Wind Engineering
Module 6.1: Cost and Weight Models
Lakshmi N. Sankar
lsankar@ae.gatech.edu
1
Overview
• In this module, we will briefly examine models
for estimating the cost of energy (in cents per
KWhr) that the operator needs to charge.
• We will look at two approaches
– Engineering models based on weight and cost
(This module 6.1)
– Models suitable for hybrid power systems
(Module 6.2)
2
Some Definitions
• Debt: Money the operator borrows to finance
a wind turbine project
• Interest on debt: Interest charged per year by
finance institution (expressed in percentage)
• Equity: Funds the operator raises by issuing
stocks
• Return on equity: Return the share-holders
expect on their investments (expressed in
percentage per $1 invested).
3
Definitions, continued..
• AWCC: Average weighted cost of capital
• Example:
–
–
–
–
20% equity
13% return on equity
80% loan
6.94% interest on loan
• AWCC for this example is (0.20*13+0.80*6.94) =
8.15%=0.0815
• Inflation-adjusted AWCC = (AWCC-Inflation)/(1+Inflation).
• For example if inflation is 3%, the inflation adjusted AWCC
is (0.0815-0.03)/(1.03) = 0.05=5%
• This is sometimes called discount rate.
4
Cost of Energy
Source: NREL /TP-500-40566
5
Definition
• FCR: fixed charge rate. It includes
– AWCC (payment to the bank loan and equity holders)
– Depreciation
– Income tax
– Property tax
– Insurance
– Other finance fees
6
Initial Capital Cost
Sum of turbine system cost for elements listed below + balance of station costs
7
Initial capital Cost (Continued..)
8
Annual operating Expenses
• Include land lease, operation and
maintenance, cost of replacing or overhauling
parts.
• Expressed in dollars per KWh.
9
Net Average Energy Production (AEP)
Overview
• Units are in KWh
• We may view this as power production integrated over time for a whole
year.
• Here is a very crude description of how this is computed.
– Power production depends on how hard wind blows and how often
– It is assumed that the wind speed at a particular site has a Weibull
distribution.
– This distribution gives the probability that the wind is blowing at a given speed
– With some knowledge of the wind turbine power characteristics (rated power,
peak Cp, tip speed ratio at which peak Cp occurs, etc), power production at
different wind speeds is estimated.
– This is multiplied by the Weibull probability that wind is blowing at that speed.
– Summation is done over all the wind speeds.
– The result is multiplied by 365 days x 24 hours/day
• Capacity Factor = AEP / (Rated Power x 365 x 24) may also be computed.
• See weibull_betz5_lswt_baseline.xls for example calculations.
10
Example: Turbine Capital Cost
NREL Report
Rating (kWs)
1500
1500
Baseline
Projected
Component Component
Component
Costs $1000 Costs $1000
Rotor
248
248
Blades
148
148
Hub
64
64
Pitch mchnsm & bearings
36
36
Drive train,nacelle
563
563
Low speed shaft
20
20
Bearings
12
12
Gearbox
151
151
Mech brake, HS cpling etc
3
3
Generator
98
98
Variable spd electronics
101
101
Yaw drive & bearing
12
12
Main frame
64
64
Electrical connections
60
60
Hydraulic system
7
7
Nacelle cover
36
36
Control, safety system
10
10
Tower
101
101
TURBINE CAPITAL COST (TCC)
921
921
11
Blade Cost
12
Example continued..
We compare baseline and projected
Rating (kWs)
Component
1500
1500
Baseline
Projected
Component
Component
Costs $1000
Costs $1000
Foundations
49
49
Transportation
51
51
Roads, civil works
79
79
Assembly & installation
51
51
Elect interfc/connect
127
127
Permits, engineering
33
33
388
388
162
162
921
921
1,472
1,472
BALANCE OF STATION COST (BOS)
Project Uncertainty
Turbine cost from previous slide
Initial capital cost (ICC)
13
Other costs
Projected
Baseline
in
In $1000
$1000
LEVELIZED REPLACEMENT COSTS (LRC)
($10.7 per kW)
16
16
O&M $20/kW/Yr (O&M)
30
30
Land ($/year/turbine)
5
5
14
Example, continued..
• We next compute
probability of wind
blowing at a particular
speed.
• Weibull probability
function is used.
• This depends on a
parameter called K
factor, and wind speed
at the hub.
15
Weibull Distribution
• K: Shape factor
• Changing k shifts
probability to the
left or right.
• l : Scale parameter
• In our example, k= 2
• l = Wind Speed at
the hub
16
Efficiency of the Turbine
100%
90%
80%
70%
Efficiency
• We next compute efficiency
of the turbine when it
operates at power other than
rated power.
• If field data is available, it is
used.
• Otherwise a simple logic is
used:
60%
50%
40%
30%
20%
10%
0%
0
0.2
0.4
0.6
0.8
1
1.2
P/P(rated)
17
Hub Power
Power Curve
1600
1400
1200
Power (kW)
• If wind velocity is less than
cut-in speed, hub power is
zero.
• If wind velocity less than
rates speed it is found from
• At higher than rated speeds,
rated power is used.
• At greater than cutout
speeds, power is zero.
• The hub power, when
multiplied by Weibull
probability and efficiency h,
gives turbine energy output
at that speed.
1000
800
600
400
200
0
0
10
20
30
40
Windspeed (m/s)
Turbine
power
18
Annual Energy Production

Turbine Energy corrected for other losses * 8760 * Availabili ty
4
• Other losses may include electrical system losses
• We divide by 4 because the wind speeds are binned (or grouped by
¼ m/sec increments.
• We will find power, for example at 2, 2.25, 2.50, and 2.75 m/sec and take
the average.
•
365 x 24 is 8760
19
Cost of Energy
• Once all the
information is
available, we can
find the cost of
energy per KWh.
20