Comparison of net present value for construction projects of
two offshore floating nuclear power plant designs, using a
monte carlo method for evaluation of the project uncertainties
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Minelli, P. et al. “Comparison of net present value for construction
projects of two offshore floating nuclear power plant designs, using
a monte carlo method for evaluation of the project uncertainties.”
Proceedings of the 2018 International Congress on Advances in
Nuclear Power Plants, ICAPP 2018, 2, (2018): 988 © 2018 The
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COMPARISON OF NET PRESENT VALUE FOR CONSTRUCTION PROJECTS OF TWO OFFSHORE FLOATING NUCLEAR POWER PLANT DESIGNS, USING A MONTE CARLO METHOD FOR EVALUATION
OF THE PROJECT UNCERTAINTIES
P. Minelli*, M. Golay, J. Buongiorno, N. Todreas
Massachusetts Institute of Technology, Nuclear Science and Engineering Department 77 Massachusetts Avenue, Cambridge, MA, 02139
*pminelli@mit.edu
The Offshore Floating Nuclear Plant (OFNP) design creatively builds on two established technologies, namely light water reactors (LWRs) and floating oil/gas platforms. Marine siting as well as several design features produce a particularly safe plant. The concept exploits the advances and experience in the construction of large floating structures in the oil/gas offshore industry and naval shipyards to decrease construction time and cost compared to standard nuclear power plants.
This work aims to compare the Net Present Value (NPV) of two different projects, when important uncertainties are taken into account:
• Construction of multiple (up to four) small modular
units (275 MW each)
• Construction of one single unit of equivalent power
(1100 MW).
Some of the major sources of uncertainties in large and complex nuclear projects are price of electricity, construction cost, discount rate, years of operation, capacity factor and transportation costs.
Such sources of uncertainty are quantified through specification of documented averages and reasonable ranges of variability. This information is first used to perform a sensitivity analysis which shows that the NPV of an OFNP project is affected most strongly by price of electricity, construction cost and discount rate.
Then, all uncertainties are assigned a probability distribution function (pdf) and combined with a Monte Carlo approach to generate a pdf for the NPV of a project.
The results show that construction of four small modular units is the preferred alternative as it is characterized by a higher average and median NPV. Additional qualitative advantages of the smaller modular units include the lower initial capital expenses, hence lower financial risk, and higher project flexibility overall.
I. BACKGROUND: OFFSHORE FLOATING NUCLEAR POWER PLANT (OFNP)
The Offshore Floating Nuclear Plant (OFNP) concept is built upon two established technologies, namely light water reactors (LWRs) and floating oil/gas platforms.
Several features produce an attractive design. First, the OFNP can be entirely built on a floating rig in a shipyard and then towed to the site, where it can be anchored between 10 and 20 km off the coast (within territorial waters), moored in relatively deep water (about 100 m). The nuclear island is below the water line, with easy access to the ocean heat sink; therefore, indefinite decay heat removal can be assured without external intervention. The plant is connected to the grid via an underwater AC transmission line such that the only structure on land is the electric switchyard. Land usage is reduced to virtually zero, the consequence of this being a substantial increase in the number of potential sites. Safety concerns from earthquakes and tsunamis are minimized [1].
The OFNP main structure is a spar-type platform with catenary mooring. A spar is a simple cylindrical, partially submerged, floating rig, with a low center of gravity for added stability. This platform design, widely used for oil/gas floating rigs, eliminates transmission of seismic loads from the ocean floor and offers the best compromise between cost and dynamic stability with respect to waves, the wind, and blast.
