Minimizing the economic cost and risk to Accelerator-Driven Subcritical Reactor technology. Part 2: The case of designing for flexibility

Nuclear Engineering and Design 243 (2012) 120–134

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Minimizing the economic cost and risk to Accelerator-Driven Subcritical Reactor technology. Part 2: The case of designing for flexibility Michel-Alexandre Cardin a,∗ , Steven J. Steer b , William J. Nuttall b,c , Geoffrey T. Parks b , Leonardo V.N. Gonc¸alves b , Richard de Neufville d a

Department of Industrial and Systems Engineering, E1A #06-25, National University of Singapore, 117576, Singapore Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, United Kingdom c Judge Business School, University of Cambridge, Cambridge CB2 1AG, United Kingdom d Engineering Systems Division, E40-245, Massachusetts Institute of Technology, Cambridge, MA 02139, United States b

a r t i c l e

i n f o

Article history: Received 16 February 2011 Received in revised form 20 November 2011 Accepted 21 November 2011

a b s t r a c t This paper presents a simple, systematic, and integrated methodology to analyse the expected Levelised Cost Of Electricity (LCOE) generation of a new nuclear technology facing significant technological uncertainty. It shows that flexibility in the design and deployment strategy of a demonstration commercial thorium-fuelled Accelerator-Driven Subcritical Reactor (ADSR) park significantly reduces the expected LCOE. The methodology recognizes early in the conceptual design a range of possible technological outcomes for the ADSR accelerator system. It suggests appropriate flexibility “on” and “in” the first-of-a-kind design to modify the demonstration park development path in light of uncertainty realizations. It then incorporates these uncertainties and flexibilities in the design evaluation mechanism. The methodology improves existing approaches for design and engineering decision-making, providing guidance for government support for a new, secure, clean, and publicly acceptable alternative technology for power generation. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Thorium-fuelled Accelerator-Driven Subcritical Reactor (ADSR) technology is a promising avenue for the transmutation of radioactive wastes (Bowman et al., 1992; Foster, 1974), and for secure, low-emission, and more publicly acceptable power generation (Carminati et al., 1993). It consists of a nuclear reactor core operating subcritically, and a high-power proton accelerator that bombards a spallation target within the reactor core to generate neutrons. These externally supplied neutrons supplement the reactor’s own neutron population and sustains a fission chain reaction, as in Fig. 1. This technology offers new opportunities to governments concerned with limiting CO2 emissions, reducing risks associated with nuclear weapons proliferation and geological waste disposal, and sustaining prosperous economic development. In countries with considerable thorium reserves (e.g. India), it has the potential to capture a non-trivial segment of the growing electricity market. In other countries, it can help diversify the portfolio of low CO2 -emitting technologies.

∗ Corresponding author. Tel.: +65 6516 5387; fax: +65 6777 1434. E-mail addresses: [email protected] (M.-A. Cardin), [email protected] (S.J. Steer), [email protected] (W.J. Nuttall), [email protected] (G.T. Parks), [email protected] (R. de Neufville). 0029-5493/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2011.11.026

Developing thorium-fuelled ADSR technology promises to be technically challenging, economically risky, and capital-intensive. Traditional nuclear power technology demands a large capital cost (Pouret et al., 2009), and requires many years of pre-development, construction, and testing before providing online capacity. An ADSR’s further requirement of high-powered accelerator technology will demand additional capital commitment, and will therefore involve significant extra financial uncertainty. Given the high upfront cost, one needs a realistic and reliable picture about the expected returns, one that explicitly recognizes how the first-of-a-kind demonstration of the technology might perform. There is much uncertainty associated with how technology will develop during the initial deployment phase of a first-of-a-kind ADSR demonstrator. This uncertainty will ultimately affect the Levelised Cost Of Electricity (LCOE) generation, which is a useful metric for evaluating economic performance and the value that a project is expected to return. One concern unique to ADSRs compared to other nuclear technology relates to the reliability of the accelerator supplying the proton-beam. If an unplanned shutdown of an accelerator leads to an ADSR shutdown, costs will be incurred due to failing to supply the electricity grid (Steer et al., 2009). Alternatively if unplanned shutdowns are eliminated through spending additional time performing maintenance on the accelerator, there is less time to schedule electricity generation and sales.

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Fig. 1. Conceptual representation of an ADSR system for power generation. Adapted from Rubbia et al. (1995).

To address these issues, this paper introduces and applies a simple, systematic, and integrated methodology to evaluate design and deployment strategies for innovative systems facing significant technological uncertainty. The starting point of the methodology for ADSRs is the technical design descriptions of a first-of-a-kind ADSR system offered in the companion paper by Steer et al. (2012). The methodology enables engineers and decision-makers to: (1) recognize explicitly uncertainty sources affecting the expected performance of the system; (2) incorporate the concept of flexibility in design and management with the goal of improving performance; and (3) evaluate the design space based on expected economic impact, to guide decision-making for large-scale investment and deployment. The integrated methodology has been applied to investigate the hypothesis that inserting flexibility early in the conceptual design of an ADSR can improve the expected economic performance while testing and validating the technology. One anticipates that flexibility will lower the expected development and deployment cost of the system. The methodology builds upon and extends standard practice for design and decision-making in engineering by considering a priori a range of uncertain outcomes affecting costs, and adequate flexible responses. This approach differs from sensitivity analyses performed after an initial design is selected. It recognizes intelligent design and pro-active system management as uncertainty unfolds. The methodology provides a framework for evaluating designs, and assessing the expected value of flexibility so it can be compared to the cost of acquiring the flexibility. The remainder of the paper is structured as follows. Section 2 provides an overview of related work in flexibility/real options analysis in an engineering context, together with previous work specifically focusing on the nuclear sector. Section 3 explains the integrated methodology, and Section 4 follows with an example application to the deployment of a demonstration commercial ADSR park. Section 5 concludes by discussing modeling assumptions and limitations, as well as findings. It also provides guidance for future work. 2. Related work 2.1. Flexibility in engineering design/real options Flexibility in engineering design enables a system to change easily in the face of uncertainty (Fricke and Schulz, 2005). It is associated to the concept of real options, providing the “right, but not the obligation, to change a project in the face of uncertainty” (Trigeorgis, 1996). Real options “on” a project tend to involve

higher-level managerial decisions such as abandoning, deferring until favorable market conditions arise, and investing in research and development (R&D) (Trigeorgis, 1996). Real options “in” a project include strategies like expanding/contracting/reducing capacity, deploying capacity over time, switching inputs/outputs, and/or mixing the above. They differ from real options “on” projects because they require careful engineering of system components, or possibly changes in their design to enable the flexibilities in operation (Wang and de Neufville, 2005). To be captured they need to be considered in the early conceptual design phase. The real options analysis (ROA) literature typically focuses on the economic valuation of flexibility (Dixit and Pindyck, 1994; Myers, 1977; Trigeorgis, 1996). It builds upon the theory of financial options developed by Black and Scholes (1973) and Cox et al. (1979). Many studies have shown that flexibility in engineering projects can bring expected performance improvements ranging between 10% and 30% compared to standard design and evaluation methods (Amram and Kulatilaka, 1999; Copeland and Antikarov, 2003; de Neufville and Scholtes, 2011). Expected performance improvements arise by affecting the distribution of system responses, rather than optimizing a pinpoint design for a set of deterministic projections. Flexibility reduces the effect from downside, risky scenarios, while positioning the system to capitalize on upside, favorable opportunities. For example, Pindyck (1993) showed that additional economic value exists when managers recognize the flexibility to abandon construction of a new nuclear plant if technology and cost evolve unfavorably. This strategy protects from downside uncertainties, which can only be resolved once the irreversible investment is made. Examples in other industries include: strategically phasing the development of airport terminals over time (de Neufville and Odoni, 2003), designing offshore platforms for future capacity expansion (Jablonowski et al., 2008), adapting supply chains flexibly to uncertain currency exchange rates (Nembhard et al., 2005), etc. It is important to consider uncertainty and flexibility early and systematically in the conceptual design phases of engineering systems. Design rigidity and relying too much on–sometimes over optimistic–deterministic projections of future conditions may contribute to the failure of an engineering system. This was the case for the Iridium satellite-based cell phone system, which filed for bankruptcy in 1999. The 77 Low Earth Orbit (LEO) satellite infrastructure, developed for the cost of U.S.$4 billion, enabled phone calls anywhere on the planet. The technology met its design goals; however, the design and management processes were centered on optimistic demand projections. This led to a rapid deployment strategy of the entire constellation between May 1997 and May 1998 (MacCormack and Herman, 2001). The projected demand did

