\section{Introduction}\label{sec1}

In the current energy crisis, surging prices for fossil fuels add to the debate on alternatives to gas, coal, and oil for energy generation. In addition to ongoing and planned efforts to expand renewable energy sources, many governments have recently declared or emphasized their intention to invest in new nuclear power plants: Japan is considering to invest in new reactors for the first time since the meltdown of the Fukushima Daiichi plant, France recently pledged to construct up to 14 new plants, although specifics remain unclear, and the United Kingdom announced funding for a Sizewell C station to pursue their target of 24 GW nuclear capacity by 2050  \citep{ft, nyt, bb}.

Currently surging prices for fossil fuels only encourage existing plans for nuclear power that pre-date the crisis and originate from government strategies to mitigate carbon emissions and combat climate change \citep{Goldstein2019}. One the one hand, from a technical perspective, nuclear power offers two advantages: First, nuclear plants are dispatchable. While today's plants do not operate flexibly and thus provide baseload supply, research suggests new reactor concepts or even established light-water reactors are capable of flexible operation \citep{Jenkins2018, Lynch2022, mit_future_2018}. As a result, nuclear power could complement fluctuating supply from renewables and ensure security of supply in decarbonized energy systems. Second, nuclear offers a great energy potential. Compared to renewables, nuclear power is far less constrained by land availability or meteorological conditions \citep{landUse}. At the same time, decarbonization in heating, industry, and transport requires electricity as a primary source of energy, either directly or indirectly using synthetic fuels produced from electricity \citep{Luderer2021,Bogdanov2021}. Therefore, nuclear power could substantially contribute to fulfilling the increasing demand for electricity.

On the other hand, there are economic arguments against investing into nuclear power. New plants are capital-intensive; especially since actual construction cost and time frequently exceed forecasts \citep{Lovins2022,Rothwell2022}. For instance, in France, offical construction costs of Flamanville 3 so far quadrupled to 12,600 €/kW while project completion is currently delayed by more than a decade \citep{edf_universal_2022,Rothwell2022}. Similarly, costs of Olkiluoto 3 in Finland tripled over a construction time of 17 years \citep{dw}. Costs of Hinkley Point C in the United Kingdom have doubled to date, and the reactor is currently scheduled to start operation in 2027---11 years after construction started \citep{bbc}. Whether this trend is reversible, is subject to debate: Drawing on the historic expansion of pressurized water reactors in France, \citet{Berthelemy2015} suggest reinforced investments and standardization could lower construction costs and time. \citet{Grubler2010} however states that the expansion of pressurized water reactors never achieved positive learning effects in the first place. 

With the high costs of nuclear power, other technologies might be more efficient to achieve decarbonization. Instead of potentially flexible nuclear plants, imports from other regions, batteries, or seasonal storage using synthetic fuels can cover demand when supply from wind and photovoltaic (PV) is low. In addition, electrification in heating, industry, and transport adds a substantial share of flexible demand. For example, electricity consumption of electrolyzers can adjust to wind and solar generation, thereby supporting the integration of renewables \citep{Wang2018}. In the same way, flexible electric heating or charging of electric vehicles can adapt to renewable supply \citep{Schill2020, Schuller2015}. Beyond flexibility, high investment costs can render nuclear power more expensive even compared to renewables in unfavorable sites, like offshore wind turbines in deep waters or PV in locations with little sunshine \citep{mckenna2014}.

Against this background, we investigate the economic efficiency of nuclear power in two steps: First, we review projected and actual costs of new nuclear capacity to compute the conceivable range of levelized costs of energy (LCOE), discuss plausibility and compare the outcome to renewables. Second, we compute the efficient share of nuclear power for previously obtained cost ranges in a decarbonized energy system with a comprehensive energy planning model \citep{Goeke2020a}. Due to its extensive scope, the model can consider all alternatives to nuclear power for the provision of flexibility, most importantly cross-border exchange of energy, flexible demand, and storage technologies. Previous research limited the scope to single regions omitting the exchange of energy as a source of flexibility, neglected the demand-side flexibility induced by electrification, or only featured short-term storage systems \citep{Duan2022,Baik2021}. The cost review focuses on OECD countries due to discrepancy of nuclear development between OECD and non-OECD countries observed in \citet{Rothwell2022}; the techno-economic analysis covers the European continent.

Inevitable simplifications of the techno-economic model are made in a way that favors investment in nuclear power. Therefore, the computed share of nuclear power in the energy mix is not an accurate estimate, but rather an upper bound of what might be if significant nuclear cost reductions were to be achieved. This applies in particular because our techno-economic analysis omits external social costs of nuclear power associated with the risk of accidents, waste management, and proliferation \citep{leveque2014,lordan2021, wheatley_reassessing_2016, lehtveer_nuclear_2015}. Although their robust quantification is difficult, external costs for nuclear typically exceed estimates for renewable energies \citep{stirling_limits_1997}.