The OFNP concept can accommodate most reactor and power cycle designs, with modifications to the size of the spar platform. The Massachusetts Institute of Technology is developing two designs in parallel: the OFNP-300 and OFNP-1100, designated according to their power rating (Figure 1). The OFNP-300 hosts a Westinghouse Small Modular Reactor [2]. It has a draft of about 48.5 m, a diameter of 45 m (hull) and the main deck is about 13 m above sea level. The OFNP-1100 is based on the Westinghouse AP1000 technology [3]. It has a draft of about 70 m, a diameter of 75 m (hull) and the
main deck is about 35 m above sea level. A water-tight underdeck hosts the nuclear island, the control room, the battery room, the spent fuel pool, the rad-waste facilities, the desalination units and the condensate storage tank. In both designs, the balance of plant and living quarters are located right below the main deck. The watertight compartments have both vertical and azimuthal bulkheads, to ensure floatation in case of breach or accidental flooding of one level. Cooling water is drawn from the bottom of the ocean, and discharged at ambient temperature at the surface, thus reducing thermal pollution.
The OFNP design aims to exploit the advances and experience in the construction of large floating structures in the oil/gas offshore industry and naval shipyards. The shipyard model potentially allows decreasing construction time and cost compared to standard nuclear power plants. This fact is crucial in light of the need to reduce the capital cost of nuclear projects. Also decommissioning is done in a centralized shipyard (just as it happens for the U.S. Navy nuclear submarine and carrier fleets) so that the site can be returned to “green field” conditions after the floating platform is towed away. The OFNP spar weight and size are well within the capabilities of modern shipyards in the U.S. and worldwide. Compared to terrestrial plants, the OFNP concept eliminates about 95% of the concrete used in a conventional nuclear power plant, thus reducing cost and removing a major potential source of delays during construction. The concrete usage in the OFNP is limited to the spent fuel pool structure and the additional protective wall for the control room.
Suitable sites are selected according to the presence of relatively deep water near shore (depth > 100m) to ensure that tsunami waves are small, the cost of other modes of electricity generation (natural gas, coal), proximity to major load centers, frequency and intensity of storms, and distance from major shipping lanes. Many such sites have been identified in established markets such as East and Southeast Asia, the Persian Gulf and Europe, but also growing markets like South America and Africa, as well as small island countries, large mining operations, and Department of Defense bases [4].
II. UNCERTAINTIES IN NUCLEAR PROJECTS
The success of nuclear power plant projects involves considerations of several factors, such as technology specifications, geographical area, political and regulatory framework. In general, it is possible to split the total costs of a generating plant into capital, operating, and external costs. Plant operating costs can be fixed or variable and include the costs of operation and maintenance (O&M), fuel, provisions for funding decommissioning, spent fuel and wastes. The external
Fig. 1. OFNP-300 (above) and OFNP-1100 (below) section views. Drawings not to scale.
costs to society from operation are defined as those actually incurred in relation to health and the environment, and could include the costs of dealing with a serious accident, if the insurance limit is exceeded. Capital costs include expenses associated with site preparation, engineering, construction and installation of components, construction materials, workforce, licensing and financing.
In nuclear reactors, the initial investment represents the largest cost component over the lifetime of the power plant, and it takes decades to be recovered. In the 2015 update of the Annual Energy Outlook Report [5], the U.S. Energy Information Administration (EIA)
estimated that the capital cost represents about 75% of the total Levelized Cost of Electricity (LCOE) of nuclear power plants. This value, in relative terms, is the largest comparing to all other dispatchable technologies.
Nuclear projects are capital intensive, whereas the expenses associated with O&M and fuel are relatively small. Traditionally, the economy of scale drives to the construction of large units, for which the initial investment can be considerable. Consequently, the capital cost is very high not only in relative but also in absolute terms. Nuclear projects are complex and they take place in a rigorous regulatory environment, whose potential instability and policy changes may affect the construction process. Also, the duration of the project is a fundamental parameter. Between the time of the investment and the starting of operations, no power is sold, and consequently there are no revenues. The financial risk increases with increasing number of years required to complete the project. Long construction periods increase the chances that the market conditions and system performance requirements will have evolved adversely between the time of investment and the time at which the plant eventually enters service [6]. For example, materials and labor cost variations can significantly affect the actual investment, and these variations are – in general – rather difficult to predict over an extended period. In a capital intensive and long project, the impact of interest rates is significant, even in the absence of delays.
