Dans l’industrie électrique, le progrès technologique apporté par les réseaux intelligents vient défier l’idée selon laquelle les consommateurs ne pourraient pas réagir aux prix des marchés de gros. L’intégration des Effacements de Demande (ED) dans le système électrique se heurte néanmoins à la question de leur efficacité économique. Cette thèse évalue la valeur économique des ED en s’appuyant sur un modèle de marché de l’énergie sous incertitude permettant de calculer les profits d’un agrégateur, par classe de consommateur et d’usage final. Le modèle appartient à la classe des problèmes linéaires stochastiques à plusieurs périodes. Sa résolution s’appuie sur Stochastic Dual Dynamic Programming. Il apparaît qu’en France, les secteurs rentables sont le load-shedding industriel et le load-shifting du ciment et du papier. Le load-shifting du chauffage électrique n’est pas profitable pour le tertiaire et le résidentiel. De plus, la valeur capacitaire des ED est déterminante. Dans l’ensemble, les ED deviennent viables mais le développement de leur potentiel semble conditionné à une baisse des coûts fixes dans les technologies de réseau intelligent. / In liberalised power markets the inability of consumers to adapt their demand in accordance to wholesale prices is increasingly challenged. Nowadays technical progress within the smart grid industry constitutes promising changes for the integration of end-users into the power system, but the deployment of Demand Response (DR) still faces the challenge of its economic viability. This thesis aims to assess the economic value of DR. We rely on an energy-only market model under uncertainty in order to quantify the revenues of DR aggregators, classified by category of consumers and end-uses of electricity. The model is formulated as a multi-stage stochastic linear problem and solved by Stochastic Dual Dynamic Programming. It appears that in France, industrial load-shedding and load-shifting of cement, paper, and pulp are profitable. For residential and tertiary consumers, load-shifting of electric heating is not profitable. We also show that the capacity value of DR is crucial. Overall, results show that DR is beginning to become economically attractive, but that fixed costs of smart grid technologies still need to come down further to fully develop its potential.

Generation and transmission investment planning in deregulated markets faces new challenges particularly as deregulation has introduced more uncertainty to the planning problem. Tradi- tional planning techniques and processes cannot be applied to the deregulated planning problem as generation investments are profit driven and competitive. Transmission investments must facilitate generation access rather than servicing generation choices. The new investment plan- ning environment requires the development of new planning techniques and processes that can remain flexible as uncertainty within the system is revealed. The optimisation technique of Stochastic Dual Dynamic Programming (SDDP) has been success- fully used to optimise continuous stochastic dynamic planning problems such as hydrothermal scheduling. SDDP is extended in this thesis to optimise the stochastic, dynamic, mixed integer power system investment planning problem. The extensions to SDDP allow for optimisation of large integer variables that represent generation and transmission investment options while still utilising the computational benefits of SDDP. The thesis also details the development of a math- ematical representation of a general power system investment planning problem and applies it to a case study involving investment in New Zealand’s HVDC link. The HVDC link optimisation problem is successfully solved using the extended SDDP algorithm and the output data of the optimisation can be used to better understand risk associated with capital investment in power systems. The extended SDDP algorithm offers a new planning and optimisation technique for deregulated power systems that provides a flexible optimal solution and informs the planner about investment risk associated with uncertainty in the power system.

