1 Department of Applied Mathematics and Computer Science, Technical University of Denmark2 Dynamical Systems, Department of Applied Mathematics and Computer Science, Technical University of Denmark3 Department of Informatics and Mathematical Modeling, Technical University of Denmark4 University of Castilla–La Mancha
To a large extent, electricity markets worldwide still rely on deterministic procedures for clearing energy and reserve auctions. However, larger and larger shares of the production mix consist of renewable sources whose nature is stochastic and non-dispatchable, as their output is not known with certainty and cannot be controlled by the operators of the production units. Stochastic programming models for the joint determination of the day-ahead energy and reserve dispatch, necessary for coping with the real-time output deviations from these sources, have been proposed in the literature. In this work, we take an alternative approach and cast the problem as an adaptive robust optimization problem. The day-ahead and reserve schedules determined in this fashion yield the minimum system cost, accounting for the cost of the redispatching decisions at the balancing stage, in the worst-case realization of the stochastic production within a specified uncertainty set. In a case-study based on a 24-node system, we assess the degree of suboptimality of the robust solution with respect to the optimal dispatch obtained with a stochastic programming approach, and compare their worst-case cost. Furthermore, we discuss the robustness of these two alternative approaches with respect to changes in the distribution of the uncertainty, as well as their computational properties.
OR in energy; Robust; Optimization; Decomposition; Electricity market; Reserve market; Renewable Energy