Nuclear Power Deployment Operation and Sustainability Part 3 potx

To date, estimates of the cost of relatively traditional alternative fuel cycle options most uranium cost increases, Yucca Mtn repository, and GNEP technology options suggest uncertainti

Assessment of Deployment Scenarios of New Fuel Cycle Technologies 59 consumption and avoidance of TRU at a given TRU CR Certainly the rate of TRU consumption from the standpoint of an individual reactor depends on the reactor power and CR; however, from the standpoint of the entire fleet, the rate of TRU consumption and avoidance additionally depends on how fast TRU-consuming reactors (burner FR in this instance) displace TRU-producing reactors (LWRs in this instance), how quickly discharged fuel can be separated and recycled material re-inserted into reactors Figure 17 shows the impact of increasing the “wet” storage time from 1 to 10 years for a 1-tier CR=0.50 fast reactor case, approximating a shift from onsite to offsite separation and fuel fabrication The total time from reactor discharge to reinsertion changes from 2 to 11 years

Fig 15 Waste, uranium, and fuel product mass for a 1-tier recycle case, CR=0.50 fast

reactors, no packaging included

Fig 16 Percent of RU and DU from LWRs used as fast reactor fuel with fast reactors and LWRs in static equilibrium

Fig 17 Long-term radiotoxicity of 1-tier fast reactor CR=0.50 with either 1 or 10 year “wet” cooling before a year of separation and fuel fabrication

5.3 Uranium utilization

To start, consider the range of estimates of world uranium resources in Table II relative to the 2006 production rate of 40,000 tonne-U.19 The current nuclear power production rate would exhaust total estimated conventional resources (16,000,000 tonnes-U) in 400 years That time scale can drop to within a century with modest nuclear power growth, but extend many centuries if unconventional resources become practical

Total estimated conventional resources

Above 4 categories, <$130/kg-U

Above 4 categories, plus “cost range unassigned”

Undiscovered + known, <$130/kg-U

Undiscovered + known, <$130/kg-U

Table 2 World Potential Uranium Resources

Assessment of Deployment Scenarios of New Fuel Cycle Technologies 61

Nuclear fuel isotopes are either fissile or fertile; fissile isotopes are much more readily

consumed The only fissile isotope in nature is U-235, which is 0.7% of uranium ore The

only fertile isotopes in nature are U-238 (99.3% of uranium ore) and Th-232 (100% of

thorium ore) To extend ore utilization substantially above 0.7%, one must convert or

“breed” fertile to fissile isotopes Fertile U-238 can be bred to fissile Pu-239, called the

uranium-plutonium fuel cycle (or plutonium for short) Fertile Th-232 can be converted to

fissile U-233, called the thorium-uranium fuel cycle (or thorium for short) The ratio of

producing fissile isotopes (from fertile) to consuming fissile isotopes is called the fissile

breeding ratio A ratio greater than 1 means that more fissile isotopes are bred than

consumed, shifting the limiting resource from fissile isotopes to fertile isotopes

All current U.S reactors have fissile breeding ratio less than 1 and thus use less than 1% of the

original uranium ore Recycling in such reactors is not sufficient to break 1% because their

fissile breeding ratios remain below 1 When the fissile breeding ratio is greater than 1, the

uranium (or thorium) utilization can exceed 1% There are exotic concepts in which maximize

in-situ breeding without recycling used fuel, it advanced materials can be developed, these

may achieve ~10% uranium utilization With recycling of used fuel in breeder reactors,

uranium and thorium utilization can approach 100%, subject to processing losses

Accomplishing 50-100x improvement in uranium utilization means near total replacement

of LWRs (or other thermal reactors) with fast reactors For example, if 10% of the reactor

fleet remains LWRs with UOX fuel with 90% of the electricity from fast breeder reactors, the

maximum uranium utilization improvement is 10x Such substantial infrastructure change

from LWRs to FRs is notoriously difficult.22 As most of the U.S LWR fleet is moving toward

a 60-year reactor lifetime, such a replacement of LWRs will take at least 6 decades from the

operation of the last LWR As an example, if fast breeder reactor deployment requires 2

decades from first deployment to 100% of new construction (i.e allowing 2 decades for

industrial scale-up and market penetration); it will be 2120 before the last LWR retires