The remainder of this paper is structured as follows: The next section \ref{methods} describes the methodology to compute LCOEs and introduces the applied energy planning model. Section \ref{main} presents the results for LCOE analysis and the planning model. In Section \ref{diss} these results are discussed and Section \ref{conclusion} concludes.

\section{Methods} \label{methods}

The first subsection \ref{lcoe} describes the computation of LCOEs for nuclear with an emphasis on the review of construction costs and financing costs during construction. Then, we introduce the energy planning model applied for a more detailed evaluation of nuclear power. The applied model uses the open AnyMOD.jl modeling framework and is described with greater detail in previous publications \citep{Goeke2023,Goeke2020a}.


\subsection{Computation of LCOEs} \label{lcoe}

Whether nuclear power is an economically efficient option for decarbonization strongly depends on its costs. Operational costs for fuel or maintenance only constitute a minor share while construction and financing account for 80\% of the total costs of nuclear power \citep{haas_historical_2019, mackerron_nuclear_1992}. At the same time, costs of construction and financing are also subject to the greatest uncertainty. Therefore, we review construction and financing costs in greater depth and vary them across the observed range in the subsequent analysis. For all other parameters, section \ref{cost_analysis} of the appendix provides a review. Table \ref{tab:assumptions} lists the assumptions used for the analysis. For these parameters, we use optimistic assumptions that correspond to at least the 25th percentile of the reviewed data. All monetary values in this paper are inflation-adjusted and given in US-\$\textsubscript{2018}. Section \ref{lcoeSup} of the appendix provides the corresponding conversion factors.


To assess the range of overnight construction costs, we reviewed different academic publications and industry reports providing 88 individual future projections or reported costs for different reactor concepts and countries \citep{nrel_2021_2021,oecd_full_2018,shirvan_overnight_2022, Rothwell2022, barkatullah_current_2017, lazard2021, wealer_investing_2021, international_atomic_energy_agency_advances_2020, green_smr_2019, rothwell_economics_2016, Duan2022, Grubler2010, stein_advancing_2022, mit_future_2018, boldon_small_2014, stewart_capital_2021, nrel_2021_2021, iea_projected_2020, tolley_economic_2004, dixon_advanced_2017}. We put a focus on light-water reactors (LWR), the most common reactor concept\footnote{Table \ref{tab:OCC_results} in the appendix shows that considering a broader range of reactor types does not give lower cost projections.}, and OECD countries since \citep{Rothwell2022} observes non-OECD estimates are not comparable. Cost projections are often provided in the means of n-th-of-a-kind cost, presenting assumptions of sometimes significant cost reductions through standardization and learning effects, e.g., \citep{shirvan_overnight_2022}. These projections however are not given in relation to a specific year or cumulated investment, complicating the comparison with cost projections for renewables.

The left boxplot in Fig. \ref{fig:OCC_boxplot} summarizes the distribution of the 45 remaining estimates. Overall, projections range from 1,914 US-\$  per kW projected by \citet{oecd_full_2018} to 12,600 US-\$ per kW, the actual costs of the Flamanville-3 project \citep{Rothwell2022}. The median is at 5,430 US-\$ per kW; 50\% of estimates are between 4,328 and 9,966 US-\$ per kW. Future projections are generally much lower than recent observations of actual costs for the European Pressurized Reactor (EPR) and the Westinghouse AP1000. Observations of actual costs are still preliminary since of the 4 relevant projects, Olkiluoto 3 has not yet started commercial operation and Flamanville 3, Hinkley Point C and Voglte Station are still under construction.\footnote{For the Shin Hanul 1 reactor that recently started operation in South Korea, final costs were not publicly disclosed. KEPCO's financial statements suggest costs as low as 3,120 US-\$ per kW \citep{kepco_interim_2022}. This seems very low when taking a construction time of approx. 12 years into account.} Some literature suggests that historically, learning rates of 5 to 10\% were achieved in the nuclear industy which would coincide with the mentioned projections \citep{Berthelemy2015, mignacca_economics_2020, lloyd_expanding_2020}. However, the discrepancy between projected and actual costs is in line with previous analyses on the actual development of nuclear construction costs in Western countries since the 1970s \citep{Grubler2010, davis_prospects_2012, koomey_reactor-level_2007, escobar_rangel_revisiting_2015, harding_economics_2007}, placing doubt on supposed learning rates.
\begin{figure}
    \centering
    \includegraphics[scale=0.1]{figures/boxplotMain.pdf}
    \caption{Boxplots for overnight construction costs and time}
    \label{fig:OCC_boxplot}
\end{figure}

