Corresponding author: Viktor M. Dekusar (

Academic editor: Georgy Tikhomirov

The authors propose an approach to the calculation of the levelized unit fuel cost (

Closing the nuclear fuel cycle solves the problem of using in a nuclear power system (NES) a second (in addition to energy) product, i.e., secondary nuclear materials recovered from spent nuclear fuel (SNF). Of the greatest interest among them is plutonium as an additional resource in nuclear power engineering at present. After the depletion of economically affordable natural uranium reserves, plutonium should become the main resource for the further development of the NES. While electric or thermal energy currently has an explicit consumer and is paid for accordingly, the associated plutonium production does not yet have a cash equivalent. At the same time, the costs of plutonium production are actually included in the levelized unit fuel cost (

One of the possible criteria for accounting for plutonium production may be a modified

At the same time, like any manufactured product, plutonium has its own cost, which, on the one hand, must cover the costs of the manufacturer for its production. On the other hand, plutonium, being an efficient energy carrier, due to its neutronic properties, makes it possible to carry out expanded reproduction of nuclear fuel in the fast neutron spectrum. Thus, plutonium-fueled fast reactor technology may actually become a renewable energy source, which is a prerequisite for the development of nuclear power in any foreseeable future.

The developed approach to determining the

This approach has been formulated for the first time.

Let us recall the main provisions of the traditional approach to calculating the

Traditionally, the

Equalization of the reduced income and fuel cycle costs makes it possible to determine the constant reduced specific fuel cost or, in the terminology of works (

The above ratio for calculating the

Let us consider the possibility of taking into account the production of plutonium in an analysis of cash and fuel flows and cost indicators of a NES, as was done in (

The additional income can be determined through the market price of the saved natural uranium. This income can also be obtained by selling the corresponding quantities of enriched uranium or fuel assemblies for thermal reactors, etc., manufactured on the basis of this uranium.

Since the release of uranium takes place throughout the entire life cycle of a nuclear power plant, the additional income should be reduced (discounted) to a specific date in the same way as it is done when fuel costs are determined (

The ratio for the discounted income _{add} received for the entire design service life of a power unit of duration

where _{add} is the is the required additional income obtained by saving natural uranium; _{0} is the base date (usually this is the moment when the reactor is commissioned); _{U} is the unit cost of products entering the market (in this case, it is natural uranium), due to which additional income is provided, $/kg; _{add} is the annual escalation of the unit price of products offered for sale (can be positive, negative or zero); Δ^{U} is the mass of products (natural uranium) that can be supplied to the market annually when thermal reactors are replaced with fast ones; Δ

To simplify the further presentation, we will assume that Δ^{U}(^{t}_{d} t_{0} can be written as

λ_{d}_{es}_{add}). (4)

The obvious (guaranteed) possibility of saving uranium occurs after loading the fuel made on the basis of separated plutonium into the reactor, i.e. at the same time, it is implicitly assumed that the “unsold” plutonium will be replaced by completely marketable uranium. This usually takes place several years after the corresponding SNF batch has been unloaded from the reactor. Consequently, in this case, the value of Δ

It is possible to earn income from the sale of saved uranium even before the corresponding equivalent is obtained in the form of separated plutonium. Moreover, in principle, this can be done even before the commissioning of a nuclear power plant with a fast reactor. This simply requires a stock of uranium in storage. In these cases, the value of

The amount of released natural uranium and the corresponding economic benefit, when thermal reactors are replaced with fast ones, can be determined as a result of mathematical modeling of a specific NES. The result obtained in this case is of a purely private nature, relating only to this NES. At the same time, the most interesting are models that claim to be somewhat versatile.

For this purpose, we shall consider the simplest mathematical model of a NES with a growing installed power. Let us assume that the power generating part of this NES includes only fast reactors of the same type with constant characteristics, operating on mixed uranium-plutonium fuel. Fast reactors are characterized by the secondary plutonium storage coefficient (

We will assume that the increase in the installed capacity of fast reactors in the NES is determined only by the capabilities of the system for the production of plutonium. In this case, additional income is understood as the saved costs that would be incurred by the NES in its development with the achievement of the same power level, but using only thermal reactors and without commissioning fast reactors.

Consider the equations describing the state of the system in time by the number of fast reactors. In this case, we will proceed from the concept of a system of reactors (

The amount of plutonium required to launch one fast reactor with the condition of filling its external fuel cycle is calculated as follows

where _{Pu}^{0} is the initial plutonium loading of the fast reactor, t; _{ext} is the duration of the external fuel cycle, years.

The annual excess plutonium from _{FR}(

where

Then the rate of change in the number of fast reactors is described by the differential equation

with the initial condition _{FR}(0) = _{FR}^{0}.

We will denote

λ_{2} = (_{ext}); (8)

λ_{2} is related to the period of doubling the power _{2} in the system of fast reactors by the ratio

λ_{2} = ln 2 /_{2}. (9)

Then equation (7) can be represented by the expression

which is solved as follows

To determine additional income, we will use formula (3). In this formula, the amount of released natural uranium is determined from the ratio

in which the number of thermal reactors is determined from the condition of equality of power generation at thermal reactors and introduced fast reactors at any time interval

_{TR}(_{TR}×_{TR} = _{FR}(_{FR}×_{FR}.

The number of introduced fast reactors depends on the amount of produced plutonium and is determined by formula (11).

In formula (12) _{FR}×_{FR})/(_{TR}×_{TR}); _{FR}^{0} is the number of fast reactors at time _{0}; _{ТР}^{U} is the annual demand of TR in natural uranium, kg.