Predicting uranium resources so far in advance is questionable

The above example assumes that the fast breeder reactors can grow faster than nuclear

power growth during its market penetration from 0 to 100%, followed by continued breeder

growth at the nuclear power growth rate once it reaches 100% of new construction The rate

of breeder deployment is constrained by fuel supply, which we have tended to assume is

transuranic material recycled from LWRs and fast reactors once operating, rather than high

enriched uranium (~30% U235)

We have derived the required TRU conversion ratio, such that LWR are not required to

supply TRU to a growing fleet of fast reactors:

(F R)

m t t

where m is the growth rate; t F is the time for cooling, separation, and fuel fabrication; t R is

the time in reactor Thus, t F is the total turnaround time As an example, if t R m  , then 0

1

CR  and the system is in balance with no LWRs Or, if one wants m  , then 0 CR  1

The higher the desired growth rate, the higher the required CR

In addition, because new fast reactors (growing at rate m) must have t  R 1 additional

years’ worth of fuel to start up, equation 1 must be multiplied by another term.2

2 A core contains t R years worth of fuel, with 1 year’s worth added each year At startup, there is

therefore an extra t -1 that must be provided

(F R)(1 ( 1))

m t t

R

At a nominal growth rate of 1.75%/yr, the time lags in the system are important If t  F 2

(example for onsite recycling) and t  , then R 4 CR 1.17 is required If t  F 11 (example

for offsite recycling) and t  , then R 4 CR 1.36 is required

Fig 18 shows the required CR as function of desired growth rate and turnaround time The

minimum turnaround time is probably ~5 years (1-year cooling, separation, fabrication and

4 years in reactor)

Fig 18 Required fast reactor TRU conversion ratio at dynamic equilibrium, as a function of

growth rate and turnaround, ignoring displacement of pre-existing LWRs or TRU

stockpiles

The theoretical maximum CR is ~1.9 because Pu239 dominates fission in a fast reactor and it

yields 2.9 neutrons/fission One neutron must induce the next fission, leaving 1.9 to make

more transuranic material from U238.3 Neutron yields vary slightly by isotope, e.g., 2.4 for

U235, 2.9 for Pu241, and 3.2 for Am242m, so the exact theoretical maximum could be

slightly different than 1.9 Of course, as neutron leakage and neutron capture by fuel and

non-fuel core material is accounted for, the practical maximum conversion ratio will be

significantly lower than 1.9 For example, if that maximum is considered to be 1.5, then the

maximum rate of breeder reactor introduction can be 4.7% with 6-year turnaround (onsite

recycling), but only 2.3% with 15-year turnaround (offsite recycling) The holdup of

transuranic material in the system impacts system performance so that short time lags, e.g.,

when facilities are co-located instead of at different locations, can lead to faster system

evolution

3 The theoretical maximum is actually smaller than 1.9 because some neutrons absorbed into fuel

necessarily lead to (n, γ) reactions instead of (n,fission) However, some of the (n, γ) products and their

successors will fission, so the reduction of the maximum below 1.9 is somewhat complicated and

beyond the scope of this illustrative calculation

Assessment of Deployment Scenarios of New Fuel Cycle Technologies 63

5.4 Proliferation resistance and physical protection

Barriers to acquisition of a nuclear weapon/explosive are called “proliferation resistance” for a host nation of nuclear facilities and “physical protection” for a subnational or terrorist group An evaluation methodology should include the four stages toward a weapon – (1) diversion (if host nation) or theft (if subnational), (2) transportation, (3) transformation, and (4) weapon fabrication and indicate how the various indicators are to be combined

First, observe that although there is significant reduction of TRU relative to once through (avoided and consumed), there remains significant TRU material throughout a fuel cycle system Figure 19 illustrates that there is substantial reduction of TRU material relative to once-through (via avoidance and consumption) but also that there is substantial TRU in many parts of the system

