Optimal Hedging Rule for Reservoir Refill Operation

Abstract:

This paper develops an optimal reservoir Refill Hedging Rule (RHR) for combined water supply and flood operation using mathematical analysis. A two-stage model is developed to formulate the trade-off between operations for conservation benefit and flood damage in the reservoir refill season. Based on the probability distribution of the maximum refill water availability at the end of the second stage, three zones are characterized according to the relationship among storage capacity, expected storage buffer (ESB), and maximum safety excess discharge (MSED). The Karush-Kuhn-Tucker conditions of the model show that the optimality of the refill operation involves making the expected marginal loss of conservation benefit from unfilling (i.e., ending storage of refill period less than storage capacity) as nearly equal to the expected marginal flood damage from levee overtopping downstream as possible while maintaining all constraints. This principle follows and combines the hedging rules for water supply and flood management. A RHR curve is drawn analogously to water supply hedging and flood hedging rules, showing the trade-off between the two objectives. The release decision result has a linear relationship with the current water availability, implying the linearity of RHR for a wide range of water conservation functions (linear, concave, or convex). A demonstration case shows the impacts of factors. Larger downstream flood conveyance capacity and empty reservoir capacity allow a smaller current release and more water can be conserved. Economic indicators of conservation benefit and flood damage compete with each other on release, the greater economic importance of flood damage is, the more water should be released in the current stage, and vice versa. Below a critical value, improving forecasts yields less water release, but an opposing effect occurs beyond this critical value. Finally, the Danjiangkou Reservoir case study shows that the RHR together with a rolling horizon decision approach can lead to a gradual dynamic refilling, indicating its potential for practical use.