Sample-Adaptive Robust Economic Dispatch With Statistically Feasible Guarantees

The high penetration of renewable energy brings significant uncertainty to the power grids. Taking economic dispatch (ED) as an example, the inaccurate prediction of renewable energy generations dramatically increases the dispatch cost and risks the power grid's reliable operation. The accurate distribution knowledge of the renewable generations enables modeling the ED as stochastic programming with joint chance constraints, which various classical methods can tackle. However, in practice, such distribution knowledge is inaccessible, and we can only observe samples from some unknown distribution. This makes conducting effective ED solely based on the observed samples challenging. It is particularly true when we need to handle the joint chance constraints. To tackle these challenges, we introduce the notions of statistical feasibility and statistically feasible ED to guarantee the satisfaction of the joint chance constraints. Specifically, we first propose a sample-adaptive robust optimization (RO) to decouple the joint constraints. We then identify that the inaccurate uncertainty set leads to RO's conservativeness, and then reconstruct the constraint-specific uncertainty sets. We design the corresponding sample-adaptive reconstruction-based RO (ReconRO) based on the reconstructed uncertainty sets to further enhance the ED's effectiveness.