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not materialize, and so the system failed to cover its financing costs. Given that it was designed to accommodate a very optimistic view of the future, the system was not capable of adapting to a different, less favorable reality. The rigidity in the design and deployment of Iridium, combined with underestimation of land-based cell phone demand, are suspected to have caused the economic failure (de Weck et al., 2004). In this case, a flexible staged deployment strategy could have improved economic performance. de Weck et al. (2004) showed that deploying the constellation in phases and adding capacity only when demand surpassed installed capacity could have saved about 20% in expected development costs. This approach, however, would have required a radically different design: one where each satellite can change orbit, so the overall orbital configuration of the constellation can be changed to accommodate changing coverage areas. 2.1.1. Challenges Designing engineering systems for uncertainty and flexibility is a challenging process. It can benefit from some guidance based on previous experience, industrial lessons, and on-going research. One difficulty resides in quantifying the benefits of flexibility relative to the additional costs and design efforts sometimes required. To this end, the work done in the ROA literature aims to allow such quantification of the economic value of flexibility in engineering systems. Another recognized issue in applying ROA to engineering systems is one of the cultural resistances, where engineers may be trained to think in a linear fashion about future operating conditions (Minai et al., 2006). Designs are often optimized for a set of forecasts, requirements and constraints, even though those are prone to change (Eckert et al., 2009). A further issue is that it may not be clear where to focus the design effort for flexibility, because so many design variables, parameters, and uncertainty scenarios can be considered (Braha et al., 2006). In addition, traditional financial tools for valuing projects based on Discounted Cash Flow (DCF) and Net Present Value (NPV) do not integrate adaptive management over time, assuming instead that the future and system will remain static or follow a predictable course (Amram and Kulatilaka, 1999; Dixit and Pindyck, 1994; Trigeorgis, 1996). This paper addresses some of these issues by suggesting an integrated methodology to guide designers and decision-makers more systematically in the conceptual process of designing a complex engineering system for uncertainty and flexibility. The methodology integrates explicitly a quantitative valuation mechanism to discriminate between different flexible design alternatives. It induces designers to think explicitly about flexibility strategies (i.e. deferring and expanding), and enablers (i.e. concrete design components enabling the strategies to be realized) more systematically, given the major uncertainty drivers facing the system. This approach differs from the work typically done in the ROA literature, which assumes that the engineering mechanism is enabled, so the focus can be on economic valuation. 2.2. Previous work on flexibility/real options in the nuclear sector Previous studies have evaluated flexibility/real option strategies in the context of nuclear technology. For instance, Kiriyama and Suzuki (2004) have assessed the value of waiting for optimal market conditions before investing in a new nuclear build (i.e. a deferral option). They used an approach similar analytically to Pindyck (2000), although relying on CO2 emission credit as the driving source of uncertainty. Rothwell (2006) studied the optimal timing for a new nuclear build in the United States. He assumed that a portfolio of tradable assets – both real and financial – was available to replicate the project cash flows, based on the dynamic programming approach by Dixit and Pindyck (1994). Abdelhamid et al. (2009) used a similar approach to evaluate the option to defer

investment in the first nuclear plant built in Tunisia. Loubergé et al. (2002) valued the optimal timing for nuclear waste disposal in deep geological formations, also a deferral option. Siddiqui and Fleten (2008a) valued a portfolio of government investments in R&D for a large-scale alternative energy source. They considered mainly nuclear energy, alongside existing renewable energy technology. Siddiqui and Fleten (2008b) also calculated the value of the flexibility to stage R&D in thorium-fuelled nuclear technology. Marreco and Carpio (2006) used a binomial lattice methodology based on the approach by Cox et al. (1979) to value the flexibility to switch between nuclear thermoelectric and hydroelectric generation in the Brazilian power system. These studies show that there is a growing interest in applying flexibility/real options techniques in the nuclear sector. Presently, most of the work focuses on valuing the flexibility to defer investment decisions in nuclear technology. These are examples of managerial real options “on” systems. They do not require significant design modifications from a detailed engineering standpoint. Only a few studies discuss the staging flexibility strategy (Siddiqui and Fleten, 2008b) and switching between technologies (Marreco and Carpio, 2006). Not much work has focused on how to design and engineer the strategies, and how to enable them concretely in the project. Specifically, to the authors’ knowledge, no study has yet focused on applying such design thinking to first-of-a-kind commercial thorium-fuelled ADSR technology for power generation. There is no study investigating the best ways to deploy a large-scale version of this technology either. This paper addresses these issues by applying the integrated methodology described in Section 3 to evaluate different design and deployment strategies under technological uncertainty. The methodology aims to exploit explicitly the concepts of flexibility/real options in engineering design, and provides the quantitative tools to discriminate between design alternatives. 3. Integrated methodology The described methodology is inspired from the four-step process described by de Neufville and Scholtes (2011) and Walker et al. (2001) for adaptive policy-making. It relies heavily on designers’ and decision-makers’ expertise with the system to identify uncertainty sources and candidate flexibilities. The methodology taps explicitly and systematically into this expertise to identify the major uncertainty source(s) to focus on, to devise flexible strategies, and enable the design to use the flexibilities in operations. As mentioned before, this is necessary because there is no “cookie-cutter” solution. Every system is different and requires special attention. Analytical tools exist at each step of the process from the literature to support this effort. Interested readers are referred to the review section in Cardin (2011). Step 1: Basic economic model development. This step consists of developing a basic economic model to measure performance of a benchmark or current design. The benchmark design typically represents current best practice. If one is interested in economic performance, a financial metric like NPV can be used. If one focuses on costs only, LCOE, measured in £/MWh, is appropriate. In electricity markets, LCOE is useful as it is directly comparable to the price of electricity – also expressed in £/MWh. Comparison of the two enables assessing profitability of a design. Step 2: Uncertainty recognition and evaluation. This step focuses on recognizing and characterizing different sources of uncertainty affecting future system performance in the benchmark design configuration. The benchmark economic model is extended to integrate considerations of uncertainty. Evaluation of the benchmark design under uncertainty follows. To simplify demonstration

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analysis presented here. Central to these pieces of work is a DCF model developed in Excel® , based on Eq. (1). The assumptions used while developing the model are listed in Table 1. Further explanatory details are given in Steer et al. (2012). All costs in the table are quoted either nominally or in 2006 money. Many of the assumptions in the model derive from Kennedy (2007) for Generation III nuclear reactors. Except where stated otherwise, this is where the values in Table 1 originate. Fig. 2. Conceptual representation of the benchmark 1 accelerator/1 reactor first-ofa-kind demonstration ADSR system.

in this paper, one major source of uncertainty is characterized, quantified, and incorporated in the benchmark economic model. Step 3: Flexibility generation/identification. This step focuses on identifying and generating candidate flexible strategies to deal with the uncertainty source(s) from Step 2. The step also identifies relevant enablers in the engineering design. The benchmark model is extended again to enable evaluation of different flexibility strategies. This step is crucial to investigate different flexible design configurations systematically in Step 4. This step is the subject of on-going research, since it is not straightforward to identify and create opportunities for flexibility in complex systems. The work by Mikaelian et al. (2011) and Cardin et al. (under review) are examples of on-going efforts to do this more systematically. Step 4: Design configuration evaluations. This step makes use of decision analysis – a simplified, more intuitive implementation of dynamic programming – to analyse the flexible alternative design and deployment strategies emerging from Steps 2 and 3. Other evaluation methods can be used, as discussed in Section 5. Design and deployment strategies are recommended based here on expected – or average – LCOE as the decision metric. Other economic metrics are introduced to demonstrate how they may affect decision-making, followed with sensitivity analysis of relevant model parameters. 4. Case application and results This section demonstrates an application of the methodology above to the deployment of ADSR technology for power generation. It identifies a major uncertainty source affecting technology required for ADSRs. It suggests a set of flexible strategies and engineering/planning enablers to deal with this uncertainty in deploying the system. It then evaluates quantitatively the flexible alternatives to recommend the best strategies to minimize expected LCOE, and favor electricity production. 4.1. Step 1: basic economic model development 4.1.1. First-of-a-kind ADSR demonstrator An ADSR accelerator system provides a high-energy, highpower proton beam impinging on a heavy metal target. This induces nuclear spallation reactions. Spallation is the act of splitting nuclei, creating a “cocktail” of species of smaller secondary nuclei. Among many other products, this generates a number of neutrons. The target is located inside the reactor core. The neutrons react with the fuel and induce additional nuclear fission reactions inside the core. These extra fissions sustain the fission chain reaction and thus energy generation, which promptly ceases if the accelerator system is turned off. Fig. 2 shows a high-level view concept diagram for the LINearACcelerator (LINAC) ADSR design. The starting point of the economic analysis is the determination of the cost of developing a single ADSR system today. In the companion to this paper by Steer et al. (2012), the technology development, design, and economics of the first-of-a-kind ADSR demonstrator are detailed. This forms a basis for the extended

