In This Issue
Fall Issue of The Bridge on Nuclear Energy Revisited
September 15, 2020 Volume 50 Issue 3
The desire to reduce the carbon intensity of human activities and strengthen the resilience of infrastructure key to economic prosperity and geopolitical stability shines a new spotlight on the value and challenges of nuclear energy.

# Chasing Cheap Nuclear: Economic Trade-Offs for Small Modular Reactors

Wednesday, September 16, 2020

The costs of first-of-a-kind small modular nuclear power reactors (SMRs) and microreactors (<10 MWe capacity) are expected to be high when compared with those of historical large-scale light water reactors (LWRs). There is widespread uncertainty in the nuclear industry about the cost drivers of small reactors after first-of-a-kind builds. “Learning by doing” could result in substantial cost declines as small reactors are deployed in series, facilitated by rapid factory production. On the other hand, scale inefficiencies in small reactors could keep their unit costs stubbornly higher than large-scale designs. These dynamics suggest a trade-off between learning effects and scaling effects in the cost trajectory of small reactors.

Background

Recent large-scale reactor builds in the United States and Europe have been prohibitively expensive as costs escalated over time. Several utilities in the Americas, Europe, and Asia are considering building small reactors as an alternative to new investment in large reactors.

SMRs can provide novel services that large designs have not, including off-grid and emergency power ­supply, and collocated industrial process heat. Additionally, hybrid energy systems could incorporate SMRs with renewables to produce a mix of electricity, heat, and hydrogen to optimize economic performance (Aumeier et al. 2011). If small reactors can achieve consistent learning effects over sustained deployment, unit-cost parity with large designs may be possible.

Because factory-produced commercial nuclear ­power reactors have never been deployed, there is little understanding of how their cost will evolve. Therefore, estimating potential learning effects is a theoretical exercise.

By combining analysis of scaling and learning effects, we explore theoretical deployment levels where SMRs and microreactors reach unit-cost parity with conventional reactors as a function of starting costs, learning rates, and scaling factors. Using ranges of possible values for each parameter, we illustrate potential pathways for microreactor cost evolution.

This study serves two purposes: first, it establishes realistic boundaries on the cost evolution of SMRs and microreactors to help inform investment policy; second, it provides empirical support for attempts to understand comparative learning and scaling effects in factory-fabricated nuclear reactors. We conclude by suggesting policies to drive learning effects and minimize dis­economies of scale.

Economies of Scale for Nuclear Power Plants

Predictions for the growth of commercial nuclear power in the 1950s were predicated on the expectation that the larger reactors of the future would be more cost-efficient. But such economies of scale were not realized.

Early commercial reactors in the United States had capacities of approximately 250–500 MWe per reactor. In the 1960s the industry began building larger reactors, approaching 1 GWe per reactor, but they were considerably more expensive, contradicting the expectation of economies of scale and contributing to the sharp decline in US nuclear construction.

The literature reports a surprisingly small number of attempts to resolve the disparity between expectation and reality for nuclear scaling economics. One study argued that the cost escalation experienced in the US nuclear power industry was caused by industry over­estimation of the scaling effect, which led to an ineffi­cient overincrease in unit size over time (­Zimmerman 1982). Another found that increases in reactor size tended to extend construction duration and thus escalate costs (Cantor and Hewlett 1988). More recently, studies have cited increased reactor size and ­complexity (­Koomey and Hultman 2007). In France, “big size ­syndrome”—the nuclear industry built inefficiently larger and more complex plants as it gained experience with the ­technology—resulted in both longer lead times and higher costs (Escobar Rangel and Lévêque 2015). In short, much of the literature argues that the larger ­nuclear designs were too complex to be built cost-effectively.

Scaling Relations

Scaling relations are used to predict the cost of scaled-up or scaled-down versions of equipment and processes. For commercial nuclear, scaling relations can connect the empirical costs of large reactors with expected costs of smaller reactors, assuming they are of similar technology.

In an attempt to quantify the trade-offs between economies of scale and other economies for SMRs, the International Atomic Energy Agency (IAEA 2013) proposes a scaling relation to predict the first-of-a-kind (FOAK) cost for an SMR, given by the following equation:

$$Cost_{SMR} = Cost_{NPP}×\left({SMR \quad NWe \over NPP \quad MWe}\right)^{n-1}$$

where CostSMR is the overnight capital cost (OCC) of the SMR per unit of capacity, CostNPP is the OCC of a large-scale nuclear power plant (NPP) per unit of ­capacity, MWe is the rated power capacity of each, and n is the scaling factor. The IAEA scaling relation applied to reactors of similar designs, so we group reactors in our dataset into fleets of similar designs. The applicability of the empirical scaling factors to a future small reactor design will depend on its similarity to existing technology.

