A comercialização de energia elétrica de fontes renováveis, ordinariamente, constitui-se uma atividade em que as operações são estruturadas sob condições de incerteza, por exemplo, em relação ao preço \"spot\" no mercado de curto prazo e a geração de energia dos empreendimentos. Deriva desse fato a busca dos agentes pela formulação de estratégias e utilização de ferramentais para auxiliá-los em suas tomadas de decisão, visando não somente o retorno financeiro, mas também à mitigação dos riscos envolvidos. Análises de investimentos em fontes renováveis compartilham de desafios similares. Na literatura, o estudo da tomada de decisão considerada ótima sob condições de incerteza se dá por meio da aplicação de técnicas de programação estocástica, que viabiliza a modelagem de problemas com variáveis randômicas e a obtenção de soluções racionais, de interesse para o investidor. Esses modelos permitem a incorporação de métricas de risco, como por exemplo, o Conditional Value-at-Risk, a fim de se obter soluções ótimas que ponderem a expectativa de resultado financeiro e o risco associado da operação, onde a aversão ao risco do agente torna-se um condicionante fundamental. O objetivo principal da Tese - sob a ótica dos agentes geradores, consumidores e comercializadores - é: (i) desenvolver e implementar modelos de otimização em programação linear estocástica com métrica CVaR associada, customizados para cada um desses agentes; e (ii) aplicá-los na análise estratégica de operações como forma de apresentar alternativas factíveis à gestão das atividades desses agentes e contribuir com a proposição de um instrumento conceitualmente robusto e amigável ao usuário, para utilização por parte das empresas. Nesse contexto, como antes frisado, dá-se ênfase na análise do risco financeiro dessas operações por meio da aplicação do CVaR e com base na aversão ao risco do agente. Considera-se as fontes renováveis hídrica e eólica como opções de ativos de geração, de forma a estudar o efeito de complementaridade entre fontes distintas e entre sites distintos da mesma fonte, avaliando-se os rebatimentos nas operações. / The renewable energy trading, ordinarily, is an activity in which mostly operations are structured under uncertainty conditions, for instance, in relation to the energy spot price and assets generation. Derives from this fact the search of the agents for strategies formulation based on computational tools to assist their decision-making process, not only seeking financial returns, but also to mitigate the risks involved. Investments analysis in renewable sources share the same challenges. In the literature, the study of optimal decision-making under uncertainty conditions is made through the application of stochastic programming techniques, which enable modeling problems with random variables and find rational solutions. These models allow the incorporation of risk metrics, as the \"Conditional Value-at-Risk (CVaR)\", to provide optimal solutions that weigh the expected financial results and the associated risk, in which the agent\'s risk-aversion becomes an essential condition for defining the operation strategy. From the perspective of generators, consumers and traders agents, the main purposes of this thesis are: (i) to develop customized optimization models with CVaR metric associated, optimized in stochastic linear programming; and (ii) to apply the models for strategic analysis of operations under the risk-return binomial, focusing on the management activities of each of these agents, and considering renewable sources as option. In this context, the emphasis is on analysis of the operations financial risks through the application of CVaR and based on the agent\'s risk-aversion level. Furthermore, the hydro and wind renewables sources are options of generation assets in order to study the seasonal generation complementarity effect among them and the consequences on energy trading strategies.

