Adaptive Robust Optimization with Data-Driven Uncertainty for Enhancing Distribution System Resilience

Abstract: Extreme weather events are placing growing strain on electric power systems, exposing the limitations of purely reactive responses and prompting the need for proactive resilience planning. However, existing approaches often rely on simplified uncertainty models and decouple proactive and reactive decisions, overlooking their critical interdependence. This paper proposes a novel tri-level optimization framework that integrates proactive infrastructure investment, adversarial modeling of spatio-temporal disruptions, and adaptive reactive response. We construct high-probability, distribution-free uncertainty sets using conformal prediction to capture complex and data-scarce outage patterns. To solve the resulting nested decision problem, we derive a bi-level reformulation via strong duality and develop a scalable Benders decomposition algorithm. Experiments on both real and synthetic data demonstrate that our approach consistently outperforms conventional robust and two-stage methods, achieving lower worst-case losses and more efficient resource allocation, especially under tight operational constraints and large-scale uncertainty.