Academic Publications

Long-term Hydro-thermal Planning


Malta Oberstufe 2

In their article “Modeling Time-dependent Randomness in Stochastic Dual Dynamic Programming“ [1], Nils Löhndorf and Alexander Shapiro, compare the effectiveness of two prominent approaches on how to represent inflow uncertainty in models of long-term hydropower planning. The planning problem is formulated as a multistage stochastic program and solved with QUASAR®’s dual dynamic programming solver.

Numerical results indicate that discretizing the stochastic inflow process to a scenario lattice yields lower system cost than sample average approximation when evaluating decisions out-of-sample. The article also demonstrates how dynamic risk measures can make the solution of a stochastic programming model robust against the model risk of using a mis-specified stochastic process. 

Interested to see the model in action and learn more about its benefits? Check out our QUASAR Cloud software solution for stochastic hydropower  optimization!
Interested to learn more about how to model and solve a stochastic hydropower optimization problem with QUASAR®?  Check out our interactive hydropower example notebook in Google Colab!


[1] Löhndorf N, Shapiro A. 2019. Modeling time-dependent randomness in stochastic dual dynamic programming. European Journal of Operational Research 273(2), 650-661.