A Stochastic Dynamic Programming Model for Hydropower Scheduling with State-dependent Maximum Discharge Constraints

<div>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%.</div>

A Stochastic Dynamic Programming Model for Hydropower Scheduling with State-dependent Maximum Discharge Constraints

<div>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%.</div>

Ensemble of constraint-handling techniques for solving reservoir scheduling problems

Reservoir scheduling based on evolutionary algorithms needs to handle potentially stringent physical and operational constraints. Both generic and reservoir scheduling problem-specific constraint-handling techniques (CHTs) have their own merits and limitations. No CHT currently available can yield better solutions than the others consistently. To ensure good reservoir operation schedules, we develop an ensemble of CHTs (ECHT) that can utilize the advantages of different individual CHTs. In the ensemble, each CHT has its own population. In every generation, the different offspring populations are mixed together and evaluated. Each CHT then assigns fitness to all individuals and selects some of them to form its new parent population. The ECHT has been tested against long-term hydropower scheduling of two large-scale reservoir systems in China. Results show that the ECHT outperforms the state-of-the-art CHTs, and its probability of returning feasible solutions is much higher. The reservoir levels optimized with the ECHT are well suited for hydropower generation, which also reduce the chance of reservoir spilling.