Beyond the technical difficulties, many costly delays are attributed to poor project management or schedule planning. Some of the large and complex components of a nuclear plant (such as the reactor pressure vessel and the steam generators) can be manufactured only by a few companies around the world. Consequently, these parts have inherently long lead times, and they must be ordered much in advance. Also the regulatory authority has a critical role in the construction phase of the power plant. Regulatory inspections can demand rework or design changes throughout the construction process. Each additional modification can lead to overruns, even if project managers usually plan for appropriate extra time built into the schedule that can allow certain tasks to run overtime without delaying the whole schedule.
In Section I we mention that a team at the Massachusetts Institute of Technology is developing two designs in parallel: the OFNP-1100 and OFNP-300. The first option favors economy of scale, whereas the second one economy of numbers. The assumption that a modular approach is beneficial is valid only if many units are built (this factor is highly uncertain). In order to achieve this goal construction should be based upon an initially-complete design and use of work oversights methods to ensure that rework amounts will be minimal. In addition to this, we expect a construction cost reduction due to the fact that the plant is built in a shipyard. In the next
section, we introduce the factor “S” to describe the gains from shipyard construction with respect to standard construction while we also realize that the shipyard approach is rewarding only if the design of the plant is completed before construction begins (this is typically not the case in traditional nuclear power plants). In other words, the shipyard construction model has a great potential only if things are done right the first time.
In conclusion, there are several “traditional” sources of uncertainties (construction cost, energy demand, construction time, etc.), as well as very important “non-standard factors” for which the uncertainties are more difficult to characterize (political support, social acceptance, etc.).
III. MODEL FOR THE DETERMINISTIC APPROACH
We set up a model to calculate the Net Present value (NPV) of an OFNP construction project. In this section we present the main parameters and assumptions of the model. We next introduce additional details for the treatment of uncertainties and other refinements. In this first deterministic approach uncertainties are not taken into account. The input required for the model is explained next. All costs are reported in 2017 USD.
Power rating, expressed in MWe. In this model,
the user can select either 275 MWe or 1100 MWe (OFNP-300 or OFNP-1100).
Capacity factor. Nuclear power plants are at the
high end of the range of capacity factors, ideally reduced only by the availability factor, i.e. maintenance and refueling. Outages management in power plants has reached extremely high levels of efficiency. However, since the OFNP is sited offshore there are necessarily uncertainties associated with operation, maintenance and refueling. Unexpected problems, marine environment, or distance from the coast can cause delays and consequently affect the capacity factor. In the deterministic case, we use 80% for both the OFNP-300 and the OFNP-1100.
Electricity price. The price at which the
electricity is sold depends on several parameters such as capital cost, operation costs, competitor’s cost, market conditions, type and profile of the demand. Is the electricity sold at a spot price or through a power purchase agreement? In what part of the world is the electricity sold? Also, how can we predict electricity prices 40 years from now? The next section discusses the price of electricity from a nuclear source and provides a reasonable range of variation. For the deterministic case we assume a fixed value for the electricity price (10 cents/kWh).
Operating costs. They include work management, training, support services, actual operations, material and services and loss prevention costs. These
costs have been rather stable in the past few decades. In the deterministic case we use the data of the Nuclear Energy Institute (NEI) [7]. We assume that the average of the US nuclear power plant reported operating costs between 2002 and 2016 is a reasonable figure. This value is about 21 $/MWh. However, since the platform is sited offshore, we assume operating costs about 10% higher (23 $/MWh).
Fuel costs. We use the NEI data between 2002
and 2016 also for the fuel costs. In the deterministic case, we assume 7 $/MWh.
