Nonconvex Environmental Constraints in Hydropower Scheduling

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 capture. This paper describes how the recently developed stochastic dual dynamic integer programming (SDDiP) method can incorporate nonconvex environmental constraints in the medium-and longterm scheduling of a hydropower system in a liberalized market context. A mathematical model is presented and tested in a multireservoir case study, emphasizing on the improvements observed when accurately modelling a particular type of nonconvex environmental constraint.

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

“…A few studies also consider accurate modelling of non-convexities by the use of SDP [18] or stochastic dual dynamic integer programming (SDDiP), such as in Refs. [19,20].…”

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

“…The challenge of representing nonconvex relationships in the SDDP algorithm has frequently been addressed in the literature by the use of approximations, e.g [14]- [17]. A few studies also consider accurate modelling of non-convexities by the use of SDP [18] or stochastic dual dynamic integer programming (SDDiP), such as in [19] and [20].…”

“…The impact of volumedependent maximum discharge in medium-term scheduling has previously been studied in [20] using SDDiP. Compared to [20], we take a broader view of state-dependencies and study a version of the maximum discharge constraint that includes dependencies on both inflow and reservoir volume. Furthermore, we apply an algorithm (SDP) that explicitly handles non-convexities, separating our work from both [30] and [20].…”

“…Compared to [20], we take a broader view of state-dependencies and study a version of the maximum discharge constraint that includes dependencies on both inflow and reservoir volume. Furthermore, we apply an algorithm (SDP) that explicitly handles non-convexities, separating our work from both [30] and [20]. We give a thorough description of the complicating elements of the constraint and elaborate on how to accurately model this type of state-dependent constraint in an SDP-based scheduling model.…”

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

“…The purpose of the constraint is to retain inflow during spring, to meet the needs of ecological habitat and recreational use for high water levels in the reservoir through summer. The impact of volumedependent maximum discharge in medium-term scheduling has previously been studied in [20] using SDDiP. Compared to [20], we take a broader view of state-dependencies and study a version of the maximum discharge constraint that includes dependencies on both inflow and reservoir volume.…”