Fig 19 Location of TRU material in a 1-tier recycle case

The second proliferation resistance observation is that the mass flow of material through separations can vary significantly both quantitatively and by type of separation, independent of separation efficiency Figure 20 shows the total mass sent through separations (the sum of the flow tonnes-TRU/yr times the number of years) as a function of fast reactor conversion ratio for a 1-tier simulation; this figure keeps the fast reactor fuel constant (metal) with onsite processing As CR increases, there are fewer LWRs hence less processing of used LWR fuel; but there are more fast reactors and more processing of fast reactor fuel These may be of different technologies and the siting strategy could differ, e.g., large centrally located aqueous separation of used UOX fuel versus at-reactor electrochemical separation of used fast reactor metal fuel In such cases, the proliferation risk posed by different technologies and locations would vary

The third proliferation resistance observation is that the recycled material composition will change significantly with time Figure 21 shows evolution of the recycle mix as TRU material is repeatedly recycled, in this case as mixed oxide fuel in LWRs.12 This calculation

uses heterogeneous inert matrix fuel (IMF)4 to keep the material fissile, i.e., each recycle is a mixture of fresh UOX and IMF made with TRU recovered from the previous recycle The figure shows that the Cm and Cf isotopes, which emit high numbers of neutrons, increase

up to four orders of magnitude between the first recycle and equilibrium Figure 21 compares MOX and metal fast reactor fuel (at CR=0.75, comparable to the CR of MOX) at the first and equilibrium recycle Both MOX-TRU and FR-TRU evolve considerably from the first to the equilibrium recycle FR-TRU has higher Pu content but lower amounts of the highest TRU isotopes (Cf) that tend to dominate neutron emission

Fig 20 Total mass of TRU material sent through separations in 1-tier recycle case as a function of fast reactor TRU conversion ratio; metal fuel, on-site processing assumed

Figure 22 shows that MOX-TRU and FR-TRU vary little after the first recycle (square data points), with major differences only in the Cf isotopes (Composition impacts many areas, not just proliferation and physical security.) At equilibrium recycle (circle data points), MOX-TRU and FR-TRU differ less than an order of magnitude below Cm244, about an order

of magnitude from Cm244 to Cm248 and over an order of magnitude for the Cf isotopes High gamma emitting isotopes are found throughout the actinide chain and therefore the total gamma comparison between MOX-TRU and FR-TRU is merely an order of magnitude The highest neutron emitters are located at the top of the TRU chain and therefore the neutron emission comparison between MOX-TRU and FR-TRU grows over an order of magnitude Still, both MOX and FR at equilibrium have higher gamma and neutron emission than either has at the start of recycling

The fourth and final proliferation resistance observation is that the quality of Pu does not change dramatically throughout the century The quality of Pu measured as the fraction of

4 MOX fuel has U and one or more TRU elements mixed in each fuel pellet and fuel pin A homogeneous IMF fuel has only TRU A heterogeneous IMF fuel is a mix of IMF fuel pins and UOX fuel pins

Assessment of Deployment Scenarios of New Fuel Cycle Technologies 65 Pu-239 to total Pu in the system only changes from 0.55 (once through) to ~0.50 for the two recycle cases

Fig 21 Isotopic mix for discharged MOX-TRU as a function of how many times transuranic material is Transmutation data from ref 16

Fig 22 Isotopic mix for discharged MOX-TRU and FR-metal-TRU for first and equilibrium recycle Transmutation data from ref 12 and 16

5.5 Economics

In any area of technology, the cheapest situation occurs when raw materials are very low cost and one is allowed to just walk away from waste As raw material cost increases, the incentive to recycle materials increase As waste disposal costs increase, the incentive to reduce, re-use, and recycle increases

Unsurprisingly, therefore, for nuclear fuel cycles, there are major uncertainties associated with the future cost of uranium (or thorium), any waste repository, and any new technologies (reactors, fuels, separation, waste forms) that may be involved Were uranium and waste disposal inexpensive, it would be difficult to economically justify new technologies

The average cost of electricity from current U.S nuclear power plants is less than

$0.018/kilowatt-hour or 18 mills/kilowatt-hour (18 mills/kW-hr) because their capital costs have mostly been depreciated Cost projections for new plants in the next decade range from

47 to 71 hr which include capital recovery Fuel cycle costs are about 6

mills/kW-hr Of this, 1 mill/kW-hr is the fee currently paid by U.S utilities to the Federal government for future geologic disposal, covering projected disposal costs