LCOE =

total life cycle cost total lifetime energy generated =

PD +

n

t=0

(It + OMf + OMv + DDt + Ft + CoFt )/(1 + r)t

n

t=0

(Et /(1 + r)t ) (1)

where PD, discounted predevelopment costs incurred before t = 0; It , capital costs incurred in year t; OMft , fixed operation and maintenance costs in year t; OMvt , variable operation and maintenance costs in year t; DDt , fixed radioactive waste disposal and decommissioning costs in year t; Ft , variable fuel costs in year t; CoFt , cost of failing to meet contracted electricity sales in year t; r, real cost of capital, or discount rate; Et , electricity sold in year t; n, years since construction of the first reactor began. In this first step of the 4-step methodology, it is assumed that in the initial development phase one accelerator and one reactor are constructed (referred to as the 1 accelerator/1 reactor configuration). This phase extends over eight years. Current accelerator technology is hypothesized to provide 70% effective operational availability (OAaccel ) (Galambos et al., 2008). The concept of effective operational availability introduced in Steer et al. (2012) is referred to here simply as effective availability (EA). Its definition is provided in Section 4.2. EA = 70% implies that the first-of-a-kind ADSR will have a slightly lower capacity factor than expectations for Generation III nuclear power stations (capacity factor of 85%). Capacity factor is defined as the ratio of actual electricity produced during the year to the total output had the plant operated at full capacity throughout the year. Throughout this paper the perspective is taken of a single profitdriven company involved in constructing the ADSR plant, and selling the electricity generated. The economic analysis is based on 3-stage LINAC technology, although equivalent analysis could be performed using another accelerator technology. LINAC technology was chosen because construction and operating cost data are more readily available. 4.1.2. ADSR reactor park demonstrator To demonstrate the notion of an ADSR reactor park a declared net capacity of 1800 MWe has been selected. This size is comparable with planned Generation III nuclear site capacities (WNA, 2009), and is considered uncontroversial at the moment to these authors’ knowledge. To attain 1800 MWe, an ADSR demonstration site might be expected to be comprised of three 600 MWe reactors and three accelerators (referred to as the 3 accelerators/3 reactors configuration). In this initial stage of modeling, each accelerator–reactor pair is considered to be independent: an accelerator can only transport its beam to one of the reactors. The stance is taken that the construction of the ADSR site is phased so that no two reactors are constructed in parallel. A 1 accelerator/1 reactor first-of-a-kind design therefore leads to a 3 accelerators/3 reactors demonstration park. Fig. 3 shows how one might expect the annual electricity generated by such a reactor park to vary through its lifetime. The figure also shows the discounted value of the electricity equivalent to if it had been generated in the first year of the first ADSR coming online. This 3 accelerators/3 reactors demonstration park design is referred as the benchmark configuration for the remainder of the paper (it extends from the

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Table 1 List of assumptions for the DCF model incorporating assumptions from the companion paper by Steer et al. (2012). Parameter

Assumption

Source/Comment

Declared net capacity (DNC) of an ADSR reactor park where each ADSR is driven by one LINAC Energy consumed by additional accelerator(s)

600 MWe per reactor

Subtract 20 MWe from the park DNC per additional accelerator

Pre-development costs

£250 million in 2006 money

Construction period of first reactor and accelerator(s)

6 years

This is a commonly cited size for a demonstrator ADSR reactor. Physics and engineering considerations have driven the decision. The energy requirement of one accelerator (20 MWe) is considered to already be subtracted from the value When operating more accelerators than reactors at the ADSR park, the park DNC is reduced by this value. The value is the same as in Steer et al. (2012) Pre-development costs (e.g. site licensing) are assumed to be insensitive to plant and park size, type of and the number of accelerators ultimately constructed. Therefore the Kennedy (2007) European Pressurized Reactor (EPR) cost has been used It is assumed that the reactor (which includes all other power plant components except the accelerator) determines the construction time and that the construction of any accelerators always fits inside this time window

Construction period of an additional reactor and accompanying accelerator(s) Timing of commencement of second phase of construction

6 years

Construction cost of first-of-a-kind power station excluding the accelerator proper and cryogenics facility Construction cost of a first-of-a-kind 1 GeV 10 mA LINAC and cryogenics facility

Construction of a second reactor begins 2 years after completion of the initial reactor (i.e. after 2 years of selling electricity). Construction begins on reactor 3 immediately following the completion of reactor 2 Per reactor: nominally £1625/kWe (£975 million) + IDC (£274 million)

Per accelerator: nominally £290 million + IDC (£82 million)

Planning for the later construction of accelerators

£20 million (nominal) is paid during the initial construction phase for each accelerator that may be constructed later. If the accelerator is constructed, the £20 million is subtracted from the build cost at that time

Construction cost of nth-of-kind power stations and accelerators with cryogenics facility Operational lifetime of a reactor Operational lifetime of a LINAC

Treated as identical to the corresponding costs for the first-of-a-kind of each technology

Operation and maintenance (O&M) of nuclear reactors

Nominally £7.70/MWh when operating a single reactor, followed by a £3.85/MWh increase per additional reactor Nominally £34 million per annum when operating a single accelerator, followed by a £17 million per annum increase per additional accelerator

O&M of accelerators

Based on Kennedy (2007) “Central” scenario for a first-of-a-kind, but increased as described in OECD/NEA (2000, p. 32), using a scale factor of n = 0.425. This is assumed to include accelerator civil works, site engineering and indirect costs Estimate from the proposed costs made by Safa et al. (2002) with a linear cost escalation of the “high-energy section” (excluding the cryogenics facility) to increase the 600 MeV beam energy to 1 GeV. A D 1 = £1 exchange rate was used. Escalating from 2002 to 2006 money and cost savings made by purchasing multiple accelerators have been neglected Taken from Steer et al. (2012). The cost of planning to construct additional reactors is neglected as in all scenarios considered three reactors are constructed successively. The uncertainty in the total cost of constructing a reactor is expected to be significantly larger than the total cost of planning for their future construction Cost reductions from experience gained and learning with the new technology have been neglected in this analysis

40 years 40 years

Operational availability of a reactor Operational availability of a LINAC

≤85%. The first 5 years of operation are 5% lower than the subsequent years

Fuel supply cost (thorium fuel)

Nominally £1.1/MWh

Combined radioactive waste disposal and decommissioning costs

Per reactor: nominally £9 million per annum, savings grow at a real rate of 2.5% annually. This is a total of £583 million after 40 years of operation

Assumed to be equal to the reactor lifetime. High-power accelerators do operate for these time scales. For example, the Swiss Paul Scherrer Institut cyclotron is still in operation after 36 years Operating reactors in parallel assumes that the O&M cost of each additional reactor is 50% of the base cost Based on reported annual running costs of the Spallation Neutron Source at Oak Ridge National Laboratory (Hickey, 2009) and the European Synchrotron Radiation Facility (ESRF, 2007, 2008). Operating accelerators in parallel assumes that the O&M cost of each additional accelerator is 50% of the base cost

80% rising to 85% after the first 5 years This is treated as a variable in the presented analysis. No benefit is gained if the average operational availability of the accelerators exceeds that of the reactors (85%) Thorium does not require enrichment. A fast thorium reactor burns nuclear fuel more efficiently than a thermal uranium reactor. Kennedy (2007) cost of uranium fuel has been modified to exclude enrichment costs (50%) and reduce the quantity of ore mined by a factor of 8 (Bryan, 2009). Mining costs per kilogram are assumed to be equal Kennedy (2007) EPR geological disposal cost is the same (£276 million at closure) and the decommissioning cost is modified to £513 million/GW. This is a simple linear extrapolation to 600 MWe of the vendor cost quotes for 1600 MWe EPRs and 1200 MWe AP1000s. Fund payments are made at a fixed rate and therefore do not vary with sensitivity analysis on the effective operation availability

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Table 1 (Continued) Assumption

Source/Comment

Contractual cost of unplanned shutdowns

Nominally £270,000 (mean loss made per 24 h ADSR shutdown)

Cost of capital

10%

Taken from the analysis performed in Steer et al. (2009) for the mean cost of a single 24 h unplanned shutdown, using the contemporary electricity price Post tax real weighted average cost of capital

Electricity Generated (TWh)

Parameter

11

Discounted

10

Nominal

9 8 7 6

5

the initial deployment phase of the first-of-a-kind demonstrator (end of year 8), as some technological performance uncertainty is resolved. This assessment is representative of typical economic valuation based on NPV/DCF. It assumes full commitment at the time of the irreversible investment, and relies on expert forecasts for the main uncertain design variables and parameters. It may prevent designers and decision-makers from recognizing other, better performing design configurations that deal with uncertainty more pro-actively.

