Data-Driven Contextual-Aware Uncertainty Set for Robust Dispatch of Power Systems

TL;DR

This paper introduces a data-driven, contextual-aware uncertainty set construction method for robust power system dispatch, leveraging side information and Gaussian mixture models to handle irregular data distributions.

Contribution

It proposes a novel uncertainty set design using conditional Gaussian mixture models and mixed integer reformulation for improved robustness in power dispatch.

Findings

Enhanced robustness in unit commitment under irregular data distributions.

Effective incorporation of side information improves uncertainty modeling.

Numerical experiments demonstrate the method's practical advantages.

Abstract

Both the level of conservativeness and the computational burden in robust optimization are critically influenced by uncertainty set design. However, contextual side information is rarely exploited in robust dispatch of power systems characterized by irregular data distributions, which hinders the explicit characterization of the relationship between covariates and uncertain parameters. To address this issue, a data-driven method for constructing contextual-aware uncertainty set is proposed in this letter. Based on a conditional Gaussian mixture model, a set of covariates is leveraged as side information to design uncertainty sets tailored to historical data exhibiting irregular distributions. The resulting set is formulated as a union-of-subsets formulation, and a mixed integer linear reformulation is adopted to describe the worst-case realization across all subsets. Finally, the effectiveness of the proposed method is demonstrated through numerical experiments applied to robust unit commitment.