To date, estimates of the cost of relatively traditional alternative fuel cycle options (most uranium cost increases, Yucca Mtn repository, and GNEP technology options) suggest uncertainties of a few mills/kW-hr, and possible increased cost (relative to once through) ranging from zero to a few mills/kW-hr, or 0-10% of total nuclear energy cost

The first is that dynamic versus static will impact economic assessments A static quilibrium

is appropriate when discount rates, the time value of money, and cash flows are not addressed A dynamic equilibrium comes closer to cash flows if the time value of money is accounted for as costs that lead others are given greater weight; cash flows that lag others are given less weight Table III lists key lead and lag items in dynamic equilibria For example, one builds LWRs relatively early in the process of generating electricity; therefore, when time value of money is considered, the relative contribution of LWRs to total cost increases Conversely, fast reactors and waste disposal are bought relatively late; therefore, their relative contribution to total cost decreases

Leading

Purchase relatively soon

Lagging Purchase relatively late Increase or decrease when

shifting from static to

dynamic equilibrium

Increase, hence factor might

be more important than predicted by static equilibrium

Decrease, smaller impact than might be predicted by static equilibrium

Material inputs Natural uranium

Depleted uranium Enriched uranium Zirconium and steel Types of reactors Number of thermal reactors

using uranium oxide fuel

Number of fast reactors Thermal efficiency increases Types of facilities Fabrication plants Separation plants

Table 3 Lead and Lag Items in Dynamic Equilibria

The fraction of fast reactors in time will be much lower than predicted by simple “static equilibrium” calculations due to multiple system constraints that impact the amount of TRU available for fueling new reactors at startup This is illustrated in figure 23

Assessment of Deployment Scenarios of New Fuel Cycle Technologies 67

Fig 23 Fraction of electricity generated by fast reactor at dynamic equilibrium (near 2100) as function of fast reactor TRU conversion rate and nuclear electricity power growth rate, calculations assumed metal fuel and onsite processing

The final observation is that fuel and separation facilities must accommodate variation in fuel mixture elemental composition This composition will vary as reactor type, fuel type, burnup, aging of used fuel, number of recycles, separation purity, etc

6 Acknowledgments

This chapter was prepared for the U.S Department of Energy Office of Nuclear Energy, Science, and Technology under DOE Idaho Operations Office Contract DE-AC07-05ID14517

7 References

[1] U S Department of Energy, Office of Nuclear Energy, Science, and Technology, Report

to Congress – Advanced Fuel Cycle Initiative: Objectives, Approach, and Technology Summary, May (2005)

[2] U S Department of Energy, Office of Nuclear Energy, Science and Technology,

Advanced Fuel Cycle Initiative (AFCI) Comparison Report, FY 2005, May (2005) [3] U S Department of Energy, Office of Nuclear Energy, Science, and Technology,

Advanced Fuel Cycle Initiative (AFCI) Comparison Report, FY 2006 Update, July (2006)

[4] J J Jacobson, A.M Yacout, G.E Matthern, S.J Piet, D.E Shropshire, R.F Jeffers, T

Schweitzer, “Verifiable Fuel Cycle Simulation Model (VISION): A tool for Analyzing Nuclear Fuel Cycle Futures”, Nuclear Technology, Volume 172, Number

2, November 2010

[5] S J Piet, “Selection of Isotopes and Elements for Fuel Cycle Analysis”, Advances in

Nuclear Fuel Management IV, April 12-15, 2009

[6] J W Forrester, Principles of Systems, Wright-Allen Press, Inc, 1971

[7] Powersim Software AS, Bergen, Norway, www.powersim.com

[8] J Grouiller, G Glamenbaum, B Sicard, M Mus, J Martin, J Devezeaux de Lavergne, O

Comellini COSI, A Simulation Software for a Pool of Reactors and Fuel Cycle Plants: Application to the Study of the Deployment of Fast Breeder Reactors Proceedings of the International Conference on Fast Reactors and Related Fuel Cycles, Kyoto, Japan, October 1991

[9] C G Bathke and E A Schneider Report of the COSI and NFCSim Benchmark Los

Alamos National Laboratory (2003) LA-UR-03-8051

[10] J A Stillman, “Homogeneous Recycling Strategies in LWRs for Plutonium,

Neptunium, and Americium Management,” Argonne National Laboratory, AFCI-124, August 2004