The right boxplot in Fig. \ref{fig:OCC_boxplot} presents a similar image for construction time. Future projections range from 5 to 9 years, but recent and ongoing projects are currently taking 10 to 17 years. These overruns drive up financing costs and can also threaten energy security.
\begin{table}
\caption{Parameters for nuclear power} \label{tab:assumptions}
\centering
\begin{tabular}{p{3cm}|p{2cm}|p{2cm}}
    \hline
    Parameter                           &Unit       &Value / Range\\
    \hline
    Overnight construction cost   &US-\$/kW     &1,914 - 12,600\\
    Annual fixed operational cost       &US-\$/kW     &88.81\\
    Variable operational cost  (incl. fuel)          &US-\$/MWh    &10.96\\
    Capacity factor                     &\%         &95\\
    Construction time             &years      &4 - 10\\
    Depreciation period        &years      &40\\
    \hline
\end{tabular}
\end{table}


Together, construction and financing costs constitute total construction costs (TCC). Financing costs reflect the interest paid and are typically calculated from the length of depreciation and the interest rate. Following the methodology for nuclear power investments introduced in \citep{rothwell_economics_2016}, our analysis additionally accounts for costs during construction. We compute the financing costs during construction $f$ using Equation \ref{idc} introduced by \citet{rothwell_economics_2016}. In the equation $i$ is the interest rate, $t$ the construction time, and $c$ the overnight construction costs.

\begin{equation} \label{idc}
f = (\frac{i}{2 \cdot t} + \frac{i^2}{6 \cdot t^2})*c
\end{equation}

For the comparison of LCOEs and analysis with the energy system model, the annuity $a$ is computed for the sum of financing and overnight construction costs according to Equation \ref{ann}. In the formula, $d$ is the depreciation period. 

\begin{equation} \label{ann}
a = (f + c) \cdot \frac{(1+i)^d \cdot i}{(1+i)^d -1}
\end{equation}

Finally, the LCOE $l$ for a single year corresponds to the sum of annuity and variable costs $v$ divided by the yearly generation. The yearly generation corresponds to the product of the utilization rate $u$ and the numbers of hours in a year.

\begin{equation}
l = \frac{a + v \cdot u \cdot 8760}{u \cdot 8760}
\end{equation}


\subsection{Energy system model} 

The deployed planning model decides on the resources and technologies to supply an exogenous demand for energy services. Fig. \ref{fig:overMod} provides an overview of the considered primary energy sources, secondary energy carriers, and the categories for final demand. Besides nuclear power, supply of primary energy is restricted to renewable sources, namely wind, hydro, photovoltaic, and biomass. To capture intermediate steps between final demand and primary supply, the model includes secondary carriers, like hydrogen or synthetic gas and oil. Finally, the model must meet the demand for residential and industrial heat, passenger and freight transport, synthetic fuels for aviation and navigation, and electricity.

\begin{figure}
	\centering
		\includegraphics[scale=0.618]{figures/modelOverview.pdf}
	\caption{Overview of model structure}
	\label{fig:overMod}
\end{figure}

To cover final demand, the model decides on the expansion and operation of predefined technologies. Technologies in the model generate, convert, store, or transport energy carriers or provide an energy service. For instance, wind turbines generate electricity that can either satisfy the final electricity demand, be temporarily stored by a battery or be converted to hydrogen by an electrolyzer or to heat by a heat pump to satisfy final demand. Overall, the model includes 22 energy carriers and 125 distinct technologies. Except for nuclear, the choice and parametrization of technologies is based on reports of the \citet{DEA} and on \citet{Robinius2020} for the transport sector. The graph in Fig. \ref{fig:powerAll2} shows all technoloiges supplying electricity. In the graph, vertices either represent energy carriers, depicted as colored squares, or technologies, depicted as gray circles. Entering edges of technologies refer to input carriers; outgoing edges refer to outputs. The appendix \ref{graphSec} provides a comprehensive graphs with all considered technologies.

\begin{figure}
	\centering
		\includegraphics[scale=0.25]{figures/powerAll_wNuclear_cropped.png}
	\caption{Technologies for electricity supply}
	\label{fig:powerAll2}
\end{figure}

The model's objective is to minimize the total system costs which consist of annualized expansion and operational costs for technologies and costs of energy imports from outside the system. Accordingly, the model takes a strictly techno-economic social planner approach and does not consider the different agents within the system, such as producers, consumers, or governments, and their behavior. The model is formulated as a linear optimization problem without constraints on unit commitment. Therefore, operational restrictions, e.g., ramping rates or start-up times, for nuclear power, or any other technology, are neglected. Previous studies agree that operational detail has little impact on results if models include options for short-term flexibility, like batteries or demand-side response \citep{Poncelet2016,Poncelet2020}. In addition, most technologies subject to considerable operational restrictions are excluded from our analysis, for instance coal power plants. As a result, the approach only creates a positive bias in favor of nuclear power, which is in line with our intention to compute an upper bound on its deployment.