Multiple studies have attempted to estimate the scaling factor for nuclear plants. A survey of 26 studies of economies of scale in nuclear power found a range from n = 0.25 to n = 1, the latter indicating no scaling effect (Bowers et al. 1983). Unfortunately, the surveyed ­studies include nuclear cost data only through 1982 and are largely restricted to US data. Despite these serious limitations, the scaling factors from the 1983 study are still widely used. For example, their use in a 2010 model of potential costs for small and medium modular reactors suggested that higher costs for smaller reactors might be offset by modularization and fabrication strategies (Carelli et al. 2010). The IAEA (2013) 250 MW SMR case study used a median value of n = 0.6, and a more recent study (Moore 2016) used the Bowers et al. midpoint value, n = 0.55, in scaling down the cost of a 1000 MW reactor to a 10 MW microreactor.

Figure 1

As an illustrative exercise, we apply the IAEA scaling relation (shown in the equation above) to the cost and size of a Westinghouse AP1000 reactor being built in the United States, assuming an OCC of $5500/kW and capacity of 1100 MW. Figure 1 shows the ­hypothetical FOAK costs for an SMR as a function of ­capacity (2.5–300 MW, with four scaling curves covering the range of scaling factors considered by IAEA, n = 0.4–0.7. While the scaling relation assumes that the scaled-down technology remains broadly similar, it can be useful to apply such an equation to advanced SMRs and microreactors as a form of benchmarking. But before we can do so, we need to reexamine what is a realistic range for scaling factor n. Past studies of nuclear costs, scaling, and learning generally had access only to US and French cost data. We use a much larger global dataset of nuclear construction costs across eight countries (Lovering et al. 2016) and group reactors broadly by technological similarity, as summarized in table 1. Table 1 To estimate the empirical scaling factors and learning rates in these groups, we construct a multiple linear regression with ordinary least squares. The regression specification is based on a simplified version of models used by Cantor and Hewlett (1988) and Escobar Rangel and Lévêque (2015), among others. $$\log(OCC_i)=\beta_0+\beta_{size}\log(\text{Capacity} _i) +$$$$\beta_{leadtime}\log(\text{Leadtime}_i) + \log(\text{CountryExp}_i)+$$$$\beta_{AtSite}(\text{AtSite} _i)+\epsilon_i$$ where we define the following variables: OCCi: overnight construction cost in 2010 USD per kW Capacityi: reactor capacity in MWe Leadtimei: time between construction start and commercial operation CountryExpi: cumulative installed capacity in MW in country prior to reactor construction start AtSitei: number of operating reactors at site at construction completion. We use the equation n = βsize + 1 to derive for each fleet the scaling factor n from the regression coefficient βsize. Although we see a large range of scaling factors from our data (table 1), the IAEA report is clear that the scaling relationship is meant only for very similar designs (i.e., just a scaled-down version of the large reactor). Past studies have drawn primarily on US data and thus primarily on LWR designs; our historical dataset includes designs for gas-cooled and heavy water reactors as well as LWRs. Many SMRs in development—high-temperature gas-cooled reactors, salt-cooled, metal-cooled, and fast—are non-LWRs. Our scaling factors thus give a more robust approximation of boundary conditions on the range of FOAK costs for SMRs and microreactors, relative to past studies restricted to LWR data. Scaling Applied to Microreactors Moore (2016) scales down costs from a 1000 MW reactor to a 10 MW microreactor using a factor of n = 0.55 and finds the microreactor OCC to be$35,000/kW—more than seven times the unit cost of the large reactor.

Two SMRs in the United States are currently going through licensing: NuScale’s 60 MW LWR and Oklo’s 1.5 MW fast reactor. Using our range of scaling factors from the historical data (n = 0.2−0.8), we estimate the FOAK costs for these two designs.

Scaling the AP1000 cost down to the 60 MW ­NuScale reactor would result in a FOAK cost ranging from $9800/kW to$56,000/kW, depending on the scaling factor. The upper figure appears unreasonably expensive, even for the most overbudget nuclear projects worldwide. Even the lower bound of nearly $10,000/kW is much higher than NuScale’s estimate of$4400/kW (NuScale 2020), which is actually less than the realized cost of the AP1000. For a smaller unit, like Oklo’s 1.5 MW reactor, the scaling relation yields even more unrealistic figures: $21,000/kW−$1.1 million/kW, depending on the scaling factor.