ANL-[11] E A Hoffman, W S Yang, R N Hill, Preliminary Core Design Studies for the

Advanced Burner Reactor over a Wide Range of Conversion Ratios,

ANL-AFCI-177, September 29, 2006

[12] E A Hoffman, “Updated Design Studies for the Advanced Burner Reactor over a

Wide Range of Conversion Ratios,” Argonne National Laboratory report, AFCI-189, May 31 (2007)

ANL-[13] E A Hoffman, “FY09 ANL AFCI Transmutation Studies,” Argonne National

Laboratory report, ANL-AFCI-271, August 31 (2007)

[14] M Asgari, B Forget, S Piet, R Ferrer, S Bays, Computational Neutronics Methods and

Transmutation Performance Analyses for Light Water Reactors,

INL/EXT-07-12472, March 2007

[15] R M Ferrer, M Asgari, S E Bays, B Forget, “Fast Reactor Alternative Studies: Effects

of Transuranic Groupings on Metal and Oxide Sodium Fast Reactor Designs,” INL/EXT-07-13236, September 2007

[16] G Youinou and S Bays, “Homogeneous recycling of Pu or Pu with Minor Actinides in

PWRs loaded with MOX-UE fuel (MOX with U-235 enriched U support), INL/EXT-09-16091, AFCI-SYSA-TRAN-SS-RT-2009-000055, June (2009)

[17] OECD Nuclear Energy Agency, Nuclear Fuel Cycle Transition Scenario Studies Status

Report (2009)

[18] S J PIET, G E Matthern, J J Jacobson, C T Laws, L C Cadwallader (INL), A M

Yacout, R N Hill (ANL), J D Smith, A S Goldmann, G Bailey (SNL), “Fuel Cycle Scenario Definition, Evaluation, and Trade-offs,” INL report, INL/EXT-06-11683, August (2006)

[19] OECD Nuclear Energy Agency and International Atomic Energy Agency, Uranium

2007: Resources, Production and Demand, NEA No 6345 (2008)

[20] J S Herring, “Uranium and Thorium Resources,” in The Encyclopedia of Energy,

Cutler J Cleveland, editor in chief, Academic Press, (2004)

[21] J J Steyn, “Uranium Resources: Need For 21st Century Advanced Fuel Cycles,”

Energy Resources International, Inc., NEI International Fuel Seminar (2003)

[22] D J Rose, Learning About Energy, Plenum Press, New York (1986)

3

The Investment Evaluation of Third-Generation Nuclear Power - From the Perspective of Real Options

Ying Fan and Lei Zhu

Center for Energy and Environmental Policy research, Institute of Policy and

Management, Chinese Academy of Sciences, Beijing

China

1 Introduction

The continued growth of world’s population and gradual increase of people’s living standards in developing countries have sped up the exhaustion of fossil fuels and caused large amount of greenhouse gas emissions Although renewable energy sources (e.g wind energy, solar energy, hydro energy and biomass energy) have developed rapidly in recent years, limitations existing in these energy sources (e.g non-continuous electricity supply of wind and solar power generation, resource constraints for hydro power and biomass energy etc.) still set barriers to launching application in large scale and fulfilling world’s energy demand in near future

Currently, great attention has been paid to nuclear technology It has been widely accepted around the world that nuclear power is a clean energy option which causes zero-emissions

of SO2, NOx, smoke dust and carbon A safely-operating nuclear power plant with strict radiation monitoring and risk management system will have little impacts on its surroundings, and the effects of radiation dose on citizens near the plant will be lower than 1% of underground natural radiation The development of nuclear energy can broaden the energy sources in energy industry, ease the limitations of fossil fuel supply, and reduce the environmental pollution caused by fossil fuel combustion The development of nuclear technology will also have significant impacts on greenhouse gas emission reduction

Asia has become the largest market for nuclear power after remarkable growth has emerged

to its economies in the last decade, especially in China and India The enjoyment of rapid economic development in Asian countries also brings the booming of energy consumption

On one hand, considering large fluctuation of international fossil energy prices (e.g oil prices) in recent years and lack of effective energy supply, Asian countries have to face more serious energy security situations; On the other hand, the consumption of fossil energy has caused severe environmental pollutions and large amount of greenhouse gas emissions, in the case of renewable energy development barriers, Asian countries need to find other new, clean, stable and extensive energy resource to meet their domestic energy demand Nuclear power is regarded as a trustworthy way to enhance Asian countries’ energy security and becomes a preferred-choice in their energy options

