Determining the maximum power system loadability, as well as preventing the system from being operated close to the stability limits is very important in power systems planning and operation. The application of optimization techniques to power systems security and electricity markets is a rather relevant research area in power engineering. The study of optimization models to determine critical operating conditions of a power system to obtain secure power dispatches in an electricity market has gained particular attention. This thesis studies and develops optimization models and techniques to detect or avoid voltage instability points in a power system in the context of a competitive electricity market. A thorough analysis of an optimization model to determine the maximum power loadability points is first presented, demonstrating that a solution of this model corresponds to either Saddle-node Bifurcation (SNB) or Limit-induced Bifurcation (LIB) points of a power flow model. The analysis consists of showing that the transversality conditions that characterize these bifurcations can be derived from the optimality conditions at the solution of the optimization model. The study also includes a numerical comparison between the optimization and a continuation power flow method to show that these techniques converge to the same maximum loading point. It is shown that the optimization method is a very versatile technique to determine the maximum loading point, since it can be readily implemented and solved. Furthermore, this model is very flexible, as it can be reformulated to optimize different system parameters so that the loading margin is maximized. The Optimal Power Flow (OPF) problem with voltage stability (VS) constraints is a highly nonlinear optimization problem which demands robust and efficient solution techniques. Furthermore, the proper formulation of the VS constraints plays a significant role not only from the practical point of view, but also from the market/system perspective. Thus, a novel and practical OPF-based auction model is proposed that includes a VS constraint based on the singular value decomposition (SVD) of the power flow Jacobian. The newly developed model is tested using realistic systems of up to 1211 buses to demonstrate its practical application. The results show that the proposed model better represents power system security in the OPF and yields better market signals. Furthermore, the corresponding solution technique outperforms previous approaches for the same problem. Other solution techniques for this OPF problem are also investigated. One makes use of a cutting planes (CP) technique to handle the VS constraint using a primal-dual Interior-point Method (IPM) scheme. Another tries to reformulate the OPF and VS constraint as a semidefinite programming (SDP) problem, since SDP has proven to work well for certain power system optimization problems; however, it is demonstrated that this technique cannot be used to solve this particular optimization problem.

Determining the maximum power system loadability, as well as preventing the system from being operated close to the stability limits is very important in power systems planning and operation. The application of optimization techniques to power systems security and electricity markets is a rather relevant research area in power engineering. The study of optimization models to determine critical operating conditions of a power system to obtain secure power dispatches in an electricity market has gained particular attention. This thesis studies and develops optimization models and techniques to detect or avoid voltage instability points in a power system in the context of a competitive electricity market. A thorough analysis of an optimization model to determine the maximum power loadability points is first presented, demonstrating that a solution of this model corresponds to either Saddle-node Bifurcation (SNB) or Limit-induced Bifurcation (LIB) points of a power flow model. The analysis consists of showing that the transversality conditions that characterize these bifurcations can be derived from the optimality conditions at the solution of the optimization model. The study also includes a numerical comparison between the optimization and a continuation power flow method to show that these techniques converge to the same maximum loading point. It is shown that the optimization method is a very versatile technique to determine the maximum loading point, since it can be readily implemented and solved. Furthermore, this model is very flexible, as it can be reformulated to optimize different system parameters so that the loading margin is maximized. The Optimal Power Flow (OPF) problem with voltage stability (VS) constraints is a highly nonlinear optimization problem which demands robust and efficient solution techniques. Furthermore, the proper formulation of the VS constraints plays a significant role not only from the practical point of view, but also from the market/system perspective. Thus, a novel and practical OPF-based auction model is proposed that includes a VS constraint based on the singular value decomposition (SVD) of the power flow Jacobian. The newly developed model is tested using realistic systems of up to 1211 buses to demonstrate its practical application. The results show that the proposed model better represents power system security in the OPF and yields better market signals. Furthermore, the corresponding solution technique outperforms previous approaches for the same problem. Other solution techniques for this OPF problem are also investigated. One makes use of a cutting planes (CP) technique to handle the VS constraint using a primal-dual Interior-point Method (IPM) scheme. Another tries to reformulate the OPF and VS constraint as a semidefinite programming (SDP) problem, since SDP has proven to work well for certain power system optimization problems; however, it is demonstrated that this technique cannot be used to solve this particular optimization problem.

