Fundamentals of Wind Energy

Paul Gipe, wind-works.org Power in the Wind

1AVP 3 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)

Paul Gipe, wind-works.org Vegetative Indicators--Wind Throw

Aude, France

Paul Gipe, wind-works.org Increase in Wind Speed Over Ridges

Paul Gipe, wind-works.org Seasonal Wind Distribution

Avg. Monthly Wind Speed (mph) 18

16     14              12        10       8     6 Amarillo, Texas 4 Erie, Penn. 2  San Francisco, Calif.

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

Paul Gipe, wind-works.org Rayleigh Wind Speed Distribution

Frequency of Occurrence % 0.16 0.14 5 m/s 6 m/s 0.12 7 m/s 0.1 0.08 0.06 0.04 0.02 0 01234567891011121314151617181920 Wind Speed Bin

Paul Gipe, wind-works.org Weibull Wind Speed Distribution For Same Average Speed

Frequency (%) Power Density (W/m2) 0.25  Tera Kora % 70  Tera Kora W/m2 0.2   60 Helgoland %  Helgoland W/m2 50 0.15       40     0.1   30         20  0.05       10             0          0 0 2 4 6 8 1012141618202224 Wind Speed (m/s)

Paul Gipe, wind-works.org Speed, Power, & Height

α V/Vo = (H/Ho)

3α P/Po = (H/Ho) 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 3.5 4 4.5 5

H/Ho

Paul Gipe, wind-works.org Increase in Power with Height

3" P=Po (H/Ho) 3.5  Wind Shear Exponent 3 0.1 0.14 (1/7) 0.2 0.25     2.5     2            1.5            1  1 1.5 2 2.5 3 3.5 4 4.5 5

H/Ho

Paul Gipe, wind-works.org Change in Wind Speed & Power with Height

2 X Height 5 X Height 25 to 50 m 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

Paul Gipe, wind-works.org Wind Resources of the Dakotas

Paul Gipe, wind-works.org Energy in the Wind Annual Energy Output (AEO) Annual Energy Production (AEP)

AEO = 1/2 ρ A V 3 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 Rotor Diameter (m) 4000 80 3000 2000 70 2000 1500 60 1000 0 50 1000 15 25 40 60 70 80 40 Diameter (meters) 30 500 20 250

10 50 0

Paul Gipe, wind-works.org Measured Efficiency of Small Wind Turbines @ Wulf Field Efficiency (%) 0.3

 0.25             0.2                          Marlec        0.15     LVM           Air 303    0.1      Air 403      BWC 850 0.05     Ampair   0  0 5 10 15 20 25 30 35 Wind Speed (mph)

Paul Gipe, wind-works.org AEO Small Wind Turbines

Paul Gipe, wind-works.org Conversion Efficiency

Medium Size Wind Turbines Measured Efficiency

0.5

0.4

0.3

Efficiency 0.2

0.1

0 0 2 4 6 8 10 12 14 16 18 20 Wind Speed (m/s) bk1/medturbeffic.wb3

L 18/80 S31 E40 V47

Paul Gipe, wind-works.org 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 V47 Diameter Swept Area Specific Yield kWh/yr m m2 kWh/m2/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*

Swept Area Yield AEO Turbine (m2) (kWh/m2/yr) (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 Kilowatts 1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 8 10121416182022242628303234363840 Wind Speed (mph)

Paul Gipe, wind-works.org Sample Power Curve Calculation Speed Distribution

Hours per Year 600

500

400

300

200

100

0 8 10121416182022242628303234363840 Wind Speed (mph)

Paul Gipe, wind-works.org Sample Power Curve Calculation Annual Energy Production

kWh/year 100

80

60

40

20

0 8 10121416182022242628303234363840 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) • 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 2002 2001

2005 Paul Gipe, wind-works.org WWW Sites • www.windpower.dk Danish Manufacturers • www.eole.org/ en français • www.wind-energie.de BWE, German Owners • wind-works.org Archive of Articles by Paul Gipe

Paul Gipe, wind-works.org Don’t Be Afraid of Foreign Language Web Sites