As we have seen, the aim of all optimizations is to minimize the cost of the energy produced by the plant. This cost includes investment cost, fuel costs, operating expenses, taxes, etc.

The reactor physicist is usually only concerned with the fuel-cycle-cost calculation, although the influence of core parameters on other investment costs must be taken into account in the optimization (e. g. the influence of the core power density on the pressure vessel size).

Expenditures and returns are strongly time dependent. For each segment of fuel expenses start long before this fuel produces energy, and continue after discharge from the reactor. Revenues are obtained from the sale of energy and in some cases from the sale of discharged fuel. Besides these costs usually change during the reactor lifetime.

The fuel cycle cost is the cost at which energy must be sold in order to recover all the expenses related to the fuel consumption and ownership. The correct value of this cost makes the total present worth of the incomes equal to the total present worth of the expenditures.

The present worth P of a payment R is defined as

P = R(l + iTy (10.18)

where і is the interest rate and у is the number of years after which the payment is made. This formula is a recognition of the fact that an interest has to be paid on money.

The factor

F = (l + iTv (10.19)

is known as “present worth factor” or “discount factor”. A discussion of the present worth method can be found in ref. 15. If interests are compounded more frequently than annually, expressions (10.18) and (10.19) are still valid if і is the interest per time period and у is the number of periods.

In order to compare fuel cycles involving slight time displacements (e. g. the difference between a cooling time of 100 or 120 days for spent fuel) the method of continuous discounting can be used."6’ The time period is divided in n intervals and the

Fig. 10.2. Time sequence of typical fuel segment (from GA-A10593).

fictitious annual interest g is introduced so that

•■—КГ

The new interest rate per period is not і In because continuous compounding would then make the annual interest greater than i. The expression for continuous compound­ing is then obtained if n -»30:

or

(1 + /) [ — e 8t (10.20)

so that

g = In (1 + і) (10.21)

and expression (10.19) is substituted by

F= e

With the present worth method all expenditures and revenues are referred to an arbitrary reference time, which is often taken to be the reactor start-up.

A difficulty may be posed by the definition of the interest rate to be used in this method. This interest must take into account taxes and the fraction of the investment represented by stocks and by bonds, each with their own required rates of return.