2.5 Specifications for Input Information

(a) Intercept Cost for Production, F1

i

The intercept cost represents the hypothetical expenditure required to establish and operate a generating facility, excluding those expenditures which depend on the plant generating capacity. For any site, the value of F, is evaluated by plotting total plant costs (sum of capital costs and operating costs during the expected plant lifetime) versus generating capacity for several plant sizes, and by extrapolating the straight line of "best fit" back to zero generating capacity (see Figure 8 in Appendix B).

(b) Load-Dependent Costs

For each plant site and load center, these costs comprise the sum of three components (for production, transmission and distribution) each of which is expressed as a product of the load center demand, and the appropriate cost rate for that component. The

cost rates are evaluated as follows:

(1) Load-Dependent Production Cost Rate,

For each plant site, the load-dependent production cost rate

is the slope of the straight line referred to in paragraph (a) above, expressed in units of cost per unit of plant generating capacity.

(2) Transmission Cost Rate, Tij

For each plant site and load center, the transmission cost rate is evaluated by dividing the total transmission costs (sum of capital costs and operating costs during the expected lifetime) by the capacity of the transmission line.

(3) Distribution Cost Rate, Dj

For each load center, the distribution cost rate is evaluated

59-068 - 71 pt. 3 ---8

by dividing the total distribution cost by the capacity of the dis

tribution system.

(c) Temperature Transfer Coefficients. A

In order to use the temperature constraint feature of the model, it is necessary to predict the effect of each thermal discharge on the temperature of the receiving water body at one or more designated sampling stations. For each plant alternative and sampling station, the temperature transfer coefficient, Ak represents the residual fraction of any initial excess temperature at the plant discharge location that would be expected to reach the sampling station (taking into account the various processes of advection, mixing and cooling). In the case of a relatively simple flow situation, such as a river, the estimation of typical transfer coefficients is exemplified in the subroutines described in Appendix B. For more complex receiving water bodies, the user must provide such data. One should expect the transfer coefficient values to depend on environmental conditions, such as quantity of flow, meteorological conditions, etc. Whether or not this dependence is sufficiently important to warrant investigation may be tested by running the model with transfer coefficients based on design conditions, and then testing the sensitivity of the solution to changes in the transfer coefficients.

(d) Temperature Rise, R.

For each plant alternative, the temperature rise is evaluated by dividing the excess temperature at the discharge location by the plant generating capacity (taking into account the effect of any proposed supplementary cooling facilities for that plant alternative).

The exact discharge location at which the value of R, is determined is not important, provided that the corresponding temperature transfer coefficients are evaluated in the same terms. For river sites, it is convenient to base R, on the mixed stream temperature (see Appendix B), but for many situations the condenser temperature rise will suffice.

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2.6 Notes on Other Applications of the Model

The model may be adapted with only minor modifications to study air quality standards instead of receiving water temperature standards. To achieve this, the transfer coefficient matrix, Aik, must be redefined and recomputed in terms of air quality criteria at each sampling station due to a unit concentration of pollutant at each discharge location. The parameter R, must also be reconstituted to express the concentration of pollutant at each discharge location divided by the generating capacity of the plant alternative at that site.

The effects of non-quantitative constraints, such as those which might prohibit the use of a particular site for political reasons, may also be evaluated using this model. First, the problem is run as if the site in question is not so constrained. If the optimal solution to this problem selects a plant alternative at that site, the total cost of this solution is noted, and the model is rerun with the plant alternatives at that site omitted. The difference in total costs between the two solutions is then a measure of how much extra the utility (and society) must spend to forgo the use of that particular site.

3. APPLICATION TO A HYPOTHETICAL SITING PROBLEM

3.1 Description of the Sample Problem

In constructing the following synthetic problem, a deliberate attempt has been made to maintain the strictest geometrical simplicity, in order to clarify the interpretation of its solution. Basically, the problem involves satisfying equal demands (of 250 MW) from each of five load centers which are spaced at uniform intervals along a straight river. Only five possible thermal plant sites are considered, one at each load center. At each of these sites there are only two proposed plant alternatives, one with abatement equipment (e.g. cooling ponds or evaporative towers) and one without. General locations of the proposed plant sites and load centers are shown diagrammatically in Figure 2. Note that, in this hypothetically simplified case, transmission costs are assumed to be negligible between each plant site and its corresponding load center at the same location.

Plant alternatives numbered 1 and 2 are located at Site 1, which is the most upstream load center, and the others are paired in sequence downstream, the furthest being plant alternatives 9 and 10 at Site 5. Thus, for computing purposes, the plant alternatives at each site may be coded simply by specifying the number of the first plant alternative at each site (e.g. NFSITE(1) 1, NFSITE(5) = 9).

=

Estimates of the input cost parameters for the problem are developed in detail in Appendix B. In summary, the production costs are characterized by a relatively small "intercept cost" (F,

=

i

$60,000 per