4 3

4.2. Step 2: uncertainty recognition and evaluation

2 1 0 0

5

10

15 20 25 30 35 40 45 50 Years Aer First Reactor Goes Online

55

60

Fig. 3. Electricity generated annually by the benchmark ADSR reactor park and the discounted equivalent value of that electricity. It is assumed here that electricity is sold for 80% of the year, rising to 85% after the first 5 years of operation for each reactor and 100% reliability.

configuration in Fig. 2 to three pairs of accelerator/reactor). It assumes a rigid/inflexible deployment to a reactor demonstration park no matter how technology evolves in the initial first-of-a-kind development phase. It is the baseline configuration with which other flexible alternatives will be compared. This staged deployment strategy enables responsive flexibility to the site design, as explained in Section 4.3. One motivation for constructing multiple reactors at the same geographical site is to benefit from significant cost savings. Operational costs savings are expected from sharing facilities, as well capital cost savings due to economies of scale, and other cost reductions from learning effects (OECD/NEA, 2000). The potential for these savings is common to all nuclear reactor designs. However unique to ADSRs and the topic of this paper, it is hypothesized that the operation of multiple reactors will be more efficient if accelerators are shared through an integrated network. Under the financial assumptions summarized in Table 1, the DCF analysis reveals a benchmark LCOE of £63.66/MWh. Fig. 4 shows in a decision tree1 that this analysis implicitly assumes that a central EA = 70% effective availability scenario arises with probability, p = 1.00. The analysis ignores all other technological scenarios, effectively setting their probability of occurrence to 0. This simplified assessment, although a necessary starting point for the analysis, is unrealistic. Apart from different cost effects, it ignores the possibility that accelerator technology may perform better, thus leading to more electricity production and a lower LCOE. It ignores the possibility that the technology may be worse, thus leading to less electricity being generated and a higher LCOE. It also ignores the possibility of making a different decision after

1 By convention, a square node corresponds to a decision point, while a circle corresponds to a “chance”, or uncertainty outcome. The probability (p) of an outcome is written under the outcome branch. The LCOE of each scenario is displayed at the terminal node, with the associated probability of occurrence. TreeAge Pro® is used for decision analysis.

4.2.1. Effective availability as main driver There are many sources of uncertainty affecting the expected performance of the proposed system. One is uranium price, an example of exogenous uncertainty. If, for example, the price of uranium remains relatively low in the future, this will not favor thorium as an alternative fuel. Another source of uncertainty is whether a strong market for waste disposal will emerge in the future, potentially favoring ADSR systems to be optimized for transmutation rather than power generation. In terms of endogenous design uncertainty, it is not yet finalised what the best choice of technology is for the coolant, reactor geometry and spallation target (e.g. with or without a beam window). Delays during construction will also affect capital cost, as for other nuclear power stations. While the exogenous uncertainties above are important, this paper focuses on the endogenous uncertainty associated with accelerator technology development. A more extensive analysis could incorporate exogenous uncertainty sources using the methodology presented here. The EA of the accelerator system is the metric that has been used presently to represent all possible technological development outcomes. Regardless of the actual reliability realized by accelerator technology, or the managerial decision taken regarding whether or not to operate the accelerator system for a larger fraction of the year but with poorer reliability or a smaller fraction of the year but with better reliability, it is always possible to equate the system’s economic performance to a theoretical system that returns the same value. This theoretical accelerator system is treated as if it exhibits 100% reliability during operation. It is, however, scheduled to only operate for the fraction of the year that equates to returning the same value as the real accelerator system returns. This accounts for the potential for real systems to fail and therefore incur costs for not meeting electricity sales contracts or for managers having chosen to forgo additional electricity sales in exchange for performing extra maintenance, and therefore improving future reliability during operation. Development is taking place to improve accelerator reliability and therefore EA (Burgazzi and Pierini, 2007; Pierini, 2007; Pierini et al., 2003; Teng, 2001). EA therefore allows for the provision of an holistic assessment of how uncertainties in accelerator technology may develop in the future. For instance, if accelerator technology development is highly successful and the accelerator is reliable (i.e. unplanned shutdowns are infrequent), EA can be high because the need for planned maintenance is limited and there are few occasions that the accelerator fails during operation. In contrast, if accelerator technology is realized to be unreliable, causing many unplanned shutdowns and/or maintenance periods, the EA will be

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Fig. 4. Decision tree assuming probability p = 1.00 for the central EA estimate.

low. The companion paper by Steer et al. (2012) provides additional details regarding EA. Similarly to the accelerator, the other reactor systems could be described in terms of an EA; however, other nuclear reactor systems are typically highly reliable and so the description is not generally necessary. Unplanned failures for these other systems are comparatively rare and so in the presented analysis they have all been treated as being 100% reliable. An ADSR can only generate electricity and therefore revenue when both the accelerator and reactor systems are working correctly. Unless the EA of the accelerator system exceeds the availability achieved by all other power plant systems, it will be the metric that dictates the capacity factor of the whole ADSR. Capacity factor is one of the main enablers of economic value for a nuclear power station. If the accelerator’s EA is high, the ADSR capacity factor can be high and more electricity generated and sold. If the accelerator EA is low, the ADSR capacity factor is low, and less electricity generated, thus lowering revenues. EA encompasses the impact of many of the key technological issues facing ADSR accelerator technology’s performance and its operation. On this basis this metric has been selected as the controlling variable in the presented economic assessment. Current ADSR accelerator designs address specific technological challenges in terms of reliability, redundancy and fault tolerance (Pierini et al., 2003). To the authors’ knowledge, however, there is no strategy in place for improving the value of ADSRs by enabling the system design to adjust responsively based on the observed performance of the technology during its development, and large-scale deployment. 4.2.2. Economic evaluation under uncertainty EA ultimately determines the economic performance returned from an ADSR demonstration reactor park. Different EA scenarios will give rise to different DCF outcomes calculated using Eq. (1). Importantly, a low (high) EA directly affects how much electricity is generated and also the costs of failing to meeting electricity supply contracts, thus it will do one or both of the following: decrease (increase) variable Et and increase (decrease) variable CoFt . Other factors affected by changes in the EA are that, for example, a low (high) EA implies lower (higher) OMvt depending on the load being placed on the ADSR components. Low (high) EA will also result in spending less (more) on fuel, thus affecting Ft . A separate consideration affecting Eq. (1) is that the act of enabling flexibility will affect the capital cost It incurred at time t, because of the sharing and construction of different infrastructures (see Section 4.3). Interested readers are welcome to request a copy of the detailed Excel® analysis from the authors, which explicitly demonstrates the impact EA has on the other factors in Eq. (1). This study assumes that uncertainty in the performance of ADSR accelerators in general can be resolved significantly during the early years of operation of the first-of-a-kind ADSR demonstration plant (i.e. during the first 6 years when the initial 1 accelerator/1 reactor first-of-a-kind system is built, and the following first 2 years of operation, as in the first stage of the decision tree in Fig. 5). The historical development of nuclear power in the United States indeed shows that the capacity factor of nuclear power plants has evolved slowly to reach today’s value of 85% and more, through steady research, development, and operations (Moen, 2010). In analogy, it is expected that a first-of-a-kind prototype will provide

Table 2 Summary of three uncertain accelerator technology scenarios considered in this analysis leading to different EA. Scenario

Effective availability (EA) estimate of a reactor driven by a single accelerator (%)

1. Optimistic 2. Central 3. Pessimistic

85 70 50

more information on how well ADSRs work for power generation. It will reveal system’s integration, socio-technical, and other systemic issues that are difficult to evaluate from a blueprint design. Three possible scenarios for technology development are considered, leading to the three EA scenarios summarized in Table 2. As explained in Steer et al. (2012), scenarios considered in this study are based on existing technology assessment (Galambos et al., 2008), discussion with accelerator operators (Findlay, 2009), and examination of accelerator reliability optimization studies (Pierini et al., 2003). Scenario 1 depicts an optimistic case where technology evolves favorably to enable EA = 85% for the reactor demonstration park. In Scenario 2, the accelerator system technology of any single-accelerator ADSR limits electricity sales to slightly less than that intended for Generation III nuclear reactors. This results in effective availability remaining at 70%, as initially hypothesized for the benchmark. Scenario 3 investigates a pessimistic view where the EA of a reactor driven by a single accelerator is no more than 50%, thus further reducing electricity generation and cost recovery. This is much lower than today’s appreciation of the technology. In this example evaluation, no particular information favors one scenario over another, and all scenarios are considered equally likely (p = 1/3 for all scenarios).2 The impact of this assumption on the results is shown in Section 4.4.5 via sensitivity analysis. The DCF cost model is modified to enable variations in the EA parameter, ultimately affecting costs, electricity generation, and LCOE for each scenario, design, and deployment plan. The decision tree in Fig. 5 shows the LCOE under each scenario, leading to an expected LCOE (E[LCOE]) of £68.09/MWh for the benchmark design under uncertainty. Fig. 5 makes clear that the deterministic benchmark assessment is only one of the several possible technology development scenarios. It also shows that E[LCOE] differs and is actually more expensive than the deterministic benchmark assessment of LCOE (£63.66/MWh). This is another manifestation of the flaw of averages, showing that E[f(x)] = / f(E[x]) for systems with a non-linear response f(x) (Savage, 2000). Fig. 6 shows a Cumulative Mass Function (CMF) – also called “target curve” by de Neufville and Scholtes (2011) – for the benchmark design with and without uncertainty recognition. For clarity, the deterministic benchmark design evaluation without uncertainty – as in Step 1 – is referred to as “benchmark” on the figure. The evaluation of the benchmark design under uncertainty is referred to as “inflexible 1 accelerator/1 reactor” (inflex. 1 accel./1 reactor for short). It refers to the fact that the 3 accelerators/3 reactors

2 Other assumptions can be used in the framework for probability distributions. The example analysis below would then give rise to other evaluations, and potentially different design choices. A sensitivity analysis is performed in Section 4.4.5 to determine threshold probability choices leading to different design decisions.

