Magee, T., E. Zagona and M. Clement (2014). “Efficient methods for Optimizing Under Uncertainty.” In Proceedings of the 11th International Conference on Hydroinformatics, New York City, August 17–21, 2014.


There are several sources of uncertainty in scheduling hydropower: reservoir inflows, power generation, demand and value, and the value of water remaining in storage at the end of the planning horizon. RiverWare is an object oriented modeling tool widely used for the operations and planning of large and small systems of reservoirs. Typically, short term optimization of hydropower is complicated by the need to meet a wide variety of prioritized non-power constraints and RiverWare is designed to satisfy these constraints to the extent possible. We present four different approaches that use deterministic methods combined with uncertainty models to efficiently optimize scheduling using RiverWare. 1) Load following reserves were used for coordinating uncertain wind generation with hydropower generation to meet uncertain load. 2) Chance constraints were used to model uncertain hydrologic inflows and inflows from dams controlled by other organizations. 3) Operating policies were designed to dynamic balancing of reservoirs with limited storage and bottlenecks to retain system flexibility while meeting anticipated load fluctuations. 4) Network stochastic programming was used to model alternative hydrologic inflow scenarios that depend on the hydrologic state. Each approach was motivated by and tested on a real system with one or more sources of uncertainty.