Formulations of optimization under uncertainty (OUU) commonly used in aerospace design—those based on treating statistical moments of the quantity of interest (QOI) as separate objectives—can result in stochastically dominated designs. A stochastically dominated design is undesirable, because it is less likely than another design to achieve a QOI at least as good as a given value, for any given value. As a remedy to this limitation for the multi-objective formulation of moments, a novel OUU formulation is proposed—dominance optimization. This formulation seeks a set of solutions and makes use of global optimizers, so is useful for early stages of the design process when exploration of design space is important. Similarly, to address this limitation for the single-objective formulation of moments (combining moments via a weighted sum), a second novel formulation is proposed—horsetail matching. This formulation can make use of gradient- based local optimizers, so is useful for later stages of the design process when exploitation of a region of design space is important. Additionally, horsetail matching extends straightforwardly to different representations of uncertainty, and is flexible enough to emulate several existing OUU formulations. Existing multi-fidelity methods for OUU are not compatible with these novel formulations, so one such method—information reuse—is generalized to be compatible with these and other formulations. The proposed formulations, along with generalized information reuse, are compared to their most comparable equivalent in the current state-of-the-art on practical design problems: transonic aerofoil design, coupled aero-structural wing design, high-fidelity 3D wing design, and acoustic horn shape design. Finally, the two novel formulations are combined in a two-step design process, which is used to obtain a robust design in a challenging version of the acoustic horn design problem. Dominance optimization is given half the computational budget for exploration; then horsetail matching is given the other half for exploitation. Using exactly the same computational budget as a moment-based approach, the design obtained using the novel formulations is 95% more likely to achieve a better QOI than the best value achievable by the moment-based design.

La modélisation de phénomènes complexes rencontrés dans les problématiques industrielles peut conduire à l'étude de codes de simulation numérique. Ces simulateurs peuvent être très coûteux en temps d'exécution (de quelques heures à plusieurs jours), mettre en jeu des paramètres incertains et même être intrinsèquement stochastiques. Fait d'importance en optimisation basée sur de tels simulateurs, les dérivées des sorties en fonction des entrées peuvent être inexistantes, inaccessibles ou trop coûteuses à approximer correctement. Ce mémoire est organisé en quatre chapitres. Le premier chapitre traite de l'état de l'art en optimisation sans dérivées et en modélisation d'incertitudes. Les trois chapitres suivants présentent trois contributions indépendantes --- bien que liées --- au champ de l'optimisation sans dérivées en présence d'incertitudes. Le deuxième chapitre est consacré à l'émulation de codes de simulation stochastiques coûteux --- stochastiques au sens où l'exécution de simulations avec les mêmes paramètres en entrée peut donner lieu à des sorties distinctes. Tel était le sujet du projet CODESTOCH mené au Centre d'été de mathématiques et de recherche avancée en calcul scientifique (CEMRACS) au cours de l'été 2013 avec deux doctorants de Électricité de France (EDF) et du Commissariat à l'énergie atomique et aux énergies alternatives (CEA). Nous avons conçu quatre méthodes de construction d'émulateurs pour des fonctions dont les valeurs sont des densités de probabilité. Ces méthodes ont été testées sur deux exemples-jouets et appliquées à des codes de simulation industriels concernés par trois phénomènes complexes: la distribution spatiale de molécules dans un système d'hydrocarbures (IFPEN), le cycle de vie de grands transformateurs électriques (EDF) et les répercussions d'un hypothétique accident dans une centrale nucléaire (CEA). Dans les deux premiers cas l'émulation est une étape préalable à la résolution d'un problème d'optimisation. Le troisième chapitre traite de l'influence de l'inexactitude des évaluations de la fonction objectif sur la recherche directe directionnelle --- un algorithme classique d'optimisation sans dérivées. Dans les problèmes réels, l'imprécision est sans doute toujours présente. Pourtant les utilisateurs appliquent généralement les algorithmes de recherche directe sans prendre cette imprécision en