In this dissertation, we focus on developing sampling-based algorithms for solving stochastic linear programs. The work covers both two stage and multistage versions of stochastic linear programs. In particular, we first study the two stage stochastic decomposition (SD) algorithm and present some extensions associated with SD. Specifically, we study two issues: a) are there conditions under which the regularized version of SD generates a unique solution? and b) in cases where a user is willing to sacrifice optimality, is there a way to modify the SD algorithm so that a user can trade-off solution times with solution quality? Moreover, we present our preliminary approach to address these questions. Secondly, we investigate the multistage stochastic linear programs and propose a new approach to solving multistage stochastic decision models in the presence of constraints. The motivation for proposing the multistage stochastic decomposition algorithm is to handle large scale multistage stochastic linear programs. In our setting, the deterministic equivalent problems of the multistage stochastic linear program are too large to be solved exactly. Therefore, we seek an asymptotically optimum solution by simulating the SD algorithmic process, which was originally designed for two-stage stochastic linear programs (SLPs). More importantly, when SD is implemented in a time-staged manner, the algorithm begins to take the flavor of a simulation leading to what we refer to as optimization simulation. As for multistage stochastic decomposition, there are a couple of advantages that deserve mention. One of the benefits is that it can work directly with sample paths, and this feature makes the new algorithm much easier to be integrated within a simulation. Moreover, compared with other sampling-based algorithms for multistage stochastic programming, we also overcome certain limitations, such as a stage-wise independence assumption.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-06-22T12:09:45Z No. of bitstreams: 1 cristinamarciabarrosdecastro.pdf: 9219339 bytes, checksum: 92fbbaf80500b5c629a4e62bcd9aa49d (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-07-13T15:29:14Z (GMT) No. of bitstreams: 1 cristinamarciabarrosdecastro.pdf: 9219339 bytes, checksum: 92fbbaf80500b5c629a4e62bcd9aa49d (MD5) / Made available in DSpace on 2016-07-13T15:29:14Z (GMT). No. of bitstreams: 1 cristinamarciabarrosdecastro.pdf: 9219339 bytes, checksum: 92fbbaf80500b5c629a4e62bcd9aa49d (MD5) Previous issue date: 2012-12-27 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Com o objetivo de atendimento à demanda de energia elétrica, buscando um baixo custo na geração de energia, é imprescindível o desenvolvimento do planejamento da operação do setor elétrico brasileiro. O planejamento da operação no horizonte de médio prazo leva em consideração a alta estocasticidade das afluências e é avaliado através da série histórica de Energia Natural Afluente (ENA). No modelo homologado pelo setor, o estudo da ENA tem sido feito por meio da metodologia Box e Jenkins, para determinar os modelos autorregressivos periódicos (PAR(p)), bem como sua ordem . Aos resíduos gerados na modelagem do PAR(p), são aplicados uma distribuição lognormal três parâmetros, como forma de gerar séries sintéticas hidrológicas semelhantes à série histórica original. Contudo, a transformação lognormal incorpora não linearidades que afetam o processo de convergência da Programação Dinâmica Dual Estocástica (PDDE). Este trabalho incorpora a técnica de bootstrap para a geração de cenários sintéticos que servirão de base para a aplicação da PDDE. A técnica estatística Bootstrap é um método alternativo a ser empregado ao problema de planejamento e que permite tanto determinar a ordem ( ) do modelo PAR(p), quanto gerar novas séries sintéticas hidrológicas. Assim, o objetivo do trabalho é analisar os impactos existentes com o uso do Bootstrap no planejamento da operação dos sistemas hidrotérmicos e, em seguida estabelecer uma comparação com a metodologia que tem sido aplicada no setor. Diante dos resultados foi possível concluir que a técnica bootstrap permite a obtenção de séries hidrológicas bem ajustadas e geram resultados confiáveis quanto ao planejamento da operação de sistemas hidrotérmicos, podendo ser usada como uma técnica alternativa ao problema em questão. / Aiming to match the long term load demand with a low cost in power generation, it is very important to improve more and more the operation planning of the Brazilian electric sector. The operation planning of medium/long term takes into account the water inflows, which are strongly stochastic, and it must be evaluated using the series of Natural Energy Inflows (NEI). In the current computational model applied to Brazilian operation planning of medium/long term, the study of ENA has been done by Box and Jenkins methodology, which determines the periodic autoregressive model (PAR (p)), as well as its order p. A lognormal distribution with three parameters is applied on the residues that are created by the PAR (p) model, as a way to generate synthetic hydrologic series similar to the original series. However, this lognormal transformation brings nonlinearities which can disturb the stability and convergence of Stochastic Dual Dynamic Programming (SDDP). This thesis incorporates the bootstrap technique to create synthetic scenarios which will be taken into account as a basis for the SDDP implementation. This statistical technique, called bootstrap, is an alternative method used to determine both the order (p) of the model PAR (p), and, after that, to produce synthetic hydrological series. Thus, the objective of this thesis is to analyze the impact of the Bootstrap technique compared to the current methodology. The results showed that the bootstrap technique is suitable to obtain adherent hydrological series. So, it was created reliable scenarios regarding the planning of the operation of hydrothermal systems. Finally, this new methodology can be used as an alternative technique to long term hydrothermal planning problems.