The temporal scope of the model consists of a single year. Using a brownfield approach, today's transmission infrastructure is available without further investment due to its long technical lifetime. In addition, the model can decide to invest into additional infrastructure. The same applies to all kinds of hydro power plants. Additional transmission capacities and all other technologies require investment to be available. Technology and demand data is based on projections for the year 2040. The model uses an hourly temporal resolution for electricity to capture fluctuations of renewables and the sensitivity of the power grid to imbalances. For other energy carriers, the model uses a coarser but at least daily resolution to reduce computational load and capture the inherent flexibility \citep{Goeke2020b}. For instance, hydrogen uses a daily resolution to capture its physical inertia and the resulting storage capabilities of pipelines. The resolutions used for other carriers are discussed in the section below. 

For timeseries of electricity demand, heat demand, and renewable supply, the model uses historic data from 2008. Since the scope only includes a single climatic year, planning does not consider extreme events with low renewable supply but high demand. On the other hand, we neither consider the risk of coincident nuclear outages threatening security of supply, for instance during the Winter of 2022/2023 in France \citep{nyt2022}.

\subsubsection{Spatial resolution and starting grid} \label{map}


The map in Fig. \ref{fig:startGrid} shows the spatial resolution of the model. The spatial scope includes the European Union plus the United Kingdom, Switzerland, Norway, and the entire Balkan region. The spatial resolution of the model divides this scope into 96 clusters with distinct energy balances and capacities. 

\begin{figure}
	\centering
		\includegraphics[scale=0.65]{figures/startGrid.pdf}
	\caption{Pre-existing grid infrastructure (solid) and new potential connections (dashed) in the model}
	\label{fig:startGrid}
\end{figure}

Representation of the electricity grid distinguishes HVAC and HVDC grids and aggregates clusters according to the balancing zones of the European power market. On the one hand, this resolution neglects interzonal congestions, but on the other hand, it allows to build on specific ENTSO-E data on limits and costs for the expansion of net-transfer capacities in the European power grid \citet{entsoe2020}. More detailed resolutions must rely on unspecific cost assumptions that range from 400 to 1,000 EUR per MW and km \citep{Fuersch2013,Gerbaulet2017}. Neglecting interzonal congestions does not impose a bias in favor of renewables and against nuclear power since nuclear capacities are typically centralized in remote areas and require substantial interzonal connection with demand centers. For renewables this is only partially true: While onshore and especially offshore wind depend on transmission grids, too, PV can be built very close to demand. In addition, we use a transport instead of flow formulation for power grid operation since previous research found this simplification to be sufficiently accurate \citep{Neumann2020a}. 

To exchange hydrogen between clusters, the model can build transmission infrastructure between neighboring clusters, or overseas in plausible cases. These pipelines are subject to costs of 0.4 million EUR per GW and km and energy losses of 2.44\% per 1,000 km \citep{DEA}. The distance between the geographic center of clusters serves as an estimate for pipeline length. 

\subsubsection{Flexibility and electricity demand}

Nuclear power has a key advantage over renewable wind or PV---it is dispatchable. In our analysis, nuclear plants are considered to be fully flexible and are not subject to operational restrictions. To what extent these characteristic drives investment strongly depends on if and how a model includes alternatives to nuclear for the provision of flexibility. One flexibility option, the interconnection of regions, is covered by the large spatial scope and consideration of transmission infrastructure in our model. This section details the representation of two additional options: energy storage and flexible demand.

First, the model includes several technologies for electricity storage. It can invest in batteries or utilize the pre-existing pumped storage and reservoir plants. Second, and more importantly, the model considers investment into storage technologies for other carriers, too. Tanks and caverns for hydrogen storage decouple electricity consumption by electrolyzers from hydrogen demand adding substantial flexibility since the modeled system requires a great amount of hydrogen for high temperature process heat and synthetic aviation fuels. In addition, using stored hydrogen for electricity generation provides an option for long-term storage that batteries or pumped storage cannot. Finally, the model includes different technologies for heat storage. At additional investment costs, electric heating systems on the consumer level can be equipped with short-term heat storages to mitigate load peaks. In heating networks storage options include water tanks for short and thermal pits for long storage durations.