The thesis deals with a general access to topological transversality in uniform spaces. / Die Arbeit behandelt einen allgemeinen Zugang zur Topologischen Transversalität in uniformen Räumen.

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No. of bitstreams: 1 DissCKT.pdf: 1622176 bytes, checksum: 694e5995257e999a079c1de6b0bbe47d (MD5) Previous issue date: 2016-12-05 / Não recebi financiamento / The current environmental situation is a worrying scenario, making it inevitable to take different measures that result in solutions that overcome social and environmental challenges, pointing to a world of sustainable societies. As an important part of the complex and articulated group of necessary measures, education is essential, since it is capable of raising awareness that mobilizes people for social transformation. Environmental education is a practice that incorporates themes that are crucial in the society development in general and, if implemented in a critical, reflexive, transformative and emancipatory perspective, can increase the power of people action in this direction, favoring the challenging inflection, now in demand. In Brazil, this practice is referred to in concepts and principles known and established, which must be followed in its exercise, in projects and programs of community interaction, or in contents worked in the school environment. In this context, based on an evaluation of the National Curriculum Parameters of the Environment Transversal Theme and the National Curriculum Guidelines in Environmental Education, this paper defined four indicators for the analysis of the the São Paulo State official curriculum of the elementary education in relation to the approach to the environmental question: knowledge, participation, values, contextualization. Bibliographic review followed by documental analysis were the procedures used in the research, complemented by surveys of empirical researches to verify the occurrence of environmental education initiatives in the hidden curriculum in school practices. From the documental analysis of the Teacher's Notebook of all disciplines, we sought, among the description of the activities proposed there, to verify the occurrence of the different indicators. It was observed that environmental education practice is still restricted mainly to the areas of Science and Geography, which contrasts with the main indication, parameters and guidelines established, that this should be a practice that transcends the curriculum, pointing to a possible interdisciplinarity. We made suggestions for insertion of the environmental theme in different situations of its absence in the materials analyzed, trying to show concretely possibilities of approaching the environmental issue in all disciplines. / A situação ambiental atual configura um cenário preocupante, tornando inevitável a tomada de diferentes medidas que resultem em soluções superadoras dos desafios socioambientais, apontando para um mundo de sociedades sustentáveis. Como parte importante do complexo e articulado conjunto de medidas necessárias, a educação apresenta-se como essencial, uma vez que é capaz de possibilitar uma tomada de consciência que mobilize as pessoas para a transformação social. A educação ambiental é uma prática que incorpora temáticas hoje cruciais no desenvolvimento da sociedade em geral e, se implementada numa perspectiva crítica, reflexiva, transformadora e emancipatória, pode ampliar a potência de ação das pessoas nessa direção, favorecendo a desafiadora inflexão ora em demanda. No Brasil, esta prática está referida em conceitos e princípios conhecidos e instituídos, os quais devem ser seguidos no seu exercício, seja em projetos e programas de interação comunitária, seja em currículos trabalhados no ambiente escolar. Nesse contexto, a partir de uma avaliação dos Parâmetros Curriculares Nacionais do Tema Transversal Meio Ambiente e das Diretrizes Curriculares Nacionais em Educação Ambiental, este trabalho definiu quatro indicadores para análise do currículo oficial do ensino fundamental do Estado de São Paulo a respeito da abordagem da questão ambiental: conhecimento, participação, valores, contextualização. Pesquisa bibliográfica seguida de análise documental foram os procedimentos empregados na pesquisa, complementados ainda por levantamento de pesquisas empíricas com vistas a verificar a ocorrência de iniciativas educativas ambientais no currículo oculto, na prática escolar. A partir da análise documental do primeiro volume do Caderno do professor de todas as disciplinas do 6º ano/5ª série, buscou-se, em meio à descrição das atividades ali propostas, verificar a ocorrência dos diferentes indicadores. Observou-se que a prática educativa ambiental ainda está restrita, principalmente, às áreas de ciências e de geografia, o que se contrapõe à principal indicação, dos parâmetros e das diretrizes instituídos/as, de que esta deva ser uma prática transversal ao currículo, apontando para uma possível interdisciplinaridade. Foram feitas, então, sugestões de inserção da temática ambiental em diferentes situações de sua ausência nos materiais analisados, procurando mostrar concretamente algumas possibilidades de abordagem da questão ambiental em todas as disciplinas.