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Fig. 5. Decision tree for the benchmark design recognizing uncertainty in accelerator reliability.

Fig. 6. Target curves for the benchmark design with and without uncertainty recognition. The solid curve represents the evaluation results for the benchmark design under uncertainty, referred as inflex. 1 accel./1 reactor for clarity – although referring to the same design and development strategies. The dashed vertical line represents the E[LCOE] of this design under uncertainty. The dashed-dotted vertical line represents the deterministic benchmark evaluation without recognizing uncertainty for reference purposes.

demonstration park ultimately starts from the 1 accelerator/1 reactor configuration. The system follows a rigid/inflexible design and development path where the reactor park is developed no matter how technology evolves in the first-of-a-kind development phase. The graphical representation in Fig. 6 is intended to help decision-makers in identifying the range of possible outcomes a particular design may produce. It changes the design paradigm from using one LCOE for decision-making (as in Step 1) to a range of probabilistic outcomes. In this example, it shows there is a one third probability of obtaining a target LCOE between £53.47/MWh and £63.66/MWh for the benchmark design when uncertainty is recognized (solid curve referred to as inflex. 1 accel./1 reactor). This quantifies the upside opportunities this kind of design may provide. Similarly, there is a one third probability of obtaining a target LCOE between £63.66/MWh and £87.15/MWh, which characterizes downside situations. E[LCOE] = £68.09/MWh is also shown as a vertical dashed line. The benchmark deterministic assessment of £63.66/MWh in Step 1 is shown as a dashed-dotted vertical line for reference. 4.3. Step 3: flexibility generation/identification 4.3.1. Flexibility strategies and enablers The three strategies in this section all aim to address the crucial issue of EA uncertainty. They are inspired from canonical strategies suggested by Trigeorgis (1996) (e.g. deferral, capacity expansion, and phasing) Represented conceptually in Fig. 7, the strategies

Fig. 7. Conceptual view on the systems-level typology of flexibility strategies, from long (top) to short (bottom) timescales.

emerge from the need in complex engineering systems to tackle uncertainty in an integrated manner, from strategic long-term system-level considerations, down to lower-level tactical, and day-to-day operations (de Neufville, 2004). The strategies enable pro-active management of technology uncertainty represented by different EA scenarios with these long-term to short-term views. Their goal is to improve expected LCOE as compared to the benchmark, inflexible 1 accelerator/1 reactor design. This can be done by mitigating the effects of downside technology scenarios (EA = 50%), while ensuring the system is positioned to capitalize on upsides (EA = 85%) in the first-of-a-kind demonstration phase. Suggestions are made from an engineering standpoint to enable these flexibilities concretely in the system design and deployment. The suggestions below are not the only ones available to designers and decision-makers. They represent feasible approaches, drawing from canonical strategies, past lessons, and

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current research on flexibility. They aim to demonstrate application of the integrated methodology, as applied to the system of interest. Strategy 1: the first, low-level, source of flexibility is an operational switching option enabled “in” the design, whereby it is possible for different accelerators to quickly deliver their beam to any of the reactors in the network, on demand. The full potential of this strategy would be realized when the reactor park features redundant accelerators as it provides the ability to switch to another accelerator if one experiences an unscheduled shutdown, or is down for planned maintenance. The strategy therefore integrates well with the scale alteration option described next (Strategy 2), which provides for the contingency to construct additional accelerators if needed. Another way in which this first strategy can be useful is when a reactor is offline for scheduled maintenance; even without explicit accelerator redundancy integrated into the reactor park (as in Strategy 2) there may be periods when a reactor is undergoing a planned closure but none of the accelerators require maintenance, the option to switch which accelerator is delivering its beam to the other two reactors provides accelerator redundancy. Finally, because all accelerator beams can be redirected to any reactor this strategy allows for any one of the accelerators to be shut down for maintenance while a reactor is also undergoing maintenance, not just a specific accelerator whose beam transport system is linked to that reactor. In essence, this strategy draws upon and extends the design approach of existing ADSR accelerator technology described by Pierini et al. (2003) to provide redundancy. Enabler 1: To be enabled, this flexibility would require a design where a single beam transport system is constructed such that all of the accelerators can quickly have their proton beam redirected to any one of the reactors as needed, at any given time. This would support the creation of an integrated reactor park with a single network of accelerators. Strategy 2: The second source of flexibility is a tactical scale alteration option “in” the engineering design. It is obtained by designing the system with contingency to add one more accelerators to increase the overall accelerator system’s EA in case it is found to be too low due to frequent unscheduled shutdowns in the initial first-of-a-kind demonstration phase, or because it is requiring extensive scheduled maintenance. It integrates naturally with flexibility Strategy 1, described above. This flexibility addresses the important issue of accelerator reliability, which is a challenge unique to ADSR technology as compared to other nuclear power generation technology. It is an important strategy as accelerator performance may have a determining effect on power generation. Although there are other facets of the ADSR design (the choice of fuel, coolant, whether or not it is operated in the fast or thermal neutron spectrum, the integrity of the target or beam window) that are expected to have a significant, possibly more significant, impact on its value. These questions are, however, wider reaching issues, some of which affect other nuclear reactor designs, and are beyond the scope of this paper. Enabler 2: To be enabled concretely and at minimum cost, this flexibility requires securing a site ahead of time so that additional ADSR systems can be added later without interfering with the existing reactor(s). It also requires designing the network carefully to share infrastructures between multiple systems, and harmonizing accelerator and reactor O&M schedules. Strategy 3: This flexibility strategy is a high-level strategic growth option “on” the system. It emerges from the idea of developing a first-of-a-kind demonstrator (referred to below as Phase 1), which is a necessary step before constructing a demonstration reactor park subsequently (referred to as Phase 2). The first-of-akind demonstration of one reactor (Phase 1) would give the “right but not the obligation” to expand to a demonstration reactor park

(Phase 2) if and only if accelerator performance (and the performance of other systems not considered in this paper) is good enough. Alternatively, development can be stopped short after Phase 1. Enabler 3: Similarly to enabler 2, this flexibility strategy requires securing a site for additional accelerator(s) and/or reactor(s). This also requires additional design efforts and planning for sharing infrastructures in the case of expansion. It requires choosing appropriate zoning, and setting all legal and financial aspects to enable the subsequent Phase 2. 4.3.2. Flexible design configurations The analysis presented in this paper focuses on the flexibility Strategies 1 and 2. As the LCOE is the chosen metric for assessment, it has been assumed that development moves on with a reactor park, regardless. These strategies are more interesting from an engineering and design standpoint, focusing on the most cost-effective way to design and deploy this complex infrastructure strategically in the long-term. Strategies 1 and 2 essentially protect from downside risks in power generation, in case technology does not perform as hoped. Analyzing flexibility Strategy 3 considers the possibility of stopping development short after the first-of-a-kind demonstrator phase, should decision-makers decide to do so. The analysis presented in the companion paper by Steer et al. (2012) give some consideration to this particular case. Integrating flexibility Strategies 1 and 2 gives rise to different design and development pathways compared to a rigid/inflexible strategy, as summarized in Fig. 8. There are two suggested flexible design configurations in the first-of-a-kind demonstration phase (Phase 1): a flexible 1 accelerator/1 reactor design, or a flexible 2 accelerators/1 reactor design. Both designs can lead to the same two possible reactor park demonstration systems in Phase 2 either a 4 accelerators/3 reactors, or a 3 accelerators/3 reactors configuration. The first flexible design starts from a 1 accelerator/1 reactor configuration, which is equivalent to the “expandable” design in the companion paper by Steer et al. (2012). It plans for the possibility of adding a fourth accelerator in Phase 2 if EA observed in Phase 1 is too low (making use of the scale alteration strategy). It is designed to be able to integrate its beam transport network with additional accelerators. It does not yet have the benefit of operational redundancy to switch accelerators in Phase 1 (flexible Strategy 1). The benefit of this design configuration is to save unnecessary capital expenditures if accelerator EA is high in Phase 1 (avoiding construction of a second accelerator), while risking producing less electricity if EA is low. After Phase 1, managers may choose to expand to either 4 accelerators/3 reactors or 3 accelerators/3 reactors configurations in Phase 2, depending how EA turns out in Phase 1. The second flexible design exploits operational switching flexibility (flexible Strategy 1) in Phase 1 and requires an additional accelerator at the outset. This is in effect the “dual” design from Steer et al. (2012). This alternative also recognizes immediately the strategic flexibility to expand to the most appropriate configuration depending on the EA realized in Phase 1 (flexible Strategy 2). This configuration starts with a 2 accelerators/1 reactor design, and has the possibility to expand to either of the 4 accelerators/3 reactors or 3 accelerators/3 reactors configurations. This configuration costs more in Phase 1 due to the construction of an additional accelerator, and shared infrastructures. On the other hand, it will generate more electricity than the flexible 1 accelerator/1 reactor design if EA is low. 4.4. Step 4: design configuration evaluations 4.4.1. Design/development pathways and evaluations At the time of irreversible investment (t = 0), decision-makers may choose between three design alternatives, represented in

