# Cost of wind

```Cost of Wind
James McCalley
Harpole Professor of
Electrical & Computer Engineering
1
Discount rate
Discount rate, i.
• the annual payment as a percentage of the amount
owed;
• the value given to possession of money now rather
than later, since having it now allows it to be
invested to earn a return. In this sense, the
discount rate is the annual income as a percentage
of the amount invested, i.e., average interest rate.
2
Moving single amounts in time
“Future”
amount of
money
1
P F
N
(1  i )
“Present”
amount of
money
F  P  (1  i)
Monetary Value
F
P
P(1+i)
1
P(1+i)2
2
3
4
Time Period
3
N
N
Number of
time periods
Observe that “F” may be a cost or a
revenue. In either case, the equivalent
amount of money in the present is
smaller.
• I prefer to incur a \$100 cost later than
a \$100 cost now.
• I prefer to obtain a \$100 revenue now
than a \$100 revenue later.
Annuitizing
“Annual”
amount of
money
i(1  i) N
A  P
(1  i) N  1
A F
i
(1  i ) N  1
Monetary Value
F
P
A
1
A
2
A
3
A
4
Time Period
4
A
A
N
Note that payment A is made at the end
of a period, so there is no payment made
at the beginning of period 1, but there is
a payment made at the end of period N.
Inflation
The discount rate does not reflect the effects of inflation.
Inflation, e, changes the buying power of money.
“Current dollars” are the actual cash flow that would
occur during a particular year, m, accounting for inflation.
“Constant dollars” are the dollars that would have been
required if the cost was paid in the “base year,” n. We
refer to this as “n dollars” as in “2012 dollars.”
F
F
(1  e) N
5
N=m-n
Inflation and discounting
The discount rate in the absence of inflation is called the
“real” discount rate, ir. The discount rate accounting for
inflation is called the “nominal” discount rate, in.
F
F
1
F
P


N
N
N
N
(1  in )
(1  ir )
(1  ir ) (1  e)
F Current dollar amount at year N (accounting for inflation)
F Constant dollar amount at year N (without inflation)
N
N
N
(1  in )  (1  ir ) (1  e)
 (1  in )  (1  ir )(1  e)
6
in  (1  ir )(1  e)  1  1  e  ir  ir e  1  e  ir
Levelized cost of energy
Data
Purchase cost
Installation cost
Levelized
fixed
charge rate
Plant rating
Capacity factor
Nominal discount
rate
Wind Turbine
\$1820/kW
\$600000
20%
1.5 MW
0.35
Levelized fixed charge rate:
• Capital cost
• Return on investment
• Depreciation
• Fed and state income taxes
• Property tax
• Insurance costs
8%
The initial investment is
(\$1820/kw)*1500kW+600000=\$3,300,000
The fixed annual charges are then 0.2*3,300,000=\$660,000.
This is called the levelized annual revenue requirements (LARR)
The average annual energy production is
=Capacity*8760hrs/yr*CapacityFactor
=1.5MW*8760hrs/yr*.35=4599MWhrs
LARR
660000
LCOE 

 \$143.51/ MWhr
AverageAnn
ualEnergyP
roduction
4599
7
Levelized cost of energy
Data
Purchase cost
Installation cost
Levelized
fixed
charge rate
Plant rating
Capacity factor
Nominal discount
rate
Wind Turbine
\$1820/kW
\$600000
11.6%
Levelized fixed charge rate:
• Return on investment
• Depreciation
• Fed and state income taxes
• Property tax
• Insurance costs
1.5 MW
0.35
8%
The initial investment is
(\$1820/kw)*1500kW+600000=\$3,300,000
The fixed annual charges are then 0.116*3,300,000=\$382,800.
This is called the levelized annual revenue requirements (LARR)
The average annual energy production is
=Capacity*8760hrs/yr*CapacityFactor
=1.5MW*8760hrs/yr*.35=4599MWhrs
LARR
382,800
LCOE 

 \$83.24 / MWhr
AverageAnn
ualEnergyP
roduction
4599
8
Levelized cost of energy
Data
Purchase cost
Installation cost
Levelized
fixed
charge rate
Plant rating
Capacity factor
Nominal discount
rate
Wind Turbine
\$1820/kW
\$600000
20%
Levelized fixed charge rate:
• Return on investment
• Depreciation
• Fed and state income taxes
• Property tax
• Insurance costs
1.5 MW
0.40
8%
The initial investment is
(\$1820/kw)*1500kW+600000=\$3,300,000
The fixed annual charges are then 0.2*3,300,000=\$660,000.
