Wind Turbine

1. Power in the Wind:
Making Statistical and Economic
Project Comparisons
April 22, 2016
This work is licensed under a Creative Commons Attribution-
NonCommercial-ShareAlike 4.0 International License.

2. Where Does the Wind Come From?
• Uneven heating of the Earth
– What if the Earth did not rotate?
CC BY-SA 3.0,
https://commons.wikimedia.org/w/index.php?curi
d=2310777
http://scioly.org/wiki/index.php/Meteorology/
Everyday_Weather

3. Where Does the Wind Come From?
• Add rotation (and thus the Coriolis effect) and
what happens?
Global Winds
"Earth Global Circulation - en"
by Kaidor - Own work based on
File:Earth Global
Circulation.jpgThe picture of
the Earth is File:Lunar eclipse
from moon-2007Mar03.png
vectorized with Inkscape..
Licensed under CC BY-SA 3.0 via
Commons -
https://commons.wikimedia.org
/wiki/File:Earth_Global_Circulat
ion_-_en.sv... (link is external)

4. Where Does the Wind Come From?
• Secondary and tertiary
circulations also occur
around the earth
– Secondary
• Hurricanes (tropical cyclones)
• Extratropical cyclones
– Tertiary
• Uneven heating due to terrain
or surface proprties
– Land/sea breezes
– Mountain/valley breezes
– Thunderstorms
– Tornadoes Land and sea breezes compared
License: CC BY-NC 3.0
Source: https://www.e-
education.psu.edu/geog497i/node/329

5. What Happens to the Wind as you Go
Up in Elevation?
A sample graph of wind speeds from 0 to 140 m
Source: NREL

6. Power in the Wind Foundations
• Density
• Volume
• Velocity
• Power
• Energy
3
[ ]
mass
volume
m kg
V m

  
3
* ]
[
area length AL m
 
[ ]
length L m
time t s


[ ]
energy J
W
time s


2 2
1 1
*( ) [ ]
2
.
2
. mass velo
K E city mv J
  
2 2 2
3
1 1 1
( ) ( )
. . 1
2 2 2
2
mv V v AL v
K
Pow
E
Av
t t t
e
t
r
 

    
Come up with an equation for power as a function only of Area, Velocity and Density:

8. Power in the Wind
• Let’s check our units:
3
1
2
W
P Av


2
kg m
s
N
J N m


3 2
2
3 3
kg m kg m
m
m s s
 
  

 
2
3
kg m N m J
s s s
  Watt


9. Let's say we'd like to know how much power is available in the wind flowing through a
hula-hoop (D= 1 m) for a wind speed of 10 m/s:
A Boeing 747 has an approximate "diameter" of 65 m, but the rotor shown in the
figure below has a diameter of 80 m. How much power is available in the wind for a
turbine of this size at a velocity of 10 m/s?
Using the 747 example from above, note the differences in available power just by
increasing the velocity of the wind by a factor of two from 10 m/s to 20 m/s:

10. Influence of Air Density… Let’s
Investigate How Air Density Changes?
• Let’s look at the Ideal Gas Law
• P= pressure, V = volume, n = # moles, T =
temperature, is the ideal gas constant 8.314
kJ/kg-K
• We are going to reconfigure this to solve for
density and apply it specifically to air.
PV T
nR

R

11. Ideal Gas Law – mass basis
• First we need to move from moles to mass:
• M is the molecular weight of the substance you
are using, and m is the mass.
• Where R is now a constant specific to the gas
used in the equation.
n
m
M

PV m
M
R
T mRT
 

12. Ideal Gas Law - rearranging
• We know that density is mass/Volume, so let’s
reorganize the terms to solve for this:
• For air, R = 286.9 J/kg-K
– Mainly composed of 78% Nitrogen (R=296.8 J/kg-
K) & 21% Oxygen (R=259.8J/kg-K)
m P
V RT
  

13. Ideal Gas Law Example
• Example:
– Calculate the air density for standard atmospheric
conditions, T = 15C, P = 101.325 kPa (Pa = N/m2):
3
[ ]
[ ]
kg P Pa
m J
R T K
kg K

 

   
 
 
 
3 3
101,325[ ]
1.225
287 (15 273.15)[ ]
kg Pa kg
m m
J
K
kg K

   
 
   
 
   

 
 

14. Density Conclusion
• Density increases with increasing pressure and
decreases with increasing temperature:
• As air rises, it becomes cooler and the
pressure decreases, thus density will?
P
RT
 
decrease

15. What Happens to Air Density in the Mile High City?
What Happens to Air Density in Cold Weather?

16. Behavior of the Wind

18. Weibull Distribution
(for your information)
k

Shape factor
Scale factor (m/s)

19. Wind Turbine Power Curves

20. 3
1
2
turbine p
P C Av



21. Calculating Energy Production
from Wind Resource Data

22. Wind Data Source
• Eastern Wind Integration Data Set
– Model data generated for wind grid integration studies.
• Not real output, but predicted for actual locations.
– No gaps in data
• No QA needed
– Lat & Long provided

23. Capacity Factor
• The amount of energy generated divided by
the amount which could be produced if the
turbine were running at its full capacity all of
the time.
– Typically considered over a year, but could be
measured over any timeframe.
• Example: If a 2 MW (2000 kW) wind turbine
generates 5,956,800 kWh of energy in a year,
what would this project’s capacity factor be?
24 365
8 0 /
/ 7
# 6
hr days
hr yr
day y
r
r
h yr 
 