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Fig. 8. Conceptual representation of the two flexible strategies for deploying a demonstration ADSR reactor park. The faintly colored reactors, accelerators and beam transport systems are planned for, but not yet constructed.

Fig. 9. Decision tree for the real options analysis of a first-of-a-kind ADSR system leading to a commercial reactor park for power generation.

Fig. 9.3 Pathways for each design configuration (1 inflexible, 2 flexible) are described. The first configuration captured by the upper branch leads to the inflexible benchmark deployment strategy, similar to the decision tree in Fig. 4. This corresponds to the inflexible 1 accelerator/1 reactor design. No adjustment is possible at the second decision node (t = 8 years). This design and deployment strategy assumes

3 Sub-optimal decision branches are marked with a double hash in the dynamic programming – backward induction – phase of decision analysis. Branches with no hashing represent the best decision at a given decision node. The expected LCOE is shown under each branch at a decision point. The recommended design is stated in the box below the first, leftmost, decision point.

full commitment to the demonstration reactor park. The LCOE is dependent on how technological uncertainties unfold during the initial first-of-a-kind phase. This design is best if technology turns out better than expected, as in the optimistic case. It provides the lowest LCOE (£53.47/MWh) of all of the scenarios, providing accelerator performance is very good. If the pessimistic EA scenario arises, however, the plant becomes the most costly (£87.15/MWh). It cannot exploit the additional redundancy provided by linking the accelerator beam transport networks to cope with poor accelerator performance. The cost of enabling this ad hoc is expected to be preventatively large. The second design starts from a flexible 1 accelerator/1 reactor configuration, planning contingency for a fourth accelerator if needed. If the optimistic EA scenario arises, the best decision is

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Fig. 10. Target curves for inflexible and flexible 1 accelerator/1 reactor demonstration park deployment strategies. The dotted curve represents the target curve for the flexible 1 accelerator/1 reactor design. The leftmost dashed-dotted vertical line represents the E[LCOE] of this design. All other curves/lines are the same as in Fig. 6.

to expand to a 3 accelerators/3 reactors configuration. In this case there is no need for an additional accelerator to increase electricity production. The LCOE (£53.78/MWh) is only slightly higher than for the inflexible design (£53.47/MWh) due to the cost of planning for – but not constructing – a fourth accelerator in Phase 1. If the central or pessimistic EA scenarios arise, it is better to exploit the scale alteration flexibility and add another accelerator. This also benefits the operational flexibility to switch between accelerators in Phase 2, thus generating more electricity. The LCOE values (£60.37/MWh and £64.99/MWh) are lower than for the inflexible design (£63.66/MWh and £87.15/MWh, respectively). This is essentially due to the increased electricity generation gained thanks to the fourth accelerator. The third design starts from a flexible 2 accelerator/1 reactor configuration. If the optimistic EA scenario arises, the reactor park only requires one more accelerator and a second reactor, followed by just a third reactor to reach a 3 accelerators/3 reactors configuration. However, the LCOE is £60.00/MWh, considerably higher than for the inflexible strategy under this scenario (£53.47/MWh). This is also more costly than for the flexible 1 accelerator/1 reactor configuration (£53.78/MWh), mainly due to the purchase of a superfluous accelerator in the first-of-a-kind phase. If the central or pessimistic EA cases arise, it is better to expand to a 4 accelerators/3 reactors configuration. The extra electricity provided thanks to the additional accelerator outweighs the additional cost. For the central EA scenario, the LCOE (£61.72/MWh) is only slightly higher than for the flexible 1 accelerator/1 reactor configuration (£60.37/MWh) due to the early purchase of a redundant accelerator. The additional power capacity gives a lower LCOE than for the inflexible case (£63.66/MWh). If the pessimistic EA scenario arises, the flexible 2 accelerators/1 reactor configuration gives the best protection against downsides. It exploits the flexibility from the redundant accelerator in both development phases, which improves electricity generation. The LCOE is £61.94/MWh compared to a high of £87.15/MWh for the inflexible, and £64.99/MWh for the flexible 1 accelerator/1 reactor design. Target curves in Fig. 10 depict graphically the information in the decision tree for the inflexible and flexible 1 accelerator/1 reactor designs only. The figure shows that a strategy recognizing uncertainty and planning for appropriate flexibility in a 1 accelerator/1

reactor design indeed provides much lower expected LCOE (leftmost dashed-dotted vertical line) than in the initial deterministic benchmark assessment of Step 1 (rightmost dashed-dotted vertical line), and also when uncertainty is factored in the benchmark analysis of Step 2 (vertical dashed line). The curves also show the probabilistic range of LCOE for the two design configurations under uncertainty (solid dark curve for the benchmark 1 inflexible 1 accelerator/1 reactor; dotted curve for flexible 1 accelerator/1 reactor). It is observed that E[LCOEflex. ] is lower than for the inflexible case mainly because it is better at protecting from downside risks in technology development (i.e. it avoids high LCOE outcomes from poor accelerator technology). 4.4.2. Design decisions The recommended design configuration depends on the utility of the decision-maker. For example, a risk-neutral decision-maker might prefer a strategy minimizing the expected – or average – LCOE (E[LCOE]). E[LCOE] is a useful metric for trading-off chances of optimistic and pessimistic EA scenarios. It will not provide, however, the possibility of attaining the lowest absolute LCOE in the decision tree. As Fig. 10 shows for the two flexible strategies, the lowest attainable LCOE is £53.78/MWh, as opposed to £53.47/MWh for the inflexible strategy. On the other hand, flexibility reduces the impact from a downside pessimistic EA scenario. The worst possible outcome is LCOE of £64.99/MWh, as opposed to the worst of all scenarios for the inflexible case (£87.15/MWh). Thus, under the assumption of a uniform prior probability distribution (i.e. complete uncertainty), a risk-neutral decisionmaker would prefer the flexible 1 accelerator/1 reactor design, with E[LCOE] = £59.71/MWh. The flexible 2 accelerators/1 reactor is not far behind at E[LCOE] = £61.22/MWh. Both flexible strategies are noticeably better when using this metric than the inflexible strategy with E[LCOE] = £68.09/MWh. 4.4.3. Other metrics for decision-making It is likely that E[LCOE] is not the only metric of concern for decision-makers. Table 3 lists other metrics useful for decisionmaking, suited for different risk profiles. For instance, a risk-averse individual might prefer a design minimizing initial capital expenditure, or reducing to the best extent possible the impact from a

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Table 3 Other metrics for evaluating alternative design and deployment strategies, with recommended decisions. Metric

Benchmark (unrealistic)

Inflexible 1 accel./1 reactor

Flexible 1 accel./1 reactor

Flexible 2 accel./1 reactor

Which is best?

