Fundamentals of Wind Energy
Paul Gipe, wind-works.org
Power in the Wind
1
3
P AV
2
Where  is air density (kg/m3),
A is area (m2), and
V is velocity (m/s).
Paul Gipe, wind-works.org
Air Density
p

R*T
Where p is air pressure (mb),
R is the gas constant, and
T is temperature (K)
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Vegetative
Indicators--Wind
Throw
Aude, France
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Increase in Wind Speed Over
Ridges
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Seasonal Wind Distribution
Avg. Monthly Wind Speed (mph)
18
16
14



12











10









8








Nov
Dec





6
Amarillo, Texas
4
Erie, Penn.
 San Francisco, Calif.
2
0
Jan
Feb
March
April
May
June
July
Month
Paul Gipe, wind-works.org
Aug
Sept
Oct
Rayleigh Wind Speed Distribution
0.16
Frequency of Occurrence %
5 m/s
6 m/s
7 m/s
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
Wind Speed Bin
Paul Gipe, wind-works.org
Weibull Wind Speed Distribution
For Same Average Speed
0.25
Frequency (%)
Power Density (W/m2)

Tera Kora %


0.2

0.15






0.1


0.05







0 






0
2
4
Tera Kora W/m2
Helgoland %
Helgoland W/m2






6
8
10

20



10








0












 

 



12
14
16
18
20
22
24
Wind Speed (m/s)
Paul Gipe, wind-works.org
50
30


60
40





70
Speed, Power, & Height
V/Vo = (H/Ho) α
P/Po = (H/Ho) 3α
Where α is the surface friction coefficient.
• 1/7 (0.14), Low Grass Prairies
• 1/4 (0.25), Suburbs
• 0.40, Urban
Paul Gipe, wind-works.org
Increase in Wind Speed with Height
V=Vo (H/Ho)
"
1.6
Wind Shear Exponent
1.5

0.1 0.14 (1/7) 0.2 0.25


1.4


1.3

1.2
1.1
1 



1






1.5


2
2.5


3
H/Ho
Paul Gipe, wind-works.org









3.5


4


4.5



5
Increase in Power with Height
3"
P=Po (H/Ho)
3.5
3

Wind Shear Exponent
0.1 0.14 (1/7) 0.2 0.25


2
1 



1





1.5




2



2.5




3
H/Ho
Paul Gipe, wind-works.org



1.5


2.5


3.5


4


4.5


5
Change in Wind Speed & Power
with Height
2 X Height
25 to 50 m
5 X Height
10 to 50 m
Wind Speed
1.1
1.25
Wind Power
1.35
1.99
1/7 (0.14), Low Grass Prairies
Paul Gipe, wind-works.org
Wind Resources of Ontario
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Wind Resources of the Dakotas
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Energy in the Wind
Annual Energy Output (AEO)
Annual Energy Production (AEP)
3
AEO = 1/2 ρ A V ή (8,760 hrs/year)
Paul Gipe, wind-works.org
AEO Estimating Methods
• Back-of-the-Envelope (Swept Area)
Simple Approximation
• Power Curve & Speed Distribution
Method Used by the Pros
Accuracy Dependent Upon Data
• Manufacturers’ Tables
Dependent Upon Honesty of Manufacturer
• Software
Must Know Assumptions Used (RETScreen)
Paul Gipe, wind-works.org
Rotor Dimensions
Paul Gipe, wind-works.org
Medium-Size & Large Wind Turbines
Swept Area (m²)
5000
80
70
60
50
40
30
20
10
0
Rotor Diameter (m)
2000
4000
3000
2000
1500
1000
1000
0
15
25
40
60
Diameter (meters)
500
250
50
Paul Gipe, wind-works.org
70
80
Measured Efficiency of Small
Wind Turbines @ Wulf Field
0.3
Efficiency (%)
     





 








 
 


 
 
 


 
 

 
  
        










 
Marlec
 
 


  
 
 

LVM







Air 303
















Air
403
 






BWC 850



Ampair

 
 





0.25
0.2
0.15
0.1
0.05
0
0
5
10
15
20
Wind Speed (mph)
Paul Gipe, wind-works.org
25
30
35
AEO Small Wind Turbines
Paul Gipe, wind-works.org
Conversion Efficiency
Medium Size Wind Turbines
Measured Efficiency
0.5
Efficiency
0.4
0.3
0.2
0.1
0
0
2
4
6
10
12
14
16
Wind Speed (m/s)
bk1/medturbeffic.wb3
L 18/80
Paul Gipe, wind-works.org
8
S31
E40
V47
18
20
California Annual Specific Yield
Annual Specific Yield (kWh/m2/yr)
1,400