Le Dynamic Line Rating est la modification dynamique des contraintes de courant sur une ligne électrique aérienne, en accord avec la météorologie. De telles modifications permettent alors d’avoir des réductions des phénomènes de congestion près de 99% du temps.De manière similaire aux énergies renouvelables, il est possible de générer des prévisions de ces contraintes modifiées, en accord avec des observations historiques, des prévisions météorologiques et des méthodes d’intelligence artificielle.Dans cette thèse, nous proposons le développement de modèles de prévision probabilistes à court terme du DLR. Nous nous concentrons plus particulièrement sur des méthodes fournissant des prévisions ayant de très faibles probabilités d’être surestimées. Cela passe par le développement et la comparaison de plusieurs méthodes de prévision, ainsi que des améliorations comme des modifications de prévisions à très bas quantile à l’aide de remodélisations des queues de distribution.Par la suite, une réflexion est faite sur l’utilisation en pratique de ces prévisions, d’abord par des cas d’étude simplifié, puis à l’aide de simulations de réseaux électrique. Ces approches nous permettent de développer de nouvelles stratégies d’utilisation des prévisions DLR, optimisant le bien-être social tout en maintenant les risques associés aux erreurs de prévision à un niveau faible.Finalement, nous évaluons les modèles de prévisions développés en fonction de leurs performances économiques à l’aide des modèles de réseaux électriques, et nous démontrons la valeur des améliorations des modèles de prévision que nous proposons. / Dynamic Line Rating is the modification of the maximal current capacity of an overhead electrical line, depending on weather characteristics. Such modifications allow important decreases of congestion phenomena, around 99% of the time.Similarly to renewable generation, it is possible to forecast the modified constraints, accordingly to some historic observations, weather predictions and artificial intelligence methods.In this document, the development of short-term probabilistic DLR forecast models. A focus is especially made on methods providing forecasts having a very low probability of being overestimated. This is made through the development and the comparison of several forecast methods, and some improvements such as the remodelling of very low quantile forecasts with tail density modelling.Following that, a reflection is proposed on the use of such forecasts in practice, first with some simplified test cases, then with electrical grid simulations. These approaches allow us developing new strategies for the use of the DLR forecasts, maximizing the social welfare while keeping risks associated with forecasts errors at low levels.Finally, an evaluation of the forecast models function of their economic value is made with the electrical grids models, and the value of the proposed modifications of the forecast models is then demonstrated.

[pt] Neste trabalho estudamos uma classe de problemas de otimização estocástica com incertezas endógenas que é formulado como um problema de programação não-linear inteira (MINLP). Esta classe de problemas difere dos problemas de otimização estocástica geralmente estudados na literatura pelo fato de que que a distribuição de probabilidade dos parâmetros aleatórios depende das decisões tomadas. Apesar de discutido dentro do contexto do problema de logística humanitária, a metodologia proposta e os resutados obtidos são válidos para uma classe geral de problemas que agrega uma variedade de aplicações. Em particular, propõe-se (i) uma técnica de convexificação de polinômios de variáveis binárias, (ii) um algoritmo de geração de cortes e (iii) a incorporação dos conceitos de importance sampling dentro do contexto de otimização estocástica de modo a permitir a solução de grandes instâncias do problema. Os resultados computacionais apresentados demonstram as vantagens da metodologia proposta ao permitir a solução de instâncias significativamente maiores que aquelas atualmente apresentadas em trabalhos relacionados. / [en] In this work we study a class of stochastic programming problems with endogenous uncertainty – i.e., those in which the probability distribution of the random parameters is decision-dependent – which is formulated as a mixed integer non-linear programming (MINLP) problem. Although discussed in the context of the humanitarian logistics problem, the proposed methodology and obtained results are also valid for a more general class of problems which comprehends a variety of applications. In particular, we propose (i) a convexification technique for polynomials of binary variables, (ii) an efficient cutgeneration algorithm and (iii) the incorporation of importance sampling concepts into the stochastic programming framework so as to allow the solution of large instances of the problem. Computational results demonstrate the effectiveness of the proposed methodology by solving instances significantly larger than those reported in related works.