Cette thèse s'inscrit dans le domaine de la théorie des hypergraphes et s'intéresse aux traverses minimales des hypergraphes. L'intérêt pour l'extraction des traverses minimales est en nette croissance, depuis plusieurs années, et ceci est principalement dû aux solutions qu'offrent les traverses minimales dans divers domaines d'application comme les bases de données, l'intelligence artificielle, l'e-commerce, le web sémantique, etc. Compte tenu donc du large éventail des domaines d'application des traverses minimales et de l'intérêt qu'elles suscitent, l'objectif de cette thèse est donc d'explorer de nouvelles pistes d'application des traverses minimales tout en proposant des méthodes pour optimiser leur extraction. Ceci a donné lieu à trois contributions proposées dans cette thèse. La première approche tend à tirer profit de l'émergence du Web 2.0 et, par conséquent, des réseaux sociaux en utilisant les traverses minimales pour la détection des acteurs importants au sein de ces réseaux. La deuxième partie de recherche au cours de cette thèse s'est intéressé à la réduction du nombre de traverses minimales d'un hypergraphe. Ce nombre étant très élevé, une représentation concise et exacte des traverses minimales a été proposée et est basée sur la construction d'un hypergraphe irrédondant, d'où sont calculées les traverses minimales irrédondantes de l'hypergraphe initial. Une application de cette représentation au problème de l'inférence des dépendances fonctionnelles a été présentée pour illustrer l’intérêt de cette approche. La dernière approche s'est intéressée à la décomposition des hypergraphes en des hypergraphes partiels. Les traverses minimales de ces derniers sont calculées et leur produit cartésien permet de générer l'ensemble des traverses de l'hypergraphe. Les différentes études expérimentales menées ont montré l’intérêt de ces approches proposées / This work is part of the field of the hypergraph theory and focuses on hypergraph minimal transversal. The problem of extracting the minimal transversals from a hypergraph received the interest of many researchers as shown the number of algorithms proposed in the literature, and this is mainly due to the solutions offered by the minimal transversal in various application areas such as databases, artificial intelligence, e-commerce, semantic web, etc. In view of the wide range of fields of minimal transversal application and the interest they generate, the objective of this thesis is to explore new application paths of minimal transversal by proposing methods to optimize the extraction. This has led to three proposed contributions in this thesis. The first approach takes advantage of the emergence of Web 2.0 and, therefore, social networks using minimal transversal for the detection of important actors within these networks. The second part of research in this thesis has focused on reducing the number of hypergraph minimal transversal. A concise and accurate representation of minimal transversal was proposed and is based on the construction of an irredundant hypergraph, hence are calculated the irredundant minimal transversal of the initial hypergraph. An application of this representation to the dependency inference problem is presented to illustrate the usefulness of this approach. The last approach includes the hypergraph decomposition into partial hypergraph the “local” minimal transversal are calculated and their Cartesian product can generate all the hypergraph transversal sets. Different experimental studies have shown the value of these proposed approaches

The thesis deals with a general access to topological transversality in uniform spaces. / Die Arbeit behandelt einen allgemeinen Zugang zur Topologischen Transversalität in uniformen Räumen.

