Technical and Economic Comparative Analysis of Nuclear Power Plants: AP1000 and SMR

Abstract

Due to the necessity of decarbonising and transforming the Polish energy mix, topic of using nuclear power plants as one of the key low-carbon generation sources is returning to the public debate. This paper compares a large, system-wide AP1000 nuclear power plant with a new concept based on small modular reactors (SMRs), specifically NuScale 60 MW_e. Computer models of secondary loops of the generating units were used for the analysis, and basic operating parameters were determined. A consistent modelling approach was used to evaluate technical, thermodynamic, and economic indicators. As a result, a relationship between total capital expenditures and unit electricity generation cost was developed. For example, if the investment outlays, taking into account the freeze, for a large-scale nuclear power plant are USD 8 billion, then the investment outlays for an SMR power plant should be below USD 0.4 billion in order to ultimately ensure a lower or equal unit discounted cost of electric energy generation. Assuming stable power demand, the AP1000 reactor power plant remains the most cost-effective technology, offering favourable economies of scale. However, modular units are characterised by shorter lead times and greater flexibility of application in different areas of the energy industry. Therefore, in the decarbonisation process, it is essential to develop both analysed technologies in parallel.

1. Introduction

The increasing energy demand, which is correlated with a growing population and rapid industrialisation, indicates that the challenges of transforming the energy sector focus on efficiency, reliability, sustainability, and environmental protection. In this context, nuclear power plants (NPPs) present an effective solution for combating global warming as they offer a cleaner alternative for the generation of electric energy. These low-carbon generation sources are characterised by relatively low fuel consumption. Furthermore, nuclear power has a negligible impact on the environment regarding greenhouse gas emissions. In contrast, power plants that utilise lignite or hard coal frequently face discussions surrounding the transfer of harmful pollutants into the atmosphere. For instance, one of Poland’s largest generating units, the Bełchatów Power Plant, emits approximately 30 million tonnes of carbon dioxide (CO₂) annually [1]. Moreover, according to the Polish transmission system operator (Polskie Sieci Elektroenergetyczne S.A., Warsaw, Poland), as of the end of 2024, coal-fired power plants accounted for about 63% of national electric energy production [2].

In contrast to Poland, where coal-fired power plants are the dominant energy source, France’s energy sector is mainly shaped by nuclear power plants. Based on [3], it can be observed that their share in total electric energy production in 2024 is almost 68%. According to information provided by the International Atomic Energy Agency, France currently operates 57 nuclear reactors [4].

The different structures of the above-mentioned energy mixes affect not only energy security but also greenhouse gas emissions. When comparing these two countries in terms of daily CO₂ emissions, clear differences can be seen. Using the example of one selected day (8 May 2024), the data presented in [5] are as follows—for Poland, generation of electric energy was charged with transferring 754 gCO₂/kWh to the atmosphere, while for France it was 18 gCO₂/kWh. Thus, the daily emission factor for the Polish power industry was almost 42 times higher than for the French power industry. In the light of global efforts to achieve climate neutrality, such a significant difference puts Poland in a particularly difficult situation.

Climate protection is a major civilizational undertaking. For this reason, it cannot be carried out within the borders of a single country. Moreover, actions related to energy transition should also focus on raising awareness among the general public. Education in the field of nuclear energy and the development of appropriate human resources are important needs that will influence further technological progress in the nuclear sector. Cizeli et al. [6] highlight the importance of a European education strategy as a kind of foundation for the future of nuclear technologies, including modern small modular reactors (SMRs) solutions. Nuclear power has been a major part of the energy mix of many countries for decades, providing electric energy in a stable, low-carbon and resilient way. The lack of appropriately qualified people may be a barrier to the further development of this sector.

For many years, technological advances in nuclear power have mainly focused on large power units, with installed capacity often exceeding 1000 MW_e. However, recently, with changing social, economic and environmental circumstances, there has been increasing interest in SMRs, which are designed to reduce capital costs through series production. The study [7] provides a comprehensive overview of the state of SMR technology worldwide, identifying both the opportunities and barriers that need to be overcome for this innovative technology to fully establish itself on the market. SMRs are seen as a potential catalyst for the expansion of nuclear power in developing countries and regions with underdeveloped transmission infrastructure. It is also important to identify the factors determining the success of SMR technology implementation. The paper [8] analysed the characteristics and potential advantages of modular solutions compared to large-scale nuclear reactors. The author described issues related to economics, safety and public acceptance. In addition, the author emphasised that technical and legal challenges (appropriate regulations or obtaining licences) may hinder the widespread implementation of SMRs. In turn, publication [9] drew attention to the need for innovative solutions in the field of operation and maintenance of modular power plants. The article describes an analysis of cost reduction strategies through the introduction of modern operational solutions, automation and design simplification. It is pointed out that such an approach can significantly increase the competitiveness of SMRs on the market. Due to the specific nature of SMRs and high safety requirements, accurate and rapid fault diagnosis is of great importance. In article [10], researchers focused on developing an intelligent method for diagnosing faults in SMRs. The authors proposed a hybrid approach combining artificial intelligence algorithms and machine learning methods. The research demonstrated high accuracy in fault classification and the effectiveness of the algorithm in conditions of measurement disturbances and uncertainty. The developed method allows for the rapid detection of any irregularities and their classification without the need for human intervention. Other factors analysed in [11] in terms of the operational capacity of a single power plant operator were the size of the facility and the simplicity and compactness of SMR solutions. The authors found that it is possible to safely supervise 3 to 5 reactors during normal operation, but only up to 2 during start-up/shutdown or refuelling operations.

