Improving operating policies in stochastic optimization: an application to the medium-term hydrothermal scheduling problem

Abstract

In decision-making under uncertainty, a robust representation of uncertainty is vital for optimal operational and strategic solutions. We extend existing methods by utilizing Fourier decomposition to create multivariate synthetic time series, capturing stochastic seasonal patterns while preserving correlations. These synthetic time series are transformed into a recombining scenario tree via K-means clustering. To enhance the resulting policy in the Stochastic Dual Dynamic Programming (SDDP) framework, we propose an additional sampling within scenario-tree nodes to consider a better representation of the cost-to-go function. A convergence proof for this sampling technique is provided. Moreover, two new stopping criteria are introduced for better solution accuracy and robustness. The first criterion extends traditional stopping rules to all scenario-tree nodes. The second criterion enforces a minimum count of Benders cuts per node, promoting accurate and robust solutions. Our approach is evaluated on the Spanish hydrothermal system, incorporating synthetic time series with seasonal-trend uncertainty in optimization and simulation. Policies from traditional SDDP and our technique were tested over a thousand realizations, demonstrating that our proposals yield reservoir operation policies closer to the thresholds set by the operator compared to traditional SDDP. Computational efficiency is maintained. The proposed sampling mitigates the impact of discretizing stochastic variables into scenario trees by evaluating more scenarios per node. Our framework offers robust policies under uncertainty through stochastic seasonal patterns by Fourier analysis, novel SDDP sampling, and additional stopping criteria.