This thesis deals with theoretical basics of risk modelling in transportation and optimization using aggregated traffic data. In this thesis is suggested the procedure and implemented the application solving network problem of shortest path between geographical points. The thesis includes method for special paths evaluation depending on the frequency of traffic incidents based on real historical data. The thesis also includes a~graphical interface for presentation of the achieved results.

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L'hydraulique est la principale énergie renouvelable produite en France. Elle apporte une réserve d'énergie et une flexibilité intéressantes dans un contexte d'augmentation de la part des énergies intermittentes dans la production. Sa gestion soulève des problèmes difficiles dus au nombre des barrages, aux incertitudes sur les apports d'eau et sur les prix, ainsi qu'aux usages multiples de l'eau. Cette thèse CIFRE, effectuée en partenariat avec Electricité de France, aborde deux questions de gestion hydraulique formulées comme des problèmes d'optimisation dynamique stochastique. Elles sont traitées dans deux grandes parties.Dans la première partie, nous considérons la gestion de la production hydroélectrique d'un barrage soumise à une contrainte dite de cote touristique. Cette contrainte vise à assurer une hauteur de remplissage du réservoir suffisamment élevée durant l'été avec un niveau de probabilité donné. Nous proposons différentes modélisations originales de ce problème et nous développons les algorithmes de résolution correspondants. Nous présentons des résultats numériques qui éclairent différentes facettes du problème utiles pour les gestionnaires du barrage.Dans la seconde partie, nous nous penchons sur la gestion d'une cascade de barrages. Nous présentons une méthode de résolution approchée par décomposition-coordination, l'algorithme Dual Approximate Dynamic Programming (DADP). Nousmontrons comment décomposer, barrage par barrage, le problème de la cascade en sous-problèmes obtenus en dualisant la contrainte de couplage spatial ``déversé supérieur = apport inférieur''. Sur un cas à trois barrages, nous sommes en mesure de comparer les résultats de DADP à la solution exacte (obtenue par programmation dynamique), obtenant desgains à quelques pourcents de l'optimum avec des temps de calcul intéressants. Les conclusions auxquelles nous sommes parvenu offrent des perspectives encourageantes pour l'optimisation stochastique de systèmes de grande taille / Hydropower is the main renewable energy produced in France. It brings both an energy reserve and a flexibility, of great interest in a contextof penetration of intermittent sources in the production of electricity. Its management raises difficulties stemming from the number of dams, from uncertainties in water inflows and prices and from multiple uses of water. This Phd thesis has been realized in partnership with Electricité de France and addresses two hydropower management issues, modeled as stochastic dynamic optimization problems. The manuscript is divided in two parts. In the first part, we consider the management of a hydroelectric dam subject to a so-called tourist constraint. This constraint assures the respect of a given minimum dam stock level in Summer months with a prescribed probability level. We propose different original modelings and we provide corresponding numerical algorithms. We present numerical results that highlight the problem under various angles useful for dam managers. In the second part, we focus on the management of a cascade of dams. We present the approximate decomposition-coordination algorithm called Dual Approximate Dynamic Programming (DADP). We show how to decompose an original (large scale) problem into smaller subproblems by dualizing the spatial coupling constraints. On a three dams instance, we are able to compare the results of DADP with the exact solution (obtained by dynamic programming); we obtain approximate gains that are only at a few percents of the optimum, with interesting running times. The conclusions we arrived at offer encouraging perspectives for the stochastic optimization of large scale problems

Cette thèse est dediée à l'alanyse numérique de méthodes numériques dans le domaine du contrôle optimal, et est composée de deux parties. La première partie est consacrée à des nouveaux résultats concernant des méthodes numériques pour le contrôle optimal de systèmes hybrides, qui peuvent être contrôlés simultanément par des fonctions mesurables et des sauts discontinus dans la variable d'état. La deuxième partie est dédiée è l'étude d'une application spécifique surl'optimisation de trajectoires pour des lanceurs spatiaux avec contraintes en probabilité. Ici, on utilise des méthodes d'optimisation nonlineaires couplées avec des techniques de statistique non parametrique. Le problème traité dans cette partie appartient à la famille des problèmes d'optimisation stochastique et il comporte la minimisation d'une fonction de coût en présence d'une contrainte qui doit être satisfaite dans les limites d'un seuil de probabilité souhaité. / This thesis is devoted to the analysis of numerical methods in the field of optimal control, and it is composed of two parts. The first part is dedicated to new results on the subject of numerical methods for the optimal control of hybrid systems, controlled by measurable functions and discontinuous jumps in the state variable simultaneously. The second part focuses on a particular application of trajectory optimization problems for space launchers. Here we use some nonlinear optimization methods combined with non-parametric statistics techniques. This kind of problems belongs to the family of stochastic optimization problems and it features the minimization of a cost function in the presence of a constraint which needs to be satisfied within a desired probability threshold.

