Hydropower Scheduling with State-Dependent Discharge Constraints: An SDDP Approach

Abstract

Environmental constraints in hydropower systems serve to ensure sustainable use of water resources. Through accurate treatment in hydropower scheduling, one seeks to respect such constraints in the planning phase while optimizing the utilization of hydropower. However, many environmental constraints introduce state-dependencies and even nonconvexities to the scheduling problem, making them challenging to represent in stochastic hydropower scheduling models. This paper describes how the state-dependent maximum discharge constraint, which is widely enforced in the Norwegian hydropower system, can be embedded within the stochastic dual dynamic programming (SDDP) algorithm for hydropower scheduling without compromising computational time. In this work, a combination of constraint relaxation and time-dependent auxiliary lower reservoir volume bounds is applied, and the modeling is verified through computational experiments on two different systems. The results demonstrate that the addition of an auxiliary lower bound on reservoir volume has significant potential for improved system operation, and that a bound based on the minimum accumulated inflow in the constraint period is the most efficient.

Optimal operation of hydropower systems with environmental constraints on reservoir management

“…The difference in reservoir management and economic performance is found to vary between the different price assumptions. In most cases, the economic loss associated with the constraint is partly reduced when the constraint is included in the medium-term scheduling, as also has been shown in previous research [36,37]. The economic gain from improved planning is found to be strongly dependent on the expected seasonal profile of the power price and the level of price variation.…”

“…Average results for all the cases are given in Table C1 and Table C2 in Appendix C. The above-discussed economic impacts are based on the assumption that the hydropower producers ignore the environmental constraints in the medium-term reservoir scheduling (i.e., do not plan for the constraints in advance). If the producers can include the environmental constraints in the strategy phase, either accurately as discussed here or by the use of approximations as in [37], the associated loss could potentially be reduced.…”

“…Furthermore, an advancement of the SDDP algorithm (SDDiP [34,35]) has been used to model this type of complex constraints in [36], demonstrating that more detailed modelling holds a potential for improved operational decision-making. Finally, the use of a tight linear approximation of the constraint in linear programming based MTHS models has been shown to give a good economic performance in [37].…”

Implications of environmental constraints in hydropower scheduling for a power system with limited grid and reserve capacity

“…If the water level in the reservoir is below a given threshold V lim h for a given period t ∈ T , discharge from the reservoir is restricted to allow only environmental flow requirements by Eq. (35).…”

“…However, such constraints have previously been demonstrated to have a considerable influence on medium-term hydropower scheduling in [33,34]. Furthermore, linear approximations for discharge constraints with dependencies on the water level in the reservoir are suggested in [35].…”