Medium-term stochastic hydrothermal scheduling with short-term operational effects for large-scale power and water networks

Andrés Navarro, Marcel Favereau, Álvaro Lorca, Daniel Olivares, Matías Negrete-Pincetic

Research output: Contribution to journalArticlepeer-review


The high integration of variable renewable sources in electric power systems entails a series of challenges inherent to their intrinsic variability. A critical challenge is to correctly value the water available in reservoirs in hydrothermal systems, considering the flexibility that it provides. In this context, this paper proposes a medium-term multistage stochastic optimization model for the hydrothermal scheduling problem solved with the stochastic dual dynamic programming algorithm. The proposed model includes operational constraints and simplified mathematical expressions of relevant operational effects that allow more informed assessment of the water value by considering, among others, the flexibility necessary for the operation of the system. In addition, the hydrological uncertainty in the model is represented by a vector autoregressive process, which allows capturing spatio-temporal correlations between the different hydro inflows. A calibration method for the simplified mathematical expressions of operational effects is also proposed, which allows a detailed short-term operational model to be correctly linked to the proposed medium-term linear model. Through extensive experiments for the Chilean power system, the results show that the difference between the expected operating costs of the proposed medium-term model, and the costs obtained through a detailed short-term operational model was only 0.1%, in contrast to the 9.3% difference obtained when a simpler base model is employed. This shows the effectiveness of the proposed approach. Further, this difference is also reflected in the estimation of the water value, which is critical in water shortage situations.

Original languageEnglish
Article number122554
JournalApplied Energy
StatePublished - 15 Mar 2024
Externally publishedYes


  • Hydrothermal scheduling
  • OR in energy
  • Optimization under uncertainty
  • Renewable energy
  • Stochastic dual dynamic programming


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