An efficient robust optimization model for the unit commitment and dispatch of multi-energy systems and microgrids

Multi-energy systems and microgrids can play an important role in increasing the efficiency of distributed energy systems and favoring an increasing penetration from renewable sources, by serving as control hubs for the optimal management of Distributed Energy Resources. Predictive operation planning via Mixed Integer Linear Programming is an effective way of tackling the optimal management of these systems. However, the uncertainty of demand and renewable production forecasts can hinder the optimality of the scheduling solution and even lead to outages. This paper proposes a new Affinely Adjustable Robust Formulation of the day-ahead scheduling problem for a generic multi-energy system/microgrid subject to multiple uncertainty factors. Piece-wise linear decision rules are considered in the robust formulation, and their potential use for real-time control is assessed. Novel features include an ad hoc characterization of the polyhedral uncertainty space aimed at reducing solution conservativeness, aggregation of uncertain factors and partial-past recourse which allows speeding up the computational time. The advantages and limitations of the Affinely Adjustable Robust Formulation are thoroughly discussed and quantified through artificial and real-world test cases. The comparison with a conventional deterministic approach shows that, despite the limitations of the affine decision rules, the adjustable robust formulation can ensure full system reliability while attaining at the same time better performances.