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 state-of-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 time-consuming 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 close the optimality gap compared to classical Benders cuts.

This paper describes a method for optimal scheduling of hydropower systems for a profit maximizing, price-taking, and risk neutral producer selling energy, and capacity to separate and sequentially cleared markets. The method is based on a combination of stochastic dynamic programming (SDP) and stochastic dual dynamic programming (SDDP), and treats inflow to reservoirs and prices for energy and capacity as stochastic variables. The proposed method is applied in a case study for a Norwegian watercourse, quantifying the expected changes in schedules, and water values when going from an energy-only market to a joint treatment of energy and reserve capacity markets.

This study describes a model for optimal scheduling of hydro thermal systems with multiple hydro reservoirs. Inflow to hydropower reservoirs, wind power and exogenously given prices are treated as stochastic variables. Power flow constraints are included through a linearised power flow model. A linearised representation of start‐up costs for generating units and pumps is provided. The model is well suited for medium‐ and long‐term hydro thermal generation scheduling and has the capability of capturing detailed system constraints by using a fine time resolution. The presented model is tested on a realistic representation of the Icelandic power system, considering some potential future system extensions.

The authors describe a method for long‐term hydro‐thermal scheduling allowing treatment of detailed large‐scale hydro systems. Decisions for each week are determined by solving a two‐stage stochastic linear programming problem considering uncertainty in weather and exogenous market prices. The overall scheduling problem is solved by embedding such two‐stage problems in a rolling horizon simulator. The method is verified on data for the Nordic power system, studying the incremental changes in expected socio‐economic surplus for expansions in both the transmission and generation systems. Comparisons are made with a widely used existing long‐term hydro‐thermal scheduling model. The results indicate that the model is well suited to valuate the flexibility of hydropower in systems with a high share of intermittent renewable generation.

Maintenance scheduling is an important and complex task in hydropower systems. In a liberalized market, the generation company will schedule maintenance periods to maximize the expected profit. This paper describes a method for hydropower maintenance scheduling suitable for a profit maximizing, price-taking and risk neutral hydropower producer selling energy and reserve capacity to separate markets. The method uses Benders decomposition principle to coordinate the timing of power plant maintenance with the medium-term scheduling of the hydropower system, treating inflow to reservoirs and prices for energy and reserve capacity as stochastic variables. The proposed method is applied in a case study for a Norwegian watercourse, and results, in terms of maintenance schedules and computational performance, are presented and discussed.