Initial capital expenditure (millions, £) Maximum LCOE (£/MWh) Minimum LCOE (£/MWh)

1305 N/A N/A

1305 87.15 53.47

1325 64.99 53.78

1595 61.94 60.00

Inflexible Flexible 2 accel./1 reactor Inflexible

Fig. 11. Sensitivity analysis over the probability assignments for Scenarios 1, 2, and 3. For brevity, only cases with p(central) = [0.0; 0.1; 0.2] are shown. For each value of p(central), light square hash areas correspond to probability combinations for optimistic and pessimistic scenarios where based on E[LCOE] the flexible 1 acclerator/1 reactor strategy is favorable over the inflexible and flexible 2 accelerators/1 reactor strategies. Dark diagonal hash areas correspond to probability combinations where the flexible 2 accelerators/1 reactor strategy is preferable over the inflexible and flexible 1 accelerator/1 reactor designs. The inflexible design is preferable for only a tiny combination of probability assignments, hardly noticeable on the bottom right of the figure for p(central) = 0.0. Blank areas correspond to infeasible probability assignments resulting in a sum greater than unity.

pessimistic technology scenario. Similarly, a risk-seeking decisionmaker might choose a design giving the lowest possible LCOE, at the risk of obtaining the worst possible outcome – as in the inflexible design – if technology is poor and effective availability is low. The best strategy thus depends on the metric used, and the decisionmaker’s utility. 4.4.4. Expected value of flexibility The expected value of flexibility can be compared to the anticipated cost of the flexible first-of-a-kind demonstrator. This is the difference in E[LCOE] between the inflexible and the best flexible strategy. As a rule of thumb, decision-makers should not be willing to pay more than this value for the additional design and engineering cost, and requirements of a flexible park demonstrator. The cost of enabling contingencies for the additional accelerator was already factored into the model (i.e. £20 million per additional accelerator). Comparing the best flexible 1 accelerator/1 reactor design to the inflexible 1 accelerator/1 reactor design shows positive expected value for the flexible strategy: E[Vflex. ] = E[LCOEinflex. ] − E[LCOEflex. ] = £68.09/MWh − £59.71/MWh = £8.38/MWh The positive value in the equation above shows the direct expected cost savings produced by flexibility. This result shows that under the described assumptions – among others, of complete uncertainty between the three EA scenarios – it would be worthwhile investing in the flexible 1 accelerator/1 reactor architecture suggested here. 4.4.5. Sensitivity analysis Thus far the analysis has assumed a uniform probability among all three scenarios considered. Decision-makers will likely want to change these probability assignments. Alternatively they might be interested in the threshold probability assignments that trigger different design decisions and development pathways.

Fig. 11 shows a sensitivity analysis on the probability assignments for Scenarios 1, 2, and 3, using the risk-neutral E[LCOE] metric for decision-making. In essence, they show that within the framework of this economic model, more value is returned by selecting a flexible design. There is a small (almost imperceptible) area in the lower right of Fig. 11 for p(central) = 0.0 where the decision to build inflexibly is more valuable, but this is the only exception. This area vanishes for p(central) ≥ 0.1. The specific probability assignments do affect whether the initial decision to go with a flexible 1 accelerator/1 reactor design or a flexible 2 accelerators/1 reactor design is more valuable. For brevity, only examples with p(central) = [0.0; 0.1; 0.2] are shown in Fig. 11. All other sensitivity analyses where p(central) > 0.2 result in the flexible 1 accelerator/1 reactor strategy being preferable over a wider area of probability assignments as compared to the flexible 2 accelerators/1 reactor design. 5. Discussion and conclusion This paper has presented and applied a simple, integrated methodology intended to improve or ratify the design of innovative technology in terms of its economic performance and costs. The impact of uncertainties associated with a technology’s future performance on its economic performance has been emphasised, specifically with relation to decisions that are made in the early conceptual design phase. Suggestions were made on how the expected cost of the case study technology, the ADSR, could be improved through the identification of specific flexibilities that could be integrated into the design, enabling it to better cope with a range of future technology performance scenarios. The paper highlighted the importance of considering uncertainty and flexibility in the early conceptual design of technological development, as opposed to later in the detailed design phase, where it would no longer be cost effective to take advantage of alternative design and development pathways. Through subjecting developing engineering systems to a cost analysis that is more

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realistic than typical DCF – i.e. by recognizing uncertainty explicitly – one ascertains a better understanding of the expected cost of the technology. Furthermore, it is possible to identify design improvements that reduce the expected cost of the technology. This knowledge is valuable not only to investors but also from a policy standpoint for public investment in research and development of such capital intensive, risky, but promising technological ventures. 5.1. Key contributions There are two central aspects to this work: first, the application of the integrated methodology was demonstrated to analyse a complex engineering system under development. This contributes to further validating the methodology, although full validation would require more applications – beyond the scope of this paper. Second, the design of ADSR nuclear reactor technology demonstrably benefited from scrutiny using the ROA-inspired methodology. This gave rise to a set of design and deployment strategies that demonstrably improved the E[LCOE] of this particular example of engineering systems. 5.1.1. Demonstration of the methodology The first key contribution was to demonstrate application of the 4-step integrated methodology to the analysis of a complex engineering system under technology uncertainty. This methodology aims to help designers and decision-makers of complex systems consider uncertainty and flexibility more systematically in the early conceptual phases of design. The general formulation presented in Section 3 involved nothing specific to ADSR systems and, although beyond the scope of this paper, it is expected that it will be applicable to the analysis of other engineering systems. It should be clear that the methodology augments typical sensitivity analyses because it incorporates decision-makers’ capacity to adapt to various situations along a development path. The economic assessment presented here was therefore more realistic than a typical DCF approach. However, it was not overly complex and therefore untenably time consuming. The analysis explicitly recognized a range of possible uncertainty scenarios, and took pro-active steps for managing these uncertainties by means of flexibility. The demonstration economic analysis used E[LCOE] as the metric for assessing flexible reactor park designs compared to a benchmark design. After defining three scenarios for the future performance of accelerator technology and assuming complete uncertainty regarding which scenario could occur, the E[LCOE] of a flexible design was found to be reduced by 12% compared to an inflexible deployment strategy (from £68.09/MWh for the inflexible 1 accelerator/1 reactor design to £59.71/MWh for the flexible 1 accelerator/1 reactor design). Even a reduction in E[LCOE] of only 1% will be significant for such a multi-billion £ investment. On the other hand, if the probability assigned to an optimistic scenario is higher compared to the central and pessimistic scenarios, the value of flexibility will reduce accordingly, and an inflexible design will be favored. Indeed, the sensitivity analysis in Fig. 11 showed that the inflexible benchmark ADSR design would become more valuable than the flexible alternatives for cases of high confidence in the good performance of the accelerator system. Such optimism would reflect a risk-seeking profile, which would amount to ignoring the possibility of central and pessimistic scenarios (i.e. uncertainty altogether). Indeed, flexibility has value only if one recognizes uncertainty, and decides to act on it in a pro-active manner. 5.1.2. Flexibility/real options strategies Regarding the second contribution, three specific real options for the accelerator system of a commercial ADSR demonstrator were suggested and investigated. They arose because of the specific focus on technology and EA uncertainty drivers. Although not

the only ones available or feasible, these strategies were suggested to enable flexibility “in” and “on” the project in the face of technology uncertainties elicited via the integrated methodology. Strategy 1 consists of an operational flexibility strategy “in” the project that requires the beam transport systems of the accelerators to be integrated into a single delivery network. Through this network, it should be possible for each accelerator to swiftly deliver its beam to any one of the reactors. This strategy builds upon and integrates with flexibility Strategy 2, which consists of a tactical scale alteration real option “in” the engineering design. Strategy 2 is obtained by designing the system with contingency to add one more accelerator to increase power generation, in case this is too low due to frequent unscheduled accelerator shutdowns, or because of extensive scheduled maintenance. These two strategies enable dynamic adjustment of the degree of accelerator redundancy provided to the reactors throughout their lifetime. It is expected that, through careful planning, another direct benefit of these strategies will be that while each reactor is successively closed for maintenance, there will be periods where a redundant accelerator is available. This redundancy will enable shutting down another accelerator if need be. This accelerator could then be visited for maintenance. This benefit has not been factored explicitly in the analytical model, and could be included in a subsequent and more detailed model of the system. Flexibility Strategy 3 is a growth option “on” the project. It gives the “right but not the obligation” to expand to a demonstration reactor park in Phase 2 if and only if accelerator performance (and the performance of other systems not considered in this paper) is good enough. This paper focused on the analysis of Strategies 1 and 2 because they require more thinking from an engineering design standpoint. These were integrated conceptually into a suggested design and development plan for commercial thorium-fuelled ADSR technology shown in Fig. 9. Strategy 3 was not studied in detail here, although the companion paper by Steer et al. (2012) gives it consideration. The design and development strategies obtained are radically different to those arising from extending current ADSR design and technology to a commercial demonstration park. Economic quantification was provided to support the design decision-making process depending on risk profiles and different probability assignments. Such explicit quantification enabled discriminating between two seemingly valuable flexible design configurations, a flexible 1 accelerator/1 reactor and a flexible 2 accelerators/1 reactor design. 5.2. Study limitations The flexibility strategies suggested here were based on the authors’ familiarity with the system. It is possible, however, that other strategies and design configurations could be crafted to favor reliable electricity production. The strategies studied here emerged by considering the canonical flexibility/real option strategies suggested by Trigeorgis (1996). They were extensions at a higher systems-level perspective of the widely used concept of redundancy in engineering practice, and current understanding of ADSR design (Pierini et al., 2003). To this end the paper provides a systematic methodology to explore other uncertainty sources and flexibility/real option strategies thoroughly and rigorously. The idea that flexibility can be used at the R&D level and later for large-scale deployment of innovative technology is applicable to other systems beyond the nuclear sector. Of course validating the generality of this statement is beyond the scope of this paper, given this study only provides one case demonstration. On the other hand, it is sensible that ideas of flexibility at the R&D level and large-scale deployment could be applied to many systems to reduce expected costs. This may help convince investors and/or funding agencies that money is used wisely all along the research process.

