SCALABLE FRAMEWORKS FOR TWO-STAGE STOCHASTIC OPTIMIZATION IN POWER SYSTEMS USING VALUE FUNCTION APPROXIMATION

Shishir Lamichhane

The increasing integration of renewable energy resources, the growing adoption ofelectric vehicles, the expansion of large-scale data centers, and the rising frequency of extreme weather events have led to a significant increase in uncertainty in modern power systems. These factors make grid planning and operations more challenging. Traditional deterministic approaches are often inadequate because they do not capture the impacts of variability and uncertainty. Two-stage stochastic optimization is a natural way to address this issue, since it incorporates uncertainty directly into the decision-making process. However, solving these problems remains difficult in practice, primarily due to the curse of dimensionality, particularly as the system size increases. To address these challenges, this dissertation develops scalable frameworks for two-stage stochastic optimization problems in power systems, focusing on different mathematical structures that arise in both long-term and operational planning problems. The work first develops a general framework based on Separable Projective Approximation Routine for Stochastic Optimal Power Flow (SPAR-OPF), and then adapts it to different problem structures, showing its use through a set of representative power systems optimization under uncertainty. The illustrated examples are selected to represent different classes of power system optimization problems under uncertainty, which capture a broad range of practical planning and operational problems. Instead of solving the full problem all at once, the proposed approach processes one scenario at a time and decomposes the original two-stage problem into smaller subproblems. This decomposition reduces computational complexity and avoids the need for large memory or high-performance computing resources, so that the framework remains applicable to large-scale systems without requiring very high computational effort, which is often a limitation in practice. The proposed framework is then adapted to different classes of stochastic optimization problems. For problems involving integer linking decisions with continuous convex recourse, a scalable formulation is developed and illustrated using a distributed generation siting and sizing problem. The results are compared with Progressive Hedging (PH) and the extensive formulation (EF), where EF is used as a benchmark. The framework also allows different planning decisions to be obtained efficiently using the learned value function, without repeatedly solving the full optimization problem. Then we extend the framework to problems with continuous and temporally coupled linking variables. These types of problems usually involve multi-period optimization, where decisions across time are coupled through linking variables. In practice, the presence of explicit first-stage objective functions and cost terms across stages can make the direct use of the proposed framework less straightforward, necessitating reformulation. A stochastic dynamic economic dispatch problem is used to illustrate this setting. The model is reformulated and solved using the proposed approach, and the results are compared with EF and PH. Finally, the dissertation considers stochastic optimization problems with integer recourse decisions, which commonly arise in restoration and resilience-related applications. A scalable framework is developed for this class of problems and is illustrated using a distribution system resilience planning problem under extreme weather conditions. Different approaches to obtain dual information (from second stage) are explored, and the performance of the proposed method is evaluated against EF and PH on larger system sizes. Overall, the results show that the proposed approach yields high-quality solutions while reducing computational effort. It also remains scalable for large system sizes where traditional approaches become difficult to apply, making it practical for real-world power system problems under uncertainty.

SCALABLE FRAMEWORKS FOR TWO-STAGE STOCHASTIC OPTIMIZATION IN POWER SYSTEMS USING VALUE FUNCTION APPROXIMATION

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