Corresponding author: Andrei A. Andrianov (andreyandrianov@yandex.ru)
Academic editor: Georgy Tikhomirov
It seems to be of current interest to consider and analyse possible electrical and nonelectrical applications of small and medium sized reactors for both the nearest and more distant future. The paper presents the results of a comparative analysis of the economic attractiveness of nuclear power plant (NPP) designs based on small and mediumsized reactor modules and a largesized reactor in order to identify conditions for increasing the investment attractiveness of NPP modular design concept. The analysis is based on the evaluation of such economic performance metrics as net present value, present value, internal rate of return, discounted payback period, and levelized cost. It was shown that, in terms of the present value and levelized costs, the NPP modular design concept is less economically attractive in comparison with the NPP design based on a largesized reactor. In terms of the net present value, internal rate of return and payback period, the NPP modular design concept can be considered economically attractive if only the predicted learning effect is observed when the modules are constructed and the scale factor is not less than 0.5. In this case, it will be economically feasible to construct an NPP based on a small number of medium sized reactor modules. If the scale factor is not less than 0.6, one may talk about the economic attractiveness of NPP designs based on reactor modules of lower power. The impact of various debt financing schemes was analysed and it was demonstrated that, in relative terms, changes in the economic performance indicators are comparable in the implementation of the NPP modular design and a large sized reactor.
At present, there is the renewed interest in developing small and medium sized reactors (SMR) and considering their possible applications in many regions of the world
The advantages of this concept are well known: relatively small absolute project implementation costs and, consequently, lower financial risk; the modular structure gives a possibility to gradually expand capacities and create an NPP with a flexible power configuration; units with small and medium sized reactors can be located closer to customers; small sized reactors can be operated without onsite refueling, thus eliminating the need for SNF and HLW handling (
Reviews of the concepts and current situations in the field of SMRs are regularly presented in publications issued by the IAEA and reports prepared under the auspices of the OECD NEA (IAEATECDOC1485, IAEATECDOC1536, IAEATECDOC881,
The liberalisation of energy markets has given high decisionmaking autonomy to business entities, which in the new conditions, first of all, seek to maximise their profits. In this context, the cash flow theory has come into use as the main tool for choosing efficient investment projects, where the criteria of net present value, present value, internal rate of return, payback period, and some others are used as the primary criteria of decisionmaking (INPRO Methodology 2014,
It is well known that the main reason for the SMR economy remaining a weak point is the so called ‘effect of economies of scale’ (scale effect) which implies that a decrease in a unit power, without making any fundamental changes, results in an increase in capital costs (
At the same time, there are factors mitigating an adverse impact of the scale effect. First of all, it is possible to simplify the reactor construction. Thus, according to the assessments in a number of studies, it has been shown that the primary circuit integral layout leads to cost saving by a factor of 0.85. If several small sized reactors are installed at the site, it will be possible to organise some common systems for them, thus reducing licensing costs. The so called ‘learning effect’ is also well known: the construction and operation of each next unit will be cheaper than the previous one. According to the estimates, it can be expected that the construction costs will be reduced by 25–30% for the fifth or sixth reactor as compared to the first one. An additional gain is associated with shorter construction periods for SMRs and costcutting for a floating NPP (
For a modular NPP, it is possible to reduce investment risks if capacity commissioning is performed on a ‘module by module’ basis without waiting for the plant to achieve its planned total power output. At the same time, the required investments will be distributed in time and may have a more attractive profile while a large unit of equal power would require investments immediately. Gradual capacity expansion reduces both the initial investment and the amount of capital at risk (
For a correct assessment of the competitiveness and economic performance of SMRs, it is required to consider the totality of factors influencing positively (multimodularity, factorymade modules, etc.) and negatively (the scale effect) their economic competitiveness. For an analysis of the concepts, it is required to collect data on capital expenditures for their construction, fuel, operating costs, etc.
An evaluation of the economic performance and competitiveness of the SMR deployment can be carried out using the economic performance indicators characterizing the attractiveness of investments and the profitability of relevant projects (INPRO Methodology 2014,
Economic Performance Indicators.
Indicator  Calculation Formula 

Net Present Value (NPV) 

Present Value (PV) 

