Continuous Time Multi-Stage Stochastic Unit Commitment with Storage

Decision models used in wholesale electricity markets are advancing to manage adequately distributed storage on the grid and grapple with increasing stochasticity and variability in net-load. The goal of this paper is to address these three issues jointly, by introducing a continuous-time stochastic multi-stage reserve unit commitment. Compared to the conventional unit commitment (UC) formulation, the one we propose a) accommodates storage devices with limited energy capacity, b) addresses load uncertainty through a multi-variate scenario tree, and c) models, through a piece-wise polynomial approximation, continuous-time changes in load and generation. In numerical simulations, we compare the system operating cost of our approach relative to relaxations of our proposed formulation, including the conventional UC. The comparisons show the relative impact of the three modeling pillars of our formulation, aimed at capturing storage constraints, uncertainty, and ramping events with inter-hourly variations.