Modelling Power Markets With Multi-Stage Stochastic Nash Equilibria

Abstract

ThanksTo all my family, specially my mother and father who stood by my side and gave me all the support one could ever dream with during this long way. Also to my brother João Pedro and my step-father Ricardo for the company.To PUC-Rio for providing an excellent environment.To my great friends that were present during all these long years.To my friends from PUC-Rio for the endless discussions, specially Gustavo Amaral, Mario Souto, Alexandre Moreira and Bruno Fanzeres.To my professors Carlos Tomei and Carlos Kubrusly for helping me to discover my interests and find my way in mathematics.To my advisor Alexandre Street who guided during most of my electrical engineering course and introduced me to optimization applied to power systems.To my good friends in UC Santa Barbara, specially my advisor over there João Pedro Hespanha.To all my friends at PSR, specially Julio Alberto Dias, Luiz Carlos da Costa Junior and Camila Metello who helped me day and night, also to Sergio Granville and Luiz Augusto Barroso for the many conversations and insights that made this work possible.To my co-advisor Mario Veiga for introducing me to the topic of this work and giving me all the support without which it would not have been possible. AbstractThe modelling of modern power markets requires the representation of the following main features: (i) a stochastic dynamic decision process, with uncertainties related to renewable production and fuel costs, among others; and (ii) a game-theoretic framework that represents the strategic behaviour of multiple agents, for example in daily price bids.These features can be in theory represented as a stochastic dynamic programming recursion, where we have a Nash equilibrium for multiple agents. However, the resulting problem is very challenging to solve. This work presents an iterative process to solve the above problem for realistic power systems. The proposed algorithm is consist of a fixed point algorithm, in which, each step is solved via stochastic dual dynamic programming method.The application of the proposed algorithm are illustrated in case studies with the real power systems. MODELAGEM DE MERCADOS DE ENERGIA COM EQUILIBRIO DE NASH STOCÁSTICO MULTI-ESTÁGIO ResumoA modelagem dos mercados de energia modernos exige a representação das seguintes características principais: (i) um processo de decisão dinâmico estocástico , com incertezas relacionadas aos os custos de produção e dos combustíveis renováveis, entre outros; e (ii) teoria dos jogos que representa o comportamento estratégico de múltiplos agentes , por exemplo, em propostas de preços diárias.Esses recursos podem ser , em teoria, representados como uma recursão de programação dinâmica estocástica, onde temos um equilíbrio de Nash para múltiplos agentes. No entanto, o problema resultante é muito difícil de resolver.Este trabalho apresenta um processo iterativo para resolver o problema acima para sistemas de energia realistas. O algoritmo proposto é composto de um algoritmo de ponto fixo, no qual, cada passo é resolvido através do mét...