SMR solutions respond to the challenges of building and operating large nuclear power plant units, which are characterised by high generating capacity, making them attractive sources of electric energy in the context of covering base load in the power system. However, their implementation is associated with high investment costs, long construction times, and complex licensing procedures. In the literature and engineering practice, the implementation of SMRs on the market is often described using the categories FOAK (first-of-a-kind) and NOAK (nth-of-a-kind) [12,13,14]. The FOAK model refers to the first unit implemented in a given technological configuration, which involves overcoming a number of regulatory, organisational and design barriers. For this reason, FOAK projects are usually characterised by higher investment costs, longer implementation times and greater technological and financial risk. In contrast, the NOAK category refers to subsequent reactors built on the basis of a proven design, which allows for the use of learning effects and standardisation. In practice, this means a reduction in capital and operating costs, a shorter implementation schedule and greater predictability of the investment process. From the point of view of the development of innovative SMR technologies, the transition from the FOAK to NOAK phase will be a necessary condition for achieving their market competitiveness and widespread implementation in national energy mixes around the world. According to data available in the literature [15,16], it can be seen that nuclear power plants can have a unit capital expenditure ratio of $2100 to $6900/kW. The lower values ($2100–3000/kW) are observed in countries with well-established nuclear programs and lower costs (e.g., China, South Korea), while the higher values ($6000–7000+/kW) are typical for first-of-a-kind units built in new markets (e.g., the USA, Europe) or in cases where significant project difficulties are encountered. In the context of SMR technology profitability analyses, the authors of publication [17] pointed to the relationship between construction costs, energy efficiency and market conditions. The conclusions presented in the paper show that SMRs can be competitive under the right investment and legal conditions. These analyses are complemented by research [18], which describes long-term forecasts and scenarios that will enable the United States to achieve climate neutrality by 2050. The paper emphasises the need for long-term investment, regulatory changes and political support to achieve these goals.

There is also a study about the increasing risk of exceeding budgets and schedules for the construction of nuclear power plants, examples of which include delays in projects such as Olkiluoto 3 (Finland)—10 years, or Vogtle units 3 and 4 (USA)—4 years [19]. Furthermore, a study by Stewart and Shirvan [20] assessed the impact of various factors that increase the risk of delays in work schedules for four types of generation III+ water reactors. It was noted that design changes and consequent performance declines were a factor causing significant delays. Another issue related to the supply chain was a small part that adversely affected the commissioning date.

In a review of the available literature, it is noticeable that there is a lack of comprehensive comparative studies that directly contrast large nuclear units with modular reactors in terms of energy analysis. Many studies devoted to technical, economic or environmental analyses of each of these solutions have already been published. Thus, there is a clear research gap that could be important for future energy strategies and investment decisions related to the ongoing energy transition.

2. Problem Description, Novelty and Original Contribution

A fundamental transformation of the Polish energy sector requires a well-considered diversification of generation sources and investment in solutions that ensure energy independence, a stable electric energy supply and low emissions. Reforming the domestic energy sector in a manner consistent with the European Union’s climate policy involves a thorough examination of alternative electric energy generation technologies. Because of the above, and the numerous discussions on the role of nuclear power in the power system, and, in particular, the newly designed modular solutions—SMRs, the selection of appropriate nuclear technologies to meet the objectives of Poland’s Energy Policy until 2040 is a significant step towards a fair transition.

There is no doubt that replacing coal power with nuclear power is the best way to reduce the CO₂ emission factor. In the national arena, a debate has appeared as to whether it is better to build a system power plant or to rely on the development of distributed energy through the use of modular solutions. This topic raises a number of questions and concerns among the public.

The research problem of this paper focuses on the development of a model to compare the two types of nuclear power plants (large-scale and modular). This will provide a more comprehensive picture of the advantages and disadvantages of the two technologies when assessing (energy or economic), which of these solutions can better meet the needs of the national power system. The results of the analyses can then serve as a tool to support decision-making in the field related to the development of the generation sector. Furthermore, the work makes an original and useful contribution through:

• The development of secondary loop models that enable the mapping of the operating parameters of various generating units, both large-scale and modular. The simulated technological systems also include a comprehensive comparative analysis from an energy perspective;
• Application of the models in the context of the transformation of the Polish energy sector—thanks to this, potential development paths for nuclear technologies can be identified, which increases the practical value of the research and its strategic importance;
• Comparison of large-scale reactors with modern, modular units, which is a valuable addition to the research conducted so far, which very often focuses only on one type of technology;
• An economic analysis examining the impact of technical and economic parameters on the relationship between the unit discounted cost of generating electric energy in a large-scale nuclear power plant and a small-scale modular power plant.

3. Model and Method Description

The research methodology was based on a comparison of two modern nuclear reactor concepts: the large unit, the AP1000, and the small modular NuScale reactor, with a unit capacity of 60 MW_e. NuScale was selected as a reference SMR due to its advanced licensing status—it is the first SMR to receive U.S. NRC design approval—as well as the availability of detailed technical data. Its integral PWR design with passive safety systems and natural circulation makes it a representative example of the current generation of light-water SMRs. While other SMRs are under development, such as the BWRX-300 (a 300 MW_e boiling water reactor) or the Rolls-Royce SMR (~470 MW_e beyond IAEA SMR definition), they differ significantly in size, cycle type or system layout. Choosing a single, well documented design allowed for a consistent comparison of economic and operational indicators.

As a first step, technical and operational data for both technologies were collected and compared. On this basis, the secondary loop of the AP1000 unit was modelled, and the technological layout of the secondary loop of a nuclear power plant with a modular reactor was designed. The results obtained were used to evaluate parameters such as gross electrical power, cooling water flow, gross power plant efficiency and nuclear fuel (heat) utilisation rate.

