Fundamentals of Wind Energy

Paul Gipe & Assoc.

Power in the Wind

3

21 AVP

Where is air density (kg/m3),

A is area (m2), and

V is velocity (m/s).

Paul Gipe & Assoc.

Air Density

TRp*

Paul Gipe & Assoc.

Where p is air pressure (mb),

R is the gas constant, and

T is temperature (K)

Paul Gipe & Assoc.Paul Gipe & Assoc.

Change in Air Density with Temperature

1.14 1.12 1.1 1.07 1.05 1.04 1.02 1 0.98 0.97 0.95 0.94 0.92 0.91 0.89

Change Relative to 15 C

0

5

10

15

20

25

30

35

40

45

50

-5

-10

-15

-20

Celsius

0

10

20

30

40

50

60

70

80

90

100

110

120Fahrenheit

Paul Gipe & Assoc.

Change in Air Density with Elevation (Normal Lapse Rate)

1 0.95 0.91 0.86 0.82 0.78 0.74 0.7 0.67

Change Relative to Sea Level

0

2

4

6

8

10

12

14Thousands (Feet)

Identifying the Wind Resource

Paul Gipe & Assoc.

Wellington, NZ

Paul Gipe & Assoc.

Vegetative Indicators--Wind

Throw

Aude, France

Increase in Wind Speed Over Ridges

Paul Gipe & Assoc.

Wind Sensors

Anemometer Wind Vane

Paul Gipe & Assoc.

Wind Direction

Paul Gipe & Assoc.

Seasonal Wind Distribution

Paul Gipe & Assoc.

Jan Feb March April May June July Aug Sept Oct Nov Dec

Month

0

2

4

6

8

10

12

14

16

18Avg. Monthly Wind Speed (mph)

Amarillo, Texas

Erie, Penn.

San Francisco, Calif.

Rayleigh Wind Speed Distribution

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Wind Speed Bin

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16Frequency of Occurrence %

5 m/s

6 m/s

7 m/s

Paul Gipe & Assoc.

Weibull Wind Speed DistributionFor Same Average Speed

Paul Gipe & Assoc.

0 2 4 6 8 10 12 14 16 18 20 22 24

Wind Speed (m/s)

0

0.05

0.1

0.15

0.2

0.25Frequency (%)

0

10

20

30

40

50

60

70

Power Density (W/m2)

Tera Kora %

Tera Kora W/m2

Helgoland %

Helgoland W/m2

Turbulence & Obstructions

Paul Gipe & Assoc.

Speed, Power, & Height

Paul Gipe & Assoc.

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

Increase in Wind Speed with Height

1 1.5 2 2.5 3 3.5 4 4.5 51

1.1

1.2

1.3

1.4

1.5

1.6

Wind Shear Exponent0.1 0.14 (1/7) 0.2 0.25

V=Vo (H/Ho)

H/Ho

Increase in Power with Height

1 1.5 2 2.5 3 3.5 4 4.5 51

1.5

2

2.5

3

3.5

Wind Shear Exponent0.1 0.14 (1/7) 0.2 0.25

P=Po (H/Ho)

H/Ho

3

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

Paul Gipe & Assoc.

1/7 (0.14), Low Grass Prairies

Typical Tower Height

20 30 50 60 70 80 100

Rotor Diameter (m)

0

20

40

60

80

100

120

140

160Tower Height (m)

Paul Gipe & Assoc.

California Wind Resources

Wind Resources of the Dakotas

Paul Gipe & Assoc.

Energy in the Wind AEO (Annual Energy Output)

AEO = 1/2 ρ A V3 ή (8,760 hrs/year)

AEO Estimating Methods

Paul Gipe & Assoc.

• Back-of-the-Envelope (Swept Area)Simple Approximation

• Power Curve & Speed DistributionMethod Used by the Pros

Accuracy Dependent Upon Data

• Manufacturers’ TablesDependent Upon Honesty of Manufacturer

• SoftwareMust Know Assumptions Used (RETScreen)

Paul Gipe & Assoc.

Rotor Dimensions

Medium-Size & Large Wind Turbines

0

10

20

30

40

50

60

70

80Rotor Diameter (m)

250

1500

1000

500

50

15 25 40 60 70 80

Diameter (meters)

0

1000

2000

3000

4000

5000

Swept Area (m²)

2000

Measured Efficiency of Small Wind Turbines @ Wulf Field

0 5 10 15 20 25 30 35

Wind Speed (mph)

0

0.05

0.1

0.15

0.2

0.25

0.3Efficiency (%)

Marlec

LVM

Air 303

Air 403

BWC 850

Ampair

AEO Small Wind Turbines

Conversion Efficiency

Paul Gipe & Assoc.

0

0.1

0.2

0.3

0.4

0.5

Effic

ien

cy

0 2 4 6 8 10 12 14 16 18 20

Wind Speed (m/s)

L 18/80 S31 E40 V47

Medium Size Wind TurbinesMeasured Efficiency

bk1/medturbeffic.wb3