A geração hidrelétrica é dependente da afluência, no entanto, é possível minimizar a variação da energia natural afluente por meio dos reservatórios. Por sua vez, a geração eólica tem como desvantagem a volatilidade devido a sua dependência em relação ao vento. Nesse sentido, uma carteira otimizada de projetos eólicos possibilita a redução da volatidade da energia gerada pelo conjunto, na medida em que aproveita as complementariedades do vento. No Brasil, os Estados da Bahia, Rio Grande do Norte, Ceará, Rio Grande do Sul e Piauí concentram 90% da capacidade instalada das usinas eólicas em operação, em construção ou contratada, com uma previsão da fonte atingir 11,6% de participação na matriz elétrica. A pesquisa tem como objetivo desenvolver uma metodologia de apoio baseada na teoria de portifólio de Markowitz que poderá ser utilizada pelo órgão de planejamento energético brasileiro para a definição da quantidade de energia a ser contratada por fonte e local, por meio de leilões de energia regionais e por fonte, com o objetivo de se obter uma carteira otimizada de empreendimentos, que reduza a volatilidade. O método também pode servir de apoio ao investidor para se obter um portfólio de usinas que minimize o risco de exposição financeira no mercado de curto prazo. Nenhum estudo aplicando a teoria de portifólio de Markowitz em usinas eólicas do Brasil foi encontrado na literatura. Os resultados obtidos demonstram que a carteira formada pelas usinas eólicas existentes não está na fronteira eficiente e poderia ser otimizada com aumento da expectativa de geração ou redução do risco. No mesmo sentido, a otimização da carteira também reduziu o risco de exposição ao mercado de curto prazo. / Even though the hydroelectric generation is highly dependent on the river flows, it is possible to minimize the volatility of the energy generation in a given period using the storage capacity of the reservoirs. In contrast, to minimize the volatility of the wind generation is burdensome due to its dependency on wind. Accordingly, an optimized portfolio of wind projects all together allows the reduction of the volatility of the energy generation for the complementarity of wind from different locations. In Brazil, the states of Bahia, Rio Grande do Norte, Ceara, Rio Grande do Sul and Piauí concentrate 90% of the installed capacity of wind power plants in operation, under construction or contracted with a font forecast to reach 11.6% share the electric matrix. The Thesis aims to develop a support methodology based in portfolio theory of Markowitz that can be used by the Brazilian-planning agency in future, to define the amount of energy to be contracted by source and location, through regional and source energy auctions, to obtain an optimized portfolio projects, with reduced volatility. The methodology can also serve to support the investor to obtain a portfolio of plants that minimize the risk of financial exposure to short-term market. No study applying Markowitz\'s portfolio theory in wind farms of Brazil was found in the literature. The results show that the portfolio of the existing wind farms is not on the efficient frontier and could be optimized with increased expectation of generating or reducing the risk. Similarly, the optimization of the portfolio also reduced the risk of exposure to short-term market.

A geração hidrelétrica é dependente da afluência, no entanto, é possível minimizar a variação da energia natural afluente por meio dos reservatórios. Por sua vez, a geração eólica tem como desvantagem a volatilidade devido a sua dependência em relação ao vento. Nesse sentido, uma carteira otimizada de projetos eólicos possibilita a redução da volatidade da energia gerada pelo conjunto, na medida em que aproveita as complementariedades do vento. No Brasil, os Estados da Bahia, Rio Grande do Norte, Ceará, Rio Grande do Sul e Piauí concentram 90% da capacidade instalada das usinas eólicas em operação, em construção ou contratada, com uma previsão da fonte atingir 11,6% de participação na matriz elétrica. A pesquisa tem como objetivo desenvolver uma metodologia de apoio baseada na teoria de portifólio de Markowitz que poderá ser utilizada pelo órgão de planejamento energético brasileiro para a definição da quantidade de energia a ser contratada por fonte e local, por meio de leilões de energia regionais e por fonte, com o objetivo de se obter uma carteira otimizada de empreendimentos, que reduza a volatilidade. O método também pode servir de apoio ao investidor para se obter um portfólio de usinas que minimize o risco de exposição financeira no mercado de curto prazo. Nenhum estudo aplicando a teoria de portifólio de Markowitz em usinas eólicas do Brasil foi encontrado na literatura. Os resultados obtidos demonstram que a carteira formada pelas usinas eólicas existentes não está na fronteira eficiente e poderia ser otimizada com aumento da expectativa de geração ou redução do risco. No mesmo sentido, a otimização da carteira também reduziu o risco de exposição ao mercado de curto prazo. / Even though the hydroelectric generation is highly dependent on the river flows, it is possible to minimize the volatility of the energy generation in a given period using the storage capacity of the reservoirs. In contrast, to minimize the volatility of the wind generation is burdensome due to its dependency on wind. Accordingly, an optimized portfolio of wind projects all together allows the reduction of the volatility of the energy generation for the complementarity of wind from different locations. In Brazil, the states of Bahia, Rio Grande do Norte, Ceara, Rio Grande do Sul and Piauí concentrate 90% of the installed capacity of wind power plants in operation, under construction or contracted with a font forecast to reach 11.6% share the electric matrix. The Thesis aims to develop a support methodology based in portfolio theory of Markowitz that can be used by the Brazilian-planning agency in future, to define the amount of energy to be contracted by source and location, through regional and source energy auctions, to obtain an optimized portfolio projects, with reduced volatility. The methodology can also serve to support the investor to obtain a portfolio of plants that minimize the risk of financial exposure to short-term market. No study applying Markowitz\'s portfolio theory in wind farms of Brazil was found in the literature. The results show that the portfolio of the existing wind farms is not on the efficient frontier and could be optimized with increased expectation of generating or reducing the risk. Similarly, the optimization of the portfolio also reduced the risk of exposure to short-term market.