compte. Nous posons trois questions. Quelle précision peut-on espérer obtenir, étant donnée l'inexactitude ? À quel prix cette précision peut-elle être atteinte ? Quels critères d'arrêt permettent de garantir cette précision ? Nous répondons à ces trois questions pour l'algorithme de recherche directe directionnelle appliqué à des fonctions dont l'imprécision sur les valeurs --- stochastique ou non --- est uniformément bornée. Nous déduisons de nos résultats un algorithme adaptatif pour utiliser efficacement des oracles de niveaux de précision distincts. Les résultats théoriques et l'algorithme sont validés avec des tests numériques et deux applications réelles: la minimisation de surface en conception mécanique et le placement de puits pétroliers en ingénierie de réservoir. Le quatrième chapitre est dédié aux problèmes d'optimisation affectés par des paramètres imprécis, dont l'imprécision est modélisée grâce à la théorie des ensembles flous. Plusieurs méthodes ont déjà été publiées pour résoudre les programmes linéaires où apparaissent des coefficients flous, mais très peu pour traiter les problèmes non linéaires. Nous proposons un algorithme pour répondre à une large classe de problèmes par tri non-dominé itératif. / The modeling of complex phenomena encountered in industrial issues can lead to the study of numerical simulation codes. These simulators may require extensive execution time (from hours to days), involve uncertain parameters and even be intrinsically stochastic. Importantly within the context of simulation-based optimization, the derivatives of the outputs with respect to the inputs may be inexistent, inaccessible or too costly to approximate reasonably. This thesis is organized in four chapters. The first chapter discusses the state of the art in derivative-free optimization and uncertainty modeling. The next three chapters introduce three independent---although connected---contributions to the field of derivative-free optimization in the presence of uncertainty. The second chapter addresses the emulation of costly stochastic simulation codes---stochastic in the sense simulations run with the same input parameters may lead to distinct outputs. Such was the matter of the CODESTOCH project carried out at the Summer mathematical research center on scientific computing and its applications (CEMRACS) during the summer of 2013, together with two Ph.D. students from Electricity of France (EDF) and the Atomic Energy and Alternative Energies Commission (CEA). We designed four methods to build emulators for functions whose values are probability density functions. These methods were tested on two toy functions and applied to industrial simulation codes concerned with three complex phenomena: the spatial distribution of molecules in a hydrocarbon system (IFPEN), the life cycle of large electric transformers (EDF) and the repercussions of a hypothetical accidental in a nuclear plant (CEA). Emulation was a preliminary process towards optimization in the first two cases. In the third chapter we consider the influence of inaccurate objective function evaluations on direct search---a classical derivative-free optimization method. In real settings inaccuracy may never vanish, however users usually apply direct search algorithms disregarding inaccuracy. We raise three questions. What precision can we hope to achieve, given the inaccuracy? How fast can this precision be attained? What stopping criteria can guarantee this precision? We answer these three questions for directional direct search applied to objective functions whose evaluation inaccuracy stochastic or not is uniformly bounded. We also derive from our results an adaptive algorithm for dealing efficiently with several oracles having different levels of accuracy. The theory and algorithm are validated with numerical tests and two industrial applications: surface minimization in mechanical design and oil well placement in reservoir engineering. The fourth chapter considers optimization problems with imprecise parameters, whose imprecision is modeled with fuzzy sets theory. A number of methods have been published to solve linear programs involving fuzzy parameters, but only a few as for nonlinear programs. We propose an algorithm to address a large class of fuzzy optimization problems by iterative non-dominated sorting. The distributions of the fuzzy parameters are assumed only partially known. We also provide a criterion to assess the precision of the solutions and make comparisons with other methods found in the literature. We show that our algorithm guarantees solutions whose level of precision at least equals the precision on the available data.

