End-to-End Learning of Correlated Operating Reserve Requirements in Security-Constrained Economic Dispatch

Abstract

Operating reserve requirements in security-constrained economic dispatch (SCED) depend strongly on the assumed correlation structure of renewable forecast errors, yet that structure is usually specified exogenously rather than learned for the dispatch task itself. This paper formulates correlated reserve-set design as an end-to-end trainable robust optimization problem: choose the ellipsoidal uncertainty-set shape to minimize robust dispatch cost subject to a target coverage requirement. By profiling the coverage constraint into a shape-dependent radius, the original bilevel problem becomes a single-stage differentiable objective, and KKT/dual information from the SCED solve provides task gradients without differentiating through the solver. For unknown distributions, a four-way train/tune/calibrate/test split combines a smoothed quantile-sensitivity estimator for training with split conformal calibration for deployment, yielding finite-sample marginal coverage under exchangeability and a consistent gradient estimator for the smoothed objective. The same task gradient can also be passed upstream to context-dependent encoders, which we report as a secondary extension. The framework is evaluated on the IEEE~118-bus system with a coupled SCED formulation that includes inter-zone transfer constraints. The learned static ellipsoid reduces dispatch cost by about 4.8\% relative to the Sample Covariance baseline while maintaining empirical coverage above the target level.