Dans cette thèse nous étudions la dynamique engendrée par une famille de flots Hamiltoniens. Un tel système dynamique à plusieurs générateurs est aussi appelé ‘polysystème’. Motivés par des questions liées au phénomène de la diffusion d’Arnold, notre objectif est de construire des trajectoires du polysystème qui relient deux régions lointaines de l’espace des phases. La thèse est divisée en trois parties.Dans la première partie, nous considérons le polysystème engendré par les flots discrétisés d’une famille d’Hamiltoniens Tonelli. En utilisant une approche variationnelle issue de la théorie KAM faible, nous donnons des conditions suffisantes pour l’existence des trajectoires souhaitées.Dans la deuxième partie, nous traitons le cas d’un polysystème engendré par un couple de flots Hamiltoniens à temps continu, dont l’étude rentre dans le cadre de la théorie géométrique du contrôle. Dans ce contexte, nous montrons dans certains cas la transitivité d’un polysystème générique, à l’aide du théorème de transversalité de Thom.La dernière partie de la thèse est dédiée à obtenir une nouvelle version du théorème de transversalité de Thom s’exprimant en termes d’ensembles rectifiables de codimension positive. Dans cette partie il n’est pas question de polysystèmes, ni d’Hamiltoniens. Néanmoins, les résultats obtenus ici sont utilisés dans la deuxième partie de la thèse / In this thesis we study the dynamics generated by a family of Hamiltonian flows. Such a dynamical system with several generators is also called ‘polysystem’.Motivated by some questions related to the phenomenon of Arnold diffusion, our aim is to construct trajectories of the polysystem which connect two far-apart regions of the phase space.The thesis is divided into three parts.In the first part, we consider the polysystem generated by the time-onemaps of a family of Tonelli Hamiltonians. By using a variational approach falling within the framework of weak KAM theory, we give sufficient conditions for the existence of the desired trajectories.In the second part, we address the case of a polysystem generated by twocontinuous-time Hamiltonian flows. This problem fits into the framework of geometriccontrol theory. In this context, we show in some cases the transitivity of a generic polysystem, by means of Thom’s transversality theorem.The third and last part of the thesis is devoted to the proof of a newversion of Thom’s transversality theorem, formulated in terms of rectifiable sets of positive codimension. Neither polysystems nor Hamiltonians are explicitly involved in this part. However, the results obtained here are used in the second part of the thesis.

Der Beitrag befasst sich mit Theaterinszenierungen und -produktionen aus einer epistemologischen, philosophischen und kulturtheoretischen Sicht vor einer historischen Perspektive. Dabei wenden neue transdisziplinäre Ansätze für die Analyse und Interpretation des Theaters, wie strukturale und poststrukturale Methoden vorgestellt bzw. Theater im Kontext transversaler, transkultureller, transmedialer zu behandeln. / The article deals with theater productions and stagings from an epistemological, philosophical and cultural-theoretical point of view in front of a historical perspective. New transdisciplinary approaches for the analysis and interpretation of theater, such as structural and poststructural methods, are presented and theater is treated in the context of transversal, transcultural, transmedial. / El artículo aborda las producciones y puestas en escena teatrales desde un punto de vista epistemológico, filosófico y teórico-cultural en una perspectiva histórica. Se presentan nuevos enfoques transdisciplinarios para el análisis y la interpretación del teatro, como los métodos estructurales y postestructurales, y se trata el teatro en el contexto de los enfoques transversales, transculturales y transmediales.