Transportation costs. The OFNP is entirely
built in a shipyard and then towed to the site. Thus, transportation costs must be taken into account (also for decommissioning and major interim maintenance). There are two main transportation modes: wet tow (the unit floats on own keel and tugs pull it to the final location) and dry tow (the unit is loaded on the deck of a transport ship and transported to the site). There are dozens of companies which can do a wet tow as there are hundreds of suitable tugs. However, there are only few companies (less than a dozen) that can do a dry tow of medium size, and currently only one which can deal with very large size structures (such as the OFNP). The most suitable option for this project, at the moment, is the Dockwise-Vanguard ship [8]. There are factors that make the cost estimation quite uncertain: route, time (dry tow is faster), flexibility (dry tow is less flexible), etc. A rough estimation is enough for this model. The DW-Vanguard was scheduled for transporting the ship Costa Concordia to China at a price of $30,000,000. In our case, a reasonable range is between $10,000,000 and $30,000,000. In this section we assume a transportation cost of $20,000,000. Transportation costs are considered not only for siting, but also for decommissioning and every time the rig is transported to the shipyard for exceptional circumstances. If these operations happen far in the future, their discounted value becomes negligibly small.
Construction cost. The construction cost of the
OFNP is highly uncertain. In our analysis, the construction cost includes:
• Construction cost of traditional nuclear power plants (“C”). Construction cost of traditional NPPs data are available from different sources. It depends on several factors such as type of technology (e.g. PWR vs. BWR vs. AGR, etc.), host country, type of financial model, extraordinary circumstances or delays, political or regulatory decisions to name the most important factors. The construction cost has a great effect on the outcome of the project since the price of nuclear electricity is highly dependent on capital cost.
• Gains from shipyard construction with respect to standard construction. One of the major advantages of the OFNP concept is that it is built in a shipyard. The cost of platform-to-shore electrical connection
(that is necessary in the OFNP design) could be significant but is not considered in this analysis. This centralized construction model aims to reduce construction costs significantly by minimizing the effect of possible delays or unpredicted circumstances typical of traditional nuclear power plant projects. In our model, this is represented by the factor “S”, defined as the fraction of cost reduction due to the gains from shipyard construction with respect to traditional stick-built construction. For example, S=0.3 means that construction cost in a shipyard is 30% lower than in a traditional site. • Gains from learning in the construction process
(“L”). One of the advantages of the OFNP is that it gives the option to build the exact same power plant over and over again, or at least production in series is easier to implement than for a traditional plant, which produces a learning effect in the construction process (e.g. the 2nd plant will be cheaper than the 1st). In this model, we do so by using the factor “L”, defined as the fraction of price reduction due to the gains from learning process. For example, L=0.25 indicates that from one plant to the next the construction cost decreases by 25% due to the learning process.
These three components (C, S, L) influence the final OFNP construction costas shown in the following equation:
)]
1
(
1
[
−
−
−
=
C
S
L
N
CC
OFNPC, S and L are defined above and N is the number of plants already built. For the deterministic case, we assume C=4000 $/kWe, S=25%, L=15%.
Years of operation. In the deterministic case we
assume 60 years.
Discount rate. The discount rate for the
deterministic case is set to 8%.
Construction time. The OFNP design exploits
the advances and experience in the construction of large floating structures in the oil/gas offshore industry and naval shipyards. The capabilities of modern shipyards worldwide are astounding. For example, the Daewoo Shipbuilding and Marine Engineering shipyards build the world’s largest oil/gas floating platforms (140 000-ton displacement, 136-m length, 30-m draft) and the largest oil supertankers (500 000-ton displacement, 380-m length, 68-m beam) in just 24 months. The Technip shipyard in Finland routinely completes construction of spar-type platforms (>40-m diameter, >100-m draft) within 20 months. Sevan Marine builds large cylindrical hull platforms (>100-m diameter) and has recently proposed this design for a 700-MW(electric) liquified natural gas (LNG)-fired power plant. Newport News Shipbuilding designs, builds, and refuels the U.S. Navy’s
nuclear-powered aircraft carriers and submarines, such as the Gerald Ford, an aircraft carrier of 100 000-ton displacement, 340-m length, 41-m deck elevation, and 12-m draft, with two nuclear reactors on board, which was assembled (hull, decks, and main internal structures) in 36 months. Samsung Heavy Industries completed in 2017 the construction of Prelude, a floating LNG plant that is also the largest offshore facility ever built (600 000 tons, 488-m length, 75-488-m width): Prelude’s hull was built in 11 months and is designed to withstand a Category 5 cyclone. These spectacular construction achievements for such large and complex structures result from the efficiencies available in today’s shipyards. The OFNP is designed like a platform to take advantage of these modern capabilities [9]. The construction time in the deterministic case is assumed to be 3 years.
