. The decomposition is an attempt to deal with the NP-hard optimization problem created by the transmission switching and unit commitment variables. The major contribution is the application of a new benders decomposition approach to the problem of transmission switching, in which the first and second stages problems are a mixed-integer program. To deal with this issue, it is used a Branch and Bound (B&B) procedure for the first-stage problem and a sequential convexification procedure for the second-stage problem.

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Les méthodes de décomposition sont une application du concept de diviser pour régner en optimisation. L'idée est de décomposer un problème d'optimisation donné en une séquence de sous-problèmes plus faciles à résoudre. Bien que ces méthodes soient les meilleures pour un grand nombre de problèmes de recherche opérationnelle, leur application à des problèmes réels de grande taille présente encore de nombreux défis. Cette thèse propose des améliorations méthodologiques et algorithmiques de méthodes de décomposition. Notre approche est basée sur l'analyse convexe et l'optimisation non-différentiable. Dans la décomposition par les contraintes (ou relaxation lagrangienne) du problème de planification de production électrique, même les sous-problèmes sont trop difficiles pour être résolus exactement. Mais des solutions approchées résultent en des prix instables et chahutés. Nous présentons un moyen simple d'améliorer la structure des prix en pénalisant leurs oscillations, en utilisant en particulier une régularisation par variation totale. La consistance de notre approche est illustrée sur des problèmes d'EDF. Nous considérons ensuite la décomposition par les variables (ou de Benders) qui peut avoir une convergence excessivement lente. Avec un point de vue d'optimisation non-différentiable, nous nous concentrons sur l'instabilité de l'algorithme de plans sécants sous-jacent à la méthode. Nous proposons une stabilisation quadratique de l'algorithme de Benders, inspirée par les méthodes de faisceaux en optimisation convexe. L'accélération résultant de cette stabilisation est illustrée sur des problèmes de conception de réseau et de localisation de plates-formes de correspondance (hubs). Nous nous intéressons aussi plus généralement aux problèmes d'optimisation convexe non-différentiable dont l'objectif est coûteux à évaluer. C'est en particulier une situation courante dans les procédures de décomposition. Nous montrons qu'il existe souvent des informations supplémentaires sur le problème, faciles à obtenir mais avec une précision inconnue, qui ne sont pas utilisées dans les algorithmes. Nous proposons un moyen d'incorporer ces informations incontrôlées dans des méthodes classiques d'optimisation convexe non-différentiable. Cette approche est appliquée avec succès à desproblèmes d'optimisation stochastique. Finalement, nous introduisons une stratégie de décomposition pour un problème de réaffectation de machines. Cette décomposition mène à une nouvelle variante de problèmes de conditionnement vectoriel (vectorbin packing) où les boîtes sont de taille variable. Nous proposons des heuristiques efficaces pour ce problème, qui améliorent les résultats de l'état de l'art du conditionnement vectoriel. Une adaptation de ces heuristiques permet de construire des solutions réalisables au problème de réaffectation de machines de Google. / Decomposition methods are an application of the divide and conquer principle to large-scale optimization. Their idea is to decompose a given optimization problem into a sequence of easier subproblems. Although successful for many applications, these methods still present challenges. In this thesis, we propose methodological and algorithmic improvements of decomposition methods and illustrate them on several operations research problems. Our approach heavily relies on convex analysis and nonsmooth optimization. In constraint decomposition (or Lagrangian relaxation) applied to short-term electricity generation management, even the subproblems are too difficult to solve exactly. When solved approximately though, the obtained prices show an unstable noisy behaviour. We present a simple way to improve the structure of the prices by penalizing their noisy behaviour, in particular using a total variation regularization. We illustrate the consistency of our regularization on real-life problems from EDF. We then consider variable decomposition (or Benders decomposition), that can have a very slow convergence. With a nonsmooth optimization point of view on this method, we address the instability of Benders cutting-planes algorithm. We present an algorithmic stabilization inspired by bundle methods for convex optimization. The acceleration provided by this stabilization is illustrated on network design andhub location problems. We also study more general convex nonsmooth problems whose objective function is expensive to evaluate. This situation typically arises in decomposition methods. We show that it often exists extra information about the problem, cheap but with unknown accuracy, that is not used by the algorithms. We propose a way to incorporate this coarseinformation into classical nonsmooth optimization algorithms and apply it successfully to two-stage stochastic problems.Finally, we introduce a decomposition strategy for the machine reassignment problem. This decomposition leads to a new variant of vector bin packing problems, where the bins have variable sizes. We propose fast and efficient heuristics for this problem that improve on state of the art results of vector bin packing problems. An adaptation of these heuristics is also able to generate feasible solutions for Google instances of the machine reassignment problem.