Multi-Stage Stochastic Programming with CVaR: Modeling, Algorithms and Robustness RNDr. Václav Kozmík Abstract: We formulate a multi-stage stochastic linear program with three different risk measures based on CVaR and discuss their properties, such as time consistency. The stochastic dual dynamic programming algorithm is described and its draw- backs in the risk-averse setting are demonstrated. We present a new approach to evaluating policies in multi-stage risk-averse programs, which aims to elimi- nate the biggest drawback - lack of a reasonable upper bound estimator. Our approach is based on an importance sampling scheme, which is thoroughly ana- lyzed. A general variance reduction scheme for mean-risk sampling with CVaR is provided. In order to evaluate robustness of the presented models we extend con- tamination technique to the case of large-scale programs, where a precise solution cannot be obtained. Our computational results are based on a simple multi-stage asset allocation model and confirm usefulness of the presented procedures, as well as give additional insights into the behavior of more complex models. Keywords: Multi-stage stochastic programming, stochastic dual dynamic programming, im- portance sampling, contamination, CVaR

[pt] A Programação Dinâmica Dual Estocástica (PDDE) constitui um dos métodos mais utilizados no planejamento hidrotérmico. Trabalhos anteriores neste campo se baseiam numa abordagem tipo acaso-decisão, enquanto a realidade está mais próxima de um processo tipo decisão-acaso. Tal dissonância entre planejamento e implementação gera um problema de inconsistência temporal, pois decisões futuras planejadas podem não ser colocadas em prática sob as mesmas condições. Se por um lado a modelagem acaso-decisão permite uma metodologia de solução cenário-decomponível eficiente, por outro, a estrutura decisão-acaso proporciona uma solução mais robusta (pessimista), já que desconsidera a antecipatividade. Neste trabalho, mensura-se o gap de inconsistência relativo a metodologia atual, assim como se propõe uma abordagem alternativa para o planejamento hidrotérmico que utiliza uma estrutura de revelação de incertezas e um processo decisório tipo decisão-acaso, aproximando o modelo de planejamento da realidade operativa. Ao invés de empregar restrições de não-antecipatividade, o que impossibilitaria a decomposição por cenário de cada subproblema estocástico de dois estágios, a metodologia proposta considera decisões de primeiro estágio como variáveis de estado a serem otimizadas via PDDE. Assim, reduz-se consideravelmente a complexidade e tempo necessário para se obter uma solução, garantindo ainda a estrutura decisória tipo decisão-acaso e não-antecipatividade das decisões de primeiro estágio. Resultados baseados no SIN indicam que tal inconsistência pode levar a um aumento considerável da geração de termelétricas mais caras, causando maior volatilidade nos preços de curto prazo e aumento no custo total de operação. Desta forma, a solução metodológica proposta, baseada na abordagem decisão-acaso via espaço de estado aumentado, constitui contribuição relevante e oportuna tanto para práticas na indústria quanto para o estado-da-arte da literatura utilizada para o planejamento da operação hidrotérmica sob incerteza. / [en] Stochastic Dual Dynamic Programming (SDDP) is currently one of the most employed methods for hydrothermal planning. All previous works on this subject are based on a hazard-decision approach, whereas reality is more closely related to a decision-hazard process. This dissonance between planning and implementation is a source of time-inconsistency, as future planned decisions under the same conditions may not be put into practice. If on the one hand the hazard-decision modeling framework allows a scenario-decomposable efficient solution methodology, on the other hand the decision-hazard structure provides a more robust (pessimistic) solution as it does not rely on anticipativity assumptions. In this work, we measure the inconsistency-gap related to the current methodology and propose an alternative approach for hydrothermal planning that utilizes an informationrevelation structure and decision process based on a decision-hazard framework, thereby approximating the planning model to realistic operational actions. Instead of relying on non-anticipativity constraints, which would prevent the scenario decomposition of each two-stage stochastic subproblem, the proposed methodology considers first-stage decisions as state variables to be optimized through the SDDP procedure. In this framework, the complexity and time required to find a solution is considerably reduced yet ensuring the decision-hazard decision structure and non-anticipativity of the first-stage decisions. Results based on the Brazilian power system indicate that this inconsistency may considerably increase generation of more expensive thermal units, leading to spikes in energy market spot prices and an increase in overall operational costs. Therefore, the proposed decision-hazard approach and augmented-state solution methodology constitute timely and relevant contributions to both industry practices and state of the art literature on the subject of hydrothermal operation planning under uncertainty.

