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Show Term 5: Annual Benefits from flood control The routing of floods through the reservoirs was not considered in the applications reported. Neither is the analysis of floods as a function of the probability of exceedance. Flood benefits are idealized as unit annual benefits R4S per unit flood storage provision. This implies an exogenous determination of flood control benefits for each reservoir as a function of storage provided, ( in the general case, a nonlinear relation could be developed and used). This is usually possible. The flood control benefits for the applications performed were expressed as R4S Fs. Such an expression is well suited for the applications presented for the Bear River basin, where the primary area of concern with respect to floods is the Great Salt Lake. The concern in these applications was the reduction of the total volume of flood flows influent into the Great Salt Lake. 5.3.5 Solution of Single Reservoir Optimization Model The optimization model formulated has a nonlinear objective function and nonlinear constraints in terms of the decision variables of the model. The nonlinear functions are defined implicitly through reservoir simulation. Table 5.1 shows the dependence between the objective function and constraints and the decision variables by showing a matrix similar to a coefficient matrix for the linear programming case. Where, a nonlinear programming algorithm ( e. g. Generalized Reduced Gradient, Successive Linear Programming) is used for model solutions, derivatives of the nonlinear functions with respect to the decision variables are evaluated numerically. Table 5.1 reflects the specification to the nonlinear programming algorithm for the evaluation of the Jacobian and the Hessian in terms of the decision variables. As can be seen from Table 5.1 all the nonlinear functions depend on each of the decision variables, leading to a very dense ( 100%) ' coefficient matrix' for the problem. Some of the entries in the table ( e. g. Mr i m with GSC, Fl with FAS) may surprise the reader. A little reflection shows that these are valid. The M& I yield dictates the monthly storages and hence available head and energy production. The generator capacity Gs selected thus depends on the degree of variability induced by Mr im. Similarly the Flood Storage Fl affects the monthly evaporation in the flood season, and could impact the final active storage FAS. The PSLP algorithm of Zhang et al ( 1985) was once again used for model solutions. Execution times for a single reservoir with 3 to 5 yields, hydropower, flood storage provision, and 432 to 660 months of data varied from 0.25 to 2.8 CPU minutes on a GOULD 9080 minicomputer. 5.3.6 Extension to a Multi- reservoir System The general scenario modeled may be illustrated using Figure 5.1 - the configuration for the largest Lower Bear River application reported on in this chapter. We presume that the candidate reservoir sites may exist on the stream system in parallel or in series, and that each is intended to serve specific demand areas for each type of demand. Return flows from each demand area are influent to an identifiable downstream section of the stream system. Local inflows into each site are identified as the difference between the gage flow record at the site and all relevant upstream reservoir site gages. Offstream reservoirs with primary inflows from a diversion from upstream reservoirs are also 114 |