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Show Hs - Firm annual release for hydropower from s Fs - Hood storage at s where s » reservoir site index m • M& I demand area index i m litigation demand area index r m reliability index The formulation presumes that the active storage capacity Ss for the reservoir s may be functionally evaluated given a candidate set of releases from the reservoir, by simulating monthly reservoir operation over a historical or synthetic streamflow record at the site. Unlike Loucks et al ( 1981), active storage capacity is not solved for in terms of within- year and over- the- year capacity. The simulation of monthly reservoir operation obviates the need for this distinction. The total storage capacity of the reservoir is then represented as a combination of the active, conservation and flood storages. It is also presumed that a determination of the optimal size Gs of the hydropower generator at the site may be made independently of the overall optimization process, by analyzing the generator costs and revenue from hydro- energy production. It is further presumed that an exogenous determination of the benefits resulting from a certain level ( storage) for flood control is possible. All system costs and revenues may then be estimated directly as a function of the decision variables ( M& I yields, irrigation yields, hydropower firm releases, conservation and flood storage). The optimization model determines the optimal yields for each purpose, and the optimal levels of conservation and flood storage by analyzing the resulting revenues and costs. A decomposition of the problem by employing simulation to describe functional relations for the reservoir storage cost, flood control benefits, hydropower revenues and costs, and generator size in terms of the decision variables is thus used to achieve a compact nonlinear optimization model. This is in contrast to formulations of the kind reported by Loucks et al ( 1981) that embed monthly or annual reservoir operation as a set of constraints in the optimization model and lead to a large linear optimization model. Procedures for estimating these functional relationships are first described. A formal statement of the resulting optimization model follows. 5.3.1 Active and Total Storage Capacity Determination The sequent peak algorithm ( Loucks et al, 1981, pp. 235- 236) is a relatively simple method for the determination of reservoir storage requirements when inflows and demands are given. One limitation of this scheme as presented in the literature, is its inability to easily model evaporation and other losses and sophisticated operation rules for the reservoir. For the screening model presented in this report, the demands on the reservoir are prescribed at each iteration of the optimization model ( as candidate values of the reservoir yields) and these demands have to be satisfied with contract specified reliabilities. The sequent peak algorithm was used as the basis for the determination of reservoir storage capacity, with modifications to account for evaporation losses. The resulting Modified Sequent Peak ( MSP) Algorithm solves the reservoir sizing problem by recursion. The structure of this algorithm is briefly described here. Define the inflow into a reservoir s in month t as QIstt and the total monthly demand on the reservoir as QRst- The monthly demands QRst on the reservoir can be expressed as: 106 |