Stepwise Flood Routing for Gated Reservoirs and Conjunctive Optimization of Hydroelectricity Income with Flood Losses

A six-stage operation policy for routing of flood hydrographs of return periods from 1.01 year up to the Probable Maximum Flood (PMF) for dams having gated spillways is suggested. The gate opening rules are determined based on the recent pool level. Without having to predict the magnitude of the incoming flood hydrograph beforehand, the fixed rules of the six-stage operation policy will provide optimum routing for any floods, which are classified into six different groups based on their return periods. 10-, 100-, 1,000-, 10,000-, 100,000-year floods, and PMF are the design hydrographs for the six groups. A definite gate opening is valid in each stage whose upper boundary is specified by a critical lake elevation. The gate opening and the critical lake level of each stage is calculated by a sequential optimization scheme based on routing of all the floods of six groups. When the PMF is routed, the rising and falling limbs of the outflow hydrograph appear like a six-step staircase each making sudden jumps and sudden drops at definite times and smoothly varying between steps. The theme of this study is twofold: 1. to reduce reliance on early flood warning systems, and 2. to reduce human intervention on gate operations during actual floods. Once such a model could be determined, it would have the advantage of being suitable for all kinds of floods from very small ones up to the PMF. Another spillway gates are automatically operated during multi-peaked floods still in an optimum way, with no need for human intervention. The optimum gate operation rules of multi-stage routing could be programmed beforehand and the gates could be adjusted automatically by a computer linked to the lift mechanism during any floods. The stepwise gate operation model devised for a six-stage case in this study can be extended up to ten stages, for example, for a more refined control of floods. Separately, an Incremental Dynamic Programming program is developed to optimize both the firm and secondary energies at monthly periods. Firstly, the six-stage flood routing program is applied sequentially to Yedigoze, Catalan, and Seyhan Dams, all on Seyhan River in Turkey, at half-hourly time increments for 18 combinations resulting from different active storages, and optimum six-stage operation policies for all the three dams are determined. Secondly, the Dynamic Programming program is applied again to these three dams with 18 combinations, using 20 number of 50-year long synthetic monthly flow data generated by HEC-4, which provides a 20-element sample series of optimized hydroelectric energy produced. Finally, the optimum active and flood retention storages for the three dams are determined so as to maximize the net difference of probability-weighted present worths of (hydroelectricity income)-(flood damage cost).