Energy and reserve dispatch with distributionally robust joint chance constraints

We develop a two-stage stochastic program for energy and reserve dispatch, which ensures the safe operation of a power system with a high penetration of renewables and a strong interdependence with the natural gas system. Distributionally robust joint chance constraints with Wasserstein ambiguity sets ensure that there is no need for load shedding and renewable spillage with high probability under any distribution compatible with the given statistical data. To make this problem tractable, we solve it in linear decision rules, and we develop a family of conditional value-at-risk (CVaR) approximations for the chance constraints. We show through extensive simulations that the proposed model dominates the corresponding two-stage stochastic program without chance constraints that models the consequences of load shedding and renewable spillage explicitly, both in terms of the mean and variability of the out-of-sample cost.