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The use of decision analysis in this study had both benefits and drawbacks. One drawback was the difficulty to consider many stages and uncertainty sources. The dimensionality of a decision tree is known to explode quickly with the number of stages and states. Another drawback was that decision analysis did not lead to an economic assessment of flexibility as rigorous as that provided by traditional ROA. On the other hand, these techniques rely on assumptions about markets and availability of data that may or may not be realistic for ADSR demonstration prototypes–and innovative technologies in general. For example, ROA based on arbitrageenforced pricing assumes markets of comparable tradable assets exist, are complete, and frictionless. This enables constructing a replicating portfolio hedging perfectly the cash flows produced by the asset, helping to deduce the value of the flexibility (Cox et al., 1979; Dixit and Pindyck, 1994; Trigeorgis, 1996). Such markets and ideal conditions may not exist for new ADSR technology. Another ROA approach based on equilibrium asset pricing makes the less stringent assumption of equilibrium within and across the markets for the relevant asset types (Arnold and Crack, 2003; Rubinstein, 1976). Such valuation, however, relies on data about market equilibrium for supply, demand, prices, together with trends and volatility for comparable assets. Although data exist for electricity supply and demand, it is not clear whether market data is readily available for establishing the costs of innovative ADSR technology. In addition, many of these economically rigorous techniques rely on concepts that may not be familiar to practicing engineers. This represents an important barrier to dissemination in real-world design and decision-making practice (Barman and Nash, 2007; Engel and Browning, 2008). Another important downside from using decision analysis related to the choice of probability distributions. As explained by Morgan and Henrion (1990), analysts must sometimes rely on educated guesses, especially when there is no historical data or clear Bayesian process to support inferences. This was the case here because no clear data existed on the probability of each EA scenario. This is why the sensitivity analysis performed over all possible distributions was conducted, and presented in Fig. 11. This analysis provided a graphical way to visualize the thresholds at which design decisions may have shifted. In this case it did show that flexibility would be valuable in most cases as opposed to a rigid, inflexible design strategy. Such decision thresholds may not be as clear for other systems. At the expense of economic rigor, decision analysis had the advantage of offering better transparency to expose the concepts above. By extension, it could help designers and decision-makers consider more explicitly in the early stages of design the different scenarios arising in the future. A graphical view of the decision nodes followed by uncertainty/chance nodes may induce more pro-active considerations of the “what-if” scenarios by means of flexibility. Another advantage of decision analysis was to enable a relatively quick evaluation and rank ordering of the different design alternatives. This was the essential value proposition for design decision-making in this paper. It was feasible without a deep understanding of the rigorous economic concepts explained above. Also, decision analysis was useful to analyse the systems exhibiting significant path dependencies. It enabled drawing explicitly the different development pathways under uncertainty, without assuming path recombination as done in traditional ROA (Copeland and Antikarov, 2003; Cox et al., 1979). Indeed, the assumption of path independence – central to these techniques – cannot be fulfilled in almost all cases of engineering systems design (Wang and de Neufville, 2005). 5.3. Future work A natural extension of this work would be to develop a simulation-based model to account for more uncertainty sources,

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scenarios, and design details in technology modeling. The same integrated methodology could be used to explore other possibilities systematically. Techniques developed by Cardin et al. (under review) and Mikaelian et al. (2011) could be used to stimulate flexibility generation and identification. If many more design alternatives arise, the analysis could build upon and extend the work by Lin et al. (2009), Wang (2005), and Yang (2009). These authors developed a screening approach based on optimizations and design of experiments to explore the design space efficiently for valuable design configurations. The analysis could also be extended to the possibility of driving ADSRs with other alternative compact accelerators, such as non-scaling Fixed-Field Alternating Gradient (ns-FFAG) accelerators, synchrotrons, or superconducting cyclotrons. Acknowledgements The authors would like to thank the U.K. Engineering and Physical Sciences Research Council (EPSRC), the Electricity Policy Research Group at the University of Cambridge, the National Science and Engineering Research Council of Canada, the M.I.T. Portugal Program, and M.I.T. Engineering Systems Division for their financial support. This work was supported, in part, by the EPSRC under grant EP/G009864/1. The authors are also grateful to the Cambridge Nuclear Energy Centre and the Electricity Policy Research Group for advice and assistance. References Abdelhamid, M.B., Aloui, C., Chaton, C., 2009. A real options approach to investing in the first nuclear power plant under cost uncertainty: comparison with natural gas power plant for the Tunisian case. International Journal of Oil 2, 44–57. Amram, M., Kulatilaka, N., 1999. Real Options: Managing Strategic Investment in an Uncertain World. Harvard Business School Press, Cambridge, MA. Arnold, T.A., Crack, T.F., 2003. Option Pricing in the Real World: A Generalized Binomial Model with Applications to Real Options Real Options Conference , Washington, DC, United States. Barman, B., Nash, K., 2007. A Streamlined Real Options Model for Real Estate Development Department of Urban Studies and Design. Massachusetts Institute of Technology, Cambridge, MA. Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654. Bowman, C.D., Arthur, E.D., Lisowski, P.W., Lawrence, G.P., Jensen, R.J., Anderson, J.L., Blind, B., Cappiello, M., Davidson, J.W., England, T.R., Engel, L.N., Haight, R.C., Hughes III, H.G., Ireland, J.R., Krakowski, R.A., LaBauve, R.J., Letellier, B.C., Perry, R.T., Russell, G.J., Staudhammer, K.P., Versamis, G., Wilson, W.B., 1992. Nuclear energy generation and waste transmutation using an accelerator-driven intense thermal neutron source. Nuclear Instruments and Methods A 320, 336–367. Braha, D., Minai, A.A., Bar-Yam, Y., 2006. Complex Engineered Systems: Science Meets Technology. Springer, Netherlands. Burgazzi, L., Pierini, P., 2007. Reliability studies of a high-power proton accelerator for accelerator-driven system applications for nuclear waste transmutation. Reliability Engineering and System Safety 92, 440–463. Bryan, A.C., 2009. Thorium as a secure nuclear fuel alternative. Journal of Security, http://ensec.org/index.php?option=com content&view= Energy article&id=187:thorium-as-a-secure-nuclear-fuelalternative&catid=94:0409content&Itemid=342 (accessed 09.14.10). Cardin, M.-A., 2011. Quantitative Performance-based Evaluation of a Procedure for Flexible Design Concept Generation. Massachusetts Institute of Technology, Cambridge, MA. Cardin, M.-A., Kolfschoten, G.L., de Neufville, R., Frey, D.D., de Weck, O.L., Geltner, D.M. Empirical evaluation of procedures to generate flexibility in engineering systems and improve lifecycle performance, under review. Carminati, F., Klapisch, J.P., Revol, J.P., Roche, C., Rubbio, J.A., Rubbia, C., 1993. An Energy Amplifier for Cleaner and Inexhaustible Nuclear Energy Production Driven by a Particle Beam Accelerator, CERN/AT/93-47. Copeland, T., Antikarov, V., 2003. Real Options: A Practitioner’s Guide. Thomson Texere, New York, NY. Cox, J.C., Ross, S.A., Rubinstein, M., 1979. Options pricing: a simplified approach. Journal of Financial Economics 7, 229–263. de Neufville, R.,2004. Uncertainty Management for Engineering Systems Planning and Design. In: Engineering Systems Symposium. Massachusetts Institute of Technology, Cambridge, MA. de Neufville, R., Odoni, A., 2003. Airport Systems: Planning, Design, and Management. McGraw-Hill Companies Inc., New York, NY. de Neufville, R., Scholtes, S., 2011. Flexibility in Engineering Design. MIT Press, Cambridge, MA.

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Non-standard abbreviations/terms Effective availability: represents the percentage of time over the year that an accelerator is not undergoing maintenance, assuming at these times the ADSR is scheduled to sell electricity Real option: a design and/or management component providing the right, but not the obligation, to change and adapt the system flexibly in the face of uncertainty resolution Target curve: a different name for Cumulative Mass Function (CMF), showing the cumulative probabilities of attaining different performance and/or cost values