Energy-secure hydropower scheduling using adaptive distributionally robust optimization

Operational planning in power systems is increasingly challenging due to growing levels of uncertainty. In this context, long-term hydro-thermal scheduling should effectively assess system flexibility and provide robust reservoir operation policies that are cost-efficient for a wide range of future scenarios. Compared to traditional multi-stage formulations, solving two-stage stochastic problems within a rolling horizon framework reduces computational complexity and enables more flexible and detailed system modeling. However, approaches based on stochastic programming operate under the premise that the underlying probability distributions are accurately identified, even though future scenarios may be inherently uncertain. Moreover, hydropower scheduling based on stochastic optimization models that focus on minimizing expected costs (or maximizing social welfare), may result in reservoirs being managed quite aggressively. Both aspects can result in operational strategies that are vulnerable to unexpected events in an increasingly uncertain future. To ensure the robustness of the scheduling scheme, we provide a distributionally robust formulation of the problem and compare its performance against a risk-neutral stochastic model, a risk-averse formulation based on Conditional Value-at-Risk and a robust optimization model. To assess the quality of the policies obtained under the different modeling approaches, we perform both in-sample and out-of-sample analyses. Our findings show that distributionally robust policies align more closely with operational practice and offer enhanced protection against both dry and wet hydrological conditions.