O planejamento de médio e longo prazo da operação hidrelétrica brasileira consiste em um problema de grande porte e que envolve muitas variáveis, onde, dentre estas, se destacam as vazões afluentes aos reservatórios. Estas vazões devem assim ser estimadas, com o objetivo de caracterizar a oferta futura de eletricidade em um horizonte de planejamento. Dentre as possíveis abordagens existentes para estimar estas vazões, se destaca a abordagem estocástica, que permite considerar variáveis em função de sua distribuição probabilística, e busca considerar o universo mais provável de manifestações. A abordagem estocástica pode se utilizar de modelos estocásticos, que costumam ser caracterizados através de árvores de cenários, que representam o universo de possibilidades de ocorrências. No entanto, devido à elevada dimensionalidade que o processo estocástico pode resultar ao se considerar árvores muito grandes, torna-se necessária a utilização de técnicas complementares, que visem a redução do número de cenários. Com base nesta contextualização, esta dissertação aborda de modo geral o processo de otimização estocástica do planejamento da geração hidrelétrica, considerando árvores de cenários e técnicas de redução de cenários, e utilizando como meio a modelagem de otimização da geração desenvolvida no SSD HIDROTERM, em linguagem GAMS. Como estudo de caso, foram desenvolvidos e adaptados algoritmos de otimização estocástica que consideram árvores com elevado número de cenários, gerados por meio de modelos estocásticos autorregressivos do tipo PAR e, sobre estas árvores, foi ainda aplicada a ferramenta de redução de cenários por agrupamento - SCENRED, desenvolvida em GAMS. As análises de sensibilidade realizadas visaram: validar o processo proposto de otimização estocástica; analisar os efeitos da utilização de diferentes árvores reduzidas de cenários de vazões, o impacto da consideração de diferentes horizontes de planejamento e a influência do regime hidrológico nos principais resultados do processo de otimização; além de estudar as vantagens e desvantagens deste processo para o planejamento da operação hidrelétrica. Os resultados indicam que o processo de otimização estocástica é eficaz ao considerar as aleatoriedades envolvidas na previsão de vazões afluentes. Estes também confirmaram tendências já esperadas no processo de otimização estocástica, como o fato de que quanto maior a árvore de cenários, mais precisos e estáveis tendem os resultados; assim como que quanto mais cenários envolvidos, maior o tempo de processamento requerido. Neste contexto, a utilização da ferramenta de redução SCENRED permitiu reduções significativas no tamanho da árvore de cenários, sem, contudo, ocasionar em perdas na qualidade e estabilidade da solução, além de viabilizar a aplicação do algoritmo de otimização estocástica proposto. / The medium and long-term planning of the Brazilian electric system consists of a complex problem with many uncertainties and variables, where, among these the inflows to the reservoirs highlight. These inflows need to be estimated in order to characterize the future availability of electricity in a planning horizon. Among the existing approaches to estimate these inflows, highlights the stochastic approach, which consider these variables according to their probability distribution, and aims to consider the most likely universe of manifestations. The stochastic approach can be developed through stochastic models, which are often characterized by scenarios trees that represent the possible universe. However, due to the high dimensionality that stochastic analyses can result when considering very large trees, it becomes necessary to use complementary tools, aimed at reducing the number of scenarios. Based on this context, this dissertation discusses in general the process of stochastic optimization of the hydroelectric generation planning, considering scenarios trees and scenario reduction tools, through the optimization modeling developed in the DSS HIDROTERM, developed in GAMS language. As a case study, it was generated and adapted stochastic optimization algorithms that consider trees with large number of scenarios, generated by autoregressive stochastic models PAR. Based on these trees it was applied the scenario reduction tool SCENRED, developed in GAMS language. The sensitivity analyzes developed intended to: validate the stochastic optimization process; analyze the effects of using different reduced scenarios trees of inflows; analyze the impacts of considering different planning horizons, analyze the hydrological influence on the main results of the optimization process, and the benefits and disadvantages of this process in the hydroelectric operation planning. The results indicate that the stochastic optimization process is effective to consider the randomness involved in the prediction of inflow to the reservoirs. These results have also confirmed some well-known trends in the stochastic optimization process, such as the fact that the larger the tree scenarios, more accurate and stable tend the results but also greater the processing time required. In this context, the use of the reduction tool SCENRED allowed significant reductions in the size of scenarios tree, without causing losses in quality and solution stability, enabling the application of the stochastic optimization algorithm proposed.