The main objective of this thesis is to investigate risk neutral and risk averse approaches to multistage stochastic programming with applications to hydrothermal operation planning problems. The purpose of hydrothermal system operation planning is to define an operation strategy which, for each stage of the planning period, given the system state at the beginning of the stage, produces generation targets for each plant. This problem can be formulated as a large scale multistage stochastic linear programming problem. The energy rationing that took place in Brazil in the period 2001/2002 raised the question of whether a policy that is based on a criterion of minimizing the expected cost (i.e. risk neutral approach) is a valid one when it comes to meet the day-to-day supply requirements and taking into account severe weather conditions that may occur. The risk averse methodology provides a suitable framework to remedy these deficiencies. This thesis attempts to provide a better understanding of the risk averse methodology from the practice perspective and suggests further possible alternatives using robust optimization techniques. The questions investigated and the contributions of this thesis are as follows. First, we suggest a multiplicative autoregressive time series model for the energy inflows that can be embedded into the optimization problem that we investigate. Then, computational aspects related to the stochastic dual dynamic programming (SDDP) algorithm are discussed. We investigate the stopping criteria of the algorithm and provide a framework for assessing the quality of the policy. The SDDP method works reasonably well when the number of state variables is relatively small while the number of stages can be large. However, as the number of state variables increases the convergence of the SDDP algorithm can become very slow. Afterwards, performance improvement techniques of the algorithm are discussed. We suggest a subroutine to eliminate the redundant cutting planes in the future cost functions description which allows a considerable speed up factor. Also, a design using high performance computing techniques is discussed. Moreover, an analysis of the obtained policy is outlined with focus on specific aspects of the long term operation planning problem. In the risk neutral framework, extreme events can occur and might cause considerable social costs. These costs can translate into blackouts or forced rationing similarly to what happened in 2001/2002 crisis. Finally, issues related to variability of the SAA problems and sensitivity to initial conditions are studied. No significant variability of the SAA problems is observed. Second, we analyze the risk averse approach and its application to the hydrothermal operation planning problem. A review of the methodology is suggested and a generic description of the SDDP method for coherent risk measures is presented. A detailed study of the risk averse policy is outlined for the hydrothermal operation planning problem using different risk measures. The adaptive risk averse approach is discussed under two different perspectives: one through the mean-$avr$ and the other through the mean-upper-semideviation risk measures. Computational aspects for the hydrothermal system operation planning problem of the Brazilian interconnected power system are discussed and the contributions of the risk averse methodology when compared to the risk neutral approach are presented. We have seen that the risk averse approach ensures a reduction in the high quantile values of the individual stage costs. This protection comes with an increase of the average policy value - the price of risk aversion. Furthermore, both of the risk averse approaches come with practically no extra computational effort and, similarly to the risk neutral method, there was no significant variability of the SAA problems. Finally, a methodology that combines robust and stochastic programming approaches is investigated. In many situations, such as the operation planning problem, the involved uncertain parameters can be naturally divided into two groups, for one group the robust approach makes sense while for the other the stochastic programming approach is more appropriate. The basic ideas are discussed in the multistage setting and a formulation with the corresponding dynamic programming equations is presented. A variant of the SDDP algorithm for solving this class of problems is suggested. The contributions of this methodology are illustrated with computational experiments of the hydrothermal operation planning problem and a comparison with the risk neutral and risk averse approaches is presented. The worst-case-expectation approach constructs a policy that is less sensitive to unexpected demand increase with a reasonable loss on average when compared to the risk neutral method. Also, we comp are the suggested method with a risk averse approach based on coherent risk measures. On the one hand, the idea behind the risk averse method is to allow a trade off between loss on average and immunity against unexpected extreme scenarios. On the other hand, the worst-case-expectation approach consists in a trade off between a loss on average and immunity against unanticipated demand increase. In some sense, there is a certain equivalence between the policies constructed using each of these methods.