Pick to Learn for Stochastic Economic Model Predictive Control with an Expected Shortfall Constraint

This paper proposes a method to find probabilistic guarantees for a scenario-based stochastic economic model predictive control (SEMPC) scheme with an empirical expected shortfall (EES) constraint. The objective function includes the minimisation of an average economic cost, desirable from an operational perspective, while keeping the risk of high costs under control through satisfaction of the EES constraint. The pick-to-learn (P2L) method is employed to find probabilistic guarantees for the solution of the proposed SEMPC problem. The suggested framework is applied to a water distribution network, and the results show a balance between economic performance and probabilistic guarantees at each time step.