A Planner-Trader Decomposition for Multimarket Hydro Scheduling

Peak/off-peak spreads on European electricity forward and spot markets are eroding due to the ongoing nuclear phaseout in Germany and the steady growth in photovoltaic capacity. The reduced profitability of peak/off-peak arbitrage forces hydropower producers to recover part of their original profitability on the reserve markets. We propose a bilayer stochastic programming framework for the optimal operation of a fleet of interconnected hydropower plants that sells energy on both the spot and the reserve markets. The outer layer (the planner’s problem) optimizes end-of-day reservoir filling levels over one year, whereas the inner layer (the trader’s problem) selects optimal hourly market bids within each day. Using an information restriction whereby the planner prescribes the end-of-day reservoir targets one day in advance, we prove that the trader’s problem simplifies from an infinite-dimensional stochastic program with 25 stages to a finite two-stage stochastic program with only two scenarios. Substituting this reformulation back into the outer layer and approximating the reservoir targets by affine decision rules allows us to simplify the planner’s problem from an infinite-dimensional stochastic program with 365 stages to a two-stage stochastic program that can conveniently be solved via the sample average approximation. Numerical experiments based on a cascade in the Salzburg region of Austria demonstrate the effectiveness of the suggested framework.

Funding: This research was supported by the Ministry of Education, Singapore, under its 2019 Academic Research Fund Tier 3 [Grant MOE-2019-T3-1-010], the National University of Singapore [Grant A-0009135-01-00], and the Swiss National Science Foundation [Grant BSCGI0_157733] as well as the Engineering and Physical Sciences Research Council [Grant EP/R045518/1].

Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2023.2456.