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-07-28T12:04:17Z No. of bitstreams: 1 rafaelbrunodasilvabrandi.pdf: 13228407 bytes, checksum: 1e92e8c2fa686ddcaea1c9ed0d33b278 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-07-28T12:16:14Z (GMT) No. of bitstreams: 1 rafaelbrunodasilvabrandi.pdf: 13228407 bytes, checksum: 1e92e8c2fa686ddcaea1c9ed0d33b278 (MD5) / Made available in DSpace on 2016-07-28T12:16:14Z (GMT). No. of bitstreams: 1 rafaelbrunodasilvabrandi.pdf: 13228407 bytes, checksum: 1e92e8c2fa686ddcaea1c9ed0d33b278 (MD5) Previous issue date: 2016-02-29 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico / O Sistema Elétrico Brasileiro (SEB) apresenta características peculiares devido às grandes dimensões do país e pelo fato da geração elétrica ser proveniente predominantemente de usinas hidráulicas. Como as afluências a estas usinas possuem comportamento estocástico e grandes reservatórios proporcionam ao sistema a capacidade de uma regularização plurianual, a utilização dos recursos hidráulicos deve ser planejada de forma minuciosa em um horizonte de tamanho considerável. Assim, o planejamento da operação de médio prazo compreende um período de 5 a 10 anos com discretização mensal e é realizado por uma cadeia de modelos computacionais tal que o principal modelo desta cadeia é baseado na técnica da Programação Dinâmica Dual Estocástica (PDDE). O objetivo deste trabalho é obter avanços nas metodologias de programação dinâmica atualmente utilizadas. Partindo-se da utilização da inserção iterativa de cortes, implementa-se um modelo computacional para o planejamento da operação de médio prazo baseado na metodologia de Programação Dinâmica Estocástica (PDE) utilizando uma discretização mais eficiente do espaço de estados (PDEE). Além disso, a metodologia proposta de PDE possui um critério de convergência bem definido para o problema, de forma que a inclusão da medida de risco CVaR não altera o processo de avaliação da convergência de forma significante. Dado que a inclusão desta medida de risco à PDDE convencional dificulta a avaliação da convergência do processo pela dificuldade da estimação de um limite superior válido, o critério de convergência proposto na PDEE é, então, base para um novo critério de convergência para a PDDE tal que pode ser aplicado mesmo na consideração do CVaR e não aumenta o custo computacional envolvido. Adicionalmente, obtém-se um critério de convergência mais detalhado em que as séries utilizadas para amostras de afluência podem ser avaliadas individualmente tais que aquelas que, em certo momento, não contribuam de forma determinante para a convergência podem ser descartadas do processo, diminuindo o tempo computacional, ou ainda serem substituídas por novas séries dentro de uma reamostragem mais seletiva dos cenários utilizados na PDDE. As metodologias propostas foram aplicadas para o cálculo do planejamento de médio prazo do SIN baseando-se em subsistemas equivalentes de energia. Observa-se uma melhoria no algoritmo base utilizado para a PDE e que o critério proposto para convergência da PDDE possui validade mesmo quando CVaR é considerado na modelagem. / The Brazilian National Grid (BNG) presents peculiar characteristics due to its huge territory dimensions and hydro-generation predominancy. As the water inflows to these plants are stochastic and a pluriannual regularization for system storage capacity is provided, the use of hydro-generation must be planned in an accurate manner such that it considersalongplanningperiod. So, thelong-termoperationplanning(LTOP)problemis generallysolvedbyachainofcomputationalmodelsthatconsideraperiodof5to10years ahead such that the primary model of this chain is based on Stochastic Dual Dynamic Programming (SDDP) technique. The main contribution of this thesis is to propose some improvements in Stochastic Dynamic Programming techniques usually settled on solving LTOP problems. In the fashion of an iterative cut selection, it is firstly proposed a LTOP problem solution model that uses an ecient state space discretization for Stochastic Dynamic Programming (SDP), called ESDP. The proposed model of SDP has a welldefined convergence criterion such that including CVaR does not hinder convergence analysis. Due to the lack of good upper bound estimators in SDDP when including CVaR, additional issues are encountered on defining a convergence criterion. So, based on ESDP convergence analysis, a new criterion for SDDP convergence is proposed such that it can be used regardless of CVaR representation with no extra computational burden. Moreover, the proposed convergence criterion for SDDP has a more detailed description such that forward paths can be individually assessed and then be accordingly discarded for computational time reduction, or even define paths to be replaced in a more particular resampling scheme in SDDP. Based on aggregate reservoir representation, the proposed methodsofconvergenceofSDDPandtheESDPwereappliedonLTOPproblemsrelatedto BNG. Results show improvements in SDDP based technique and eectiveness of proposed convergence criterion for SDDP when CVaR is used.