Internal Rate of Return (IRR)  The interest rate at which the NPV is equal to 0. 
Discounted Payback Period (DPP)  The period of time required for the revenue generated by the investment, taking into account the discount, to cover the investment cost. 
Levelized Cost (LC) 

where D_{t} is the operating income at the time t; R_{t} is the operating costs at the time t; W_{t} is the current power generation; d is the rate of discount; Т_{1} is the construction period (years); Т_{2} is the project lifetime (years); t is the discrete time. 
Depending on the task at hand, it is necessary to use one or another set of performance criteria. For example, in the case of orientation mainly to investors, the main indicator is the net present value which depends on an indefinite electricity tariff. In the case of owner orientation (when the construction of NPPs is mainly paid by the State), the main indicators for assessing the costeffectiveness of NPP designs usually are total discounted costs. Generally, it is necessary to take into account the entire spectrum of performance indicators that reflect different aspects of the project.
While performing evaluation of economic performance and competitiveness of SMR deployment, it is necessary to consider not only the main factors influencing the economic indicators of SMRs but also a possibility of involving debt financing. The initial data are external conditions (price per unit of electricity sold, nuclear fuel cost, plant factor, discount rate, income tax rate), financing scheme (share in total capital investment, credit payment period, credit interest), unit performance parameters (installed capacity, construction time and unit cost, fixed cost, operation and maintenance costs, fuel burnup, plant efficiency, annualized share of capital investment). The basic set of initial data used in the present study, which corresponds to some hypothetical (country neutral) situation is shown in Table
Initial data.


