Optimal Multipurpose-Multireservoir Operation Model with Variable Productivity of Hydropower Plants

Stochastic dual dynamic programming (SDDP) is one of the few methods available to solve multipurpose-multireservoir operation problems in a stochastic environment. This algorithm requires that the one-stage optimization problem be a convex program so that the efficient Benders decomposition scheme can be implemented to handle the large state-space that characterizes multireservoir operation problems. When working with hydropower systems, one usually assumes that the production of hydroelectricity is dominated by the release term and not by the head (storage) term to circumvent the nonlinearity of the hydropower production function. Although this approximation is satisfactory for high head power stations for which the difference between the maximum and the 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 nonlinear hydropower function through a convex hull approximation of the true hydropower function. A network of hydropower plants and irrigated areas in the Nile Basin is used to illustrate the difference between the two SDDP formulations on the energy generation and the allocation decisions.