Further reduction, however, has negligible effect on total costs in this case. This apparently erratic sensitivity of the optimal solution to variations in temperature standards emphasizes the importance of using this technique to ensure that arbitrary decisions involving temperature standards are not made without a full appreciation of their consequences.

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3.6 Sensitivity to Variations in Stream Flow

The sensitivity runs involving variations in stream flow were designed to test the dependence of the results of the previous section on the values of the stream flows on which the excess temperature computations are based. An excess temperature standard of 10°F was used for these runs because it was considered to represent a more practical level for this purpose than the 15°F value (which had been arbitrarily inflated for the first set of runs in order to ensure that the basic solution would be unconstrained):

Runs 28 to 32 in Table IV, plotted in Figure 7, indicate that reducing the stream flow from 3000 cfs to 500 cfs involves four shifts in optimal solution pattern and similar increases in total costs to those observed in the preceding section. A comparison of Figures 6 and 7 shows that both tests began with the basic pattern B and shifted through patterns C and F to pattern H as conditions in the stream became more restrictive. It is apparent, therefore, that both stream flows and maximum permissible temperatures warrant a similarly high degree of attention.

Ultimately, it would be desirable to base the maximum temperature considerations on a low flow with a specified probability of occurrence (rather than to choose a historical low flow, which may be statistically extreme) and to test the optimal siting model for sensitivity to temperature criteria at this level. For discussion of a proposed siting model with such probabilistic temperature constraints, the reader is referred to Appendix C.

Notes:

STREAM FLOW (cfs)

4. SUMMARY

The results of this study demonstrate that physical factors which influence the siting of proposed generating plants in a localized electric power system can be successfully modelled in mathematical form. Such models can be used to obtain information concerning the sensitivity of their optimal solutions to various cost and environmental factors, which results in a generally improved understanding of the system as a working unit.

In particular, the zero-one integer model has been developed for use in determining the optimal choice of locations for thermal generating plants in a sample problem, based on the lowest total cost of satisfying the demand for power in a given region. This application has demonstrated that, in the sample problem, the optimal solution depends critically and unpredictably on the temperature constraints assumed for the receiving water body.

Such an analysis can be of inmense value to public regulatory agencies and industry executives faced with siting decisions.

Work on the less restrictive but currently unsolved mixed-integer and probabilistic models is the next step in the development of optimal siting models for thermal plants with temperature constraints. This constitutes a current objective of the physical program of the EEI Cooling Water Discharge Project.