Beyond storage, the model captures to what extent final demand is elastic and can adapt to supply. To represent this, it varies temporal resolution by energy carrier. For the final demand for electricity, we assume no elasticity and use an hourly resolution.

The demand for residential and industrial heat uses a 4-hour resolution, but the generation profile of each individual heating system on the consumer level is fixed to match demand. Technologies within heating networks can instead operate flexible but must jointly meet the final demand of the connected consumers, similar to the power grid. In residential heating, the 4-hour resolution captures the thermal inertia of buildings \citep{Heinen2017}; in heating networks the inertia of the network  itself \citep{Triebs2022}; and in industrial heating the possibility to reschedule processes. It should be noted that despite the 4-hour resolution, industrial heating is mostly inflexible in this approach, because demand is almost constant, and systems must continuously operate close to full capacity.

Demand from BEVs is flexible within limits: First, an hourly profile restricts charging and reflects when BEVs are connected to the grid. Second, for each day the sum of charged electricity must match consumption. To implement the latter, transport services use a daily resolution in the model. This approach is a compromise regarding the flexibility of BEVs in future power systems which is still subject to significant uncertainty. On the one hand, we assume charging can be flexible to some degree and can adapt to supply \citep{Strobel2022}. On the other, we do not consider bidirectional loading, also known as vehicle-to-grid, where BEVs can operate like regular batteries and supply energy back to the grid \citep{Hannan2022}. Apart from BEVs, other electricity consumption in the transport sector, for instance for rail transport, is inflexible and uses an hourly resolution. 

\subsubsection{Renewable supply} 

In the model, the level of investment into nuclear power depends on the potential and costs of its alternative renewable energy. Therefore, this section provides further details on the used assumptions regarding renewable supply.

Assumptions on the technical potential of wind and solar can vary substantially. In our study, we use data from \citet{Auer2020} for the potential of wind and solar. To put these numbers into context, we compare them against results of a meta-analysis on renewable potential in Germany in the appendix \ref{supEE} \citep{Risch2022}. The material demonstrates that the assumed potential is in line with results of the meta-analysis, except for PV, for which our assumptions are more conservative.

To reflect that sites for renewables differ in quality, wind and PV technologies are further subdivided. Onshore wind and openspace PV each have three sub-technologies; rooftop PV has two. Energy yield and capacity potential for each sub-technology are computed for each of the 96 clusters based on the respective distribution of full-load hours. Offshore wind is subdivided into two technologies with identical full-load hours, but different investment costs representing shallow and deep waters. Figures in section \ref{supEE} of the appendix sort the entire potential of different renewables by full-load hours and demonstrate how increased deployment results in smaller yields.

The use of biomass in each country is subject to an upper energy limit that sums to 1,081 TWh for the entire model \citep{jrc2015}. In addition to domestic production, the model can import renewable hydrogen by ship at costs of 131.8 US-\$\textsubscript{2018} per MWh and by pipeline from Marocco or Egypt at 90.7 and 86.8 US-\$\textsubscript{2018} per MWh, respectively \citep{Hampp2021}.


\section{Results} \label{main}

This section \ref{main} first compares the computed range of LCOEs for nuclear power with renewable sources. Afterwards, we present the results of the more elaborate analysis applying the energy planning model.


\subsection{Levelized cost comparison}

Based on the review of construction projections, we compute a conceivable range for LCOE for nuclear power using the formula presented in section \ref{lcoe}. Fig. \ref{fig:lcoe} compares this range against historic LCOEs on the left side (a) and against cost projections for renewable energy on the right (b). Historic LCOEs for all energy sources build on the corresponding reports by \citeauthor{lazard2021} from 2009 to 2021.\footnote{To exclude subsidies and harmonize interest rates, we re-computed LCOEs based on the reported techno-economic assumptions instead of directly copying the values in the Lazard reports \citep{lazard2009,lazard2010,lazard2011,lazard2012,lazard2013,lazard2014,lazard2015,lazard2016,lazard2017,lazard2018,lazard2019,lazard2020,lazard2021}.} The projection for nuclear results from the parameters in Table \ref{tab:assumptions}, projections for renewable sources use 2040 data from \citet{DEA} for cost assumptions and the 10th to 90th percentile of respective energy yield in Europe for full-load hours. For a full documentation of assumptions on costs and renewable potential, see the respective sections in the appendix \ref{cost_analysis} and \ref{lcoeSup}.

\begin{figure}[!htbp]
	\centering
		\includegraphics[scale=0.1]{figures/lcoeComparison.pdf}
	\caption{Comparison of LCOEs for generation technologies}
	\label{fig:lcoe}
\end{figure}

The comparison of historic LCOEs shows how, in the past, costs for nuclear power increased but dropped for renewable energy, in particular for PV. Current costs for nuclear power reported by Lazard are at the upper end of our projections for the future. For wind, current costs are already within the project range; for PV, current costs are above projections implying a continuous degression of costs. Overall, the comparison of projected LCOEs suggests that nuclear can only compete with renewables if the industry can reverse the historic trend and achieve substantial learning effects and economies of scale to reduce project costs.

