Energy from Wind

Methods of Calculating AEO Swept Area Method Manufacturers Estimates Power Curve Method

Swept Area Method

Wind Speed Distributions Credit: Paul Gipe

Wind Speed Distributions Wind is empirically known to follow a Weibull probability distribution Weibull curve: has shape parameter k Average k in US: k = 2 (Raleigh distribution)

Specifications Rotor Diameter: 8.2 ft (2.5 m) Rotor Area: 53 ft2 (4.9 m2) Rated Power: 1,000 W Peak Power: ~1,800 W Rated Wind Speed: 24.6 mph (11 m/s) Rated Rotor Speed: 490 RPM Start-up Wind Speed: 6.7 mph (3 m/s) Cut-in Wind Speed: 5.6 mph (2.5 m/s) Furling Wind Speed: 29 mph (13 m/s) Cut-out Wind Speed: None Max. Design Wind Speed: 120 mph (54 m/s) Net Weight: 75 lbs (34 kgs) Shipping Weight: 95 lbs (43 kgs) Power Curve

Specifications Rotor Diameter: 20.2 ft (6.2 m) Rotor Area: 320 ft2 (30.2 m2) Rated Power: 10 kW (Grid), 7.5 kW (Battery) Peak Power: ~11 W (Grid), ~ 8.5 kW(Battery) Rated Wind Speed: 31 mph (14 m/s) Rated Rotor Speed: 300 RPM Start-up Wind Speed: 7.5 mph (3.4 m/s) Cut-in Wind Speed: 7.5 mph (3.4 m/s) Furling Wind Speed: 36 mph (16 m/s) Cut-out Wind Speed: None Max. Design Wind Speed: 120 mph (54 m/s) Net Weight: 1,020 lbs (464 kgs) Shipping Weight: 1,250 lbs (568 kgs) Power Curve

Turbine Ratings are weird Bergey XL.1 Rated Power 1 kW Does it produce 1000W all of the time? NO! Only a small percentage of time….

Turbine Ratings are weird Swept Area 10.1 m² (110 sq. ft.) Rated Power 2.5 kW

Turbine Ratings are weird Whisper 500 About 500 kWh/month at a site with a 12 mph annual average wind speed Rated Power 3.0 kW

Turbine Ratings are weird AWP3.6 Rotor Diameter 11.8 ft. (3.6 m) Rated Power 850W(24V) 1000W  (48V) 1600W  (Grid Connect)

Turbine Ratings are weird Vestas V90-3.0 MW Rotor Diameter 90m (295 ft) Rated Power 3,000,000 W or 3,000 kW or 3 MW

Power Curve Southwest Windpower Whisper 100 and Whisper 200 Similar rated power Difference in energy

Power Power: Rate at which energy is delivered Power = Energy Time Measured in Watts (W), kilowatts (kW), or horsepower Power is an instantaneous quantity Power does not accumulate Think gallons per minute

Energy Energy: Ability to do something Measured in kilowatt  Hours (kWhrs) Why? Since Power = Energy/Time, then Power  Time = Energy Energy does accumulates over time Think gallons Gallons = (gallons/min)  minutes

Wind Resource At any instant, the only question that makes sense is “What’s the power of the wind?” Answer depends on 2 quantities Instantaneous wind speed, v Air density, , which depends on Elevation Temperature Weather At sea level and 77F (standard conditions), air density  = 1.225 kg/m3 At 5,000 ft elevation,  is ~16% less than at sea level

Power Density of the Wind Power Density: P/A P/A = ½  v3 (in W/m2) Example: Suppose the wind speed is 8.0 m/s, and air density is 1.0 kg/m3, then P/A = ½ (1.0 kg/m3)(8.0 m/s)3 = 256 W/m2 For each square meter of area, there are 256 W of power Use Metric Units! If wind speed doubles, power density increases by 8

Swept Area The single most important parameter of a wind turbine is its rotor’s swept area A

Power of a Wind Turbine The power of a wind turbine is P = ½  v3 A CP A: swept area of rotor CP: rotor efficiency Example: A 2.5 m diameter turbine with a 25% efficient rotor in our 8.0 m/s wind will have P = ½ (1.0 kg/m3)(8.0 m/s)3 [ (2.5 m/2)2](0.25) = 314 W

Energy in the wind How much energy can this turbine produce? Need a constant wind speed and time Example: If the wind speed is a constant 8.0 m/s, then in 1 month our turbine will produce (314 W)(30 days)(24 hrs/day) = 226 kWhrs The average home in NC uses around 850 kWhrs/month

Method of Bins There are limitations to this method… Wind speed is not constant! Rotor efficiency depends on wind speed! Small turbines furl in high winds Here’s a better method: Method of Bins Need to know (or approximate) your wind distribution Power Curve of turbine

Wind Distribution Wind is known to follow a Weibull distribution =WEIBULL(v, k, vavg, 0) Rayleigh Distribution if k=2 Credit: Paul Gipe

Power Curve The turbine’s manufacturer will provide you with its power curve Bergey XL.1

Method of Bins Calculate Energy = Power  Time for each wind speed bin Sum ‘um up!

Method of Bins Power Curve Wind Distribution (data) Annual Energy Output

How? How do you get a power curve? How do you get a wind distribution? From the manufacturer Measure power and wind speed and make bins; follow IEC standards How do you get a wind distribution? Measure the wind speed and make a histogram Use the Weibull function assuming a Rayleigh distribution How do you do the calculations? Excel WinCAD or cheat…

AEO Charts from Manufacturer Example (6 m/s,13.44 mph, 250 W/m2, 3.6 m Diam.): AEO ≈ 325-375 kWh/mo

AWP 3.6 from Beech

Power Curve Verification

Example Whisper 200 Use real data from a met tower What is the Annual Energy Output (AEO)? Use a Rayleigh distribution How does the AEO compare?