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Optimizing power system investments is a complex network optimization challenge, involving a vast and growing system governed by non-convex physics and subject to significant uncertainty. The diversity of generation technologies and configurations introduces many binary decisions, requiring model simplifications to ensure tractability. As the grid evolves with new technologies and shifting demand patterns, past assumptions may no longer hold, necessitating new approaches to investment planning that enhance resilience and efficiency.
This work develops methods for optimizing long- and medium-term grid investments under uncertainty. We first address long-term transmission-level capacity expansion, balancing cost with resilience to extreme events. We propose a conditional sampling technique to reduce the number of scenarios needed to capture high-impact, low-frequency risks, incorporating it into a bi-objective optimization framework. We also introduce a statistical model for generating spatially correlated extreme temperature scenarios. A large-scale case study shows that conditional sampling helps effectively identify cost-risk tradeoffs and that modeling temperature dependence and spatial correlation significantly affects investment decisions.
At the distribution level, we propose a model for medium-term investment in distributed energy resources and control devices to enhance reliability during outages, and we develop a scalable solution using network flow approximations and Benders decomposition. The model balances reliability improvements during outages with normal-operation cost savings from resources like distributed solar. We find that the network flow approximation offers effective guidance for planning decisions and that small adjustments to operational policies can significantly affect the accuracy of the approximation and the efficiency of computation.