Wind power
Part 2: Resource Assesment
San Jose State University
FX Rongère
February 2009
Wind resource characterization
 Energy provided by the wind



dE 
  QA   WA   m A .(hA  k A  A )

dt  Open A
A
A


v A2
v 3A
A WA  A mA . 2  A  A . 2
Available power is proportional to the cube of the wind velocity
Power Capacity Calculation
 Use of Probability Density Function (Pdf)
 Since





W  A. .v , W  A. . v
2
2
3
3
 We will use the Pdf(v):

W
 

0
W (v).Pdf (v).dv


0
Pdf (v).dv
 It has been shown that the Rayleigh’s approximation
gives good results for wind power capacity calculation
2



 .v

.v 
 
Pdf (v) 
. exp  
2
 
2
.
v

2. v
 
 

Rayleigh’s Distribution
 Using the mathematical properties of the Rayleigh’s
Distribution we can show that:
 The most frequent wind speed is equal to 0.8 times the
average wind speed.
Pdf (v) max is located at :
2

Rayleigh's function
0.4
0.35
Pdf(v)
0.3
0.25
0.2
0.15
0.1
0.05
0
0
0.5
1
1.5
V/Vav er ag e
"Vaverage=2m/s"
"Vaverage=5m/s"
"Vaverage=10m/s"
2
 v  0.80 . v
Most contributing wind
 The most contributing wind speed is equal to 1.6 times the
average wind.

8
v3 .Pdf (v) max is located at :

 v  1.60 . v
Most contributing wind to the power
0.8
0.7
3
v . Pdf(v)
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
V/Vav er ag e
Vaverage=2m/s
Vaverage=5m/s
vaverage=10m/s
2
Average power
 The average power is equal to 1.91 times the power
corresponding to the average wind speed

v3 


0
v 3 .Pdf (v).dv

Pdf (v).dv
0
v3 
6


3

 v  1.91 . v
3




W  A. .v 3
2

W  A. . v
2

3


W (v)  1.91 . W v
Example of power distribution
 Lee Ranch Facility in Colorado
 Actual measures probability of wind
and power
 Curves use the Rayleigh’s distribution
More complex Pdf
 Weibull’s distribution is a more general
form than Rayleigh’s distribution:
k. 
Pdf (v) 
2.v
  .v 

.

