Fundamentals of Wind Energy Paul Gipe, wind-works.org Power in the Wind P1 AV3 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 Vestas 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) • 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 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 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 .