No description available.

[pt] A contratação de energia elétrica no Brasil por parte de grandes consumidores é feita de acordo com o nível de tensão e considerando dois ambientes: o Ambiente Regulado e o Ambiente Livre. Os grandes consumidores são aqueles que possuem carga igual ou superior a 3 MW, atendidos em qualquer nível de tensão e a energia pode ser contratada em quaisquer desses ambientes. Um grande desafio para esses consumidores é determinar a melhor alternativa de contratação. Para tratar este problema, é preciso ter em conta que o consumo de energia e a demanda de potência requerida são variáveis desconhecidas no momento da contratação do consumidor, sendo necessário estimá-las. Esta dissertação propõe atacar este problema por uma metodologia que envolve simulação de cenários futuros de demanda máxima de potência e energia total consumida e otimização estocástica dos cenários simulados para definir o melhor contrato. Dada a natureza estocástica do problema, empregou-se o CVaR (Conditional Value at Risk) como medida de risco para o problema de otimização. Para ilustrar, os resultados da contratação foram obtidos para um grande consumidor real considerando a modalidade Verde A4 no Ambiente Regulado e um contrato de quantidade no Ambiente Livre. / [en] The energy contracting in Brazil for large consumers is done according to the voltage level and considering two environments: the Regulated Environment and the Free Environment. Large consumers are those characterized by installed load equal to or greater than 3 MW, supplied at any voltage level and its energy contract can be chosen between any of these two environments. A major challenge for these consumers is to determine the best alternative of contracting. To address this problem, it must be taken into account that the energy consumption and the required power demand are unknown variables by the time of consumer contracting, being necessary to estimate them. This dissertation proposes to tackle this problem by a methodology based on the simulation of future scenarios of maximum power demand and total consumed energy and on stochastic optimization of these simulated scenarios in order to define the best contract. Given the stochastic nature of the problem, it was used the CVaR (Conditional Value at Risk) as a measure of risk for the optimization problem. To illustrate, the contracting results were obtained for a large real consumer considering the Green Tariff group A4 in the Regulated Environment and a quantity contract in the Free Environment.

[pt] Com o advento do novo modelo do setor elétrico a partir de 2004, foi permitida aos agentes de mercado a comercialização de energia no ambiente de contratação livre. Considerando a natureza destas operações e a influência de variáveis meteorológicas na formação e volatilidade dos preços, as decisões no âmbito da comercialização de energia são tomadas sob condições de incerteza, levando os agentes a buscarem estratégias de contratação para maximização do retorno dos ativos e/ou mitigação dos riscos envolvidos. No setor elétrico brasileiro, a gestão do risco de mercado é realizada principalmente por contratos a termo, de forma a reduzir os impactos adversos da flutuação do PLD. Neste contexto, os objetivos deste estudo são avaliar a aplicabilidade de dois modelos de otimização sob incerteza, estágio único e estocástico de dois estágios, na tomada de decisão de uma comercializadora e comparar as decisões recomendadas pelos modelos. Estes modelos utilizaram uma função de preferência que permite representar a variação do nível de aversão ao risco considerando diferentes bandas de preferência, tendo os seus parâmetros determinados pelo método Analytic Hierarchical Process. Para a construção das curvas forward do modelo estocástico de dois estágios, foi ponderado o preço de mercado observado e as 2.000 séries do PLD da previsão oficial do ONS. Os resultados evidenciaram a efetividade na mitigação do risco para os produtos avaliados. Ademais, devido à redução do custo do arrependimento a partir da modelagem do problema de otimização em dois estágios, este modelo apresentou soluções mais rentáveis quando comparado ao modelo de único estágio. / [en] With the advent of the new model for the electricity sector in 2004, market agents were allowed to sell energy in the free market. Considering the nature of these operations and the influence of meteorological variables on the formation and volatility of prices, energy trading decisions are taken under conditions of uncertainty, leading agents to seek contracting strategies to maximize the return on assets or mitigation of the risks involved. In the Brazilian electricity sector, market risk management is mainly accomplished through forward contracts, in order to reduce the adverse impacts of PLD fluctuation. In this context, the objectives of this study are to evaluate the applicability of two optimization models under uncertainty, single-stage and two-stage stochastic, in the decision making of a trading company and to compare the decisions recommended by the models. These models used a preference function that allows representing the variation of the risk aversion level considering different preference groups, having its parameters determined by the Analytic Hierarchical Process. For the construction of the forward curves of the two-stage stochastic model, the observed market price and the 2,000 PLD series of the ONS official forecast were weighted. The results evidenced the effectiveness in risk mitigation for the evaluated products. Furthermore, due to the reduction in the cost of regret from the two-stage optimization problem modeling, this model presented more cost-effective solutions when compared to the single-stage model.