1,200











1,000

800



600


















Cal. Avg.
400
 San Gorgonio Farms
200
0
86 87 88 89 90 91 92 93 94 95 96 97 98 99 '00 '01 '02 '03
Year
Paul Gipe, wind-works.org
Tararua New Zealand Yields
Tararua Wind Plant New Zealand Specific Yields
Vestas V47
Diameter Swept Area Specific Yield
kWh/yr
m
m2
kWh/m 2/yr
Approximate
Low
1,457,901
47
1,735
840
800
Median
2,500,000
47
1,735
1,440
1,500
High
3,050,622
47
1,735
1,760
1,800
WindStats, Spring 2005, Vol. 18, No. 2, pg 13.
Paul Gipe, wind-works.org
AEO Medium & Large Turbines
Paul Gipe, wind-works.org
Estimating AEO
Swept Area Method for 7 m/s*
Turbine
Swept Area
(m2)
Yield
(kWh/m2/yr)
AEO
(kWh/yr)
36 m; .5 MW
1,000
1,000
1,000,000
50 m; .75 MW
2,000
1,000
2,000,000
62 m; 1 MW
3,000
1,000
3,000,000
80 m; 2 MW
5,000
1,000
5,000,000
Paul Gipe, wind-works.org
*At Hub Height
Sample Power Curve Calculation
Power Curve
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Kilowatts
8
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
Wind Speed (mph)
Paul Gipe, wind-works.org
Sample Power Curve Calculation
Speed Distribution
600
Hours per Year
500
400
300
200
100
0
8
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
Wind Speed (mph)
Paul Gipe, wind-works.org
Sample Power Curve Calculation
Annual Energy Production
100
kWh/year
80
60
40
20
0
8
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
Wind Speed (mph)
Paul Gipe, wind-works.org
Net Generation from Wind Plants
Net
Availability
98%
Electrical
97%
Array Interference
90%-95%
Total
86%-90%
Paul Gipe, wind-works.org
Measures of Productivity
• Capacity (Plant) Factor
Misleading Indicator
Used for Fossil-Fired Plants
Not Suited for Wind Energy Use
• kWh/kW/yr (for Planning Purposes)
When Sufficient Data is Unavailable
• Annual Specific Yield (kWh/m2/yr)
The Only Measure Specific to Wind Energy
Paul Gipe, wind-works.org
Measures of Cost
• $/kW of Installed Capacity
Often a Misleading Indicator
• $/m2 of Installed Swept Area
Most Useful When Resource is Unknown
• $/kWh/yr of Annual Generation
Most Important Criteria in the End
Paul Gipe, wind-works.org
Wind Energy Software
• Spreadsheets
Integrated (Tom Wind)
Fully Integrated (RETScreen)
• Wind Farm Design Tools
WAsP (Risø)
WindFarm (ReSoft)
WindFarmer (Garrad Hassan)
WindPro (EMD)
WindMap (Brower)
Paul Gipe, wind-works.org
Wind Turbine Standards
Small Turbines
Caveat Emptor (Buyer Beware)
You Get What You Pay For
Big Turbines
Minimum Design Stds. (GL)
Power Curve Field Tests
Warranteed Power Curves
Performance Guarantees
Field Experience Best Guide
Paul Gipe, wind-works.org
Trade Magazines
•
•
•
•
•
•
•
•
Windpower Monthly
WindStats
WinDirections
RE World
New Energy
Neue Energie
North American Windpower
Systèmes Solaires
Paul Gipe, wind-works.org
Measured Performance Data
•
•
•
•
Power Curves
Noise
Power Factor
Flicker
Paul Gipe, wind-works.org
Pricing
•
•
•
•
•
Model
Tower
Transformer
€/kWh/annum
€/m2
Paul Gipe, wind-works.org
New Wind Books
2002
Paul Gipe, wind-works.org
2002
2001
2005
WWW Sites
• www.windpower.dk
Danish Manufacturers
• www.eole.org/
en français
• www.wind-energie.de
BWE, German Wind Turbine Owners
• wind-works.org
Archive of Articles by Paul Gipe
Paul Gipe, wind-works.org
Don’t Be Afraid of Foreign
Language Web Sites