This thesis aims at Multi-Objective Optimization under Uncertainty in structural design. We investigate Polynomial Chaos Expansion (PCE) surrogates which require extensive training sets. We then face two issues: high computational costs of an individual Finite Element simulation and its limited precision. From numerical point of view and in order to limit the computational expense of the PCE construction we particularly focus on sparse PCE schemes. We also develop a custom Latin Hypercube Sampling scheme taking into account the finite precision of the simulation. From the modeling point of view, we propose a multifidelity approach involving a hierarchy of models ranging from full scale simulations through reduced order physics up to response surfaces. Finally, we investigate multiobjective optimization of structures under uncertainty. We extend the PCE model of design objectives by taking into account the design variables. We illustrate our work with examples in sheet metal forming and optimal design of truss structures. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

[pt] No Brasil, as distribuidoras (DisCos) devem suprir seu crescimento de carga por meio de contratos comercializados em leilões centralizados de Energia Nova, nos quais são leiloados contratos com entrega 4 anos a frente. No entanto, projetar a demanda de energia para vários anos à frente é muito desafiador, pois o consumo de energia é muito dependente da taxa de crescimento da economia, da possibilidade de surgimento de uma nova solução/tecnologia (geração solar distribuída) e da migração de consumidores cativos para o mercado livre. Embora as distribuidoras possam repassar os custos do excedente contratual de até 5 por cento nas tarifas de energia, esse limite tem se mostrado insuficiente desde que a última crise econômica no Brasil (2015) derrubou as expectativas de crescimento do consumo, deixando as distribuidoras com um superavit de contrato enorme. Essa situação tornou-se um problema para as distribuidoras, uma vez que esses contratos são liquidados no mercado spot, expondo-as ao preço spot, variável demasiadamente volátil no Brasil, e comprometendo assim a os seus fluxos de caixa. Neste contexto, criou-se o Mecanismo de Venda de Excedentes - MVE, um importante instrumento regulatório para gerenciamento do portfólio das distribuidoras. Por meio deste mecanismo as distribuidoras são capazes de vender, em um leilão centralizado, seus excedentes contratuais, reduzindo assim sua exposição ao mercado spot. Assim, este trabalho tem como objetivo propor uma metodologia para otimizar a estratégia das distribuidoras nos processamentos de MVE utilizando o conceito de Decisão sob Incerteza. Em outras palavras, o modelo indicará uma estratégia de venda de contratos no MVE, considerando o perfil de aversão ao risco do agente, avaliando os diferentes custos de oportunidade existentes neste processo de tomada de decisão. / [en] In Brazil, distribution companies (DisCos) must supply their expected load growth with contract purchases in centralized New Energy Auctions, in which commercial operation date – COD of generation projects being sold is (at least) 4 years ahead. Projecting energy demand for several years ahead is very challenging as energy consumption is very dependent on economy growth rate, the possibility of a surge of a new solution/technology (solar distributed generation) and the migration of captive consumers to the free market, to name a few. Even though distribution companies are allowed to pass through the costs of contract surplus of up to 5 percent in energy tariffs, this threshold was shown insufficient when the latest economic crisis in Brazil (2015) has knocked over consumption growth expectations, leaving distribution companies with huge contract surplus. This situation became a problem for the distribution companies since these contracts must be settled in the spot market, exposing them to the spot price, which is very volatile, and compromising their cash flow. In this context, the Mecanismo de Venda de Excedentes - MVE was created, an essential regulatory instrument to help distribution companies manage their energy portfolio. Through this mechanism, DisCos can sell in a centralized auction their contracts surplus, reducing their position in the spot market. This work aims to propose a methodology to optimize the distribution companies strategy in the MVE auctions using the theory of the Decision under Uncertainty. In other words, the model will indicate a strategy to sell contracts in the MVE, considering the agent s risk aversion profile, evaluating all the opportunity costs involving in this decision-making.

[pt] Os combustíveis de baixo impacto ambiental estão em destaque na mídia e na sociedade, atualmente. Neste contexto, o hidrogênio, fonte de energia limpa, tem um grande potencial. Entretanto, ainda não existe uma infraestrutura adequada para sua comercialização. O crescimento da demanda por hidrogênio é de difícil previsão, gerando um alto grau de incerteza na definição das necessidades de capacidades futuras de sua rede logística. Esta dissertação propõe uma metodologia para o planejamento do projeto da cadeia de suprimentos de hidrogênio para uso em transporte. Para representar o problema e avaliar diferentes alternativas de investimentos em infraestrutura logística foi desenvolvido um modelo matemático estocástico de dois estágios utilizando programação linear inteira mista (PLIM). O elevado nível de incerteza desta cadeia aumenta a complexidade do modelo, requerendo uma grande quantidade de cenários, inviabilizando sua otimização. Para contornar esta dificuldade, foi utilizada a técnica de aproximação