loading page

A Stochastic Dynamic Programming Model for Hydropower Scheduling with State-dependent Maximum Discharge Constraints
  • Linn Schäffer ,
  • Arild Helseth ,
  • Magnus Korpås
Linn Schäffer
Norwegian university of science and technology

Corresponding Author:[email protected]

Author Profile
Arild Helseth
Author Profile
Magnus Korpås
Author Profile


We present a medium-term hydropower scheduling model that includes state-dependent environmental constraints on maximum discharge. A stochastic dynamic programming algorithm is used to enable modelling of nonconvex relationships in the problem formulation. The model is applied in a case study of a Norwegian hydropower system with multiple reservoirs. We find that the maximum discharge constraint significantly impacts the water values and simulated operation of the hydropower system. A main finding is that the nonconvex characteristics of the environmental constraint is reflected in the water values, implying a nonconvex objective function. Operation according to the computed water values is simulated for cases with and without the environmental constraint. Even though operation of the system changes considerably when the environmental constraint is included, the total electricity generation over the year is kept constant, and the total loss in expected profit limited to less than 0.8%.
Jul 2022Published in Renewable Energy volume 194 on pages 571-581. 10.1016/j.renene.2022.05.106