\subsection{Planning model analysis}

However, comparing LCOEs for nuclear and renewables is of limited insight because nuclear and renewables ultimately provide different goods: nuclear plants are dispatchable and can, within limits, adapt supply to demand; renewable energy sources like wind and PV cannot. Therefore, we elaborate our comparison and deploy a techno-economic planning model of the European energy system for further analysis. The model captures fluctuations of wind and PV and assumes fully flexible operation of nuclear plants. Its objective is to minimize the sum of investment and operational costs for meeting energy demand in a fully decarbonized system.

Fig. \ref{fig:costShare} presents the key results of the energy system model analysis. On the left axis, the graph shows the share of nuclear power in total electricity generation depending on the overnight construction costs and time. The right axis provides the corresponding distribution of cost projections in the literature and actual costs reported by recent projects.

\begin{figure}[!htbp]
	\centering
		\includegraphics[scale=0.1]{figures/costShare.pdf}
	\caption{Generation share of nuclear and distribution of overnight cost projections}
	\label{fig:costShare}
\end{figure}

The results confirm the tentative conclusion from the LCOE analysis. Only if construction costs and time drop substantially, nuclear power provides a significant share of electricity. At 7 years construction time, overnight costs must drop to 4,120 US-\$ per kW to achieve a 10\% share in generation, at 4 years construction time this threshold increases to 4,450 US-\$ per kW. At the same time, only 20\% of overnight construction cost projections are below 4,120 US-\$ per kW and actual costs of recent projects lie above 8,000 US-\$ per kW. At the lowest construction costs, projected by \citet{oecd_full_2018}, nuclear power provides up to 52 \% of total electricity generation. Non-nuclear electricity generation largely corresponds to wind and PV. Other sources are hydro which is kept at today's level supplying 540 TWh. Biomass supplies at most 13.6 TWh since the model predominantly deploys the limited potential to cover the demand for synthetic fuels instead.

Despite its assumed flexibility, nuclear power rather substitutes than complements fluctuating supply from wind and PV generation. In the most extreme case with a 52 \% generation share, nuclear power plants are operating at a utilization rate of 94.4\%; close to the 95\% limit. This changes only slightly at smaller nuclear and consequently higher renewable shares. At a nuclear share of 7.9\%, utilization still amounts to 88.7\%, which is above the average of European nuclear plants operating today \citep{wealer_ten_2021}. This implies that even if technically capable, nuclear power is economically not well suited to provide system flexibility due to its high investment costs.

To highlight the system's renewable integration, Fig. \ref{fig:durCur} exemplarily compares the residual load curves of Germany for a system with the highest nuclear share of 52\% and no nuclear capacity at all. Residual load is the remaining electricity demand after subtracting supply of fluctuating renewables from total demand. Plotted in descending order, the curve shows the residual peak load on the y-axis, the amount of residual demand as the area above the x-axis, and excess energy as the area below the x-axis. Appendix \ref{timeSeries} shows an extract of the hourly model results from which the duration curves were computed.

\begin{figure}[!htbp]
	\centering
		\includegraphics[scale=0.1]{figures/durationCurve.pdf}
	\caption{Residual load curve for Germany in a system with a nuclear share of 52\% (left) and no nuclear at all (right)}
	\label{fig:durCur}
\end{figure}

In the graphs, there are two residual load curves: 'Flexible demand' shows the actual residual load in the model; 'inflexible demand' is computed ex-post assuming demand cannot adapt to supply. To what extent demand is flexible depends on its use. The conventional final demand for electricity is inflexible, but only constitutes around 39\% of total demand, exact shares differing from case to case. Additionally, the creation of synthetic fuels takes up 24\%, electrified transportation 20\% and heating 17\% of total electricity demand. This demand can be flexible within specific restrictions detailed in Section \ref{methods}. Some of this flexibility comes without costs, like flexible charging of battery electric vehicles, but most require the model to invest, for instance into heat or hydrogen storage.