por média amostral (SAA). Esta abordagem gera soluções, cuja qualidade pode ser estatisticamente avaliada utilizando-se um número reduzido de cenários. A metodologia proposta foi aplicada em um estudo de caso com dados reais da cadeia de suprimentos de hidrogênio líquido da Grã-Bretanha. Os gaps de otimalidade gerados nestes testes foram inferiores a 1 por cento, demonstrando a adequação do método desenvolvido. Mesmo com o alto nível de incerteza do problema, o SAA possibilitou definir como, quando, e onde investir. Os resultados obtidos devem contribuir para proporcionar avanços na criação de uma infraestrutura apropriada para a comercialização do hidrogênio. / [en] Nowadays, fuels with low environmental impact are highlighted in media and society. In this context, hydrogen, as a clean energy source, has a great potential. However, there is still no appropriate infrastructure for its commercialization. The prediction of demand for hydrogen is difficult, generating a high degree of uncertainty in the definition of capacity needs in the future for its logistics network. This work proposes a methodology for the design of the hydrogen supply chain for use in transportation. To represent the problem and evaluate alternatives to invest in logistics infrastructure, a two-stage stochastic mixed-integer programming was developed. The high degree of uncertainty in this chain increases the complexity of the mathematical model, requiring a huge number of scenarios which makes its optimization impossible. To overcome this difficulty, the technique of sample average approximation (SAA) is used. This approach generates solutions, whose quality can be statistically evaluated using a reduced number of scenarios. The proposed methodology was tested in a study case with real data from Great Britain s liquid hydrogen supply chain. The optimal gaps generated in these tests were below 1 percent, demonstrating the adequacy of the developed methodology. Even with the high level of uncertainty of the problem, the propose methodology using SAA technique can define how, when, and where to invest. The results should be helpful in advancing the creation of an appropriate infrastructure for hydrogen commercialization.

Cette thèse développe des algorithmes pour les problèmes de plus court chemin sous cont-rain-tes de ressources, et les applique à l'optimisation des rotations des avions et des équipages d'une compagnie aérienne dans le cadre d'approches par génération de colonnes.Les problèmes de plus court chemin sous contraintes de ressources sont généralement résolus grâce à une énumération intelligente de tous les chemins non dominés. Les approches récentes utilisent des bornes sur les ressources des chemins pour éliminer des solutions partielles. L'efficacité de la méthode est conditionnée par la qualité des bornes utilisées. Notre principale contribution au domaine est l'introduction d'une procédure générique pour calculer des bornes qui s'applique à la plupart des problèmes de chemins sous contraintes, et en particulier les problèmes stochastiques. A cette fin, nous introduisons une généralisation du problème de plus court chemin sous contraintes dans laquelle les ressources des chemins appartiennent à un monoïde ordonné comme un treillis. La ressource d'un chemin est la somme des ressources de ses arcs, le terme somme désignant l'opérateur du monoïde. Le problème consiste à trouver parmi les chemins qui satisfont une contrainte donnée celui dont la ressource minimise une fonction de coût croissante de la ressource des chemins. Nous généralisons les algorithmes d'énumération à ce nouveau problème. La théorie des treillis nous permet de construire une procédure polynomiale pour trouver des bornes de qualité. L'efficacité pratique de la méthode est évaluée au travers d'une étude numérique détaillée sur des problèmes de chemins déterministes et stochastiques. Les procédures de calcul des bornes peuvent être interprétées comme des généralisations aux monoïdes ordonnés comme des treillis d'algorithmes de la littérature définis pour résoudre un problème de chemin pour lequel les ressources des chemins prennent leur valeur dans un semi-anneau.Nos algorithmes de chemins ont été appliqués avec succès au problème de crew pairing. Étant donné un ensemble de vols opérés par une compagnie aérienne, les problèmes d'aircraft routing et de crew pairing construisent respectivement les séquences de vols opérées par les avions et par les équipages de manière à couvrir tous les vols à moindre coût. Comme certaines séquences de vols ne peuvent être réalisées par un équipage que s'il reste dans le même avion, les deux problèmes sont liés. La pratique actuelle dans l'industrie aéronautique est de résoudre tout d'abord le problème d'aircraft routing, puis le problème de crew pairing, ce qui aboutit à une solution non-optimale. Des méthodes de résolution pour le problème intégré ont été développées ces dix dernières années. Nous proposons une méthode de résolution pour le problème intégré reposant sur deux nouveaux ingrédients : un programme linéaire en nombre entier compact pour le problème d'aircraft routing, ainsi que de nouveaux pour le problème esclave de l'approche usuelle par génération de colonnes du problème de crew pairing. Ces algorithmes pour le problème esclave sont une application de nos algorithmes pour le problème de plus court chemin sous contraintes. Nous généralisons ensuite cette approche de manière à prendre en compte des contraintes de probabilités sur la propagation du retard. Ces algorithmes permettent de résoudre quasiment à l'optimum les instances industrielles d'Air France / This thesis develops algorithms for resource