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Optimal price-based scheduling of a pumped-storage hydropower plant considering environmental constraints


The paper proposes a novel medium-term scheduling model for a hydropower system composed by a pumped storage hydropower plant connected to a traditional hydropower plant subject to three types of environmental constraints; these deal with the maximum water abstraction from the reservoir thought the turbines and through the pump for energy production, the minimum environmental water flow and the ramping capabilities of water volumes inside the system’s reservoirs. The scheduling problem is formulated for a planning horizon of 1 year with weekly decision stages. The methodology to determine the optimal operation of the plant is based on a stochastic dynamic programming algorithm which allows for an accurate representation of the uncertainties associated to the water inflows and energy prices. Moreover, it facilitates the handling of the non-convex characteristic of the state-dependent constraint on maximum water abstraction from the reservoir. The model is applied to the case of a real hydropower system based on a cascaded watercourse with two conventional hydropower plants in south of Norway to assess the economic benefits of having a pumping unit and the technical impact of the above-mentioned environmental constraints. Furthermore, this work proposes a methodology to analyze the optimal operation of the hydropower system, computed for different temporal resolutions, in order to investigate the techno-economic impact of the constraints involving dependencies on the states of the system, the different environmental constraints and other seasonal effects on the accuracy and the applicability of medium-term scheduling models. Further case studies assess the computational burden and the precision of the results when adopting a finer discretization of the state variables of the dynamic-programming-based methodology. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.


Academic article


  • Research Council of Norway (RCN) / 320794





  • University of Trento
  • Norwegian University of Science and Technology
  • SINTEF Energy Research / Energisystemer
  • Imperial College London



Published in

Energy Systems, Springer Verlag





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