2
.
v


k 1
   .v  k 
 
. exp  
  2.v  


 Rayleigh’s distribution: k=2
Wind Shear
 In general wind is stronger with altitude
because of the friction on the ground
ground cover
smooth surface ocean, sand
low grass or fallow ground
high grass or low row crops
tall row crops or low woods
high woods with many trees suburbs, small
towns
n
0.1
0.16
0.18
0.2
100
low grass or fallow
ground
80
60
high grass or low row
crops
40
20
tall row crops or low
woods
0
1
1.2
1.4
1.6
v(z)/v(10m)
0.3
smooth surface
ocean, sand
Wind shear
Altitude (m)
 z 
v( z )  v( z0 ). 
 z0 
n
1.8
2
high woods with
many trees suburbs,
small towns
Wind shear is much more complex than friction
on the ground. Analysis must be performed for
each specific case
Class of wind power density
 Locations are rated following the table:
10 m (33 ft)
Wind
Power
Class
1
Wind Power
Density
50 m (164 ft)
Wind Power
Density
(W/m2)
0
Average
Speed m/s
(mph)
0
(W/m2)
0
Average
Speed m/s
(mph)
0
100
4.4 (9.8)
200
5.6 (12.5)
150
5.1 (11.5)
300
6.4 (14.3)
200
5.6 (12.5)
400
7.0 (15.7)
250
6.0 (13.4)
500
7.5 (16.8)
300
6.4 (14.3)
600
8.0 (17.9)
400
7.0 (15.7)
800
8.8 (19.7)
1000
9.4 (21.1)
2000
11.9 (26.6)
2
3
4
5
6
7
Assuming a Rayleigh distribution and a wind shear provided
by the power law with an exponent equals to .14
Wind scale
Wind speed
Beaufort number
Description
Wave height
kt
km/h
mph
m/s
0
0
0
0
0-0.2
1
1-3
1-6
1-3
2
4-6
7-11
4-7
3
7-10
12-19
8-12
4
11-15
20-29
13-18 5.5-7.9 Moderate breeze 1
3.3
5
16-21
30-39
19-24 8.0-10.7 Fresh breeze
2
6.6
6
22-27
40-50
25-31 10.8-13.8 Strong breeze
3
9.9
7
28-33
51-62
32-38 13.9-17.1 Near gale
4
13.1
8
34-40
63-75
39-46 17.2-20.7 Gale
5.5
18
9
41-47
76-87
47-54 20.8-24.4 Severe gale
7
23
10
48-55 88-102 55-63 24.5-28.4 Storm
9
29.5
11
56-63 103-119 64-73 28.5-32.6 Violent storm
11.5
37.7
12
64-80
14+
46+
120
m
ft
Calm
0
0
0.3-1.5
Light air
0.1
0.33
1.6-3.3
Light breeze
0.2
0.66
0.6
2
3.4-5.4 Gentle breeze
74-95 32.7-40.8 Hurricane
Wind resource in the USA
Wind Farms in the USA
Wind resource in the USA
Wind resource in the USA
Wind resource in California
Solano
415 MW
Altamont Pass
586 MW
Wind resource in California
Pacheco
16 MW
Tehachapi
665 MW
San Gorgonio
619 MW
Altamont Pass
586 MW
6,000 wind turbines
Early 80s
Repowering has started
38 Mitsubishi (1MW in 2006)
Pacheco Pass
16 MW
167 wind turbines
Mid 80s
Project by Enel with
Vestas 660kW
Tehachapi
665 MW
2,000+ wind turbines
Early 80s
Repowering started in 1999
Micon 700 kW
GE 1.5 MW
Mitsubishi 1 MW
San Gorgonio
619 MW
1,000+ wind turbines
Early 80s
Repowering started in 1999
Zond 750 kW
Vestas 650 kW
Mitsubishi 600 kW
GE 1.5 MW
Wind Resource in California
45 miles
Projects
Project
Alta Mesa IV
Utility/Developer
Location
Tenderland Power/ CHI
Enel
San Gorgonio Pass
Altamont Power
Altamont Power, LLC
Altamont Pass
Pacific Renewable
PG&E
Montezuma
Status
NA
MW
Cap
40
Online date/
Turbine
NA
Vestas 660 kW
(61)
NA
36
NA / NEG Micon
800kW
(45)
Lompoc
83
NA
FPL Energy
Solana
32
NA
Pine Tree Wind
Project
Zilkha/ LA Dept of PW
Mojave (North)
Proposed
120
NA
Tehachapi Wind
Project
Western Wind
Tehachapi
Proposed
50
NA
San Gorgonio Wind
Project
SeaWest Windpower
San Gorgonio
Proposed
37
NA
Tehachapi Wind
Project
Coram Energy
Tehachapi
Proposed
12
NA
Recent Projects
Name
Power
Capacity
Location
(MW)
Turbine
Mfr.
Units
Edom Hills
repower
20
8 Clipper
Alite Wind
Farm
24
8 Vestas
Dillon
45
45
Solano Wind
Project
Solano
63
21
Buena Vista
Altamont
Pass
38
38
Shiloh Wind
Power Project
Solano
County
150
100
Solano IIA
Solano
County
24
8
Coram Energy
(Aeroman
repower)
Tehachapi
10.5
7
East of
San Diego
50
Victorville
prison
0.75
Kumeyaay
Wind Power
Project
Victorville Wind
Project
Developer
BP Alternative
Energy
Owner
Power
Purchaser
BP Alternative
SCE
Energy
California
Portland
Cement
Southern
Iberdrola
Iberdrola
Mitsubishi
California
Renewables
Renewables
Edison
Sacramento
Sacramento
Sacramento
Vestas
Municipal Utility Municipal
Municipal Utility
District
Utility District District
Babcock &
Babcock &
Pacific Gas &
Mitsubishi
Brown
Brown
Electric
PG&E, Modesto
Irrigation
GE Energy PPM Energy
PPM Energy
District & City
of Palo Alto
Utilities
Sacramento
Sacramento
Sacramento
Vestas
Municipal Utility Municipal
Municipal Utility
District
Utility District District
Southern
GE Energy Coram Energy Coram Energy California
Edison
Allco/Oak
Creek Energy
Year
Online
2008
2008
2008
2007
2006
2006
2006
2005
25 Gamesa
Superior
Renewable
Energy
Babcock &
Brown
San Diego Gas
& Electric
2005
1 Vestas
NORESCO
NORESCO
Victorville
Prison
2005
Under-construction Projects
Name
Power
Capacity
Location
(MW)
Pine Tree Wind north of
Project
Mojave
120
San Gorgonio San
Farms repower Gorgonio
5
Northern
California
150
Shiloh II
Units
Turbine
Mfr.
Developer
Owner
Power
Purchaser
80 GE Energy
Los Angeles
Department of
Water and
Power
Los Angeles
Los Angeles
Department of Department of
Water and
Water and
Power
Power
10 Vestas
San Gorgonio
Farms
San Gorgonio
Farms
75 REPower
enXco
enXco
Year
Online
PG&E
Source: American Wind Energy Association
Assessment Techniques
 Wind Tower




