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

Oil and Gas Production Profiles

36

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