Since the model presented in the report is not developed in the context of a system, the nature of the complications introduced by system interdependence are not considered. This particular feature of the report should be viewed with some caution, since the implications generated by not incorporating this interdependence are indeed fundamental.

Accompanying this foreword is a Power System Planning Chart (Figure 1) depicting a general scheme by which the choice can be made of a plant program which minimizes the entire system cost subject to constraints such as meeting specified future demand loads and simultaneously satisfying effluent quality requirements. Cost is defined here as the present worth of all net future expenditures on the construction, maintenance and operation of the generating, transmission and distribution system. The general investment (not strictly location) model in the context of the system is strategic rather than tactical; it relates to the decisions that must be made when choosing what types of plants to install and where they should be installed in a given future period. As a result, different types of plant mixes may be examined to determine the most efficient use of the system as a whole.

FIGURE 1.

COSTING MODEL Calculates production costs, adds transmission costs, performs present worth calculations

OUTPUT

Present worth of all future
costs to meet load demand

with specific service
standard

Power System Planning Chart

(Adapted from Westinghouse Eng., Sept. 1960, p. 130)

AN OPTIMAL SITING MODEL FOR THERMAL PLANTS

WITH TEMPERATURE CONSTRAINTS

The choice of location for a power generating station is a function of many complex and interrelated factors, including the locations and types of demand loads to be met, the types of generating facilities available and their capacities, the supply of raw fuel, the transmission of energy produced, the disposal of wastes and various political and aesthetic constraints. For water-cooled thermal plants, it is important that the generating stations be located near water bodies that have adequate cooling capacity.

On a small stream, or in areas of high thermal waste loads, the heat discharged may have environmental effects which make the receiving water less serviceable to some of its other users. To protect against this possibility, governmental agencies are establishing temperature standards for many receiving waters. Plant siting policy with regard to water temperature standards may take several forms: (a) alternative cooling facilities may be incorporated at each plant site in order to reduce the heat load reaching the water body; (b) smaller plants in greater number may be dispersed along the water body in order to lessen the heat impact at any particular point; or (c) some combination of these two alternatives may be selected.

The type of temperature standard* may affect the location decision. For example, a particular set of alternatives might be chosen if the standard specified a maximum permissible absolute temperature for the receiving water, whereas if the standard was expressed in terms of a maximum permissible excess above its normal ambient temperature, then a different set of alternatives may prove to be optimal. Both of these optimal solutions might be dependent on regulatory policies concerning compliance with maximum temperature standards during statistically extreme weather conditions. The type of temperature standard may also influence the type of abatement equipment used, as well as the location selected, depending on the cost trade-offs involved.

The task is to search among the many combinations of feasible alternatives to find that set which, for the least overall cost, satisfies both the demand loads and the temperature standards. This report presents an approach by which the environmental aspects of this task may be taken into account.

Before describing the optimal siting models in detail, it is important to appreciate the nature of their capabilities. The staffs of both utilities and regulatory agencies involved in plant siting decisions need a great deal of information in order to decide upon an appropriate course of action at any time. Answers to many questions must be sought,

*The uniform application of standards, as used in this report, is for purposes of illustrations only, and is not necessarily considered optimal from an economic standpoint. For efficient management of water resources, the costs of extra treatment should be balanced against the downstream benefits derived from higher quality effluents. It is evident that different kinds and levels of treatment might be justified depending upon other uses of the water. These could vary from region to region and from time to time, so that the application of fixed standards might result in undesirable inefficiencies, i.e., too much or too little treatment in light of the benefits and costs perceived in a region.

such as (a) How sensitive is the decision criterion to errors in estimating such items as property values, fuel prices, transmission costs and future demand loads?, (b) Which type of stream temperature standard affects the optimal location pattern most?, and (c) How much does compliance with temperature standards cost? The optimal siting models presented in this report may be used to examine all of these questions, particularly by manipulating the input data and constraints in such a way as to show how environmental quality standards affect the optimal location pattern and consequently the cost of satisfying the demand loads. Thus, the role of the models is to provide additional information to assist the decision-maker faced with a major investment in plants which can affect the environment.

Three siting models are presented in this report. The first, which is described in the main body of the report, is a zero-one integer model. Although this model is somewhat restrictive in its assumptions (see Section 2.2), it has the advantage of a readily available solution technique. The other two less restrictive models, a mixed integer model and a probabilistic model, are formulated and discussed in

Appendix C, although working solutions for these less restrictive models are not yet available.