Energy from Wind
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
PowerkW
(kilowatts)
EnergykWh
(kilowatt hours)
Think gpm
Think gallons
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 77F (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 rotorCP: 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
How NOT to estimate 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/month– The average home in NC uses around 850
kWhrs/month• The wind speed is not constant
10 Minute Wind Data
0 10 20 30 40 500
2
4
6
8
Fre
qu
ency
(%
)
Probability Distribution Function
50WS HI (mph)
Actual data Best-f it Weibull distribution (k=2.04, c=15.96 mph)
Wind Speed Distributions
Using the Annual Average Wind Speed to Calculate Energy Production is Problematic
• Using the average Annual wind speed will under estimate energy production because of the cubic relationship between wind speed and power.
• Need to cube each 10 minute wind speed• The average of the cubes is greater than the
cube of the average
Cube of Average vs Average of Cubes for site with 6.5 m/s average annual wind speed
• Cube of the Average– Class 3 site @ 30 meters
= 6.5 m/s– P/A = .6125 x 6.53
– P/A = 168 watts/m2
Too Low
• Average of CubesP/A of 10.0 m/s = 612P/A of 5.0 m/s = 76.56P/A of 4.6 m/s = 59.6
19.6/3748.16/3
6.5 m/s 249 w/m2
Energy Pattern Factor (EPF) = Average of cubes / cube of average = 249 / 168 = 1.48
10 minute datamph20 std dir F
10/1/2006 0:00 1.00 0.6 0 5010/1/2006 0:10 1.00 0.5 202 5010/1/2006 0:20 3.10 1 270 5010/1/2006 0:30 3.60 0.9 248 5010/1/2006 0:40 4.00 1.6 225 5110/1/2006 0:50 6.70 2.4 225 5310/1/2006 1:00 5.50 2.1 202 5410/1/2006 1:10 8.90 2.5 202 5410/1/2006 1:20 8.50 2.2 202 5510/1/2006 1:30 7.50 2.8 225 5510/1/2006 1:40 5.40 1.9 225 5510/1/2006 1:50 4.50 1.9 225 5510/1/2006 2:00 4.00 2 270 55
Average of Cubes is Greater than Cube of Average
Time Stamp Speed (mph) m/s P/A1/1/2006 15:50 7.6 3.39 23.921/1/2006 16:00 8.2 3.66 30.051/1/2006 16:10 9.2 4.11 42.441/1/2006 16:20 10.5 4.69 63.091/1/2006 16:30 10.6 4.73 64.911/1/2006 16:40 9.8 4.38 51.291/1/2006 16:50 10.3 4.60 59.551/1/2006 17:00 10.6 4.73 64.911/1/2006 17:10 12.4 5.54 103.901/1/2006 17:20 10.9 4.87 70.571/1/2006 17:30 11.4 5.09 80.741/1/2006 17:40 12.2 5.45 98.96
average speed 4.60
P/A of Average 59.69 watts/m2Average of Cubes 62.86 watts/m2
Energy Pattern Factor
• Average of Cubes divided by Cube of Average• 62.86 / 59.69 = 1.05• EPF = 1.05• Typical EPF = 1.9• Multiply power density calculated from
average annual wind speed by 1.9 to get more accurate average annual power density
Estimating Average Annual Power Density from Annual Average Wind Speed
• What would be a reasonable estimate of an annual average power density when the average annual wind speed was 12 mph (5.35 m/s) and elevation was 4,000’
• Annual Average P/A = ½ Density x V3 (in meters/sec) x 1.9• AA P/A of 12 mph = ½ (1.225 x .88) x 5.353 x 1.9• AA P/A of a 12 mph wind at 4,000’ = 156 watts/m2
Air Density Changes with Elevation
Density Change with Elevation
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
10,000
70 75 80 85 90 95 100
Density Change Compared to Sea Level, %
Ele
vati
on
, ft
Swept Area Method of Estimating Energy Production (AEO)
• AEO = (Average annual power density x 1.9) x area of rotor (m2) x efficiency x hours/year
Swept Area• Power is directly related to the area intercepting the
wind• Doubling the swept area will double power available
to it• Nothing tells you more about a wind turbines
potential than area swept by rotor• Area = πr2 or πd2/4• Relatively small increases in blade length produce
large increase in swept area• Doubling diameter will quadruple swept area
Credit: Paul Gipe
Swept Area
A = Pi D2 / 4
1 m = 3.3 ft
Area = πr2
Swept Area of Bergey XL.1
• Bergey XL.1 has three blades each 4’ long and a rotor diameter of 8.2’
• 8.2’ / 3.28 (ft/m) = 2.5 meter diameter
• Radius = 1.25 meter• Area = πr2
• Area = πr2 = π 1.252 = 4.9 m2
Power Intercepted by Bergey XL1 with 4.9 m2 of Wind Power at 4,000’, 00, in 7 m/s wind
• Power = ½ density x area x velocity3
• Power = ½ (1.218 kg/m2) x 4.9 m2 x 73
• Power = .609 x 4.9 m2 x 73
• Power = .609 x 4.9 x 343• Power = 1,023 watts
Estimating Annual Energy Output of XL.1 with Swept Area Method @ class 3 site; 6.5 m/s @ 5,000’
• AEO in watts = Annual Average P/A x Swept Area x efficiency x hours per year
• AEO = (1/2 air density) x (v3) x (1.9) x 4.9 x .20 x 8760
• AEO = ½ (1.225 x .860) x (6.53) x 1.9 x 4.9 x .20 x 8760
• AEO = 2,359 Kwh
Power Curve Method or Method of Bins
2 Things Needed
Need to know (or approximate) your wind distribution
Power Curve of turbine
Wind Distribution• Wind is known to follow a Weibull distribution
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240
500
1000
1500
2000
2500
3000
Distribution of Wind Speeds
Frequency
Wind Speed (m/s)
# o
f O
ccu
rren
ces
Wind Distribution• Wind is known to follow a Weibull distribution • =WEIBULL(c, k, vavg)• Rayleigh Distribution if k=2
Credit: Paul Gipe
Wind Speed Distributions
k = 2
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Pro
b.
den
sity
k = 3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Pro
b.
den
sity
k = 1.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Pro
b.
den
sity
• Wind is empirically known to follow a Weibull probability distribution
• Weibull curve: has shape parameters: c & k• Average k in US: k = 2 (Raleigh distribution)
Method of BinsWind Distribution: From your logger!
Power Curve• The turbine’s manufacturer will provide you
with its power curve
Bergey XL.1
Whisper Power Curves
Utility Scale Power Curve (GE)
Method of BinsPower Curve (kW)
Wind Distribution (hrs)
AEO (kWhrs)H
ours
Ener
gy (k
Whr
)
Method of Bins• Calculate Energy = Power Time for each wind
speed bin• Sum ‘um up!
Charts from Manufacturer