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-05-10T12:15:28Z No. of bitstreams: 1 alexandredasilvafernandes.pdf: 3326554 bytes, checksum: f4dfcfe70bde99c5ebe4501f03add83e (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-05-22T15:33:53Z (GMT) No. of bitstreams: 1 alexandredasilvafernandes.pdf: 3326554 bytes, checksum: f4dfcfe70bde99c5ebe4501f03add83e (MD5) / Made available in DSpace on 2018-05-22T15:33:53Z (GMT). No. of bitstreams: 1 alexandredasilvafernandes.pdf: 3326554 bytes, checksum: f4dfcfe70bde99c5ebe4501f03add83e (MD5) Previous issue date: 2018-02-20 / O planejamento da operação do Sistema Interligado Nacional constitui-se uma tarefa de alta complexidade, seja pela quantidade acentuada de usinas hidrelétricas e termelétricas distribuídas nos quatro submercados interligados, ou pelas características marcantes da operação das hidrelétricas, no que diz respeito às incertezas dos cenários hidrológicos futuros e aos acoplamentos espacial e temporal. O objetivo deste planejamento é a determinação de uma política ótima de despacho das usinas do sistema de modo a minimizar o valor esperado dos custos operativos no horizonte considerado. Uma importante restrição do problema é o suprimento da demanda de energia elétrica, dado pela diferença entre a carga efetiva de cada submercado e a geração das usinas não simuladas, esta última composta pela energias alternativas (eólica, solar, biomassa), pequenas centrais hidrelétricas, entre outros. Entretanto, a crescente penetração da geração renovável, aliada às incertezas das fontes naturais como eólica e solar (pois dependem de fatores climáticos e por isso são imprevisíveis), contribui com a necessidade de representação da demanda em diversos cenários para um correto despacho das usinas e uma operação do sistema mais confiável. Sabendo que os modelos oficiais atuais tratam apenas as incertezas oriundas dos cenários hidrológicos, devido à dificuldade de implementação e alocação de memória na consideração de outras incertezas na Programação Dinâmica Dual Estocástica, o trabalho desenvolvido nesta dissertação propõe metodologias que incluem os diversos cenários de demanda, além de representar com maior detalhe a geração das hidrelétricas. Além disso, são propostos algoritmos de representação analítica da Função de Custo Imediato em sistemas isolados e com múltiplas áreas na busca por uma redução das dimensões do problema tratado. Finalmente, são realizados testes em sistemas tutorias e os resultados são analisados para avaliar as performances computacionais das metodologias propostas. / The operation schedulling of Brazilian System constitutes a task of high complexity, either due to the large number of hydro and thermal plants distributed in the four interconnected submarkets, or due to the outstanding characteristics of the hydro plants, with respect to the uncertainties in the hydrological scenarios future and due to spatial and temporal couplings. The objective of this planning is the determination of an optimal dispatch policy of plants that minimizes the expected value of the operating costs in the considered horizon. An important constraint is the supply of demand, which is obtained by the difference between the effective load of each submarket and the generation of non-simulated plants, composed of renewable energies (wind, solar, biomass), small hydropower plants, and others. However, the growing penetration of renewable generation, coupled with the uncertainties of natural sources such as wind and solar (because they depend on climatic factors and are therefore unpredictable), contributes to the need to represent demand in different scenarios for a correct dispatch of the plants and a more reliable system operation. Knowing that the current official models deal only with the uncertainties arising from the hydrological scenarios, due to the difficulty of implementation and memory allocation in the consideration of other uncertainties in Stochastic Dual Dynamic Programming, this work proposes methodologies that include the several scenarios demand, besides representing in greater detail the generation of hydroelectric plants. In addition, algorithms are proposed for analytical representation of the Immediate Cost Function in isolated systems with multiple areas in the search for a reduction of the dimensions of the problem. Finally, tests are performed on tutorial systems and the results are analyzed to evaluate the computational performances of the proposed methodologies.