This is called the levelized annual revenue requirements (LARR)
The average annual energy production is
=Capacity*8760hrs/yr*CapacityFactor
=1.5MW*8760hrs/yr*.40=5256MWhrs
LARR
660000
LCOE 

 \$125.58/ MWhr
AverageAnn
ualEnergyP
roduction
5256
9
Levelized cost of energy
Data
Purchase cost
Installation cost
Levelized
fixed
charge rate
Plant rating
Capacity factor
Nominal discount
rate
Wind Turbine
\$1820/kW
\$600000
11.6%
Levelized fixed charge rate:
• Return on investment
• Depreciation
• Fed and state income taxes
• Property tax
• Insurance costs
1.5 MW
0.40
8%
The initial investment is
(\$1820/kw)*1500kW+600000=\$3,300,000
The fixed annual charges are then 0.116*3,300,000=\$382,800.
This is called the levelized annual revenue requirements (LARR)
The average annual energy production is
=Capacity*8760hrs/yr*CapacityFactor
=1.5MW*8760hrs/yr*.40=5256MWhrs
LARR
382,800
LCOE 

 \$72.83/ MWhr
AverageAnn
ualEnergyP
roduction
5256
10
Levelized cost of energy
Resource
PC plant
NGCC plant
Nuclear plant
Wind, CF=0.35, FCR=20%
Wind, CF=0.35, FCR=11.6%
Wind, CF=0.40, FCR=20%
Wind, CF=0.40, FCR=11.6%
LCOE
\$59.94/MWhr
\$99.64/MWhr
\$66.49/MWhr
\$143.51/MWhr
\$83.24/MWhr
\$125.58/MWhr
\$72.83/MWhr
Levelized cost of energy
annual operating expenses (AOE). This includes land lease
cost, levelized O&M cost, and levelized replacement cost:
AOE=LLC+LOM+LRC
with units of \$/year. So the expression for LCOE is
LARR  AOE
LCOE 
AverageAnnualEnergyProduction
AOE is generally only about 2% of the purchase cost.
The above expression is sometimes expressed as:
LARR
LCOE 
 AOE
AverageAnnualEnergyProduction
12
which implies AOE is given in \$/MWhr.
Levelized cost of energy
Data from Electric Power Research Institute
13
Nuclear Energy Institute, “The cost of new generating capacity in perspective,” Sept., 2011, available online at
www.nei.org/resourcesandstats/documentlibrary/newplants/graphicsandcharts/the-cost-of-new-generating-capacity-in-perspective.
Levelized cost of energy
Data from US DOE Energy Information Administration
14
Nuclear Energy Institute, “The cost of new generating capacity in perspective,” Sept., 2011, available online at
www.nei.org/resourcesandstats/documentlibrary/newplants/graphicsandcharts/the-cost-of-new-generating-capacity-in-perspective.
Levelized cost of energy
National Research Council (National Academies of Science
and of Engineering)
15
Nuclear Energy Institute, “The cost of new generating capacity in perspective,” Sept., 2011, available online at
www.nei.org/resourcesandstats/documentlibrary/newplants/graphicsandcharts/the-cost-of-new-generating-capacity-in-perspective.
Representative split – capital costs
This is for capital (investment) costs.
It is for a representative wind turbine
design, but one should recognize that
there are different designs. But it does
provide some indication of relative splits
among major wind turbine components.
Source: P. Jamieson, “Innovation in wind turbine design,” Wiley, 2011.
Note – this book has an entire chapter dedicated to “Cost of Energy.”
16
Component
Cost fraction
0.177
Hub
0.077
Gearbox
0.143
Generator
0.076
Yaw system
0.019
Nacelle cover
0.020
Nacelle structure
0.040
Tower
0.219
Variable speed system
0.073
Pitch system
0.043
Rotor brake
0.006
Couplings
0.003
Shaft
0.041
Other
0.063
Total turbine
1.00
Representative
split
- LCOE
Initial capital costs
Turbine
0.820
0.569
Rotor
Nacelle systems
Source: P. Jamieson, “Innovation in
wind turbine design,” Wiley, 2011.
Note – this book has an entire
chapter dedicated to “Cost of
Energy.”
Electrics and control
O&M
0.180
17
Rotor lock
0.0057
0.1037
Hub
0.0142
Gearbox
0.0961
Generator
0.0378
Rotor brake
0.0085
Nacelle cover
0.0142
Nacelle structure
0.0193
Couplings
0.0057
Shaft
0.0171
Yaw system
0.0171
Bearings
0.0171
Pitch system
0.0365
Variable speed system
0.0551
Tower
0.0896
Other
0.0313
Balance of plant
0.0221
0.251
Electrics and grid con
0.0761
Assembly & insttlltn
0.0073
Transportation
0.0365
Foundations
0.0675
Financial and legal
0.0414
Labor
0.0792
Parts
0.0630
Operation
0.0216
Equipment
0.0090
Facilities
0.0072
0.180
```

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