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Future and Challenge of Nuclear Energy
Lecture 10
Economics of Nuclear Energy
Global Collaborative Summer Program in Sustainable Developments
towards a Green Planet
July 2010
YOON IL CHANG
Electricity Generation Cost
Electricity generation cost for nuclear is composed of the
following 4 components:
– Capital cost (annualized fixed charge rate)
– Operations and maintenance (O&M) cost
– Fuel cycle cost
– Decommissioning cost
Quantification of each component is not simple, and
hence a consistent comparison between different reactor
types or energy options is illusive.
The goal here is to provide a broad understanding of the
factors involved rather than definitive quantification.
2
Energy Accounting Principles
Time value of money
– Money received now is worth more than money
received in the future.
– Expenses occurring at different times need to be
normalized to a given reference point – concept of
“present worth”.
Present worth = future worth/(1 + r)n
– “Inflation rate” is used to escalate expenses in nominal
dollars.
– “Interest rate” reflects cost of money
Interest rate = inflation rate + real cost of money
– “Discount rate” is used to reflect opportunity costs
Discount rate = interest rate + risk premium
3
Capital Cost Amortization
P = principal amount
A = annual payment for interest and repayment of
principal
P = A{1/(1+r) + 1/(1+r)2 + 1/(1+r)3 + - - - }
= A[(1+r)n – 1]/r(1+r)n
This formula applies for mortgage payment as well.
Equal monthly (or yearly) payments consists of interest
and principal. Initially mostly interest and small amount
of principal, but increasingly smaller interest and larger
principal.
4
Capital Cost
“Fixed charge rate” is used to translate the capital cost
into annualized revenue requirements:
Fixed charge rate = capital amortization based on
average rate of return (bond and equity) + revenue tax
+ insurance, etc.
= 15-20% per year.
Interest expenses during construction are included in
the initial capitalization.
For comparative purposes, it is a common practice to
include only capital amortization in the capital cost.
5
Simple Analysis
“Overnight” cost ignores interest expenses and
escalation in nominal dollars during construction.
“Constant dollar” analysis ignores inflation.
Nominal dollar = constant dollar x (1 + r)n
Reactor plant capital cost is commonly quoted as an
overnight cost in terms of $/kWe.
6
Capital Cost
Capital cost consists of two components:
– Direct cost
– Indirect cost
7
Typical Cost Breakdown (% of Direct Cost)
Account Description %
21
22
23
24
25
26
Structure and Improvement
Reactor Plant Equipment
Turbine Plant Equipment
Electrical Plant Equipment
Misc. Plant Equipment
Heat Rejection System
26
30
24
11
4
5
Total Direct Cost 100
91
92
93
94
Construction Services
Home Office Engineering
Field Office Engineering
Owner’s Costs
21
33
16
-
Total Indirect Cost 70
8
Capital Cost Contribution to Generation Cost
Assuming an overnight cost of $2000/kWe and fixed
charge rate of 15%/yr:
– $2000x0.15 / (365x24x0.9) = $0.038/kwhr
= 3.8 cents/kwhr
Operations and maintenance cost for a 1000 MWe
plant is about $100 million/yr:
– 100M / (1Mx365x24x0.9) = 1.3 cents/kwhr
9
LWR Fuel Cycle Cost
Discrete cost component for each step of the fuel cycle:
– Uranium ore (U3O8)
– Conversion to UF6
– Enrichment
– Fabrication
– Backend fuel cycle
•Storage
•Reprocessing
•Disposal
10
Cost Assumptions
Uranium Ore, $/lbU3O8 30
UF6 Conversion, $/kg 8
Enrichment, $/SWU 100
Fabrication, $/kgHM 275
Disposal Fee, mill/kwhr 1
Reprocessing, $/kgHM 1,000
MOX Fabrication, $/kgHM 1,500
Fuel Cycle Cost
Fuel cycle cost can be calculated without considering
the mass flow data for the entire core.
We will first calculate the cost for 1 kg of fresh fuel and
then convert it to a cent/kwhr basis.
We will assume a 50,000 MWD/T burnup case, which
requires 4.5% enrichment.
