A stochastic dynamic programming model for hydropower scheduling with state-dependent maximum discharge constraints

Abstract

We present a medium-term hydropower scheduling model that includes inflow- and volume-dependent environmental constraints on maximum discharge. A stochastic dynamic programming algorithm (SDP) is formulated to enable an accurate representation of nonconvex relationships in the problem formulation of smaller hydropower systems. The model is used to assess the impact of including state-dependent constraints in the medium-term hydropower scheduling on the calculated water values. 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 are 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 is limited to less than 0.8%.