As part of the economic comparative analysis, a general correlation was derived for the difference between the unit discounted generation costs of a large-scale nuclear power plant and a modular power plant. The derivation of the correlation made it possible to define the parameters determining the advantage of economic reasonableness of the compared technologies to each other.

The results of the analysis provide a basis for determining the efficiency (cost-effectiveness) of the implementation of each technology, depending on local demand.

3.1. Energy Analysis

Computer models of nuclear power units with PWR-type reactors of 60 and 1100 MW electrical output were used for the comparative analysis. Based on the data contained in [21,22] and using the EBSILON^®Professional 16.0 programme, schematics of the thermal systems of the mentioned generating units were developed. The models are presented in Figure 1 and Figure 2.

Despite differences in reactor design, most modern nuclear power plants use the Rankine cycle—this is a proven thermodynamic cycle in which heat from nuclear fission is converted into mechanical energy and then into electricity. In NPP systems where a saturated steam thermal cycle is used, the expansion of the working fluid in the high-pressure part of the turbine leads to its partial condensation (it changes to a wet steam state). The unwanted phenomenon can be seen from the course of the parameter changes shown in the temperature-entropy diagrams (Figure 3). Therefore, one method of improving the efficiency of the saturated steam cycle was applied to the process systems studied. Steam driers (moisture separation) were modelled along with interstage superheating. In addition, it can be seen from the T-s diagrams that the steam expansion on the last turbine stage is characterised by a moisture content that does not exceed the allowed 13%. It should also be added that the cycle begins in the condenser, where the working fluid is in a wet vapour state, as it has expanded at the individual stages of the steam turbine (thermodynamic transformation 1–2). Waste heat is removed from the system by cooling water flowing through pipes inside the condenser. The process of condensing the working fluid is visible on the T-s diagrams as an isobaric and isothermal transformation (2–3). The use of low- and high-pressure regenerative heaters improves the efficiency of the Rankine cycle and increases the temperature of the feed water. The working fluid is then compressed by a pump to the pressure prevailing in the steam generator so that it can be heated in the next step (isobaric transformation 3–4) by absorbing heat from the fission reaction of atomic nuclei and evaporating to a saturated vapour state (isothermal and isobaric transformation 4–5). The steam is directed to the high-pressure part of the turbine, where it partially expands (transformation 5–6), performing work. As mentioned above, the parameters of the working fluid decrease, so in order to prevent further deterioration, a dryer (isothermal transition 6–7) and an interstage superheater (isobaric transition 7–1) are brought into the system. After increasing the parameters of the working medium, it is directed to the low-pressure part of the turbine, thus closing the thermodynamic cycle.

To ensure a consistent comparison between the large-scale AP1000 unit and the selected SMR design, the thermal cycle of the small modular reactor was modelled with steam reheat, analogous to the AP1000 configuration. Although the reference SMR design (NuScale, 60 MW_e) is an integral pressurised water reactor with a simplified, once through steam generator and no provision for steam reheat, this modelling assumption was made intentionally. The goal was to maximise the thermal efficiency of the SMR cycle for the purpose of comparison under equivalent boundary conditions. While integral SMRs do not include reheat within the reactor pressure vessel, certain multi-module plant configurations could potentially include a reheat system in the shared secondary loop, improving the overall efficiency. Without reheat, the thermal efficiency of such an SMR unit would be expected to drop to approximately 30%, due to lower steam parameters and simplified turbine design. Nevertheless, this assumption does not affect the general conclusions of the study, as the economic trends and relative performance between the two technologies remain the same or very similar.

In the case of feedwater preheating systems, four preheaters—two low-pressure and two high-pressure—as well as a deaerator, are designed in the SMR solution. Feedwater reheating in the higher power unit is carried out using two heat exchangers on the high-pressure side and four low-pressure heaters. Important parameters taken from data sheets for the modelled nuclear technologies are summarised in

Table 1. Selected technological parameters of the analysed nuclear power plants own elaboration based on [21].

Parameter		Unit	AP1000	SMR 1
thermal power of the reactor		MWt	3400	200
gross (and net) electrical power		MWe	1200 (1100)	60 (57)
reactor coolant	mass flow	t/h	51,480	2397.6
	pressure	MPa	15.513	13.8
	temperature (inlet)	°C	279.4	265
	temperature (outlet)	°C	324.7	321
fresh steam	pressure	MPa	5.76	4.3
	temperature	°C	272.8	-
condenser pressure		kPa	9.1	-
feedwater temperature		°C	226.7	-
calculated efficiency of the power plant		%	34.7	33.3

¹ parameters for one module.

.

Performing further energy analysis of the secondary loops of the modelled units focused on simulating different loads on the nuclear reactor side. Thus, it was possible to examine the changes in individual parameters in the simulated systems. In addition, the usage of the simulation results obtained, as well as Equation (1), allowed the determination of operating characteristics for the subsequent comparison of large-scale technology with modular technology.

The following equation was used to determine the nuclear fuel utilisation rate:

$$q={\displaystyle \frac{3.6}{{\eta }_{el}}}\left[{\displaystyle \frac{\mathrm{G}\mathrm{J}}{\mathrm{M}\mathrm{W}\mathrm{h}}}\right]$$

(1)

where

η_el—gross power plant efficiency.

In addition, the indicators that were determined in EBSILON^®Professional are:

• Fresh steam flow—D;
• Cooling water flow in the condenser—D_cw;
• Gross electrical power—P_{el_gross};
• Gross power plant efficiency—η_el.

