1. Energy from Wind

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

3. Swept Area Method

4. Wind Speed Distributions
Credit: Paul Gipe

5. 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)

6. 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: 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

7. 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

8. 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….

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

10. 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

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

12. Turbine Ratings are weird
Vestas V MW
Rotor Diameter
90m (295 ft)
Rated Power
3,000,000 W
or 3,000 kW
or 3 MW

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

14. 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

15. 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

16. 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  = kg/m3
At 5,000 ft elevation,  is ~16% less than at sea level

17. 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

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

19. 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

20. 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

21. 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

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

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

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

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

26. 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…

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

28. AWP 3.6 from Beech

29. Power Curve Verification

30. 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?