constrained shortest path problems, and uses them to solve the pricing subproblems of column generation approaches to some airline operations problems.Resource constrained shortest path problems are usually solved using a smart enumeration of the non-dominated paths. Recent improvements of these enumeration algorithms rely on the use of bounds on path resources to discard partial solutions. The quality of the bounds determines the performance of the algorithm. Our main contribution to the topic is to introduce a standard procedure to generate bounds on paths resources in a general setting which covers most resource constrained shortest path problems, among which stochastic versions. In that purpose, we introduce a generalization of the resource constrained shortest path problem where the resources are taken in a lattice ordered monoid. The resource of a path is the monoid sum of the resources of its arcs. The problem consists in finding a path whose resource minimizes a non-decreasing cost function of the path resource among the paths that satisfy a given constraint. Enumeration algorithms are generalized to this framework. We use lattice theory to provide polynomial procedures to find good quality bounds. The efficiency of the approach is proved through an extensive numerical study on deterministic and stochastic path problems. Interestingly, the bounding procedures can be seen as generalizations to lattice ordered monoids of some algebraic path problem algorithms which initially work with resources in a semiring.Given a set of flight legs operated by an airline, the aircraft routing and the crew pairing problem build respectively the sequences of flight legs operated by airplanes and crews at minimum cost. As some sequences of flight legs can be operated by crews only if they stay in the same aircraft, the two problems are linked. The current practice in the industry is to solve first the aircraft routing, and then the crew pairing problem, leading to a non-optimal solution. During the last decade, solution schemes for the integrated problem have been developed. We propose a solution scheme for the integrated problem based on two new ingredients: a compact integer program approach to the aircraft routing problem, and a new algorithm for the pricing subproblem of the usual column generation approach to the crew pairing problem, which is based on our resource constrained shortest path framework. We then generalize the algorithm to take into account delay propagation through probabilistic constraints. The algorithms enable to solve to near optimality Air France industrial instances

Au stade de projet amont, les ingénieurs utilisent souvent des modèles de basse fidélité possédant de larges erreurs. Les approches déterministes prennent implicitement en compte les erreurs par un choix conservatif des paramètres aléatoires et par l'ajout de facteurs de sécurité dans les contraintes de conception. Une fois qu'une solution est proposée, elle est analysée par un modèle haute fidélité (test futur): une re-conception peut s'avérer nécessaire pour restaurer la fiabilité ou améliorer la performance, et le modèle basse fidélité est calibré pour prendre en compte les résultats de l'analyse haute-fidélité. Mais une re-conception possède un coût financier et temporel. Dans ce travail, les effets possibles des tests futurs et des re-conceptions sont intégrés à une procédure de conception avec un modèle basse fidélité. Après les Chapitres 1 et 2 qui donnent le contexte de ce travail et l'état de l'art, le Chapitre 3 analyse le dilemme d'une conception initiale conservatrice en terme de fiabilité ou ambitieuse en termes de performances (avec les re-conceptions associées pour améliorer la performance ou la fiabilité). Le Chapitre 4 propose une méthode de simulation des tests futurs et de re-conception avec des erreurs épistémiques corrélées spatialement. Le Chapitre 5 décrit une application à une fusée sonde avec des erreurs à la fois aléatoires et de modèles. Le Chapitre 6 conclut le travail. / At the initial design stage, engineers often rely on low-fidelity models that have high uncertainty. In a deterministic safety-margin-based design approach, uncertainty is implicitly compensated for by using fixed conservative values in place of aleatory variables and ensuring the design satisfies a safety-margin with respect to design constraints. After an initial design is selected, high-fidelity modeling is performed to reduce epistemic uncertainty and ensure the design achieves the targeted levels of safety. High-fidelity modeling is used to calibrate low-fidelity models and prescribe redesign when tests are not passed. After calibration, reduced epistemic model uncertainty can be leveraged through redesign to restore safety or improve design performance; however, redesign may be associated with substantial costs or delays. In this work, the possible effects of a future test and redesign are considered while the initial design is optimized using only a low-fidelity model. The context of the work and a literature review make Chapters 1 and 2 of this manuscript. Chapter 3 analyzes the dilemma of whether to start with a more conservative initial design and possibly redesign for performance or to start with a less conservative initial design and risk redesigning to restore safety. Chapter 4 develops a generalized method for simulating a future test and possible redesign that accounts for spatial correlations in the epistemic model error. Chapter 5 discusses the application of the method to the design of a sounding rocket under mixed epistemic model uncertainty and aleatory parameter uncertainty. Chapter 6 concludes the work.