3.2. Economic Analysis

To make economic comparisons of different types of power plants, the calculated costs of electricity generation should be used, as they include all cost elements. Calculated costs of generating electricity are the own costs increased by the costs of servicing investment outlays used to build the power plant (capital servicing costs), including interest on the loan taken out for construction. It is permissible to include interest on capital (accumulation) and depreciation in a total rate, dependent on the interest rate on capital and the depreciation period of the power plant, expressed by the discount rate.

Investment outlays, operational costs and production effects should be reduced to comparable values using discounting. A commonly used methodology is that developed in the late 1970s by UNIPEDE and then adopted by the European Union and other countries, according to which the unit discounted cost of generation is determined as the ratio of the total discounted costs of building and operating a power plant during its “life”, including investment outlays, maintenance and repair costs and fuel costs, to the discounted amount of electric energy produced during that period:

$$k^j={\displaystyle \frac{I_{\left[0\right]}+\sum _{t=1}^N\frac{{KU}_t+A_t·k_{pt}}{{(1+p)}^t}}{\sum _{t=1}^N\frac{P_t·T_t}{{(1+p)}^t}}}$$

(2)

where

$I_{\left[0\right]}$—capital expenditure taking into account the freeze during the construction of the power plant;

$N$—lifespan of a power plant;

${KU}_t$—maintenance and repair costs per year $t$;

$A_t$—amount of electricity produced in a year $t$ ($A_t=P_t·T_t$);

$k_{pt}$—cost of fuel used to produce a unit of energy;

$p$—discount rate;

$P_t$—installed capacity of power plants in the year $t$;

$T_t$—time of use of installed capacity $t$ [23].

The amount of electric energy produced is taken into account in calculations as net energy introduced into the power system. This means the electric energy generation after taking into account the consumption for the power plant’s own needs, which translates into the value of the time of use of the installed capacity [23].

Investment outlays taking into account the freeze during the power plant construction period $I_{\left[0\right]}$ are calculated from the correlation:

$$I_{\left[0\right]}=\sum _{t=0}^{t=-(B-1)}{I}_t·{(1+p)}^{-t}$$

(3)

where

$B$—construction period [years];

$I_t$—capital expenditure in the year $t$ (nominal) [23].

A general quantitative comparison of electric energy generation costs in large-scale nuclear power plants with those in small-scale modular power plants is a difficult task due to large discrepancies in published, estimated, and forecasted economic data for various types of nuclear projects. As the literature review has shown, the incurred or forecasted capital expenditures and, consequently, the unit discounted cost of electric energy generation may take on extremely different values [24,25,26].

In order to analyse the factors influencing the relationship between the costs of electric energy generation in a large-scale nuclear power plant and a small-scale modular nuclear power plant, a relationship for their difference was defined:

$${∆k}^j=k_{LSNPP}^j-k_{SMR}^j$$

(4)

If $k_{LSNPP}^j>k_{SMR}^j$, then ${∆k}^j>0$. This means that the unit discounted cost of electricity generation in a large-scale nuclear power plant is higher, thus electricity production is more profitable in the case of SMR technology.

If $k_{LSNPP}^j<k_{SMR}^j$, then ${∆k}^j<0$. This means that the unit discounted cost of electricity generation in a small-scale modular nuclear power plant is higher, and therefore electricity production is more profitable in the case of a large-scale nuclear power plant.

Equation (4), describing ${∆k}^j$, is expanded below in order to determine the relation of electric energy generation costs in the compared technological variants taking into account the main techno-economic factors:

$$\begin{array}{c}{∆k}^j=k_{LSNPP}^j-k_{SMR}^j=\\ ={\displaystyle \frac{I_{\left[0\right],LSNPP}+\sum _{t=1}^N\frac{{KU}_{t,LSNPP}+A_{t,LSNPP}·k_{pt,LSNPP}}{{\left(1+p\right)}^t}}{\sum _{t=1}^N\frac{P_{t,LSNPP}·T_{t,LSNPP}}{{\left(1+p\right)}^t}}}-{\displaystyle \frac{I_{\left[0\right],SMR}+\sum _{t=1}^N\frac{{KU}_{t,SMR}+A_{t,SMR}·k_{pt,SMR}}{{\left(1+p\right)}^t}}{\sum _{t=1}^N\frac{P_{t,SMR}·T_{t,SMR}}{{\left(1+p\right)}^t}}}\end{array}$$

(5)

where

$LSNPP$—large-scale nuclear power plant;

$SMR$—small modular reactor.

It was assumed that:

• Maintenance and repair costs (fixed costs) are proportional to the installed capacity of the nuclear power plant (single-core system), i.e.,:

  $${KU}_{t,LSNPP}=k_{UT}^j·P_{t,LSNPP}$$

  (6)

  $${KU}_{t,SMR}=k_{UT}^j·P_{t,SMR}$$

  (7)

  where
  $k_{UT}^j$—unit cost of maintenance and repairs (fixed) [USD/kW].
• The installed capacity of the power plant is constant throughout the entire life of the facility, i.e.,:

  $$P_{t,LSNPP}=const=P_{LSNPP}$$

  (8)

  $$P_{t,SMR}=const=P_{SMR}$$

  (9)
• The time of use of the installed power is constant throughout the entire life of the facility and the same for both investments under consideration, i.e.,:

  $$T_{t,LSNPP}=T_{t,SMR}=const=T$$

  (10)
• The cost of fuel used to produce a unit of electricity expressed in [USD/MWh] can be expressed as the product of the cost of fuel (primary energy) expressed in USD/GJ and the unit consumption of nuclear energy by individual power plants, expressed in GJ/MWh, constant throughout the entire life of the facility, i.e.,:

  $$k_{pt,LSNPP}\left[{\displaystyle \frac{\mathrm{U}\mathrm{S}\mathrm{D}}{\mathrm{M}\mathrm{W}\mathrm{h}}}\right]=k_{pt,LSNPP}\left[{\displaystyle \frac{\mathrm{U}\mathrm{S}\mathrm{D}}{\mathrm{G}\mathrm{J}}}\right]·q_{pt,LSNPP}\left[{\displaystyle \frac{\mathrm{G}\mathrm{J}}{\mathrm{M}\mathrm{W}\mathrm{h}}}\right]=const=k_{p,LSNPP}·q_{LSNPP}$$

