AN OPTIMAL SITING MODEL FOR THERMAL PLANTS

WITH TEMPERATURE CONSTRAINTS

1. INTRODUCTION

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 leads to be met, the types of genera= ting 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. Te protect against this possibility, governmental agencies are estab= lishing 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 (e) 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.

The siting problem is developed in the following manner. Suppose there are many possible plant sites in or near a region for which estimates of future power demands at load centers within the region have been made. At each of these potential sites, there are several alternative sizes and types of generating facilities that might be built. The costs of providing power for the region involve both the capital costs of constructing generating facilities, transmission lines and distribution systems, and the operating costs involved in fuel supply, equipment maintenance, insurance and taxes, etc. It is evident, therefore, that the total enumeration of all possible combinations of sites, plants and cooling facilities may be an enormous task, perhaps an insurmountable one.

The problem is to find the optimum number, size and location of facilities required to satisfy the given demand loads, in such a manner as to minimize the total cost (i.e., capital costs plus lifetime operating costs) while complying with the following constraints:

(a) the predicted power demands of the region must be

satisfied, and

(b) the temperature standards for the coolant receiving

waters must not be exceeded.

It is recognized that this may appear to be a somewhat idealized concept of the problem, in that its relationship with an existing power system is not defined, and that it approaches the satisfaction of est

imated future demand loads in a "static mode" rather than in the context of a dynamically growing system. It should be remembered, however, that the siting model is not intended to solve a problem by a single, one-run application, but is useful only when the optimality of its solution is tested under various conditions of costs and constraints. When considered in this multiple-run context, with the possibility of testing various time horizons for costs and demand loads, the applicability of the model becomes more apparent.