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201442 https://hdl.handle.net/2286/R.2.N.201442 http://rightsstatements.org/vocab/InC/1.0/ All Rights Reserved 2025 189 pages Doctoral Dissertation Academic theses en Zhang, Shaobo Hedman, Kory W Byeon, Geunyeong Ramapuram Matavalam, Amarsagar Reddy Wu, Meng Arizona State University Partial requirement for: Ph.D., Arizona State University, 2025 Field of study: Electrical Engineering The rapid growth of variable energy resources (VER) and distributed energy resources (DER) brings many benefits; at the same time, it presents challenges such as the substantially increased computational complexity, and the increased requirement for operation flexibility. To help tackle these challenges, this research studies algorithmic improvements to region-based decomposition algorithms for security constrained unit commitment (SCUC), and proposes enhancements to the formulation of Do-Not-Exceed limits that measures flexibility from operation reserves. Regarding the modeling of transmission constraints in SCUC, the computational advantage of the shift-factor formulation over the phase-angle formulation has not been fully explored in region-based decomposition algorithms. This research studies two strategies depending on the degree of decomposition. For small degrees of decomposition, the strategy is to reformulate the transmission constraints in each region with regional shift factors. The second strategy is to directly decompose the shift-factor formulation by exploiting the sparsity in the shift-factor matrix and active transmission constraints. Numerical results on a 3012-bus test case show that both strategies improve the computational speed. Furthermore, the full N-1 transmission contingencies are represented through constraint screening. A warm start strategy is proposed for the incremental changes from the screening process. The nonconvexity of SCUC problems causes oscillation problems. Thus, this research proposes a dynamic overlapping decomposition scheme. Regions are expanded to include foreign generators with significant PTDF influence on the oscillating lines. Simulation results show that the overlapping approach removes most of oscillation units in the 3012-bus test case, which significantly improves the solution quality. The original DNE limit formulation finds the largest uncertainty set that can be accommodated with operating reserves. However, it does not consider the probability distribution of uncertainty, which is critical for characterizing VERs' demand for flexibility. Thus, the obtained DNE limits does not fully capture the flexibility of reserves. This research enhances the original formulation by finding the largest uncertainty set that minimize the expected costs of energy curtailments and reserve shortages. As a result, VER curtailments can be reduced. Also, the sensitivities of the objective can help to determine locations to increase reserves in the long term. Electrical Engineering Computationally Challenging Power System Problems due to Uncertainty: Formulations and Algorithm Advances