As the world’s largest developing country which is struggling with limited energy resources, growing energy demand, increasing dependence on imported oil, deteriorating

environment, and enormous greenhouse gas emission, China has taken nuclear power as one of main directions in future energy development to cope with serious threats on domestic energy security China’s power generation portfolio aims to gradually reduce the proportion of coal-fired power in the total power-generation mix and to promote the diversification of electrical energy sources, the power industry’s ‘Eleventh Five-Year Plan’ (NDRC, 2007) has been proposed to optimize the development of nuclear power Furthermore, the objective of ‘Mid and Long-term Nuclear Power Development Plan’ (NDRC, 2007) is to achieve a new capacity of 40 GW Nuclear Power in the year 2020, which will account for 4% of total generating capacity At the end of 2009, China has owned the largest scale of nuclear power plants under construction over the world, and the plants in progress have reached 21.92 GW with a total of 20 units

After the development of first two generations of nuclear power, China proposed to pioneer the demonstration and deployment of third-generation nuclear power with advanced reactors (Generation III nuclear reactor) in order to further enhance the level of self-developed nuclear power technology The third-generation reactors have: 1) a standardized, simpler and more rugged design for each type to expedite licensing; 2) higher availability and longer operating life expectancy; 3) comparatively lower possibility of core melt accidents; 4) resistance to serious damages; 5) higher burning temperature to reduce fuel use and the amount of waste and burnable absorbers to extend fuel life In 2007, as one of the Generation III nuclear reactor technologies on basis of a comprehensive technology transfer, Westinghouse AP1000 has been selected by China National Nuclear Cooperation to build four nuclear reactors in two demonstration projects in Zhejiang Sanmen and Shandong Haiyang Currently, nuclear reactors built in Zhejiang Sanmen are the only third-generation nuclear power units in the world

2 Uncertainties of China's third-generation nuclear power technology

investment

Some scholars have already studied the third-generation nuclear power from different perspectives Yim (2006) has discussed the relationship between the future expansion of nuclear power and the prospect for world nuclear nonproliferation, he concludes that the development of nuclear power and expansion of advanced nuclear technology will not result in nuclear proliferation Popa-Simil (2008) has proposed that the micro-bead heterogeneous fuel mesh gives the fission products the possibility to acquire stable conditions outside the hot zones without spilling and the high temperature fission products free fuel with near perfect burning, which is important to the future of nuclear power development Marcus (2008) has studied the characteristics of advanced nuclear reactor in order to extensive demands worldwide, including the role of nuclear power in the world power generation, introduction of innovative nuclear technologies, nuclear path forward and international initiatives of advanced nuclear technologies Tronea (2011) has discussed the European quest for standardisation of nuclear power reactors, including nuclear power design, new reactors standard and nuclear safety Yan et.al (2011) has introduced the development of nuclear power and third-generation nuclear power demonstration projects

in China, and they also have forecasted the future demand of uranium fuel in China

In the study of the economics of nuclear power, Kessides (2010) has discussed nuclear power investment from the perspective of economic risks and uncertainties He points out that several elements should be considered in nuclear power valuation, including

The Investment Evaluation of Third-Generation

environmental benefits of nuclear power investments (the contribution of greenhouse gas emissions), fuel costs, costs of radioactive waste disposal, risks associated with radio activity release from all fuel cycle activity, with the capital or nuclear power construction costs with the greatest importance However, as a technology that is currently in the research and development stage, China is facing numerous uncertainties in demonstration and deployment of third-generation nuclear power, including:

1 The uncertainty from the technology itself As a large-scale and capital-intensive technology, third-generation nuclear power is still in the development and demonstration stage which exhibiting unsolved technology uncertainties During the technology deployment process, uncertainties around the technology mainly come from the plant design and construction, reactor installation, and equipment commissioning And this corresponds to the uncertainties of investment cost and construction period which are in need for technology deployment

