Uncertainty Set Learning for Adaptive Robust Economic Dispatch

In robust optimization for power system operations, striking a balance between solution robustness and performance is crucial. Unlike conventional interval-based uncertainty sets, which treat random variables as independent entities, our approach introduces a compact, coupled representation of these variables. We establish theoretical benchmarks to assess the benefits of employing this coupled uncertainty set in the context of the economic dispatch problem. Moreover, we have devised a pioneering data-driven algorithm capable of autonomously learning the shape of the parametric uncertainty set. This algorithm concurrently optimizes performance and furnishes solutions with statistical guarantees in terms of generalization capabilities. The effectiveness of this algorithm is validated through case studies on both a synthetic dataset and a real-world problem.