In the 52\% nuclear system, wind and PV only account for 10\% of generation in Germany and the need for flexibility is small. The residual load is flat and does not substantially adapt to supply. For the system without nuclear, results are contrary. To reduce the amount of residual demand and excess energy, demand substantially adapts to supply. For instance, electrolyzers operate more flexibly, thereby causing their full-load hours to decrease to 3,343 compared to 5,979 in the 52\% nuclear system while more than doubling their capacity from 35.9 to 77.1 GW. Investments in heat and hydrogen storage provide additional flexibility. Storage capacities for district heating increase to 40.9 TWh compared to 18.2 Twh in the 52\% nuclear system; for hydrogen even to 12.4 from 1.7 TWh.

Coloured areas in the graph indicate how the system covers the residual load. In the 52\% nuclear system, 132 GW of nuclear operate at full capacity and cover the predominant share of residual load. Additional imports of 86.9 TWh from neighboring countries cover peak loads. Vice versa, Germany exports 78.5 TWh of excess supply. In the system without nuclear, the residual load is smaller, but imports are higher and cover 244 TWh of demand---the predominant share of residual load. Dispatchable thermal plants fueled by hydrogen and biogas only provide 7.3 TWh of generation. In both cases, there is no additional investment in electricity storage and both systems only deploy the existing pumped storage and hydro reservoirs.

Although the integration of renewables requires additional investments, nuclear power is only a cost-efficient alternative at very low construction costs as shown previously. Otherwise, investment costs of nuclear significantly outweigh the costs of renewables and corresponding flexibility options. For instance, the system without nuclear shows 9.7 billion US-\$ of additional annualized investment into demand side flexibility compared to the 52\% nuclear system. Adding 8.2 billion US-\$ for additional grid infrastructure and 3.0 billion US-\$ for thermal plants, total costs of renewable integration add up to 20.9 billion US-\$. But on the other hand, even if overnight construction costs of nuclear drop to 5,430 US-\$ per kW, the median of projections in Fig. \ref{fig:costShare}, the 52\% nuclear system is already 46.9 billion US-\$ more expensive than the system without nuclear. This 46.9 billion US-\$ difference is composed of a 67.8 billion US-\$ increase in generation costs only partially offset by 20.9 billion US-\$ of additional integration costs in the system without nuclear exclusively deploying renewables. For reference, the total costs of renewable generation amount to 150.5 billion US-\$ in this case.

Fig. \ref{fig:mapRes} further investigates the role of import and export for both systems. It shows electricity generation and net exchange of hydrogen and electricity by high-voltage alternating current (HVAC) or direct current (HVDC) grids for each country. Exchange of hydrogen and electricity increases substantially in the system without nuclear reflecting the 8.2 billion US-\$ rise of costs for grid infrastructure. The maps show that this infrastructure not only serves renewable integration but reduces generation costs as well because it allows to utilize renewables where full-load hours are highest, for instance in southern Europe for PV or in the North Sea for offshore wind.

\begin{figure}[!htbp]
	\centering
		\includegraphics[scale=0.65]{figures/mapResults.pdf}
	\caption{Electricity generation and exchange the 52\% nuclear system (top) and the system without nuclear (bottom)}
	\label{fig:mapRes}
\end{figure}

For a comprehensive overview of energy flows and conversion processes in the compared energy systems, see appendix \ref{sankey}. 

\section{Discussion} \label{diss}

Although building on an extensive review of cost projections and a detailed planning model, our analysis faces some inevitable limitations. Overall, these limitations impose a positive bias on nuclear power, so results are rather an upper bound than reliable estimates for the cost-efficient share of nuclear. 

First, there are simplifications of the techno-economic model itself. We consider construction cost of nuclear (and all other technologies) as exogenous, although costs can depend on the level of investment due to learning effects. Therefore, cases in Fig. \ref{fig:costShare} with low nuclear shares, but construction costs dropping below 5,000 US-\$ per kW, are implausible. If learning can in fact achieve such a drop in costs, it will require capacity investments that will already raise the share of nuclear in power generation above 10\%. To achieve this share, 41 GW of nuclear would have to be built which approximately corresponds to 25 EPR-sized reactors. A nuclear share of 50\% requires 132.5 GW of capacity, i.e. 83 EPR-sized reactors. Given the current state of ongoing projects in France, Finland and the UK, this seems rather challenging \citep{Rothwell2022}. Considering learning effects endogenously is not an option, due to the uncertainty of their existence and computational limits \citep{Berthelemy2015,Grubler2010, harding_economics_2007}.