A comercialização de energia elétrica de fontes renováveis, ordinariamente, constitui-se uma atividade em que as operações são estruturadas sob condições de incerteza, por exemplo, em relação ao preço \"spot\" no mercado de curto prazo e a geração de energia dos empreendimentos. Deriva desse fato a busca dos agentes pela formulação de estratégias e utilização de ferramentais para auxiliá-los em suas tomadas de decisão, visando não somente o retorno financeiro, mas também à mitigação dos riscos envolvidos. Análises de investimentos em fontes renováveis compartilham de desafios similares. Na literatura, o estudo da tomada de decisão considerada ótima sob condições de incerteza se dá por meio da aplicação de técnicas de programação estocástica, que viabiliza a modelagem de problemas com variáveis randômicas e a obtenção de soluções racionais, de interesse para o investidor. Esses modelos permitem a incorporação de métricas de risco, como por exemplo, o Conditional Value-at-Risk, a fim de se obter soluções ótimas que ponderem a expectativa de resultado financeiro e o risco associado da operação, onde a aversão ao risco do agente torna-se um condicionante fundamental. O objetivo principal da Tese - sob a ótica dos agentes geradores, consumidores e comercializadores - é: (i) desenvolver e implementar modelos de otimização em programação linear estocástica com métrica CVaR associada, customizados para cada um desses agentes; e (ii) aplicá-los na análise estratégica de operações como forma de apresentar alternativas factíveis à gestão das atividades desses agentes e contribuir com a proposição de um instrumento conceitualmente robusto e amigável ao usuário, para utilização por parte das empresas. Nesse contexto, como antes frisado, dá-se ênfase na análise do risco financeiro dessas operações por meio da aplicação do CVaR e com base na aversão ao risco do agente. Considera-se as fontes renováveis hídrica e eólica como opções de ativos de geração, de forma a estudar o efeito de complementaridade entre fontes distintas e entre sites distintos da mesma fonte, avaliando-se os rebatimentos nas operações. / The renewable energy trading, ordinarily, is an activity in which mostly operations are structured under uncertainty conditions, for instance, in relation to the energy spot price and assets generation. Derives from this fact the search of the agents for strategies formulation based on computational tools to assist their decision-making process, not only seeking financial returns, but also to mitigate the risks involved. Investments analysis in renewable sources share the same challenges. In the literature, the study of optimal decision-making under uncertainty conditions is made through the application of stochastic programming techniques, which enable modeling problems with random variables and find rational solutions. These models allow the incorporation of risk metrics, as the \"Conditional Value-at-Risk (CVaR)\", to provide optimal solutions that weigh the expected financial results and the associated risk, in which the agent\'s risk-aversion becomes an essential condition for defining the operation strategy. From the perspective of generators, consumers and traders agents, the main purposes of this thesis are: (i) to develop customized optimization models with CVaR metric associated, optimized in stochastic linear programming; and (ii) to apply the models for strategic analysis of operations under the risk-return binomial, focusing on the management activities of each of these agents, and considering renewable sources as option. In this context, the emphasis is on analysis of the operations financial risks through the application of CVaR and based on the agent\'s risk-aversion level. Furthermore, the hydro and wind renewables sources are options of generation assets in order to study the seasonal generation complementarity effect among them and the consequences on energy trading strategies.

The future of the electric grid requires advanced control technologies to reliably integrate high level of renewable generation and residential and small commercial distributed energy resources (DERs). Flexible loads are known as a vital component of future power systems with the potential to boost the overall system efficiency. Recent work has expanded the role of flexible and controllable energy resources, such as energy storage and dispatchable demand, to regulate power imbalances and stabilize grid frequency. This leads to the DER aggregators to develop concepts such as the virtual energy storage system (VESS). VESSs aggregate the flexible loads and energy resources and dispatch them akin to a grid-scale battery to provide flexibility to the system operator. Since the level of flexibility from aggregated DERs is uncertain and time varying, the VESSs’ dispatch can be challenging. To optimally dispatch uncertain, energy-constrained reserves, model predictive control offers a viable tool to develop an appropriate trade-off between closed-loop performance and robustness of the dispatch. To improve the system operation, flexible VESSs can be formulated probabilistically and can be realized with chance-constrained model predictive control. The large-scale deployment of flexible loads needs to carefully consider the existing regulation schemes in power systems, i.e., generator droop control. In this work first, we investigate the complex nature of system-wide frequency stability from time-delays in actuation of dispatchable loads. Then, we studied the robustness and performance trade-offs in receding horizon control with uncertain energy resources. The uncertainty studied herein is associated with estimating the capacity of and the estimated state of charge from an aggregation of DERs. The concept of uncertain flexible resources in markets leads to maximizing capacity bids or control authority which leads to dynamic capacity saturation (DCS) of flexible resources. We show there exists a sensitive trade-off between robustness of the optimized dispatch and closed-loop system performance and sacrificing some robustness in the dispatch of the uncertain energy capacity can significantly improve system performance. We proposed and formulated a risk-based chance constrained MPC (RB-CC-MPC) to co-optimize the operational risk of prematurely saturating the virtual energy storage system against deviating generators from their scheduled set-point. On a fast minutely timescale, the RB-CC-MPC coordinates energy-constrained virtual resources to minimize unscheduled participation of ramp-rate limited generators for balancing variability from renewable generation, while taking into account grid conditions. We show under the proposed method it is possible to improve the performance of the controller over conventional distributionally robust methods by more than 20%. Moreover, a hardware-in-the-loop (HIL) simulation of a cyber-physical system consisting of packetized energy management (PEM) enabled DERs, flexible VESSs and transmission grid is developed in this work. A predictive, energy-constrained dispatch of aggregated PEM-enabled DERs is formulated, implemented, and validated on the HIL cyber-physical platform. The experimental results demonstrate that the existing control schemes, such as AGC, dispatch VESSs without regard to their energy state, which leads to unexpected capacity saturation. By accounting for the energy states of VESSs, model-predictive control (MPC) can optimally dispatch conventional generators and VESSs to overcome disturbances while avoiding undesired capacity saturation. The results show the improvement in dynamics by using MPC over conventional AGC and droop for a system with energy-constrained resources.