Of course, this scaling relation was meant to apply to similar technologies, and Oklo is a very different reactor from the AP1000. Even NuScale’s LWR is likely too dissimilar to make a scaling relation applicable. However, it is useful to note that early solar photo­voltaic (PV) panels started at similarly exorbitant costs—about $100,000/kW in the 1970s—and are now below$2000/kW (Nemet 2006). And while solar panels may seem like a “simpler” technology (that could therefore experience faster learning), the same cost trajectory is seen with the modern jet engine turbine, a very complicated piece of engineering with peak output >10 MW: its costs are now less than $1000/kW. The discrepancy between modeled and projected FOAK costs highlights an important point: economies of scale and reactor capacity are not the only factors that will affect the cost of an SMR in comparison to a large NPP. NuScale (2020), for example, explains the lower cost estimate for its SMR based on design simplicity, as its proposed reactor has “no reactor coolant pumps, no external steam generator vessels, and no large-bore reactor coolant piping.” The IAEA report notes that other nonscaling factors (e.g., learning effects, expedited construction schedules, and rapid deployment rates) may outweigh most of the diseconomies of scale. The report looks at a case study comparing four 250 MW SMRs with a single 1000 MW NPP. Using the scaling equation above, it finds that the OCC of the FOAK SMR will be 74 percent higher, but the benefits from other factors reduce the total capital investment of the project to only 9 percent more than the large-scale plant. The biggest contributor to that reduction is the learning associated with the construction of multiple units at the same site. Learning Curves As microreactors are deployed in series, unit costs are likely to decline in a process known as economies of volume or learning by doing. For large stick-built (i.e., nonmodular) power plants, the more common metric is to look at how capital costs decline with cumulative installed capacity. These so-called “experience curves” track industrywide learning across a country or region, rather than on an assembly line. Early studies of cost trends for nuclear power found that the technology had experienced positive learning (Cantor and Hewlett 1988): construction costs decreased with increased firm experience. But more recent analyses have found negative learning, or forgetting by doing, where costs increase as firms or countries gain experience (Cooper 2010; Grubler 2010).[1] Since no country has constructed a series of commercial SMRs, it is difficult to predict what the learning curve will be with factory fabrication.[2] While China has brought more than 40 reactors online over the last decade, with another 10 under construction, they were all large-scale stick-built construction projects. Learning rates of other electricity-generating technologies may provide useful context. Rubin and colleagues (2015) aggregated learning rates from the literature and found rates ranging from −11 percent for onshore wind and combined cycle natural gas to 47 percent for PV solar panels (table 2). Table 2 Using our multifactor regression and a dataset of 369 reactors in 8 countries, our model finds that most fleets experienced statistically significant negative learning (table 1). To convert from our regression coefficient for country experience to a learning rate, we use the following two equations: b = eβexp and LR = 1 – 2b. With the exception of South Korea, none of the countries experienced significant positive learning—they all got more expensive with cumulative country experience. Great Britain, the US early phase, and the French early phase do show positive learning, but the result is not significant (likely because of the small number of reactors and confounding factors in those groups). However, with stick-built large infrastructure like the large NPPs in this dataset, it is difficult to achieve the same degree of learning that is possible from serialized factory fabrication. (A recent survey of learning rates for energy technologies finds that learning effects are stronger for smaller-capacity technologies; Sweerts et al. 2020.) Trade-Offs Between Economies of Scale and Learning Effects How is it possible to determine the trade-offs between large and small reactors before building the first SMR? On one side are those who argue that bigger nuclear power plants, if built successfully, will be cheaper thanks to economies of scale. On the other are proponents of SMRs, who argue that the benefits of factory fabrication will accelerate learning effects and drive down costs with successive builds. To start, we analyze the theoretical intersection of these two effects and put boundaries on the relevant parameters based on historical nuclear data and lessons from other electricity-generating technologies. To find this hypothetical crossover point, we assume two different nuclear reactor technologies: Reactor1 is a conventional, large LWR, while Reactor2 is an SMR. Using the standard learning curve formulation, the cost of the uth unit built for each reactor is given by the equations for c1 and c2 below, where c1,0 and c2,0 are the FOAK cost for each reactor, and b1 and b2 are the learning ­factors for each reactor. $$c_1(u_1)=c_{1,0}u_1^{b_1}$$ $$c_2(u_2)=c_{2,0}u_2^{b_2}$$ To calculate break-even deployment, each learning curve must be formulated as a function of deployed capacity, rather than units, so we replace u1 = G/s1 and u2 = G/s2, where G is the total capacity deployed for each reactor, and s1 and s2 are the sizes of each reactor. Plugging these into the equations for c1 and c2 above, setting them equal, and solving for G: $$c_{1,0}(G/s_1)^{b_1}=c_{2,0}(G/s_2)^{b_2}$$ $$G=\left(c_{2,0}s_1^{b_1}\over c_{1,0}s_2^{b2}\right)^{1\over b_1-b_2}$$ This provides an analytical expression for the break-even deployment, G—that is, how many SMRs are needed to reach cost parity with the large reactor. The units of G will be the same as the units of s1 and s2, whether in kW, MW, or GW. We apply these break-even equations to our 60 MW SMR and 1.5 MW microreactor examples to see the range of cost trajectories. If economies of scale are significant (n = 0.2) and learning is slow (LR = 5 percent), then it is infeasible for either reactor to reach cost parity with the AP1000 (if learning by doing is the only cost reduction mechanism). However, if economies of scale are less important (n = 0.8) and learning occurs faster (LR = 25 percent), then it would be necessary to deploy only 230 MW of the 60 MW reactor (4 units) or 32 MW of the 1.5 MW reactor (21 units). And if these scaling relations simply do not apply (i.e., the technologies are too dissimilar), the simplified break-even equation can be used to understand the effects of reactor size and learning rate. Figure 2 shows the break-even volume for a 60 MW and a 1.5 MW reactor, assuming they both have FOAK costs of$11,000/kW (twice the cost of the AP1000). Even at slower learning rates, smaller reactors experience faster cost reductions, because more units are being built.