This project investigates the applicability of the originalversion of Markowitz’s mean-variance model for portfoliooptimization to real-world modern actively managed portfolios.The method measures the mean-variance model’s capability toaccurately capture the riskiness of given portfolios, by invertingthe mathematical formulation of the model. The inversion of themodel is carried out both for fabricated data and real-world dataand shows that in the cases of real-world data the model lackscertain accuracy for estimating risk averseness. The method hascertain errors which both originate from the proposed estimationmethods of input variables and invalid assumptions of investors. / Projektet undersöker lämpligheten att använda den ursprungliga versionen av Markowitzs ”Mean-Variance model” för portföljoptimering för moderna aktivt förvaltade portföljer. Metoden mäter modellens förmåga att tillförlitligt beräkna risken för givna portföljer genom att invert-era den matematiska formuleringen av modellen. Inversionen av modellen utförs både för simulerad data och verklig data och visar att i fallet med verkliga data saknar modellen viss noggrannhet för att uppskatta riskpreferens. Metoden har vissa fel som både uppstår från de föreslagna uppskattningsmetoderna för inputvariabler och ogiltiga antaganden för investerare. / Kandidatexjobb i elektroteknik 2021, KTH, Stockholm

The increasing penetration of proactive agents in distribution systems (DS) has opened new possibilities to make the grid more resilient and to increase participation of responsive loads (RL) and non-conventional generation resources. On the resiliency side, plug-in hybrid electric vehicles (PHEV), energy storage systems (ESS), microgrids (MG), and distributed energy resources (DER), can be leveraged to restore critical load in the system when the utility system is not available for extended periods of time. Critical load restoration is a key factor to achieve a resilient distribution system. On the other hand, existing DERs and responsive loads can be coordinated in a market environment to contribute to efficiency of electricity consumption and fair electricity tariffs, incentivizing proactive agents' participation in the distribution system. Resiliency and market applications for distribution systems are highly complex decision-making problems that can be addressed using modern optimization techniques. Complexities of these problems arise from non-linear relations, integer decision variables, scalability, and asynchronous information. On the resiliency side, existing models include optimization approaches that consider system's available information and neglect asynchrony of data arrival. As a consequence, these models can lead to underutilization of critical resources during system restoration. They can also become computationally intractable for large-scale systems. In the market design problem, existing approaches are based on centralized or computational distributed approaches that are not only limited by hardware requirements but also restrictive for active participation of the market agents. In this context, the work of this dissertation results in major contributions regarding new optimization algorithms for market design and resiliency improvement in distribution systems. In the DS market side, two novel contribution are presented: 1) A computational distributed coordination framework based on bilateral transactions where social welfare is maximized, and 2) A fully decentralized transactive framework where power suppliers, in a simultaneous auction environment, strategically bid using a Markowitz portfolio optimization approach. On the resiliency side, this research proposed a system restoration approach, taking into account uncertain devices and associated asynchronous information, by means of a two-module optimization models based on binary programming and three phase unbalanced optimal power flow. Furthermore, a Reinforcement Learning (RL) method along with a Monte Carlo tree search algorithm has been proposed to solve the scalability problem for resiliency enhancement. / Doctor of Philosophy / Distribution systems (DS) are evolving from traditional centralized and fossil fuel generation resources to networks with large scale deployment of responsive loads and distributed energy resources. Optimization-based decision-making methods to improve resiliency and coordinate DS participants are required. Prohibitive costs due to extended power outages require efficient mechanisms to avoid interruption of service to critical load during catastrophic power outages. Coordination mechanisms for various generation resources and proactive loads are in great need. Existing optimization-based approaches either neglect the asynchronous nature of the information arrival or are computationally intractable for large scale system. The work of this dissertation results in major contributions regarding new optimization methods for market design, coordination of DS participants, and improvement of DS resiliency. Four contributions toward the application of optimization approaches for DS are made: 1) A distributed optimization algorithm based on decomposition and best approximation techniques to maximize social welfare in a market environment, 2) A simultaneous auction mechanism and portfolio optimization method in a fully decentralized market framework, 3) Binary programming and nonlinear unbalanced power flow, considering asynchronous information, to enhance resiliency in a DS, and 4) A reinforcement learning method together with an efficient search algorithm to support large scale resiliency improvement models incorporating asynchronous information.