Stochastic unit commitment and reserve scheduling: A tractable formulation with probabilistic certificates

The increased penetration of renewable energy sources to the network highlights the necessity of constructing stochastic variants of the standard unit commitment and reserve scheduling problems. Earlier approaches to such problems are either restricted to ad-hoc methodologies (at the expense of a suboptimal solution), or lead to computationally intractable formulations. In this paper we provide a unified framework to deal with such planning problems for systems with uncertain generation, while providing a-priori probabilistic certificates for the robustness properties of the resulting solution. Our methodology is based on a mixture of randomized and robust optimization and leads to a tractable problem formulation. To illustrate the performance of the proposed methodology we apply it to the IEEE 30-bus network, and compare it by means of Monte Carlo simulations against an algorithm based on a deterministic variant of the unit commitment problem.