Price per unit of electricity sold (cent/kWh)  10.5 
Nuclear fuel cost (dollar per kg of U)  1800 
Plant factor  0.8 
Discount rate (%)  5 
Income tax rate  24 
Unit performance parameters  
Installed electric power (MW)  1200 
Construction period (years)  6 
Unit construction cost ($/kW)  4500 
Fixed service, maintenance and repair costs ($MM/yr)  90.00 
Fuel burnup (MWth d/kg U)  43.00 
Plant efficiency (%/100)  0.334 
Annualized constant capital investment (%)  16.7 
Financing scheme  
Share in total capital investment (%)  0–100 
Credit payment period (years)  15–20 
Credit interest (%)  7–10 
The effect of economies of scale implying that an increase in unit power leads to a reduction in installed cost per kW works in the case when one reactor design similar to itself increases or decreases in power. The following correlation between capital costs and power unit is established according to the formula (
where OCC are the Overnight Construction Costs, the scale factor n is in the range from 0.4 to 0.7, P is the reactor unit capacity. Different reactor technologies are characterized by their own scale factor. It should be noted that an increase in its value entails reducing the cost sensitivity to the power unit. In particular, if the scale factor value is equal to 1, there will be no economies of scale and the capital costs will no longer depend on the power unit.
Figure
Figure
Figure
The internal rate of return (IRR) of the project, i.e. the interest rate at which the NPV is equal to 0, for the considered scenarios is 11.7, 10.5, and 9.2%, respectively. It is believed that the higher the IRR and the greater the difference between its value and the predetermined discount rate, the more profitable the project is.
If the investor is the owner, for example, the State, the main economic performance indicators are usually the present value (PV), which for the considered investment projects are 4827, 5475, and 5634 million dollars, respectively. In this case the indicator of levelized costs (LC) will be 4.14, 4.68, and 5,28 cents per kWh, respectively.
As is seen from the estimations under the presented assumptions, the construction of one 1200 MW unit is more economically attractive. However, the implementation of the modular NPP concept based on small modular reactors includes provisions that increase their competitiveness due to the factors that determine the specifics of SMRs (in addition to traditional advantages of the modular concept such as high quality of manufacture and assembly of the main equipment at the factory, short production time, the possibility of transporting reactor units by rail, etc). In this regard, it seems appropriate to perform evaluations aimed at identifying areas where the implementation of the modular concept may be beneficial. To solve this problem, the following options have been considered: the possibility of building up to 20 units, the scale factor n is in the range from 0.4 to 0.7, assessments are made both including and excluding the learning effect (in accordance with (
Figure
Figure
The discounted payback period and internal rate of return are important additional metrics of the investment project characterizing its economic performance and stability. Figures
Figure
One of the arguments in favor of the SMR is that the deployment of a nuclear energy system based on them can reduce the risks associated with the loss of capital investment (
Figure
The general conclusion that can be drawn from these evaluations, is as follows. In terms of the costs (present value and levelized cost), the economic attractiveness of the modular concept is missing. In terms of the net present value, internal rate of return and discounted payback period, it is possible to talk about the modular NPP feasibility in case the predicted learning effect is observed during the construction of the modules and the scale factor is not less than 0.5. In this case, it seems economically reasonable to construct an NPP from a small number of medium sized modules. If the scale factor is not less than 0.6, one can talk about the feasibility of constructing units of lower power.
Change in NPV with time.
Net Present Value.
Present Value.
Discounted Payback Period.
Internal Rate of Return.
Levelized Costs.
VaR.
Choosing the optimal SMR deployment strategy is a multicriteria problem: it is reasonable to use the NPV and VaR indicators as the main criteria. These indicators are conflicting in nature: an improvement of one entails a deterioration of another. Therefore, it is necessary to look for compromise SMR deployment options: which would maximise the net present value on the one hand and minimise the value at risk on the other hand. The parameters that require definition are the power and startup time of a reactor module. Selection of nondominated deployment strategies makes it possible to define compromise deployment options of the system.
The values of NPV and VaR indicators for various SMR deployment scenarios are presented in Fig.
The final choice of the most appropriate option from a set of tradeoff ones should be made based on an analysis of the NPV and VaR indicators substitution curve, taking into account an additional alternative analysis using other performance indicators and experts’ judgments as well as the entire set of graphic and attribute data with due regard for the sensitivity analysis results. Such an analysis will make it possible not only to select a scenario (capacity and commissioning periods for reactor modules) which will provide an acceptable value of one indicator for a given constraint on the other, but also to formulate recommendations on how to increase the overall economic performance keeping associated risks at the acceptable level.
NPV and VaR values for various SMR deployment scenarios.
Relative changes in performance indicators, depending on the share of debt capital in the total investments.
Let us compare the effect of debt financing on the values of economic effectiveness indicators for the NPP based on SMRs and a large nuclear reactor for the following scenarios: one 1200 MW unit, two 600 MW units, and four 300 MW units. The last two are constructed on a module by module basis. The evaluations are made on the assumption that n = 0.6, excluding the learning effect.
The following are three financing schemes of the investment project: (1) at its own expense without involving outside investors (zero share of external credit); (2) credit financing scheme (share in the total investment is 100%); (3) debt financing (share of the total investment is 10–90%). The credit payment period is 15–20 years. The interest rate is 7–10%. The values of performance indicators for financing the construction at its own expense without involving outside investors, corresponding to the zero share of external credit, are listed above.
As can be seen in Fig.
A comparison of different credit schemes from the standpoint of changes in the economic performance during the implementation of the modular NPP and the NPP based on a large nuclear reactor shows that the scaling effects are comparable in these cases. This does not make SMR more sensitive to a share of debt capital in the total capital investments, nor does it substantially deteriorate their adaptation to financing with the involvement of external credits as compared to large nuclear reactors.
The comparative analysis of the investment attractiveness of the NPP designs based on SMR modules and a large nuclear reactor has shown that, in terms of the total discounted and levelised costs, the NPP modular design concept has no economic attractiveness in comparison with a large nuclear reactor. In terms of the net present value, internal rate of return and payback period, the NPP modular design concept can be considered economically attractive if only the predicted learning effect is observed when the modules are constructed and the scale factor is not less than 0.5. In this case, it will be economically feasible to construct an NPP based on a small number of medium sized modules. If the scale factor is not less than 0.6, then we can talk about the feasibility of NPP designs based on reactor modules of lower power. The analysis of the impact of various debt financing schemes has demonstrated that, in relative terms, changes in the economic performance indicators are comparable in the implementation of the NPP modular design and a large sized reactor.
* Russian text published:Izvestiya vuzov. Yadernaya Energetika (ISSN 02043327), 2018, n. 4, pp. 89–101.
According to the classification adopted by the IAEA, small reactors are reactors with an equivalent electric power of less than 300 MW(e) and medium sized reactors are reactors with an equivalent electric power of between 300 and 700 MW(e).