[pt] O planejamento hidrotérmico estocástico multi-etapa se destaca como um dos problemas mais importantes do setor elétrico, principalmente devido à sua grande relevância na operação do sistema. Este problema refere-se a determinar o despacho ótimo das usinas que minimizam o custo de operação sob as restrições físicas do sistema. Uma das principais dificuldades do problema reside nas representações de incerteza, pois a decisão de despacho deve considerar os diferentes cenários possíveis de afluência de água, geração renovável e demanda. Mais recentemente, o grande aumento de fontes renováveis variáveis trouxe a atenção dos pesquisadores para como melhorar a granularidade do modelo sem aumentar muito o tempo computacional. Neste trabalho é proposto uma nova formulação para um despacho econômico estocástico multi-etapa com unit-commitment. O modelo usa regras de decisão afins para ser computacionalmente tratável. A relação entre regras de decisão e o scenario approach é explorada e, ao construir o conjunto de incertezas, tanto a viabilidade da política da regra de decisão quanto a restrição probabilística do balanço de carga são automaticamente respeitadas. / [en] Multi-stage stochastic hydrothermal planning stands as one of the most critical problems in the power systems industry, mostly due to its vast implication in the system operation. The multi-stage stochastic hydrothermal scheduling refers to determining the economic dispatch of the power plants that minimize the global operation cost under the system s physical constraints. One of the main difficulties of the problem lies in the representations of uncertainty, as the dispatch decision must consider the different possible scenarios of water inflow, renewable generation, and the demand. More recently, we have seen a worldwide speed up in the integration of variable renewable sources. Nonetheless, these sources have a greater uncertainty in the short-term than the world has ever experienced. Therefore, to support the dispatch scheduling, the models must accurately represent the uncertainties without increasing computational time. In this work it is proposed a novel formulation for a multistage stochastic week-ahead economic dispatch with unit-commitment. The model uses affine decision rules to be computationally tractable. The relationship between the decision rules and the scenario approach is explored, and by building the uncertainty set with the scenario approach, both the feasibility of the decision rule policy and the chance-constraint on the load balance are respected.

[pt] Mudanças recentes em mercados de energia com alta penetração de fontes renováveis destacaram a necessidade de estratégias complexas que, além de maximizar o lucro, proporcionam proteção contra a volatilidade de preços e incerteza na geração. Neste contexto, este trabalho propõe um modelo dinâmico para representar a tomada de decisão sequencial no cenário atual. Ao contrário de trabalhos relatados anteriormente, este método fornece uma estrutura para considerar as incertezas nos níveis estratégico (longo prazo) e operacional (curto prazo) simultaneamente. É utilizado um modelo de programação estocástica multiestágio em que as correlações entre previsões de vazão, geração renovável, preços spot e preços contratuais são consideradas por meio de uma árvore de decisão multi-escala. Além disso, a aversão ao risco do agente comercializador é considerada por meio de restrições intuitivas e consistentes no tempo. É apresentado um estudo de caso do setor elétrico brasileiro, no qual dados reais foram utilizados para definir a estratégia ótima de comercialização de um gerador de energia eólica, condicionada à evolução futura dos preços de mercado. O modelo fornece ao comercializador informações úteis, como o montante contratado ideal, além do momento ótimo de negociação e duração dos contratos. Além disso, o valor desta solução é demonstrado quando comparado a abordagens estáticas, através de uma medida de desempenho baseada no equivalente de certo do problema multiestágio. / [en] Recent market changes in power systems with high renewable energy penetration highlighted the need for complex profit maximization and protection against price volatility and generation uncertainty. This work proposes a dynamic model to represent sequential decision making in this current scenario. Unlike previously reported works, we contemplate uncertainties in both strategic (long-term) and operational (short-term) levels, all considered as pathdependent stochastic processes. The problem is represented as a multistage stochastic programming model in which the correlations between inflow forecasts, renewable generation, spot and contract prices are accounted for by means of interconnected long- and short-term decision trees. Additionally, risk aversion is considered through intuitive time-consistent constraints. A case study of the Brazilian power sector is presented, in which real data was used to define the optimal trading strategy of a wind power generator, conditioned to the future evolution of market prices. The model provides the trader with useful information such as the optimal contractual amount, settlement timing, and term. Furthermore, the value of this solution is demonstrated when compared to state-of-the-art static approaches using a multistage-based certainty equivalent performance measure.