5,956,800 /
0.34 34%
2000 8760 /
kWh yr
kW hr y
F
r
C  



24. Wind Turbine Power Curves [kW]
Wind Speed
[m/s]
Alstom Eco
74/1670 Class
II
Alstom
Eco
80/1670
Class II
Alstom
Eco
80/2000
Class II
Siemens
SWT-2.3-
113
Siemens
SWT-2.3-
93
Siemens
SWT-2.3-
82 VS
Vestas
V126 -
3.0 MW
Vestas
V126-3.3
MW IEC
IIIA
Vestas
V110-2.0
MW
Vestas
V90-2.0
MW
GE 1.6-
100
3 0 1 0 70 0 0 14 20 23 0 0
4 32 33 32 223 98 42 179 162 140 97 47
5 98 94 98 409 210 136 416 395 314 220 180
6 185 197 200 722 376 276 712 694 549 392 449
7 301 346 339 1074 608 470 1148 1060 900 616 745
8 460 538 522 1570 914 727 1713 1714 1347 927 1058
9 671 771 766 2009 1312 1043 2219 2432 1775 1275 1371
10 938 1033 1054 2191 1784 1394 2566 2999 1972 1622 1523
11 1232 1288 1370 2270 2164 1738 2858 3260 1999 1899 1585
12 1495 1489 1668 2298 2284 2015 3000 3300 2000 2000 1600
13 1634 1607 1894 2300 2299 2183 3000 3300 2000 2000 1600
14 1669 1655 1981 2300 2300 2260 3000 3300 2000 2000 1600
15 1670 1668 2000 2300 2300 2288 3000 3300 2000 2000 1600
16 1670 1670 2000 2300 2300 2297 3000 3300 2000 2000 1600
17 1670 1663 2000 2300 2300 2299 3000 3300 2000 2000 1600
18 1670 1638 2000 2300 2300 2300 3000 3300 2000 2000 1600
19 1670 1596 1982 2300 2300 2300 3000 3300 2000 2000 1600
20 1670 1549 1936 2300 2300 2300 3000 3300 2000 2000 1600
21 1670 1499 1876 2300 2300 2300 3000 3300 2000 2000 1600
22 1670 1449 1824 2300 2300 2300 3000 3300 2000 2000 1600
23 1670 1401 1772 2300 2300 2300 0 3300 2000 2000 1600
24 1670 1356 1712 2300 2300 2300 0 3300 2000 2000 1600
25 1670 1314 1660 2300 2300 2300 0 3300 2000 2000 1600

25. Procedures for the Competition
• Choose a location and its accompanying data for this
exercise
• Create a histogram
• Select a Power Curve
• Calculate the energy produced from the selected turbine at
your site using the histogram and the power curve
• Calculate and record the Levelized cost of energy
• Calculate and record the capacity factor
• Iterate until you believe you have found the best turbine for
your location.
• Compare results with the class and see who came up with
the lowest LCOE and highest CF. Discuss!

26. Calculating Energy
• https://youtu.be/GVHc1zpLnXw
25 /
0 /
[ ]
m s
at each velocit
v
y
m s
Power t
Energ me
y i


 
Wind Speed
[m/s]
Alstom Eco
74/1670 Class
II
Al
80
Cl
3 0
4 32
5 98
6 185
7 301
8 460
9 671
10 938 1
11 1232 1
12 1495 1
13 1634 1
14 1669 1
15 1670 1
16 1670 1
17 1670 1
18 1670 1
19 1670 1
20 1670 1
21 1670 1
22 1670 1
23 1670 1
24 1670 1
25 1670 1

27. Wind Energy Economics

28. Levelized Cost of Energy
• en = energy, to be calculated from wind resource data
and selected wind turbine power curve
• TIC = total installed cost for project (equation to be
provided for educational purposes)
• fcr = fixed charge rate - an annualized presentation of
the cost of financing a wind project
• rc = recurring charges. Typically provided per unit of
energy, e.g. $/kWh. For instance, operation and
maintenance costs.
TIC rc
LCOE fcr
en en
  

29. LCOE Example Problem
• Under the following conditions for a wind turbine
project, calculate the levelized cost of energy for
this project:
• Total installed cost for the project is $30,000,000
• Average amount of energy produced at the project
site is 61,320,000 kWh/yr
• Fixed charge rate (fcr) = 0.09
• Operation & Maintenance charges (recurring
charges rc/en) = $0.01/kWh
$30,000,000*0.09
$0.01/ $0.054 /
61,320,000
kWh kWh
kWh
LCOE  
TIC rc
LCOE fcr
en en
  

30. Competition
We are supplying wind data for several locations.
You will form teams and choose which data set you
would like to work with. You will then characterize
this wind resource with a histogram and calculate
the energy production by applying a power curve.
Several are provided to you. Cost data has also
been provided. Your objective is to minimize the
LCOE of your wind turbine installation by choosing
an optimal turbine for your location. You will also
calculate the resulting capacity factor of your
design.

32. Levelized Cost of Energy
• en = energy, to be calculated from wind resource data
• TIC = total installed cost, to be calculated from the
following equation which is a function of the turbine
size:
 𝑇𝐼𝐶 = $150 ∗ 𝑠𝑤𝑒𝑝𝑡 𝑎𝑟𝑒𝑎 𝑚2
+ $250 ∗ 𝑟𝑎𝑡𝑒𝑑 𝑝𝑜𝑤𝑒𝑟 𝑘𝑊 +
$1,500,000 (𝑏𝑎𝑙𝑎𝑛𝑐𝑒 𝑜𝑓 𝑠𝑦𝑠𝑡𝑒𝑚)
:
0.11
$0.015 /
TIC rc
LCOE fcr
en en
Assumptions
fcr
rc
kWh
en
  