[pt] Nesta tese é abordado o problema de planejamento de investimentos para a cadeia de fornecimento de petróleo sob incerteza. Neste contexto, um modelo de programação estocástica de dois estágios é formulado e resolvido. Tal modelo busca representar com precisão as características particulares que são inerentes ao planejamento de investimentos para a infra-estrutura logística de petróleo. A incorporação da incerteza neste contexto inevitavelmente aumenta a complexidade do problema, o qual se torna rapidamente intratável conforme cresce o número de cenários. Tal dificuldade é contornada baseando-se na aproximação por média amostral (AMA) para controlar o número de cenários necessários para atingir um nível pré-especificado de tolerância em relação à qualidade da solução. Além disso, é considerado o desenvolvimento de técnicas que resolvam de maneira eficiente o problema, explorando sua estrutura especial, através de decomposiçãoo por cenários. Seguindo esta ideia, propõe-se duas novas abordagens para decompor o problema de forma que o mesmo possa ser eficientemente resolvido. O primeiro algoritmo é baseado na decomposição estocástica de Benders, a qual é aprimorada usando-se novas técnicas de aceleração propostas. O segundo consiste de um novo algoritmo baseado em decomposição Lagrangeana que foi projetado para lidar com o caso onde temos variáveis inteiras no problema de segundo estágio. A característica inovadora desse algoritmo está relacionada com a estratégia híbrida utilizada para atualizar os multiplicadores de Lagrange, combinando subgradientes, planos de cortes e regiões de confiança. Em ambos os casos as abordagens propostas foram avaliadas considerando um exemplo de grande escala do mundo real e os resultados sugerem que os mesmos apresentam desempenho superior quando comparados com outras técnicas disponíveis na literatura. / [en] In this thesis we investigate the investment planning problem for the petroleum supply chain under demand uncertainty. We formulate and solve a two-stage stochastic programming model that seeks to accurately represent the particular features that are inherent to the investment planning for the petroleum logistics infrastructure. The incorporation of uncertainty in this case inevitably increases the complexity of the problem, which becomes quickly intractable as the number of scenarios grows. We circumvent this drawback by relying on Sample Average Approximation (SAA) to control the number of scenarios required to reach a prespecified level of tolerance regarding solution quality. We also focus on efficiently solving the stochastic programming problem, exploiting its particular structure by means of a scenario-wise decomposition. Following this idea, we propose two novel approaches that focus on decomposing the problem in a way that it could be efficiently solved. The first algorithm is based on stochastic Benders decomposition, which we further improve by using new acceleration techniques proposed in this study. The second is a novel algorithm based on Lagrangean decomposition that was designed to deal with the case where we have integer variables in the second-stage problem. The novel feature in this algorithm is related with the hybrid strategy for updating the Lagrange multipliers, which combines subgradient, cutting-planes and trust region ideas. In both cases, we have assessed the proposed approaches considering a large-scale realworld instances of the problem. Results suggests that they attain superior performance.

