Constructing Uncertainty Sets From Covariates in Power Systems

Robust optimization (RO) immunizes against uncertainties in power systems through uncertainty sets that control the robustness and conservativeness of the underlying optimization problem. Despite earlier work in their structure and properties, there are few suggestions on calibrating their size. In this paper, we propose a method to determine (predict) the uncertainty set size using machine learning models and mixed-integer optimization (MIO), leveraging historical data that consist of covariates or features. In essence, we utilize covariates to simultaneously predict the uncertain parameters and construct an uncertainty set around the nominal prediction based on the confidence in the prediction itself. In addition, we introduce optional amendments to our framework so that the uncertainty set bounds are covariate-dependent and also develop an outer approximation scheme for efficiently solving the underlying MIO problem in larger datasets. We apply our framework to uncertainty sets for available wind resource capacity in the Adaptive Robust Unit Commitment (ARUC) problem. We show that our approach gives lower probabilities of constraint violation than commonly used statistical approaches, without necessarily exhibiting an increase in the cost.