2 It is claimed in the design that the operating costs of third-generation nuclear power will

be equal or even lower than that of second-generation It should be noted that nuclear fuel cost has accounted for a large proportion in nuclear power operating costs Currently, the price of nuclear fuel is relatively stable because uranium resources in each country are under government control, as more nuclear power plants will be put into use in the coming future, increasing demand of uranium resources worldwide may result in price increasing and fluctuation This will add more price risk to generating cost

3 Although the design of third-generation nuclear power is much safer than first two generations, because the lack of actual operational experiments, the potential risk of radiation can not be completely under control China’s National Nuclear Security Regulations require the Probabilistic Safety Assessment (PSA) must be carried out by all nuclear power plants Nuclear accidents are unexpected events with small probability, and previous studies in nuclear power valuation have not considered the impacts of nuclear accidents and losses (or damage) caused by nuclear plants operation

4 The uncertainty in electricity price mechanism Currently, China’s electricity price of nuclear power is set by the government, which is a cost-benefit pricing mechanism and each nuclear power plant has its own constant electricity price So the electricity prices vary a lot among different nuclear plants With the continuous electricity market reform, the electricity price will be gradually pushed forward to market-oriented One important feature of electricity price marketization is “price bidding” among different kinds of power plants Liberalized electricity price will be affected by seasonal demand for electricity, fuel price changes, and other factors And thus it is uncertain Electricity price mechanism and price level will directly affect the valuation of third-generation nuclear power investment

5 Regarding climate policy, nuclear power can be viewed as an emission reduction option Compared to thermal power with identical installed capacity, the operation of nuclear power does not produce greenhouse gas emissions, but this part of emission reduction can not be verified in current Clean Development Mechanism (CDM) So the application of nuclear power can not have Certification Emission Reduction (CER) and trade in CDM In fact, the nuclear industry is promoting nuclear power CDM credits If nuclear power can be included in Clean Development Mechanism, the uncertainties in climate policy and trading mechanism of CDM (Bilateral or Unilateral) will also affects the investment of third-generation nuclear power

As NPV based evaluation method can not fully catch the impacts of these uncertainties on nuclear power investment, it is necessary to develop a proper method to handle such kinds

of uncertainties to evaluate the demonstration and deployment of third-generation nuclear power plants in China

Real options approach is suitable for evaluation of large-scale investment projects with great uncertainties Brennan and Schwartz (1985) first introduced a real options approach to natural-resource investment decisions After that, real options approach has been applied more frequently in the evaluation of energy investment (Paddock et al, 1988, Smith and Nau, 1995, Smith and McCardle, 1998, 1999, Fan and Zhu, 2010) For power investment projects, real options approach can consider the uncertainties of the market environment, generating fuel prices, environmental factors, electricity demand and supply and so on (Venetsanos et.al, 2002, Davis and Owens, 2003, Siddiqui et al, 2007, Abadie and Chamorro, 2008a, 2008b, Fuss et.al, 2008, Fleten and Näsäkkälä, 2009) Therefore, the real options approach would be useful for evaluation of advanced generating technologies In the valuation of nuclear investment, Gollier et al (2005) apply real options approach with the consideration of electricity price uncertainty to compare the critical value between flexible sequence of small nuclear power plants and a nuclear power plant of large capacity They show that the option value of modularity has a sizeable effect on the optimal dynamic strategy of the producer, particularly in terms of the optimal timing of the decision to invest

in the first module

This paper applies real options theory with Monte Carlo method to establish a nuclear power investment evaluation model, incorporating the world's first third-generation nuclear power project-Sanmen nuclear power plant in Zhejiang province, to evaluate the value of third-generation nuclear power plant from the perspective of power generation enterprises Several technical and economic uncertainty factors (deployment cost, generating cost and nuclear accident), and two price mechanisms (electricity price and CDM) have been considered in the model and it is solved by Least Squares Monte Carlo (LSM) method As the model can be used

as a policy analysis tool, under a given period of nuclear power operation, first we have evaluated the value of Sanmen third-generation nuclear power plant in current constant electricity price set by the government to see whether it is worth investing or not Then the impacts of different electricity and CDM mechanisms on the valuation of third-generation nuclear power have been discussed And we have also analyzed the acceptable level of investment cost for third-generation nuclear power in China

