Optimization under uncertainty with power system applications
(2024)
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- Abstract
- The transition of the energy sector towards decarbonization involves the integration of more renewable sources, which introduces unpredictability from solar and wind energy. This necessitates sophisticated decision-making models to manage such variability effectively. Emphasizing the importance of innovative modeling approaches, this thesis highlights how effective modeling serves as a critical strategy to utilize these mathematical techniques in practical scenarios. By presenting examples, including a novel perspective on uncertainty in multi-interval real-time markets and reformulation strategies for multi-area reserve sizing problems, the dissertation demonstrates significant computational efficiency gains and the potential for solving large-scale, practical power system challenges. The first part of this dissertation explores the dynamics of multi-interval real-time markets, where the unique characteristics of rolling implementation pose significant challenges for both optimal dispatch decisions and pricing models. Through theoretical and empirical analyses, this chapter uncovers the difference between these two models and introduces a method that leverages the stochastic gradient algorithm. This innovative approach circumvents the complexities of multi-stage stochastic programming, yielding near-optimal solutions swiftly for large-scale problems and highlighting the significance of advanced modeling in reducing opportunity costs. The second part of this dissertation considers the multi-area reserve dimensioning problem, aiming to optimize reserve allocations within the constraints of system reliability. Beginning with a foundational two-stage chance-constrained programming model, this chapter evaluates three distinct reformulations. The final approach is particularly notable for the development of an efficient solution method that not only solves real-world problems optimally but also has been adopted by a Nordic Transmission System Operator for a number of planning functions. This example underlines the impact of modeling, especially in handling integer variables. Collectively, the dissertation underscores the role of modeling as a foundational element for optimization under uncertainty in power systems, presenting modeling not just as a theoretical endeavor, but as a practical tool that addresses specific and complex requirements, thereby bridging the gap between computational capabilities and practical needs in the power industry.
- Affiliations
UCLouvain SST/ICTM/INMA - Pôle en ingénierie mathématique
Citations
Cho, J. (2024). Optimization under uncertainty with power system applications. https://hdl.handle.net/2078.5/30159