Expensive
Punctual information
Telecommunication
Limited height (50 m)
Wind vane
anemometer
Source: Wes Slaymaker
Commercial Wind Site Assessment
Madison, WI February 2005
Sodar
 Acoustic signal modified by the wind
velocity by Doppler effect:
Frequency is higher in front of the moving source and lower behind
 w 
f ' 
. f
 wv
f: emitted frequency
f’: observed frequency
w: velocity of the wave
v: velocity of the source
Sodar
 Sound velocity:


M
Effect of Temperature on Sound Speed
Cp

Cv
R: Boltzmann’ constant 8.314 Jmol
T: Temperature K
M: Mass of one mole of gas
γ: 1.4 for dry air
 .R.T
350
-1K-1
Sound Speed (m/s)
w  .
P
Depends on Temperature
and Humidity
340
330
320
310
300
-10
0
10
Temperature (C)
20
30
Sodar
 Sound is reflected and scattered by the
eddies carried by the turbulent wind
 The amplitude of the received wave
characterizes the stability of the
atmosphere
Using several sodar
sources allows to capture
the different components of
the wind velocity
Vertical range : 200 m. to 2,000 m.
Frequency: 1,000 Hz 4,000 Hz
Sodar signal
Satellite based measurements
 Sea waves scatter and reflect radar signal
 Direction and Wave length of the waves provide
wind information
 Accuracy of ±2m/s and ±20o
 Not valid close to the coast because of effect on
waves
Numerical simulation
 Objective:
 To get detailed wind calculation in specific location
from general atmospheric observations
 Categories of models from the general to
detailed
 Mesoscale models (n00 km x n00km x 10 km) ex KAMM
 Microscale linear models (n km x n km x n km) ex WAsP
 Navier-Stokes non-linear models with turbulence (n00 m
x n00 m x n00 m)
 They are usually used in conjunction with local
measured data to be adjusted
Source : Wind Flow Models over Complex Terrain for Dispersion Calculations COST Action 710 - 1997
References
 http://rredc.nrel.gov/wind/pubs/atlas/maps.html#2-1
 http://www.wasp.dk/Courses/Index.htm
 http://www5.ncdc.noaa.gov/documentlibrary/pdf
 Companies to follow:
www.awstruewind.com (Albany)
 www.windlogic.com (St Paul)
 www.3tiergroup.com (Seattle)
 www.garradhassan.com (UK)
Application
 At Ilio Point on Molokai (Hawaii)
 The average wind speed at 30m is 8.1m.s-1
 The shear exponent is .14 and the wind follows the
Rayleigh’s distribution
 What is the average speed at 50m?
 What is the class of the site?
 What is the power density available at 50m?
 What is the most probable wind speed at 50m?
 What is the most contributing wind speed at 50m?
 What is the probability to have a wind speed greater
than 25 m.s-1 at 50m?
Ilio Point