Aquaplan project

Working paper : Variable productivity of hydropower function in Aquaplan model

by Q. Goor¹ , D. Pinte¹ , and A. Tilmant²

¹ Dept of Environmental Sciences and Land Use Planning, Université catholique de Louvain (Louvain-la-Neuve, Belgium)

² Dept of Management and Institutions, UNESCO-IHE (Delft, The Netherlands)

Stochastic Dual Dynamic Programming (SDDP) is an extension of SDP that removes the computational burden found in discrete SDP through sampling and decomposition. In SDDP, the one-stage optimization problem must be a convex program, such as a linear program (LP), so that the Kuhn-Tucker conditions for optimality are necessary and sufficient. When dealing with hydropower systems, one usually assumes that the production of hydroelectricity is dominated by the release term and not by the head term to circumvent the non-convexity of the hydropower production function. Although this approximation is satisfactory for high head power stations where the difference between the maximum and minimum head is small compared to the maximum head, it may no longer be acceptable when a significant portion of the energy originates from low and/or medium head power plants. Recent developments improve the representation of the non-linear and mildly non-convex hydropower function through a convex hull approximation of the true hydropower function. A cascade of hydropower plants in the Nile basin is used to illustrate the difference of the two SDDP formulations on the release decisions.