Energy from Wind Methods of Calculating AEO Swept

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 v Rotor Diameter: 8. 2 ft (2. 5 m) v Rotor Area: 53 ft 2 (4. 9 m 2) v Rated Power: 1, 000 W v Peak Power: ~1, 800 W v Rated Wind Speed: 24. 6 mph (11 m/s) v Rated Rotor Speed: 490 RPM v Start-up Wind Speed: 6. 7 mph (3 m/s) v Cut-in Wind Speed: 5. 6 mph (2. 5 m/s) v Furling Wind Speed: 29 mph (13 m/s) v Cut-out Wind Speed: None v Max. Design Wind Speed: 120 mph (54 m/s) v Net Weight: 75 lbs (34 kgs) v Shipping Weight: 95 lbs (43 kgs) Power Curve

Specifications v Rotor Diameter: 20. 2 ft (6. 2 m) v Rotor Area: 320 ft 2 (30. 2 m 2) v Rated Power: 10 k. W (Grid), 7. 5 k. W (Battery) v Peak Power: ~11 W (Grid), ~ 8. 5 k. W(Battery) v Rated Wind Speed: 31 mph (14 m/s) v Rated Rotor Speed: 300 RPM v Start-up Wind Speed: 7. 5 mph (3. 4 m/s) v Cut-in Wind Speed: 7. 5 mph (3. 4 m/s) v Furling Wind Speed: 36 mph (16 m/s) v Cut-out Wind Speed: None v Max. Design Wind Speed: 120 mph (54 m/s) v Net Weight: 1, 020 lbs (464 kgs) v Shipping Weight: 1, 250 lbs (568 kgs) Power Curve

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

Turbine Ratings are weird • ARE 110 • Swept Area 10. 1 m² (110 sq. ft. ) • Rated Power 2. 5 k. W

Turbine Ratings are weird • Whisper 500 • About 500 k. Wh/month at a site with a 12 mph annual average wind speed • Rated Power 3. 0 k. W

Turbine Ratings are weird • AWP 3. 6 • Rotor Diameter – 11. 8 ft. (3. 6 m) • Rated Power – 850 W(24 V) – 1000 W (48 V) – 1600 W (Grid Connect)

Turbine Ratings are weird • Vestas V 90 -3. 0 MW • Rotor Diameter – 90 m (295 ft) • Rated Power – 3, 000 W – or 3, 000 k. W – 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 (k. W), 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 (k. Whrs) • 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/m 3 • At 5, 000 ft elevation, is ~16% less than at sea level

Power Density of the Wind • Power Density: P/A = ½ v 3 (in W/m 2) • Example: Suppose the wind speed is 8. 0 m/s, and air density is 1. 0 kg/m 3, then P/A = ½ (1. 0 kg/m 3)(8. 0 m/s)3 = 256 W/m 2 – 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 v 3 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/m 3)(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 k. Whrs – The average home in NC uses around 850 k. Whrs/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? – 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 – Win. CAD – or cheat…

AEO Charts from Manufacturer Example (6 m/s, 13. 44 mph, 250 W/m 2, 3. 6 m Diam. ): AEO ≈ 325 -375 k. Wh/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?