The model focuses on the single year 2040, but decarbonization of the energy system is a process over several decades. Computational limits however require to limit the analysis to one year. On the one hand, this year should be sufficiently far in the future to allow for learning effects of nuclear. On the other hand, years further into the future will increasingly favor renewables since learning effects are expected to keep reducing their costs, too \citep{DEA}. Against this background, we choose 2040 as the earliest date until that substantial reductions of costs are conceivable, an optimistic assumption considering the construction times of recent European nuclear projects.

On the more technical side, we omit unit commitment constraints, as already mentioned. Of all considered technologies, these operational restrictions are most pronounced for nuclear power. The method section discusses further technical limitations like the representation of extreme events and grid constraints.

Second, some adverse characteristics of nuclear power escape the techno-economic perspective of the analysis. For instance, costs of managing nuclear waste and decommissioning old plants are substantial but not included in our analysis due to unavailability of reliable data and the long time frame \citep{lordan2021, Lovins2022}. Furthermore, nuclear power carries the risk of severe accidents, proliferation of nuclear material and radioactive contamination \citep{leveque2014, wheatley_reassessing_2016, lehtveer_nuclear_2015}. Although robust quantification of these externalities is difficult and therefore not part of the analysis, their social costs typically exceed estimates for renewable energy \citep{stirling_limits_1997}.

\section{Conclusion} \label{conclusion}

Our least-cost analysis indicates that nuclear power is only a cost efficient option for full decarbonization of Europe's energy system if construction costs at least half and drop below 4,000 US-\$\textsubscript{2018} per kW. In contrast, costs and construction time for nuclear power in the last ten years have been increasing rather than decreasing. This assessment uses optimistic assumptions for other characteristics of nuclear, like availability and operational costs, and still omits social costs, like the risk of accidents or waste management, since these externalities escape robust quantification.

Results show that nuclear power reduces investments into system flexibility. Since nuclear plants are, in contrast to wind or PV, dispatchable, their system integration induces lower costs for grid infrastructure, energy storage, demand-side flexibility, or thermal backup plants. However, if generation costs of nuclear do not drop substantially, they outweigh this benefit. For instance, assuming overnight construction costs of 5,430 US-\$ per kW, the median of compiled projections, a 52\% generation share of nuclear will reduce investments into system flexibility by 20.9 bn US-\$ per year but increase generation costs by 67.8 bn US-\$ or 44\% compared to a fully renewable system. 

A crucial detail to understand these results is that apart from grid infrastructure, most investments into system flexibility occur outside of the power sector. Instead of battery storage or conventional demand-side management, new electricity demand induced by the decarbonization of heating, transport, and industry adds substantial flexibility. For instance, hydrogen production, accounting for 25\% of electricity demand, supports renewable integration by adapting to renewable supply and using storage to match production with demand.

Results do not indicate that fluctuating renewables and flexibly operated nuclear plants are economic complements. Even when neglecting operational restrictions, nuclear power runs at utilization rates close to 90\%. From a cost perspective, it is preferable to invest into system flexibility rather than running capital-intensive nuclear plants at low utilization rates.

Our analysis puts previous least-cost analyses on nuclear power that were limited to the power sector and a single country into perspective. As we showed, this setup omits two key options for system integration of fluctuating renewables: First, grid infrastructure connecting regions with different generation profiles, and second, the potential flexibility of electricity demand added to decarbonize the heating, transport, and industry sector. As a result, previous analyses overestimated the value of dispatchable nuclear power plants. Not considering other types of firm generation, like hydrogen or biogas fueled plants, adds to this bias.

Our results suggest that efforts to advance nuclear technology---if undertaken at all---should focus on reducing costs and construction time. If plans to extend nuclear capacity are followed through, and renewable investments consequently neglected, project construction delays might put European energy security at risk. Concepts for more flexible operation are not promising because even fully flexible plants almost exclusively operate at full capacity for economic reasons. Since the share of nuclear also affects investments into grid infrastructure and energy storage, path dependencies in system development arise. The risk of nuclear power not achieving substantial cost reductions should thus be accounted for in long-term planning. Potential non-electrical applications for nuclear power, such as high temperature provision for industrial processes, are not considered in this paper but should be addressed in future research.

\section*{Supplementary material}

All data and running scripts used in this paper are openly available here: \url{https://github.com/leonardgoeke/EuSysMod/tree/greenfield_nu} Due to their size, model outputs are not part of the repository but are available upon request.

The applied model uses the open AnyMOD.jl modeling framework \citep{Goeke2020a}. The applied version of the tool is openly available under this link. \url{https://github.com/leonardgoeke/AnyMOD.jl/releases/tag/flexibleElectrificationWorkingPaper}

\section{Acknowledgments}

The research leading to these results has received funding from the Deutsche Forschungsgemeinschaft (DFG) under project number 423336886.

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