The transition of the power network towards cleaner and sustainable energy generation requires appropriate planning of the future power infrastructure, considering both the technical and economic aspects. With this thesis, I propose an optimization model to address the arising challenges and provide the necessary tools to effectively solve energy planning problems. The proposed optimization model simultaneously incorporates a multi-stage formulation, a finitely supported Markov structure of random processes, and the alternating current (AC) nature of power flow dynamics, filling a gap in the existing literature.
First, I propose a semi-metric for Markov processes involved in linear stochastic optimization problems. The distance aims to assess the accuracy of a discrete approximation and its influence on the optimal value of a multi-stage stochastic optimization. The distance relies on transportation metrics and depends on problem parameters, allowing for consideration of randomness in both the objective function and the constraints.
Next, I provide a solution strategy for multi-stage stochastic optimal power flow (OPF) problems. This strategy is based on recent developments in convex semi-definite programming relaxations of OPF problems and the adaptation of the stochastic dual dynamic programming (SDDP) algorithm. I discuss the convergence conditions and properties of the algorithm.
Lastly, I set up an extensive case study focusing on renewable expansion and storage integration planning within the IEEE RTS-GMLC network. The study illustrates the applicability and computational tractability of the presented framework.
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The transition of the power network towards cleaner and sustainable energy generation requires appropriate planning of the future power infrastructure, considering both the technical and economic aspects. With this thesis, I propose an optimization model to address the arising challenges and provide the necessary tools to effectively solve energy planning problems. The proposed optimization model simultaneously incorporates a multi-stage formulation, a finitely supported Markov structure of rand...
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