  (11)

  $$k_{pt,SMR}\left[{\displaystyle \frac{\mathrm{U}\mathrm{S}\mathrm{D}}{\mathrm{M}\mathrm{W}\mathrm{h}}}\right]=k_{pt,SMR}\left[{\displaystyle \frac{\mathrm{U}\mathrm{S}\mathrm{D}}{\mathrm{G}\mathrm{J}}}\right]·q_{pt,SMR}\left[{\displaystyle \frac{\mathrm{G}\mathrm{J}}{\mathrm{M}\mathrm{W}\mathrm{h}}}\right]=const=k_{p,SMR}·q_{SMR}$$

  (12)

  where
  $q$—unit consumption of nuclear fuel energy [GJ/MWh].
• Fuel cost [USD/GJ] is independent of technology:

  $$k_{p,LSNPP}=k_{p,SMR}=k_p$$

  (13)
• The operating period N is the same for both power plants considered.

Taking into account the above assumptions, Formula (5) can be written in the form:

$$\begin{array}{c}{∆k}^j=\\ ={\displaystyle \frac{I_{\left[0\right],LSNPP}+\sum _{t=1}^N\frac{k_{UT}^j·P_{LSNPP}+P_{LSNPP}·T·k_p·q_{LSNPP}}{{\left(1+p\right)}^t}}{\sum _{t=1}^N\frac{P_{LSNPP}·T}{{\left(1+p\right)}^t}}}-{\displaystyle \frac{I_{\left[0\right],SMR}+\sum _{t=1}^N\frac{k_{UT}^j·P_{t,SMR}+P_{SMR}·T·k_p·q_{SMR}}{{\left(1+p\right)}^t}}{\sum _{t=1}^N\frac{P_{SMR}·T}{{\left(1+p\right)}^t}}}=\\ ={\displaystyle \frac{I_{\left[0\right],LSNPP}}{\sum _{t=1}^N\frac{P_{LSNPP}·T}{{\left(1+p\right)}^t}}}+{\displaystyle \frac{\sum _{t=1}^N\frac{k_{UT}^j·P_{LSNPP}}{{\left(1+p\right)}^t}}{\sum _{t=1}^N\frac{P_{LSNPP}·T}{{\left(1+p\right)}^t}}}+{\displaystyle \frac{\sum _{t=1}^N\frac{P_{LSNPP}·T·k_p·q_{LSNPP}}{{\left(1+p\right)}^t}}{\sum _{t=1}^N\frac{P_{LSNPP}·T}{{\left(1+p\right)}^t}}}\\ \hspace{1em}-{\displaystyle \frac{I_{\left[0\right],SMR}}{\sum _{t=1}^N\frac{P_{SMR}·T}{{\left(1+p\right)}^t}}}-{\displaystyle \frac{\sum _{t=1}^N\frac{k_{UT}^j·P_{t,SMR}}{{\left(1+p\right)}^t}}{\sum _{t=1}^N\frac{P_{SMR}·T}{{\left(1+p\right)}^t}}}-{\displaystyle \frac{\sum _{t=1}^N\frac{P_{SMR}·T·k_p·q_{SMR}}{{\left(1+p\right)}^t}}{\sum _{t=1}^N\frac{P_{SMR}·T}{{\left(1+p\right)}^t}}}=\\ \hspace{1em}\hspace{1em}\hspace{1em}={\displaystyle \frac{1}{T·\sum _{t=1}^N{\left(1+p\right)}^{-t}}}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}·[{\displaystyle \frac{I_{\left[0\right],LSNPP}}{P_{LSNPP}}}+k_{UT}^j·{\displaystyle \sum _{t=1}^N}{\left(1+p\right)}^{-t}+T·k_p·q_{LSNPP}·{\displaystyle \sum _{t=1}^N}{\left(1+p\right)}^{-t}-{\displaystyle \frac{I_{\left[0\right],SMR}}{P_{SMR}}}-k_{UT}^j\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}·{\displaystyle \sum _{t=1}^N}{\left(1+p\right)}^{-t}-T·k_p·q_{SMR}·{\displaystyle \sum _{t=1}^N}{\left(1+p\right)}^{-t}]=\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}={\displaystyle \frac{1}{T·\sum _{t=1}^N{\left(1+p\right)}^{-t}}}·\left[{\displaystyle \frac{I_{\left[0\right],LSNPP}}{P_{LSNPP}}}-{\displaystyle \frac{I_{\left[0\right],SMR}}{P_{SMR}}}+T·k_p·{\displaystyle \sum _{t=1}^N}{\left(1+p\right)}^{-t}·(q_{LSNPP}-q_{SMR})\right]\end{array}$$

(14)

The analysis aims to compare unit costs of electricity generation for nuclear power plants on a diametrically different scale. It is worth mentioning that the initial capital cost for 1 core only can be distributed over multiple cores. Such an approach lowers the value of unit capital costs. However, this economic indicator was not considered. Instead of it, the economic analysis assesses the range of total capital expenditures for a single investment, taking into account the freeze.

The presented economic analysis assumes that SMR cost estimates were taken as projected future costs after some learning (approaching NOAK costs), rather than one-off prototype costs (FOAK). Additionally, the considered capital expenditures refer to a power plant with a single core and the necessary facility. For this reason, the value of repair and maintenance costs was assumed at a stable and proportional level without scaling for multiple cores.

