Nonconvex Medium-Term Hydropower Scheduling by Stochastic Dual Dynamic Integer Programming

Abstract

Hydropower producers rely on stochastic optimization when scheduling their resources over long periods of time. Due to its computational complexity, the optimization problem is normally cast as a stochastic linear program. In a future power market with more volatile power prices, it becomes increasingly important to capture parts of the hydropower operational characteristics that are not easily linearized, e.g. unit commitment and nonconvex generation curves.Stochastic dual dynamic programming (SDDP) is a stateof-the-art algorithm for long-and medium-term hydropower scheduling with a linear problem formulation. A recently proposed extension of the SDDP method known as stochastic dual dynamic integer programming (SDDiP) has proven convergence also in the nonconvex case. We apply the SDDiP algorithm to the medium-term hydropower scheduling (MTHS) problem and elaborate on how to incorporate stagewise dependent stochastic variables on the right-hand sides and the objective of the optimization problem. Finally, we demonstrate the capability of the SDDiP algorithm on a case study for a Norwegian hydropower producer.The case study demonstrates that it is possible but timeconsuming to solve the MTHS problem to optimality. However, the case study shows that a new type of cut, known as strengthened Benders cut, significantly contributes to closing the optimality gap compared to classical Benders cuts.

Medium-Term Hydropower Scheduling with Variable Head under Inflow, Energy and Reserve Capacity Price Uncertainty

“…The work carried out in this paper is based on earlier work on developing improved methods to solve the MTHS problem, as in [7,16]. The main contributions are:…”

“…Similar behavior might also be imposed by environmental constraints, such as minimum discharge limits for certain periods of the year. While operating at low power outputs, the linear optimization model will observe a higher power output than what is physically feasible and thus overestimate the system's potential profit, as discussed in [7,16]. This overestimation can be avoided by more accurate modeling of the generation function.…”

“…Thus, the aim for the long-term reservoir is to store as much water for usage in the most remunerated hours during the year, while the short-term reservoirs need to be properly managed in order to avoid spillage. This system was also used as a study case in [7,24].…”

“…The MTHS problem normally covers a planning horizon of one to three years, aiming at maximizing a single producer's expected profit. We have from ongoing research experienced that SDDiP requires considerably more computational force than SDDP [7]. Nevertheless, an improved type of the Benders (B) cuts, called strengthened Benders (SB) cuts, derived from the SDDiP method, show promising results by improving the convergence of the algorithm with a reasonable increase in computation time.…”

Medium-Term Hydropower Scheduling with Variable Head under Inflow, Energy and Reserve Capacity Price Uncertainty

“…In this work we investigate how improvements in the SDDP algorithm, derived from the Stochastic Dual Dynamic integer Programming (SDDiP) algorithm [6], can be used to improve the Medium-Term have from ongoing research experienced that SDDiP requires considerable more computational force than SDDP [7]. Nevertheless, an improved type of the Benders (B) cuts, called Strengthened Benders (SB) cuts, derived from the SDDiP method, show promising results by improving convergence of the algorithm with an reasonable increase in computation time.…”