[pt] O investimento em fontes renováveis, apesar do crescimento recente, ainda é dificultado devido à volatilidade dos mercados de curto prazo. Contratos forward são essenciais mesmo em mercados de balcão como o Ambiente de Contratação Livre (ACL) Brasileiro. Contatos forward permitem a redução da incerteza sobre a receita, ajudam a garantir a adequação do fornecimento graças à sinalização de preços para a expansão e podem também ser obrigatórios para realização do project finance de novos empreendimentos. Apesar da oferta de contratos, as fontes renováveis ainda possuem o risco adicional em sua geração, o que pode, combinando-se altos preços spot em um momento de baixa geração, ocasionar uma exposição ao risco de preço-quantidade. Investimento em fontes renováveis pode ser incentivado através da aplicação de técnicas de gestão de riscos como contratação forward, diversificação e definição do momento ótimo de investimento. Através da negociação de contratos e aproveitando complementariedades sazonais entre as fontes, é possível minimizar a exposição aos riscos do mercado. O problema de investimento em centrais de energia renovável pode ser visto como um modelo de otimização estocástica multiestágio com variáveis inteiras, de difícil resolução. As principais soluções disponíveis na literatura simplificam o problema ao reduzir a dimensionalidade da árvore de cenários, ou assumindo hipóteses simplificadoras sobre os processos estocásticos. Nosso objetivo é apresentar um framework para valoração de investimentos em energia renovável, considerando as principais fontes de incerteza e alternativas para composição de uma carteira de investimentos. A principal contribuição desse trabalho é uma metodologia para resolver, utilizando técnicas de decomposição, o problema de investimento ótimo em centrais renováveis complementares no mercado elétrico brasileiro. Este é um problema estocástico multiestágio e não convexo. Nossas políticas de investimento são geradas através de um algoritmo baseado em Programação Dinâmica Dual Estocástica (SDDP). Restrições de integralidade são consideradas no passo forward, onde as políticas são avaliadas, e relaxados no passo backward, onde as políticas são geradas, para garantir a convexidade das funções de recurso. Os resultados numéricos mostram que não é possível assumir independência entre estágios dos processos estocásticos de preços. A estrutura Markoviana dos processos estocásticos é preservada usando uma discretização do espaço de probabilidade, que é resolvida utilizando uma conhecida extensão do SDDP. A avaliação da performance é feita utilizando os dados originais, validando nossa heurística. Nosso framework requer um modelo para o preço forward de energia. Nós aplicamos o modelo Schwartz-Smith usando dados do mercado spot e de balcão para construir a curva forward do mercado brasileiro. O framework contempla as particularidades do ACL no mercado brasileiro, mas também pode ser utilizado em mercados similares. Utilizando medidas coerentes de risco, incorporamos aversão a risco e avaliamos as estratégias concorrentes utilizando conceitos modernos de gestão de riscos. / [en] Despite recent trend for investment in renewable energy, high volatility in shortterm markets still may hinder some opportunities. Forwarding contracting is essential even in Over The Counter (OTC) markets such as the Brazilian Free Trading Environment. Forward contracts allow reducing revenue uncertainty, help ensure supply adequacy by signaling generation expansion and may also be required for project financing in new ventures. Still, renewable sources face the additional risk of uncertain generation, which, in low periods, combined with high spot prices, pose the hazardous price-quantity risk. Renewable investment may be fostered by applying risk management techniques such as forward contracting, diversification and optimal investment timing. By trading contracts and exploiting the seasonal complementarity of the renewable sources, it is possible to reduce risk exposure. The problem of investment in renewable energy plants may be seen as a multistage stochastic optimization model with integer variables, which is very hard to solve. The main approaches in the current literature simplify the problem by reducing the dimensionality of the scenario tree or by assuming simplifying hypothesis on the stochastic processes. Our objective is to introduce a renewable investment valuation framework, considering the main uncertainty sources and portfolio investment alternatives. The main contribution of this work is a method to solve, by applying decomposition techniques, the problem of optimal investment in seasonal complementary renewable plants in the Brazilian energy market. This is a multistage stochastic and non-convex problem. Our investment policies are devised using an algorithm based on Stochastic Dual Dynamic Programming (SDDP). Integrality constraints are considered in the forward step, where policies are evaluated, and relaxed in the backward step, where policies are built, to ensure convexity of the recourse functions. Numerical results show that it is not possible to assume stagewise independence of the price processes. We maintain the Markovian property of the stochastic processes by a discretization of the probability space, solvable by a known extension to the SDDP method. Performance evaluation is carried out using the original data, validating our heuristic. A forward energy price model is required in our framework. We apply the Schwartz-Smith model with spot and OTC data of the Brazilian market to build such a forward price curve. The framework is able to represent the characteristics of the Brazilian FTE and may be applied to similar markets. We incorporate risk aversion with coherent measures of risk and evaluate alternative strategies based on modern risk management concepts.