3 Model description and parameter settings

As stated above, Sanmen third-generation nuclear power project has been chosen for evaluation object, the model established here is based on real options theory with Monte Carlo method and solved by Least Squares Monte Carlo (LSM) simulation The valuation includes nuclear power plant construction period and operation period As a large-scaled investment project, it will take time to complete nuclear power investment And the power generation enterprise has the right to exercise the abandon option to terminate the nuclear project in the investment stage So at each step of the investment stage, the enterprise can re-evaluate the nuclear project to decide whether to continue or abandon the investment

Assuming the total period for nuclear power construction and operation is T years, for the purpose of valuation we divide the T years into N periods, each with a length of

The Investment Evaluation of Third-Generation

/

t T N

  , and define t n  , 0,1, n t n N All the units for the parameters described below is displayed in table 1

3.1 Modeling third-generation nuclear power operation

At nuclear power plant operation period, first it is in need to calculate the cash flow during nuclear power operation Assuming at any period t n, the generating capacity of third-generation nuclear power is Q Elec n( )t , and all the electricity generated by nuclear power can

be sold to grid Considering the possibility of nuclear accident, after nuclear power investment has been completed, the cash flow CF t( )i earned by the power enterprise through electricity selling from nuclear power at t i period should be:

And r is the risk free rate

During nuclear power plant operation period, we have considered the impact of three electricity price mechanism, two CDM price mechanism, generating cost (uranium fuel price) uncertainty, and unexpected events with small possibility on the nuclear power plant operating cash flow and value

First, we can assume nuclear generating cost following a geometric Brownian motion:

1/2 1

Nuclear accidents are unexpected events with small possibility Here we apply a Poission process to describe the unexpected events (nuclear accidents) during nuclear power plant

operation period Let q be a Poission process, then we have:

Where  is the average probability for the unexpected events (nuclear accidents), and at

any time horizon t , the probability of nuclear accidents happen will be  and the t

probability of nuclear accidents do not happen will be 1  ; u represents the damage or t

loss caused by nuclear accidents during nuclear operation, and       S M L 1

Considering different level of nuclear accidents will cause different damage or loss, we define three levels of nuclear accidents which correspond to different probability:

1 Minor accident, the probability is  , there is a small loss S u S for nuclear power plant and it will not affect plant operation

2 Moderate accident, the probability is  , there is a moderate loss M u M for nuclear power plant And the plant will pause power generation in next two years in order to have necessary reactor security maintenance and monitoring nuclear leak, which

For CDM, two following forms of CDM have been modelled in this paper:

1 In bilateral CDM, the carbon price is constant, of which P t C i( 1)P t C i( )

2 In unilateral CDM, referring to previous research related carbon price modeling (Abadie and Chamorro, 2008, Heydari et.al, 2010), assuming the carbon price in unilateral CDM follows a geometric Brownian motion:

1/2 1

3.2 Modeling third-generation nuclear power investment

At nuclear power plant construction period, we apply a controlled diffusion process to describe the uncertainty of third-generation nuclear power investment K Nu is the expected total investment cost for power generation enterprises to deploy third-generation nuclear

The Investment Evaluation of Third-Generation

power technology and the total deployment investment remaining at period t i is K Nu i( )t Assume that K Nu follows the controlled diffusion process:

F  V 

At the time period t before investment is completed, the value of the nuclear power i

investment opportunity that the enterprise owns is equal to:

3.3 LSM Solution to the model

The abandon option F Nu i( )t of third-generation nuclear power investment is computed by the Least Squares Monte Carlo (LSM) method The LSM method was developed for valuing American options and is based on Monte Carlo simulation and least squares regression (Longstaff and Schwartz, 2001; Schwartz, 2004) The model also computes the related greenhouse gas emission reduction which is avoided by applying nuclear power to take place

of thermal power Take  to represent the time that the third-generation nuclear power g

investment is completed in path g Thus, the greenhouse gas emission reduction from the

adoption of nuclear power during the given observation period can be computed as:

ER g  e Q  T 

Where ER g( ) is the emission reduction amount during path g ; e is the emission factor for

existing thermal power Taking the average over all the paths, the total emission reduction amount through investing in third-generation nuclear power technology can be obtained LSM method described has been implemented in Matrix Laboratory (MATLAB), and all solution procedure is vividly described in figure 1