Finally, all the parameters discussed above are used in a cash flow calculation to find the NPV of different OFNP projects. The construction of four OFNP-300 (assuming that each OFNP-OFNP-300 generates 275 MWe) generates an NPV of 2,484 million dollars. The construction of one single OFNP-1100 generates an NPV of 2,226 million dollars.
The calculation assumes that construction of the four OFNP-300 occurs in a staggered series of four years (i.e. the units are brought into operation one year apart). The analysis (deterministic case) shows that the project based on four OFNP-300 has a higher NPV than one single OFNP-1100.
IV. SENSITIVITY ANALYSIS AND TORNADO DIAGRAM
A complex project has many uncertain variables. Our objective is to understand relevant issues and develop improved designs. The major uncertainties that are likely to impact the success and/or the performance of the project are:
Electricity price. the average retail price of
electricity in US between 1960 and 2011 (in 2015 cents per kWh, including taxes and transmission) approximately ranges between a minimum of 7 cents/kWh to a maximum of about 11 cents/kWh. Potentially, the OFNP can be built and sited in many places around the world. Thus, if we want to evaluate a reasonable range of change in the electricity price, we should take other regions of the world into account. Figure 2 shows the data reported by IEA, EIA, National Electricity Boards, and ONADA on the average national electricity prices in 2011. The numbers are converted in 2017 USD/kWh. We can see that the data range between about 9 US cents/kWh (India and China) to about 45 US cents/kWh (Denmark). The United States is approximately in the middle of the range (13 cents/kWh).
To account for electricity prices variations in the future, one option is to look at their projections. However, forecasts are almost always wrong, so we do not use these charts. Instead, we assume that 5 cents/kWh is a reasonable lower bound for the electricity price for the project and the time range we are considering. As an upper bound we take the Denmark figure (45 cents/kWh). The base case is the electricity price in the United States shown in the chart below (13 cents/kWh).
Number of years of operation. Lower and
upper bounds are determined as follows:
• Lower bound = 1 year. For whatever reason the project might be abandoned immediately and the production of electricity stops.
• Upper bound = 60 years. This is the life time for which nuclear power plants are typically deigned nowadays.
• Base case = 40 years. Conservatively assumed lower than 60 years to account for unexpected degradation of the plant in the marine environment.
Fig. 2. Cost of electricity worldwide in 2017 $/kWh. [10]
Capacity factor. According to the Nuclear
Energy Institute (NEI), the US nuclear capacity factors significantly increased between 1980 and 2000, and later on reached an asymptote around a value of about 90%. The United Kingdom Department of Energy and Climate Change database reports nuclear capacity factors in the UK grid from 59.6% in 2007 to 75.1% in 2015 (a significant lower value compared to the US). In addition, the OFNP is sited offshore and in a marine environment. Thus, we might expect a reduction of capacity factor of some extent (at least for the first units). In conclusion, we assume the following reasonable range:
• Lower bound = 50% • Upper bound = 90% • Base case = 80%
Construction cost. Let us start with the
construction cost of traditional power plants. Figure 3 is taken from a report of the World Nuclear Association
(WNA), and it shows the uncertainty associated with the construction cost of completed nuclear power plant projects in different regions of the world. Data are collected from various publications and studies for nuclear plant construction costs, since 2008.