After performing the integration in (3), we obtain the following formula for determining the additional income:

In formula (13), the function

where λ = λ_{2} – λ_{d}_{es}_{d}_{es}

The

Then the

The notations here are the same as in the previous formulas.

From here, we can obtain the following relation for the

The first term on the right in expression (15) represents the fuel component in the one-product model (production of electricity only); let us denote it as _{0}.

Then expression (15) can be rewritten as

or

_{0} – Δ(

The value of Δ(

Passing from summation to integration over time and making the necessary transformations, we obtain

where 8766 is the average number of hours per year;

where λ_{d}_{2} = λ_{2} – λ_{d}

Function

Among the variables on which the

The _{2} value (the time of doubling the installed capacity of the fast reactor system) is responsible for the reactor and the fuel cycle. It is determined by the plutonium storage coefficient, the duration of the fuel campaign in the reactor, and the duration of the external fuel cycle. The latter mainly depends on the technological features of the fuel cycle and the radiation characteristics of the irradiated fuel.

Let us consider the application of the described method for calculating the

The calculations are based mainly on the physical and technical characteristics of a high-power power unit, adopted in accordance with (

The following time intervals are accepted: after unloading from the reactor, the SNF is kept for two years in the in-reactor storage, then for one year in the spent fuel pool, and for another year the SNF is reprocessed, fresh fuel is produced and transported. Thus, the duration of the external fuel cycle is assumed to be four years.

The data on fuel loads and unit costs for redistribution of the nuclear fuel cycle were taken from (

The results of calculations of the _{0} at discount rates (^{–3} $).

As can be seen from the data in the table, when the discount rate changes from 0 to 10%, the _{0} first decreases and then slightly increases. The nonmonotonic dependence of the _{0} as a function of the discount rate _{0} of the initial and final stages of the fuel cycle.

Let us consider the effect of saving natural uranium when a VVER-TOI thermal reactor is replaced with a fast reactor of the same power. The _{ТР}^{U} value can be taken equal to 200 tons, which corresponds to approximately 22.5 tons of enriched (4.3% in ^{235}U) uranium per year. The results of calculations of the

As can be seen from the presented results, the production of plutonium makes it possible to obtain serious additional income (from 0.11 to 3.6 B$ depending on the price of natural uranium and the discount rate) by selling the saved natural uranium on the market. Accounting for this income in an equivalent way leads to a noticeable decrease in the _{0}”) and 2 shows that at a price of natural uranium equal to $50/kg, taking into account the production of plutonium reduces the

Figure _{0} values.

At non-zero values of the escalation, a rather strong dependence of the _{2}.

Figure

With an escalation of the price of natural uranium by 5%, the calculations show that the picture does not change qualitatively, but the

The performed computational studies show that for a power unit with a fast sodium reactor and a fuel cycle with a doubling time of about 50 years, a discount rate of 5% and at an initial price of natural uranium of $100/kg and its annual escalation of 3% with zero Δ

Taking into account that the contribution of

_{0} [mills/kWh] for a high-power fast reactor at discount rates of 0, 5 and 10%

Stages of the fuel cycle | |||
---|---|---|---|

Initial | 6.45 | 7.45 | 8.87 |

Final | 3.95 | 1.60 | 1.18 |

Full _{0} |
10.40 | 9.05 | 10.05 |

Technical and economic indicators of a fast reactor of high power, taking into account the market value of the released natural uranium at _{2} → ∞

Uranium price, $/kg | Δ( |
Additional income, B$ | |||||
---|---|---|---|---|---|---|---|

50 | 1.04 | 9.36 | 8.01 | 9.01 | 0.60 | 0.20 | 0.11 |

100 | 2.07 | 8.33 | 6.98 | 7.98 | 1.20 | 0.39 | 0.21 |

150 | 3.10 | 7.30 | 5.95 | 6.95 | 1.80 | 0.58 | 0.31 |

200 | 4.14 | 6.26 | 4.91 | 5.91 | 2.40 | 0.78 | 0.42 |

250 | 5.18 | 5.22 | 3.87 | 4.87 | 3.00 | 0.97 | 0.52 |

300 | 6.21 | 4.19 | 2.84 | 3.84 | 3.60 | 1.16 | 0.63 |

The _{0}(_{0}(_{0}(

The

The authors propose an approach to determining the Levelized Unit Fuel Cost (

At the same time, the additional income from the production of plutonium in fast reactors is estimated at the cost of saved natural uranium while the fleet of thermal reactors using this uranium is reduced, being replaced with fast reactors using plutonium fuel. The saved uranium has a real market price and can be sold on the market. The proposed approach is based on the energy value of the produced plutonium and thus eliminates the expensive mechanism for assessing its cost. On the basis of these assumptions, a mathematical model was constructed and relations for calculating the

The analysis of the obtained relations showed that the

As an example, a computational study of the

The technique can be useful for comparative analytical studies to justify the choice of a strategy for the development of a two-component NES with thermal and fast reactors in a single closed NFC.

A characteristic feature of the proposed technique is that the recipients of income from the saved uranium are structures that are sufficiently removed from NPPs (up to the level of a state as a whole). However, there is no doubt about the role of a nuclear power plant with a fast reactor in creating this possibility. It is at NPPs, as a result of nuclear physical processes, that weakly fissionable ^{238}U is converted into an additional raw energy resource, i.e., plutonium. The developed technique makes it possible to see and take into account this income in the technical and economic indicators of a nuclear power plant.

* Russian text published: Izvestiya vuzov. Yadernaya Energetika (ISSN 0204-3327), 2021, n. 3, pp. 5–17.