Energy and reserve scheduling under ambiguity on renewable probability distribution

Publication Type

Journal Article

Date Published





This paper presents a novel methodology to devise a least-cost energy and reserve scheduling under uncertainty in renewable energy sources (RES) and equipment outages. The uncertainty in renewable production is accounted for by exogenously simulated scenarios, as customary in stochastic programming, whereas outages of generators and/or transmission lines are addressed via adjustable robust optimization. The precise characterization of the RES output by means of a unique probability distribution is a challenging task. Hence, we provide a general formulation that allows the consideration of a set of “credible” probability distributions. In this manner, the system operator's ambiguity aversion to uncertainty in renewable production is accounted for. Our proposed methodology determines the least-cost energy and reserve scheduling through a three-level model. Structurally, the upper level defines a least-cost scheduling and, under uncertainty in renewable production, the middle level identifies the worst contingency for the given operating point. The lower level then utilizes the scheduling provided by the upper-level to determine the best redispatch. In order to control the system equilibrium, we adapt risk constraint techniques to handle the system imbalance uncertainty and ensure a reliable operating level. To solve the multi-level problem, we propose an algorithm that combines Benders decomposition and column-and-constraint generation techniques to approximate the risk measure while scheduling power and reserves. The effectiveness of the proposed model and the importance of considering ambiguity are demonstrated through a case study with real data from the Great Britain power system network.


Electric Power Systems Research



Year of Publication