Both large-scale reactor (AP1000) and the selected small modular reactor (SMR) are light-water reactors operating with standard low-enriched uranium (LEU) fuel. Consequently, both units are assumed to rely on the same conventional fuel supply chains, with no significant differences in uranium procurement, enrichment, or fabrication technologies.

Therefore, the assumption that the unit fuel cost per unit of thermal energy is the same for both technologies, which is justified for the purposes of this comparison. This simplification ensures consistency in the economic model and allows a clearer focus on the influence of other plant-scale parameters, such as thermal efficiency and capital intensity.

Based on the above equation, the following conclusions can be drawn:

• The relationship between the unit discounted costs of electric energy generation for a large-scale nuclear power plant and a small-scale modular nuclear power plant depends primarily on the capital expenditures and the cost of the fuel used to produce a unit of electricity, or more precisely, at the same fuel purchase price, on the fuel primary energy used per unit of electricity produced.
• Due to the so-called “scale effect”, the unit consumption of nuclear energy fuel in a large-scale nuclear power plant translates into reduced operating costs compared to a small-scale modular power plant.
• It is predicted that the relative (per unit of installed capacity) investment outlays of modular power plants will be reduced in relation to large-scale power plants. This is supported by the expected dissemination of technology, serial production, shorter implementation time, etc.
• The relation between the unit electricity generation costs of the variants under consideration will be determined by the strength of the above effects. In other words, will the difference in costs be influenced to a greater extent by the “scale effect” and the reduction in fuel costs in a large-scale power plant, or will the effect of serial production and the reduction in relative investment outlays prove to be more significant?
• Since both factors: investment outlays and unit consumption of nuclear fuel energy, strongly depend on the technology used and the specificity of the project, in order to obtain a clear answer in the decision-making process, each case should be considered individually.

4. Results and Discussion

The results obtained from simulation studies carried out on models implemented in the EBSILON^®Proffesional environment provided valuable information from both technical and energy and economic aspects. These results provide a basis for understanding the differences between the nuclear technologies studied and their potential applications in the context of the transformation of the Polish energy sector.

4.1. Energy Analysis

Large-scale power plants are characterised by lower specific fuel consumption, which makes them extremely advantageous for large national investments. In addition, the slightly higher fresh steam parameters achieved in a nuclear power plant equipped with an AP1000 reactor result in higher fuel energy efficiency when operating at near-rated unit power (90–100)%P_el. The efficiency of the large-scale power plant analysed reaches about 34.7%, compared to about 33.3% for the modular solution.

Another important aspect is the possibility of integration into the National Power System (NPS). The AP1000 technology is better suited to the needs of replacing large centralised generating units (currently operating coal-fired power plants). On the other hand, the SMR solution, thanks to its modularity, offers greater flexibility both in terms of installed capacity and the possibility of locating it close to final consumers or industrial plants (adaptation to the needs of distributed generation).

The analysis of the obtained characteristics allows the assessment of the correlations between the different operating parameters of nuclear generating units. The adopted power variation range of (25–100)% of rated power is consistent with the physical design constraints of nuclear reactors. It not only minimises the risk of fuel damage, but also allows electricity production to be adapted to the fluctuating demand in the power system (load following operation). Thus, a spike or drop in load will not lead to the activation of the steam discharge system or the need to shut down the reactor.

Moreover, the very wide range from 25% to 100% of nominal power for both type of reactors was adopted for the purposes of sensitivity analysis, representing a theoretical scenario such as load following operation or emergency power reduction. AP1000 is technically capable of load-following operation by reducing power output to approximately 20–30% of nominal capacity if required. However, in practice, such low-load operation is not optimal and very rare in large power systems. The 25% power level should not be seen as a typical operating point for AP1000, but rather as a boundary case for modeling purposes. In a PWR, reducing power to such level can be achieved by adjusting control rods position or increasing boron concentration in water.

Figure 4 shows the dependence of reactor thermal power as a function of gross electrical power generated for the two technologies compared.

From the study, it can be seen that, in both the high-powered unit and the modular unit (SMR), increasing the thermal output of the reactor results in a linear increase in the generated electrical output. Maintaining the stability of power processes in a power plant involves a number of factors, including proportional changes on the electricity generation side or the fresh steam flow rate. If more heat is supplied to the steam generator, it will be possible to increase the output energy of the plant (production of the working medium). This will then translate into an increasing load on the steam turbine—increased electricity generation and the need to remove a significant amount of waste heat from the system (an increase in the demand for D_cw cooling water (Figure 5) necessary for condensation of the steam in the condenser). This relationship follows directly from the energy balance (conservation of energy principle).

When selecting a location for an NPP, it is important to bear in mind the need for cooling water to receive waste heat from the steam-water cycle. It becomes important to select a suitable site, which should be close to large reservoirs of water (river, lake, sea or ocean), with modular SMR technology offering greater location options due to the much lower cooling water requirements of the thermal cycle. A cooling water flow of approximately 150,000 t/h must be assumed for operation of the AP1000 at rated output for Δt_cw = 12 °C. For SMR operation at rated output, the cooling water flow is 8500 t/h.

Figure 6 shows the relationship between the nuclear-to-electricity conversion efficiency as a function of the unit load.

From Figure 6, it can be seen that as the amount of heat generated in the reactor increases, the gains in primary energy efficiency decrease. In the considered load range of the AP1000 nuclear power plant generator, the efficiency decreases from the nominal value of 34.5% by about 4 p.p., while in the case of the SMR, the efficiency relative to the nominal load decreases by about 1 p.p. This is due to the modularity of the solution and the much smaller range of variation in steam parameters as a function of load. From the point of view of power plant operation, aiming to operate in the highest efficiency range will minimise costs and energy losses.