Fig. 3. Overnight capital cost of NPPs (in USD/kW) and relative uncertainty by region. The numbers above the bars are the sample size.
All data are overnight capital costs (expressed in 2013 USD), which are useful to compare the economic feasibility of building various plants. The overnight capital cost does not take into account financing costs or escalation, and hence is not an actual estimate of construction cost [5].
North America and Europe are characterized not only by larger average construction costs, but also by larger ranges of uncertainty compared to Asia and the Middle East. In this sensitivity analysis we do not draw a distinction between construction costs of large monolithic units and Small Modular Reactors (SMRs). We refine this model in the next section. For the purposes of this analysis, the following boundaries are appropriate: • Upper boundary = 7000 USD/kW (2017) • Lower boundary = 1500 USD/kW (2017) • Base case = 4000 USD/kW (2017)
It is rather difficult to find data for the factors “L” and “S”. In this analysis, we assume the following to be reasonable values:
• “L” ranges between 0 (no learning effect) and 0.3 (cost reduction of 30% from one plant to the next). The base case is 0.15.
• “S” ranges between 0 (no advantages from shipyard construction) and 0.5 (50% cost reduction with respect to traditional power plants). The base case is 0.25.
The discount rate is a crucial parameter, capturing the perceived financial risk of the project,
which in turn depends on a myriad of country, company and time-dependent factors. For the purpose of this analysis, we assume that the following are reasonable values:
• Upper boundary = 15% • Lower boundary = 5% • Base case = 8%
In conclusion, the values used for base case, lower and upper boundaries to build the tornado diagrams are shown in Table I.
TABLE I. Ranges of change of different uncertain parameters.
Base Case Lower Boundary Upper Boundary Electricity Price 10 US cents/kWh 5 US cents/kWh 45 US cents/kWh Construction Cost 4000 $/kW, L=0.15, S=0.25 1500 $/kW, L=0.3, S=0.5 7000 $/kW, L=0, S=0 Years of Operation 40 1 60 Discount Rate 8% 5% 15% Capacity Factor 0.8 0.5 0.9
Building the tornado diagram is conceptually similar to calculating the partial derivative of the utility function (in this case NPV) with respect to each one of the uncertain parameters. Using the ranges in Table I, we get the tornado diagrams shown in Figure 4 and Figure 5 (respectively for the OFNP-300 and OFNP-1100).
The results in the tornado diagram are normalized to the base case NPV (divided by base case NPV and subtract 1). In the tornado diagrams, black indicates a plus in the NPV and red indicates a minus.
Electricity price is the factor with the largest variation in the positive direction. The sites with electricity prices similar as those of Denmark are upside opportunities. The promoters of the projects might prefer to consider markets with high electricity prices. Construction cost is also important (in both positive and negative directions). Discount rate and years of operation are important in the negative direction. All these trends are reasonable and expected.
Fig. 4. Tornado diagram (OFNP-300)
Fig. 5. Tornado diagram (OFNP-1100)
V. REFINEMENTS TO INCLUDE
UNCERTAINTIES AND CONDITIONAL DECISIONS
In this section we explain how we refine the analysis to take into account uncertainties. Let us compare the new model, which is probabilistic, with the deterministic approach and list the factors that are affected by the new probabilistic approach.
Capacity factor. To take into account the
variability of the input, we assume it to be normally distributed with mean and standard deviation equal to 0.8 and 0.03, respectively.
Electricity price. We choose a mean equal to 10
cents/kWh and a standard deviation of 2 cents/kWh. A new value of the electricity price is drawn every year from the distribution. In addition to this, we also consider the possibility that the price of electricity can drop dramatically due to external circumstances, e.g. the development of fracking and cheap natural gas as well as the build-up of intermittent renewable capacity have determined an electricity price collapse in the past 5 years. The user can easily set the probability that this happens (in this analysis 5% per year). If the electricity price drops, its value is drawn from a uniform distribution with parameters that the user can specify (in this analysis, 3 cents/kWh 1.5 cents/kWh). Figure 6 shows the histogram of electricity prices for one single simulation of a 60-year project. Note the characteristic shape of the normal distribution on the right side but also a second
peak around 2-3 cents/kWh due to the unexpected price drops.
