Approximating Ramping Constraints in Hydropower Scheduling

This work concerns the modeling of ramping constraints on discharge in medium-term hydropower scheduling models applied in a liberalized market context. Such models often apply a coarse time discretization to ensure reasonable computation times. Consequently, ramping constraints at a fine time-resolution are challenging to represent. To address this challenge, we derive a quadratic transition-cost term capturing the power production shifted to time periods with less favorable prices due to ramping constraints. We approximate the quadratic term by linearization so that it can be embedded in an existing hydropower scheduling tool based on stochastic linear programming. A prototype hydropower scheduling model, including the approximated transition-cost term, was tested on a realistic hydropower system in Norway. We demonstrate that the improved modeling of ramping constraints significantly impacts discharge patterns and comes at a significant, but not prohibitive, increase in computation time.