1. Energy from Wind

2. The Rating Game

3. 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….

4. Turbine Ratings are weird ARE110 Swept Area 10.1 m² (110 sq. ft.) Rated Power 2.5 kW

5. 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

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

7. 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

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

9. 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

10. 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

11. 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

12. Power Density of the Wind Power Density: P/A 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

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

14. Power of a Wind Turbine The power of a wind turbine is P = ½  v 3 A C P A: swept area of rotor C P : 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

15. 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

16. 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

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

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

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

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

21. 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 –WinCAD –or cheat…

22. AEO Charts from Manufacturer Example (6 m/s,13.44 mph, 250 W/m 2, 3.6 m Diam.): AEO ≈ 325-375 kWh/mo

23. AWP 3.6 from Beech

24. Power Curve Verification

25. 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?