Transportation cost. We assume a uniform
distribution between 10 and 30 million USD.
Construction cost. For the OFNP-1100 we
describe this variable as a normal distribution with mean of 4000 $/kWe and standard deviation 800 $/kWe. The construction cost of modular reactors is typically assumed to be larger than for monolithic constructions on a $/kWe basis. A satisfactory literature regarding construction costs of SMRs is absent. In this paper we assume that the construction cost of the OFNP-300 is normally distributed
Fig. 6. Electricity prices for one random simulation.
Fig. 7. Construction costs (“C”) distribution used for the OFNP-300 (orange) and the OFNP-1100 (blue).
with mean 10% larger than for the OFNP-1100 and same standard deviation (see Figure 7). Every time a new unit is built, a new value is drawn from this distribution.
Construction time. The OFNP construction
time in the deterministic case is 3 years. However, delays in nuclear power plant constructions are, unfortunately, very common. These are often major contributors to cost overruns. In this model, every time a unit is built, the construction time is drawn from a distribution that starts from a minimum of 3 years and decreases exponentially. The users can specify the parameters of the exponential function (in our model lambda is 3). Generating capacity
(thus revenues) are added only after construction is completed.
Decommissioning costs. These are traditionally
assumed to be about one third of total construction costs. We make this assumption in our model. Note that if decommissioning happens far in the future, its discounted value becomes quite small.
Maintenance and extraordinary repairs. The
model distinguishes between regular maintenance and extraordinary repairs. The former happens offshore (no need of towing) every 10 years and it takes three months to complete (i.e. one fourth of the yearly revenues are subtracted). The latter is assumed to be a rare event and requires the rig to be towed back to the shipyard. The probability of this extraordinary circumstances is set to 1% per unit, per year. If the platform needs extraordinary repairs in any given year, the following costs are applied: loss of revenues (3 months), transportation costs, cost of extraordinary repair (e.g. material, labor, shipyard). Cost of extraordinary repairs is drawn from a normal distribution with mean and standard deviation equal to 100 million $ and 10 million $. In order to have a realistic model, if extraordinary repairs are needed in the last 10 years of the plant lifetime, the OFNP is permanently shut down.
Multiple units. If the user selects the 1100 MWe
unit option, the model assumes that only one unit is built (one OFNP-1100). If the user selects the 275 MWe unit option (OFNP-300), the model assumes that multiple units (up to a maximum of four) can be built. The necessary condition to build an additional unit is that the electricity price during the previous year is higher than a certain threshold (e.g. 9 cents/kWe). This can be seen as a measure of whether the market is favorable or not.
VI. RESULTS
In this section we compare again the performance of the following projects on the base of the probabilistic model described in the previous section: 1. Construction of multiple (up to four) OFNP-300 (275
MWe each);
2. Construction of one single OFNP-1100 (1100 MWe). The Monte Carlo method is used to propagate uncertainties. The sample size of the Monte Carlo simulation is equal to 2000 runs in each project. For each project, we show the cumulative distribution functions (Figure 8 and 9) from the Monte Carlo simulation.
Table II is a summary of average, standard deviation, ranges of simulation results, minimum and maximum results as well as the values of 5th and 95th
percentiles, and .
Fig. 8. CDF for the construction of four OFNP-300.
Fig. 9. CDF for the construction of one OFNP-1100.
TABLE II. Simulation results for NPV of the OFNP-300 and OFNP-1100 projects
4 OFNP-300 1 OFNP-1100 Average NPV (M$) 1,723 1,337 Standard Deviation (M$) 410 845 Average range (M$, 95% confidence) 1,705 - 1,740 1,300 - 1,374 (M$) 1,000 -100 (M$) 2,400 2,700 Minimum (M$) 350 -1,400 Maximum (M$) 3,290 4,300
Based on these results, construction of four OFNP-300 units is a better project because the average NPV is about 1.3 times higher than the OFNP-1100 case and the uncertainty is far lower.