12
Natural Uranium and Enrichment Requirement
Natural uranium requirement:
F/P = (Xp – Xt) / (Xf –Xt) = (4.5 – 0.2) / (0.711 - .2) =
8.414 kgU x 1.1792 x 2.2046 = 21.9 lbU3O8
Uranium cost = 21.9 x 30 = $660/kg of enriched U
Conversion cost = 8.414 x $8/kg = $67/kgU
Enrichment cost = (6.544 + 8.851)/2 = 7.70 x
$100/SWU = $770/kgU
Fabrication cost = $275/kg
13
Conversion between $/kg and cent/kwhr
Example: Uranium cost
(660$/kg x 100 cent/$) / (50 MWD/kg x 0.33 e/th x
1000 kw/MW x 24 hr/D)
= 0.17 cent/kwhr
= 1.7 mills/kwhr
14
Spent Fuel Disposal Fee
U.S. Nuclear Waste Policy Act mandated 1 mill/kwhr
disposal fee. (1 mill = 0.1 cent)
This translates to:
– $240/kg for 30,000 MWD/T burnup
– $400/kg for 50,000 MWD/T burnup
15
Time Value of Money
Because each fuel cycle step expense occurs at
various time step prior to the electricity generation,
present worth approach has to be used to be more
accurate.
Since the time difference is within a year or two, we will
ignore the present worth approach.
16
Once-Through Fuel Cycle Cost (U.S. Perspective)
$/kgHM mills*/kwhr
Uranium 660 1.7
Conversion 70 0.2
Enrichment 770 1.9
Fabrication 275 0.7
Disposal Fee 240-400 1.0
Total 2015-2175 5.5
*1 mill = 0.1 cent
Nuclear Electricity Generation Cost (cents/kwhr)
Capital Cost 3.8
Operating & Maintenance Cost 1.3
Fuel Cycle Cost 0.6
Decommissioning Cost 0.2
Total 5.9
18
Fuel Cycle Cost for Recycle Case
The front end fuels cycle costs are the same as the
once-through cycle.
The back end fuel cycle costs occur about 10 years or
more after the electricity generation, therefore in this
case we should use the present worth approach.
19
Delayed Reprocessing Cost
If reprocessing occurs after 10 years from the reactor
discharge, then the cost should be present- worthed to
the time when the electricity is generated.
Assume a discount rate of 5% per year.
Then $1000/kg / (1.05)10 = $610/kg
The disposal cost is assumed to be 1/2 of the direct
spent fuel disposal case and also discounted at the
same rate as the reprocessing.
20
Closed Fuel Cycle Cost (Europe/Japan Perspective)
$/kgHM mills/kwhr
Uranium 660 1.7
Conversion 70 0.2
Enrichment 770 1.9
Fabrication 275 0.7
Reprocessing* 610 1.5
Disposal Fee** 120 0.3
Total 2,505 6.3
*Present worth based on 5%/yr discount rate for 10 years
**Assumed to be ½ of once-through cycle, discounted as above
Recycle Credits
The fuel cycle cost for the reprocessing case is about
15% higher than the once-through cycle even after a
heavy discounting.
But the recycle of plutonium can offset the reprocessing
cost.
22
MOX Comparison in Closed Fuel Cycle, $/kgHM (Europe/Japan Perspective)
UOX MOX
Uranium 660 78
Conversion 70 8
Enrichment 770 0
Fabrication 275 1500
Reprocessing 610 763*
Disposal Fee 120 120
Total 2505 2469
*MOX reprocessing cost was assumed to be 25% more
expensive due to higher Pu content.
Key Difference between Once-Through and Closed Fuel Cycle
In closed fuel cycle, the reprocessing and subsequent
waste disposal costs are levied against the fuel batch
as it generates electricity, and hence the present worth
of these costs are discounted since reprocessing is
carried out after significant delay in storage.
Treatment for MOX recycle cost is also drastically
different:
– For closed fuel cycle, Pu is a byproduct and hence
there is no acquisition cost since reprocessing has
been paid for.
