To a large extent, electricity markets worldwide still rely on deterministic procedures for clearing energy and reserve auctions. However, increasing shares of the production mix consist of renewable sources whose nature is stochastic and non-dispatchable, as their output is uncertain and cannot be controlled by the operators of the production units. Stochastic programming models allow the joint determination of the day-ahead energy and reserve dispatch accounting for the uncertainty in the output from these sources. However, the size of these models gets quickly out of hand as a large number of scenarios are needed to properly represent the uncertainty. In this work, we take an alternative approach and cast the problem as an adaptive robust optimization problem. The resulting day-ahead energy and reserve schedules yield the minimum system cost, accounting for the cost of the redispatch decisions at the balancing (real-time) stage, in the worst-case realization of the stochastic production within a specified uncertainty set. We propose a novel reformulation of the problem that allows considering general polyhedral uncertainty sets. In a case-study, we show that, in comparison to a risk-averse stochastic programming model, the robust optimization approach progressively trades off optimality in expectation with improved performance in terms of risk. These differences, however, gradually taper off as the level of risk-aversion increases for the stochastic programming approach. Computational studies show that the robust optimization model scales well with the size of the power system, which is promising in view of real-world applications of this approach. 
A robust optimization approach to energy and reserve dispatch in electricity markets