The OFNP-300 project has a further advantage. Since it involves the construction of modular, small units, the initial investment required is lower than for the OFNP-1100. The CapEx (e.g. the capital expenditure needed to start the project) is lower, making it easier for the investors to take the risks. This could translate in a lower discount rate for the OFNP-300, which was not accounted for in this analysis. Modularity means also that
managers can decide to “control” the capacity of the power plants park as the uncertainties unfold. For instance, they can decide to build less plants than originally planned if the market conditions are not particularly favorable. If the project has to be abandoned in the first years, the OFNP-300 limits financial losses as not all capacity has been built yet. By contrast, decision makers can easily build additional capacity if the conditions are particularly favorable.
Finally, the model allows users to exercise different “options”, a decision made in response to an (uncertain) event. An example would be the possibility to add capacity in response to a particularly favorable market. These are types of decisions that are made in reality and therefore must be taken into account in the analysis. We highlight the importance of such options by considering an example of a significant uncertainty: the possibility to lose support from the government. Loosing political support can have drastic consequences on the success of the project. An example is the decision by a local public utility commission to withdraw support for a new nuclear power plant.
We can set the probability per year that the project loses support from the government (e.g. 0.5% per year). In addition, we can specify whether the plant can be relocated to a different site or must be decommissioned. The crucial difference is that in the second case, we give managers the “option” to limit potentially huge losses deriving from the loss of political support. For example, the plant could be relocated from the UK to Singapore. In each year of the project, the model performs the following steps:
1. Determines if the project loses political support (probability = 0.5%)
2. If so and the plant cannot be relocated, the project proceeds to decommissioning.
3. If political support is lost, but the plant can be relocated, the model adds cost of towing to new site as well as additional relocation costs (switchyard, new contracts, licenses, etc...). Then operations are re-started the next year.
Let us compare the results when the model includes the possibility of losing support and (i) the plant cannot be relocated, and (ii) the plant can be relocated. The way the results are presented is similar to the previous section. For simplicity, we will consider only the case of the OFNP-300.
The NPV may become significantly negative if political support is lost and it is not possible to relocate the plant. However, if we allow for relocation after losing support, the distribution is much more skewed towards positive values of the NPV.
Fig. 10. CDF for the base case (orange), the case in which we introduce the possibility of losing political support and no option to relocate the plants (blue), and the case in which we introduce the possibility of losing political support as well as the option to relocate the plants (green).
Table III shows that the average NPV for the second case is higher, and the financial risk is also lower (the maximum losses are limited compared to the first case). At the same time, the maximum gains are comparable. Therefore, the possibility to relocate provides the OFNP concept with an important edge against loss of political support.
TABLE III. Simulation results for OFNP-300 NPV when the plant can and cannot be relocated.
Plants cannot be relocated Plants can be relocated Average NPV (M$) 1,410 1,710 Standard Deviation (M$) 908 420 Average range (M$, 95% confidence) 1,370 - 1,450 1,690 - 1,730 (M$) -1,000 1,000 (M$) 2,400 2,400 Minimum (M$) -2,700 300 Maximum (M$) 3,100 3,000 VII. CONCLUSIONS
In this paper we compared the NPV of two different OFNP deployment projects (one based on multiple small modular reactors OFNP-300 and one based on a single large OFNP-1100 unit), with consideration of the important uncertainties via sensitivity analysis and a probabilistic approach.
Based on the analyses presented here, we conclude that the OFNP-300 project is economically more promising as its average NPV is higher and the standard deviation is smaller.
We also show that the possibility to relocate an OFNP plant during its service lifetime provides the OFNP concept with an important economic edge against loss of political support at the site of initial deployment
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