– For once-through cycle, the reprocessing cost to
acquire Pu should be charged to MOX recycle.
MOX Comparison in Once-Through Cycle, $/kgHM (U.S. Perspective)
UOX MOX
Pu acquisition 7800*
Uranium 660 -923**
Conversion 70 -95**
Enrichment 770 -393**
Fabrication 275 1500
Disposal Fee 400 400
Total 2175 8289
*7.8 kgHM is reprocessed to acquire the Pu equivalent to 1 kgHM UOX
**Credits for uranium recovered in the process of acquiring Pu are given
whether recycled or not.
26
Once-Through vs. Recycle Cost, $/kgHM (A Proper Comparison)
Once-
Through
U and Pu
Recycle
Reprocessing Cost 1000
U Recycle Credit -140
Pu Recycle Credit -191
Pu Fabrication Penalty 157
Disposal Fee Collected 400 200
Present Worth Adder* 430
Total 830 1026
*Based on 5%/yr for 15 years
Backend Fuel Cycle Cost
If reprocessing cost is charged to the electricity
produced by the spent fuel as practiced in Europe and
Japan, the fuel cycle cost penalty is affordable.
Reprocessing plants have been amortized and the
reprocessing cost can be heavily discounted due to 10-
20 years time lag. MOX recycle is also economical.
However, if the reprocessing plant and MOX
fabrication infrastructure does not exist, then there is
absolutely no economic incentives to reprocess and
recycle in LWRs.
Impact of Uranium Price on Fuel Cycle Cost
0
2
4
6
8
10
12
0 20 40 60 80 100 120 140 160
Uranium Price, $/lb
Fu
el
Cy
cle
Co
st,
mil
ls/k
wh
r
Disposal Fee
Conversion + Fabrication
Enrichment
Uranium
Total Fuel Cycle Cost
Once-Through vs. Recycle Cost
0
200
400
600
800
1000
1200
0 20 40 60 80 100 120 140 160
Uranium Price, $/lb
$/k
g
Once-Through
Pu Recycle Only
U Recycle Only
U + Pu Recycle
U + Pu Recycle
at $500/kg Rep Cost
30
Uranium Spot Market Price Trend
Euratom Average U Price: Spot vs. Long-term
U.S. Utilities Average Uranium Price
0
5
10
15
20
25
30
35
40
1994 1996 1998 2000 2002 2004 2006 2008
$/lb
Spot Market
Purchase
Weighted
Average
Long-Term
Contracts
U.S. Electricity Generation Costs
O&M Costs Fuel Costs Total
Nuclear 1.46 0.51 1.97
Coal 0.60 2.20 2.80
Natural Gas 0.53 7.27 7.80
Petroleum 1.94 15.69 17.63
33
A Quote from Daniel Yergin, “Ensuring Energy Security”
“Energy security does not stand by itself but is lodged
in the larger relations among nations and they interact
with one another… The renewed focus on energy
security is driven by an exceedingly tight oil market and
by high oil prices, which have doubled over the past
three years… But it is also fueled by the threat of
terrorism, instability in some exporting nations, … , and
countries’ fundamental need for energy to power their
economic growth. In the background – but not too far
back – is renewed anxiety over whether there will be
sufficient resources to meet the world’s energy
requirements in the decades to come.”
34
Relative Rarity of Carbon-based Resources
World crude oil production depends heavily on the
production from a remarkably small number of fields.
There is a generally accepted consensus on
conventional oil production: it’s now at its highpoint.
Natural gas is linked to oil.
Coal outlook is the least well-defined. Recoverable
coal is the issue.
Carbon based fuel will soon become increasingly less
avaiable.
35
Renewable Energy
Renewable energy uses will increase rapidly in the
near future.
But they are diluted energy source requiring a large
scale land usage.
Economics is favorable.
Availability limits capacity factor in the range of 25%.
37
38
39
Solar Photovoltaic Plant (40 MW)
40
Solar Thermal Plant (10 MW and 20 MW)
41
Geothermal Plant in Iceland
42
Geothermal Plant Cooling Tower
43
Ocean Tidal Wave Plant in Portugal
44
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