Figure 7 shows the relationship between the nuclear fuel utilisation factor and the gross electrical power generated.

As the load increases, the value of the ratio of the use of nuclear energy of the fuel for the production of electric power decreases, while for the AP1000 technology in the considered range of power changes of 200–1200 MW, the q ratio changes its value in the range of 11.9–10.36 GJ/MWh, while for SMR the value of the q ratio changes in the load range by a small value of 0.32 GJ/MWh. The small change in the value of the q index is due to the modular design of the solution and the selection of parameters, already at the design stage, so that the operation of the SMR units in the partial load ranges is characterised by the highest possible efficiency. Thus, the examined parameter indicates that the power plant gains clearly in energy efficiency only at higher reactor thermal power values (increased electricity generation). The values of q were taken into account in the economic analysis.

4.2. Economic Analysis

For example, the derived relationship (Formula (14)) was used to compare a large-scale nuclear power plant with an AP1000 reactor and a NuScale 60 MW SMR. Considering that the ratio of installed powers of the compared power plants is 20 $\left({\displaystyle \frac{P_{LSNPP}}{P_{SMR}}}={\displaystyle \frac{1200 \mathrm{M}\mathrm{W}}{60 \mathrm{M}\mathrm{W}}}\right)$, the equation for the difference in the unit cost of electricity generation can be written as:

$$\begin{array}{c}{∆k}^j={\displaystyle \frac{1}{T·\sum _{t=1}^N{\left(1+p\right)}^{-t}}}·\left[{\displaystyle \frac{I_{\left[0\right],LSNPP}}{20·P_{SMR}}}-{\displaystyle \frac{I_{\left[0\right],SMR}}{P_{SMR}}}+T·k_p·{\displaystyle \sum _{t=1}^N}{\left(1+p\right)}^{-t}·\left(q_{SMR}-q_{p,SMR}\right)\right]=\\ ={\displaystyle \frac{{0.05·I}_{\left[0\right],LSNPP}-I_{\left[0\right],SMR}}{T·\sum _{t=1}^N{\left(1+p\right)}^{-t}·P_{SMR}}}+(q_{LSNPP}-q_{SMR})·k_p\end{array}$$

(15)

In order to answer the question under what techno-economic conditions the generation of electricity in SMRs will be more economically viable than in a large-scale nuclear power plant, the following condition should be defined:

$${∆k}^j>0$$

(16)

Using Equation (15), the above condition becomes:

$${\displaystyle \frac{{0.05·I}_{\left[0\right],LSNPP}-I_{\left[0\right],SMR}}{T·\sum _{t=1}^N{\left(1+p\right)}^{-t}·P_{SMR}}}+(q_{LSNPP}-q_{SMR})·k_p>0$$

(17)

After mathematical transformations:

$$I_{\left[0\right],LSNPP}>{20·I}_{\left[0\right],SMR}-20·(q_{LSNPP}-q_{SMR})·k_p ·T·\sum _{t=1}^N{\left(1+p\right)}^{-t}·P_{SMR}$$

(18)

The following data were adopted for further analysis:

• Fuel cost (primary energy)—k_p = 1.4 [USD/GJ];
• Unit consumption of nuclear energy fuel for AP1000 when working at rated power—$q_{LSNPP}=10.36 \left[{\displaystyle \frac{\mathrm{G}\mathrm{J}}{\mathrm{M}\mathrm{W}\mathrm{h}}}\right]$;
• Unit consumption of nuclear energy fuel for SMR when working at rated power—$q_{SMR}=10.81 \left[{\displaystyle \frac{\mathrm{G}\mathrm{J}}{\mathrm{M}\mathrm{W}\mathrm{h}}}\right]$;
• Period of operation of the power plant—N = 60 years;
• Annual time of use of installed power, with availability of 90%—T = 7884 h;
• Discount rate—p = 0.07.

After taking into account the above values of selected quantities in the condition regarding the difference in unit discounted costs of electricity generation, the relationship between investment outlays for the compared technologies is obtained:

$$I_{\left[0\right],LSNPP}>{20·I}_{\left[0\right],SMR}-20·(q_{LSNPP}-q_{SMR})·k_p ·T·\sum _{t=1}^N{\left(1+p\right)}^{-t}·P_{SMR}$$

(19)

$$I_{\left[0\right],LSNPP}>{20·I}_{\left[0\right],SMR}-20·(10.36-10.81)·5 ·7884·\sum _{t=1}^{60}{\left(1+0.07\right)}^{-t}·60$$

(20)

$$I_{\left[0\right],LSNPP}>{20·I}_{\left[0\right],SMR}+83.7·{10}^6$$

(21)

Expressing the relationship in billions of USD:

$$I_{\left[0\right],LSNPP}>{20·I}_{\left[0\right],SMR}+83.7$$

(22)

The above condition defines the relationship between capital expenditures taking into account the freeze for the compared power plants. If the condition is met, the unit discounted cost of generating electricity in a small-scale NuScale 60 MW modular nuclear power plant is lower than the cost for a large-scale nuclear power plant with an AP1000 reactor.

Figure 8 shows the relationship between the capital expenditures taking into account the freeze for a large-scale nuclear power plant with an AP1000 reactor and the expenditures for a small-scale NuScale 60 MW modular nuclear power plant, ensuring that the unit discounted generation costs in these plants are equal: $k_{LSNPP}^j=k_{SMR}^j$.