Figure 2

Policy Implications of a Transition to Small Modular Reactors

From the historical cost data, it is clear that most countries experienced economies of scale in their large ­reactor fleets, from a scaling factor of 0.2 in Canada to 0.8 in the United States. However, these were fleets of very similar technology, and it is unclear how well these scaling factors would apply to radically different types of advanced reactors and microreactors.

But the historical data also show that almost every country experienced negative learning (costs rose with cumulative country experience). In contrast, for other energy technologies that are modular, like gas turbines and solar panels, positive learning rates could be as high as 35–45 percent. With even modest learning rates of 10–20 percent, SMRs could reach cost parity with large reactors after a dozen units, even if they start out at twice the cost. This is certainly relevant to the fledgling industry, and has significant policy implications for the future competitiveness of smaller reactors.

While the goal of SMR and microreactor vendors may be full factory fabrication, the first few units will likely be built on site. These FOAK costs may be much higher than the eventual factory-fabricated units. ­Policies to support demonstration and deployment of SMRs should build in resiliency to higher FOAK costs, for example through direct government procurement, public-private partnerships for demonstrations, and loan guarantees for manufacturing facilities.

Vendors will likely need orders for tens of reactors to justify the investment in factory facilities to manufacture modular reactors. For comparison, Boeing and ­Airbus line up a few hundred orders for new aircraft before the first one rolls off the assembly line (Lovering et al. 2017).

Federal policy that stimulated demand is ultimately what led to large cost declines for solar technologies (Nemet 2006). For small and microreactors, similar ­policies could include production and investment tax credits, federal power purchase agreements, state-level clean energy mandates, direct government procurement, and a streamlined licensing process for modular reactors.

Conclusion

The International Energy Agency and Nuclear Energy Agency argue that global nuclear capacity will need to double by 2050 to meet aggressive climate targets and match growing demand for energy (IEA and NEA 2015). This implies adding roughly 400 GW of new nuclear capacity and another 200 GW to replace ­retiring units. Most of the new capacity will likely come from large reactors, but if just 25 percent comes from SMRs that will equate to 2500 60 MW reactors or 100,000 1.5 MW reactors—large enough volumes to experience significant learning by doing and cost reduction.

While SMRs and microreactors are considered appropriate for niche markets today, this analysis shows that with significant volume, there is potential for their cost to decline enough to be competitive with large nuclear power plants. With targeted policies and fast learning rates, SMRs could reach cost parity with fossil fuels before 2050.

References

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Cantor R, Hewlett J. 1988. The economics of nuclear power: Further evidence on learning, economies of scale, and regulatory effects. Resources and Energy 10(4):315–35.

Carelli MD, Garrone P, Locatelli G, Mancini M, Mycoff C, Trucco P, Ricotti ME. 2010. Economic features of ­integral, modular, small-to-medium size reactors. Progress in ­Nuclear Energy 52(4):403–14.

Cooper M. 2010. Policy challenges of nuclear reactor construction, cost escalation and crowding out alternatives. Institute for Energy and the Environment, Vermont Law School.

Escobar Rangel L, Lévêque F. 2015. Revisiting the cost escalation curse of nuclear power: New lessons from the French experience. Economics of Energy and Environmental ­Policy 4(2).

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[1]  Nuclear power is not alone in experiencing negative learning rates: one study found that onshore wind and natural gas combined cycle plants also experienced negative learning over specific time periods (Rubin et al. 2015).

[2]  An obvious exception is, of course, nuclear navies. The US, Russian, UK, and French navies have built small modular propulsion reactors for their nuclear submarines and aircraft carriers. While their cost data would be quite illustrative for commercial SMRs, attempts to obtain this information have been futile. Similarly, cost data are scarce for large-scale commercial power reactors recently built in China.

About the Author:Jessica Lovering is a doctoral student in the Engineering and Public Policy Department at Carnegie Mellon University. Jameson McBride is a senior research analyst at the Breakthrough Institute and a graduate student in the Technology and Policy Program at MIT.