[pt] Os novos elementos conectados nos sistemas de distribuição de energia elétrica aumentam a complexidade do planejamento e operação destas redes. Os benefícios da implementação de técnicas clássicas, como Conservation Voltage Reduction (CVR), combinadas com uma operação coordenada dos recursos energéticos distribuídos, podem contribuir para o aumento de eficiência nos sistemas de distribuição de energia elétrica e reduzir o consumo de energia. Na técnica CVR, as tensões são reduzidas objetivando redução de picos de demanda e consumo de energia. Este trabalho propõe um modelo de otimização para o planejamento da operação do dia seguinte nos sistemas de distribuição de energia elétrica, considerando sistemas desequilibrados e com penetração de geração distribuída (GD) fotovoltaica. A técnica CVR será aplicada em uma abordagem determinística, estocástica e robusta, considerando a incerteza nos seus parâmetros e, consequente, na modelagem de carga. O modelo de otimização proposto considera a atuação de elementos de controle tradicionais, como transformador On Load Tap Changers (OLTC) na subestação e bancos de capacitores (BC), além de elementos modernos, como inversores fotovoltaicos inteligentes, para minimização do consumo de energia observado na subestação. O problema, fundamentalmente de programação não-linear inteira mista, é transformado em um problema de programação linear de natureza contínua. Os resultados são avaliados no sistema teste IEEE 123-barras para as diferentes estratégias modeladas. A economia de energia obtida foi significativa nas abordagens propostas, mas o modelo de otimização robusta se mostrou mais adequado para reduzir os riscos de violação de tensão. / [en] The new elements connected in electrical distribution systems increase the complexity of grids planning and operating. The benefits of classical techniques, such as Conservation Voltage Reduction (CVR), combined with a coordinated operation of distributed energy resources, can contribute to increasing efficiency and reducing energy consumption of the distribution systems. In the CVR technique, voltages are reduced in order to reduce peak demand and energy consumption. This paper proposes an optimization model for the day-ahead operation planning of unbalanced distribution systems with photovoltaic distributed generation (DG) penetration. The CVR technique will be applied in deterministic, stochastic and robust approach, considering the uncertainty in its parameters and consequently, in the load modeling. The proposed optimization model considers the operation of traditional control elements, such as On Load Tap Changers (OLTC) at substation and capacitor banks (CB), in addition to modern elements, such as intelligent photovoltaic inverters, to minimize the energy consumption at the substation. The problem, originally of mixed-integer nonlinear programming, is transformed into a continuous linear programming problem. The results are evaluated in the IEEE123-bus test system for the different optimization approaches. The energy savings obtained were significant in all the proposed approaches, but the robust optimization model proved to be more adequate since it reduces the risk of voltage violations.

[pt] Os incêndios florestais podem ser uma fonte de vulnerabilidade para sistemas de potência. Esses eventos podem afetar especialmente a operação de sistemas de distribuição, interrompendo o fornecimento de energia, aumentando os custos, e diminuindo a confiabilidade. Nesta dissertação, é considerada a relação entre as decisões operativas e a probabilidade de falha nas linhas sob o contexto de queimadas. Este tipo de estudo ainda não foi devidamente avaliado pelo meio acadêmico. Ao não reconhecer este aspecto, o funcionamento dos sistemas de potência pode estar sendo prejudicado. A modelagem adequada dessa dependência poderia reduzir a incidência de queimadas e perda de carga. Considerando este aspecto, um problema de otimização distributivamente robusto de dois estágios com incerteza endógena foi desenvolvido para considerar a operação multiperíodo de sistemas de distribuição. O primeiro estágio determina a topologia da rede e os investimentos nas linhas, e o segundo estágio avalia o custo operacional esperado no pior caso. Nessa estrutura, a incerteza é modelada de forma dependente das decisões do modelo, onde as probabilidades de falha da linha são em função do fluxo de potência das próprias linhas. Um método iterativo é proposto para resolver este modelo e uma análise fora da amostra é desenvolvida para validação através de diferentes estudos. Os resultados mostraram que, ao negligenciar a dependência da incerteza, uma maior perda de carga e um maior custo operacional são esperados. Ao considerar esta nova abordagem, a confiabilidade da rede pode ser melhorada e as consequências dos incêndios podem ser mitigadas com ações mais econômicas. / [en] Wildfires can be a source of vulnerability for power systems operations. These events can especially affect the operation of distribution systems. They can interrupt energy supply, increase costs, and decrease grid resilience. Numerous approaches can be executed to prevent them. In this dissertation, it is considered the relationship between operative actions and the probability of wildfire disruption. This type of study has not been properly evaluated in technical and scientific literature. By not recognizing this aspect, the operation of power systems may be impaired. Properly modeling this dependency could lower wildfire disruption and loss of load. Considering this, a two-stage distributionally robust optimization problem with decision-dependent uncertainty is developed to consider distribution system multiperiod operation. The first stage determines the optimal switching actions and line investments, and the second stage evaluates the worst-case expected operation cost. It is designed a decision-dependent uncertainty framework where the line failure probabilities are a function (dependent) of its power flow levels. An iterative method is proposed to solve this model and an out-of-sample analysis is developed to validate it through different case studies. Results showed that, by neglecting the uncertainty dependency on operative decisions, there could be a higher expected loss of load and a higher operational cost. By considering this new approach when operating power lines, the grid s resilience could be improved and wildfire consequences can be mitigated with less costly actions.