Figure 8 addresses the large variability of possible estimates in terms of costs connected to nuclear power plants. Instead of estimating and indicating single specific values of capital expenditures for comparing investments, the ranges of these quantities and their influence on relation between unit electricity generation costs were considered. Figure 8 shows the line defining capital expenditures configurations for which unit electricity generation costs are equal in both compared investments. Additionally, there are defined the spaces over and under this line, which consists of configurations resulting in an opposing relationship between unit electricity generation costs—respectively: $k_{SMR}^j<k_{LSNPP}^j$ and $k_{SMR}^j>k_{LSNPP}^j$.

According to the relationship presented in Figure 8, if, for example, the investment outlays, taking into account the freeze, for a large-scale nuclear power plant are USD 8 billion, then the investment outlays for an SMR power plant should be below USD 0.4 billion in order to ultimately ensure a lower or equal unit discounted cost of electric energy generation.

The presented method of relative economic evaluation of two compared nuclear technologies allows for determining the impact of technical and economic parameters on the mutual relationship between the discounted unit costs of generating electricity without the need to determine their exact value. Determining the value of the discounted unit cost of generating electricity for nuclear technologies is challenging due to the difficulties in estimating the level of costs incurred for construction and operation. The presented method of economic analysis is therefore universal and generalised. The main determinants, which have by far the greatest impact on the unit cost of generating electric energy in nuclear technologies and on the obtained results, are the investment outlays. Their values can significantly differ and be shaped depending on the degree of complexity and organisational constraints of large-scale projects, or the development and popularisation of SMR technology.

5. Conclusions

Both compared investments—AP1000 nuclear power plant and the 60 MW_e SMR power plant—can have a crucial role to play in the transformation of the Polish power generation sector, with the AP1000 as the foundation for large-scale zero-carbon electric energy generation (system base operation), and the SMR as a distributed and flexible solution to support the decarbonisation of industry. The implementation of nuclear technologies could significantly reduce CO₂ emissions, improve energy security, as well as ensure a stable electric energy supply in conditions of constantly increasing shares of renewable energy sources in Poland’s energy mix.

As the reference SMR in this analysis, the NuScale 60 MW_e was chosen, primarily because it is a pressurised water reactor, the same type as the AP1000. This ensures that the comparison between the two technologies is made on the basis of comparable thermodynamic and safety principles, even though they differ significantly in scale. Furthermore, NuScale was seriously considered for deployment in Poland, similarly to AP1000, which reinforces its relevance in our context. It also has the most advanced licensing status.

Comparing the two technologies, it can be seen that the AP1000 reactor has a higher electric energy generation efficiency when operating at rated power (approximately 34.7% compared to 33.3% for the SMR system). This translates into a lower nuclear fuel utilisation rate of between 10.36 and 11.88 GJ/MWh for the AP1000, compared to 10.81–11.15 GJ/MWh for the SMR unit. This dependence translates into a difference in operating costs related to the purchase of nuclear fuel.

Despite the lower efficiency, modular solutions can offer a number of advantages, such as shorter investment lead times, the possibility of series production and greater location flexibility. Investments can be made close to end-users or in areas with underdeveloped transmission infrastructure. In terms of cooling water requirements, this is one factor that is important in the choice of location, making SMRs more suitable for regions far from large water reservoirs or with limited water resources. However, in unit terms, the difference is insignificant.

Since facilities of completely different scales were compared, the unit discounted cost of electricity generation was used as the evaluation parameter. The economic analysis shows that the cost-effectiveness of both solutions is strongly dependent and the most sensitive on capital expenditures. As the main variable, the investment outlays taking into account the freeze during the power plant construction period $I_{\left[0\right]}$ was used. Moreover, the sensitivity of the results on these quantities for both investments was examined. It is worth mentioning that the impact of changes in discount rate was examined indirectly, because, it affects the value of the investment outlays taking into account the freeze during the power plant construction period: $I_{\left[0\right]}=\sum _{t=0}^{t=-(B-1)}{I}_t·{(1+p)}^{-t}$. The advantage of the method is the lack of necessity to specify the value of unit investment outlays, which characterises significant variability.

The presented methodology of economic analysis is adequate for single-module power plants. It is particularly significant in the case of SMR units, because initial costs for 1 core only can be distributed over multiple added cores. Such an approach lowers the value of unit capital cost or unit maintenance and repair costs. In order to take into account the effect of modularity on economic efficiency, a relationship should be developed that scales unit costs with the number of cores in the reactor building. However, the closer the number of modules used in an SMR brings its rated power to that of the AP1000, the less justified their use as a replacement for a large-scale power plant seems. Therefore, the analysis focuses on comparing a large-scale power plant with a small-capacity unit, whose roles in the system may be complementary.

As the two technologies can complement each other, a hybrid deployment strategy should be considered. High-capacity reactors should be built in regions with adequate grid infrastructure and access to water, while SMRs can act as distributed sources to replace decommissioned coal-fired units or serve as process heat sources for industry.

The developed model, with its potential for further expansion, is a valuable tool to support the much-needed decision-making associated with the implementation of nuclear power in the country. In future research work, it is worth extending the analysis to include external factors such as regulatory risk, energy market development scenarios and the potential for integration of nuclear technology in hybrid energy systems (e.g., cogeneration, district heating, hydrogen production).

It may be particularly important to deepen research into the application of small modular reactors (SMRs) in the district heating sector, which in Poland faces challenges related to the need to reduce greenhouse gas emissions and decarbonise the heating infrastructure.

Extending the current model to include variants for the use of SMRs for district heating production would allow the development of scenarios for their implementation in district heating systems. However, a comprehensive legal framework, institutional support and outreach activities aimed at increasing public acceptance of nuclear power in heating applications will be required for the successful implementation of this technology.