My dissertation considers solving of linear programming problems with p-order conic constraints that are related to a class of stochastic optimization models with risk objective or constraints that involve higher moments of loss distributions. The general proposed approach is based on construction of polyhedral approximations for p-order cones, thereby approximating the non-linear convex p-order conic programming problems using linear programming models. It is shown that the resulting LP problems possess a special structure that makes them amenable to efficient decomposition techniques. The developed algorithms are tested on the example of portfolio optimization problem with higher moment coherent risk measures that reduces to a p-order conic programming problem. The conducted case studies on real financial data demonstrate that the proposed computational techniques compare favorably against a number of benchmark methods, including second-order conic programming methods.

The objective of the proposed research is to develop methods that couple an expert user's guidance with automatic image segmentation and registration algorithms. Often, complex processes such as fire, anatomical changes/variations in human bodies, or unpredictable human behavior produce the target images; in these cases, creating a model that precisely describes the process is not feasible. A common solution is to make simplifying assumptions when performing detection, segmentation, or registration tasks automatically. However, when these assumptions are not satisfied, the results are unsatisfactory. Hence, removing these, often times stringent, assumptions at the cost of minimal user input is considered an acceptable trade-off. Three milestones towards reaching this goal have been achieved. First, an interactive image segmentation approach was created in which the user is coupled in a closed-loop control system with a level set segmentation algorithm. The user's expert knowledge is combined with the speed of automatic segmentation. Second, a stochastic point set registration algorithm is presented. The point sets can be derived from simple user input (e.g. a thresholding operation), and time consuming correspondence labeling is not required. Furthermore, common smoothness assumptions on the non-rigid deformation field are removed. Third, a stochastic image registration algorithm is designed to capture large misalignments. For future research, several improvements of the registration are proposed, and an iterative, landmark based segmentation approach, which couples the segmentation and registration, is envisioned.

This thesis presents a model that simulates and solves power system dispatch problems utilizing stochastic linear programming. The model features the ability to handle single period, multiple bus, linear DC approximated systems. It determines capacity, energy, and reserve quantities while accounting for N-1 contingency scenarios (single loss of either generator or line) on the network. Market systems applying to this model are also proposed, covering multiple real-time, day-ahead, and hybrid versions of consumer costing, transmission operator payment, and generator remuneration schemes. The model and its market schemes are applied to two test systems to verify its viability: a small 6-bus system and a larger 66-bus system representing the Ontario electricity network.

This thesis presents a model that simulates and solves power system dispatch problems utilizing stochastic linear programming. The model features the ability to handle single period, multiple bus, linear DC approximated systems. It determines capacity, energy, and reserve quantities while accounting for N-1 contingency scenarios (single loss of either generator or line) on the network. Market systems applying to this model are also proposed, covering multiple real-time, day-ahead, and hybrid versions of consumer costing, transmission operator payment, and generator remuneration schemes. The model and its market schemes are applied to two test systems to verify its viability: a small 6-bus system and a larger 66-bus system representing the Ontario electricity network.