Cette thèse est une contribution au calcul des variations et à la théorie du contrôle optimal dans les cadres discret, plus généralement time scale, et fractionnaire. Ces deux domaines ont récemment connu un développement considérable dû pour l’un à son application en informatique et pour l’autre à son essor dans des problèmes physiques de diffusion anormale. Que ce soit dans le cadre time scale ou dans le cadre fractionnaire, nos objectifs sont de : a) développer un calcul des variations et étendre quelques résultats classiques (voir plus bas); b) établir un principe du maximum de Pontryagin (PMP en abrégé) pour des problèmes de contrôle optimal. Dans ce but, nous généralisons plusieurs méthodes variationnelles usuelles, allant du simple calcul des variations au principe variationnel d’Ekeland (couplé avec la technique des variations-aiguilles), en passant par l’étude d’invariances variationnelles par des groupes de transformations. Les démonstrations des PMPs nous amènent également à employer des théorèmes de point fixe et à prendre en considération la technique des multiplicateurs de Lagrange ou encore une méthode basée sur un théorème d’inversion locale conique. Ce manuscrit est donc composé de deux parties : la Partie 1 traite de problèmes variationnels posés sur time scale et la Partie 2 est consacrée à leurs pendants fractionnaires. Dans chacune de ces deux parties, nous suivons l’organisation suivante : 1. détermination de l’équation d’Euler-Lagrange caractérisant les points critiques d’une fonctionnelle Lagrangienne ; 2. énoncé d’un théorème de type Noether assurant l’existence d’une constante de mouvement pour les équations d’Euler-Lagrange admettant une symétrie ; 3. énoncé d’un théorème de type Tonelli assurant l’existence d’un minimiseur pour une fonctionnelle Lagrangienne et donc, par la même occasion, d’une solution pour l’équation d’Euler-Lagrange associée (uniquement en Partie 2) ; 4. énoncé d’un PMP (version forte en Partie 1, version faible en Partie 2) donnant une condition nécessaire pour les trajectoires qui sont solutions de problèmes de contrôle optimal généraux non-linéaires ; 5. détermination d’une condition de type Helmholtz caractérisant les équations provenant d’un calcul des variations (uniquement en Partie 1 et uniquement dans les cas purement continu et purement discret). Des théorèmes de type Cauchy-Lipschitz nécessaires à l’étude de problèmes de contrôle optimal sont démontrés en Annexe. / This dissertation deals with the mathematical fields called calculus of variations and optimal control theory. More precisely, we develop some aspects of these two domains in discrete, more generally time scale, and fractional frameworks. Indeed, these two settings have recently experience a significant development due to its applications in computing for the first one and to its emergence in physical contexts of anomalous diffusion for the second one. In both frameworks, our goals are: a) to develop a calculus of variations and extend some classical results (see below); b) to state a Pontryagin maximum principle (denoted in short PMP) for optimal control problems. Towards these purposes, we generalize several classical variational methods, including the Ekeland’s variational principle (combined with needle-like variations) as well as variational invariances via the action of groups of transformations. Furthermore, the investigations for PMPs lead us to use fixed point theorems and to consider the Lagrange multiplier technique and a method based on a conic implicit function theorem. This manuscript is made up of two parts : Part A deals with variational problems on time scale and Part B is devoted to their fractional analogues. In each of these parts, we follow (with minor differences) the following organization: 1. obtaining of an Euler-Lagrange equation characterizing the critical points of a Lagrangian functional; 2. statement of a Noether-type theorem ensuring the existence of a constant of motion for Euler-Lagrange equations admitting a symmetry;3. statement of a Tonelli-type theorem ensuring the existence of a minimizer for a Lagrangian functional and, consequently, of a solution for the corresponding Euler-Lagrange equation (only in Part B); 4. statement of a PMP (strong version in Part A and weak version in Part B) giving a necessary condition for the solutions of general nonlinear optimal control problems; 5. obtaining of a Helmholtz condition characterizing the equations deriving from a calculus of variations (only in Part A and only in the purely continuous and purely discrete cases). Some Picard-Lindelöf type theorems necessary for the analysis of optimal control problems are obtained in Appendices.