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CATs
COHERENT APPLICATION
WindTHREADS
Turbines
Supplemental Learning Module
ME 366 PROBABILITY AND
STATISTICS
Statistics and Distributions
Don Wroblewski
Associate Professor, Mechanical Engineering
Associate Chair, Aerospace Engineering
Undergraduate Program
ACTUAL WIND DATA HISTOGRAM
Typical Annual Wind Speed Histogram
10 Minute Averages in 1 m/s Bins
Annual Mean Wind
Speed: 10/m/s
WEIBULL DISTRIBUTION FIT
Probability Density
Function
 V k 
V k 1
f (V)  k k exp  
c
 c  
k = shape parameter*
c = scale parameter (related to mean wind speed)

Best fit Weibull distribution
k = 2.18 c = 11.0
* k=2 is a Rayleigh distribution, often used if only
mean wind speed is known
ANNUAL ENERGY UTILIZATION
ESTIMATE
Annual Wind Speed
Weibull Distribution
Annual Energy Distribution
700
400
500
400
Annual Energy MWh
# hours per year
600
300
200
100
0
0
2
4
6
8
10
12
14
16
Wind Speed, m/s
Turbine Power Curve
Power, kW
2000
300
200
100
0
1500
0
1000
2
4
6
8 10 12 14 16
Wind Speed, m/s
500
0
0
5
10
15
Wind Speed, m/s
20
TURBULENCE INTENSITY & BLADE FATIGUE
Wind Speed over 10 minutes Interval
V =9.5 m/s
sV =1.15 m/s
Turbulence intensity=
sV
V
Turbulence intensity
(12.1% for plot
above)
Blade fatigue
TURBULENCE INTENSITY & BLADE FATIGUE
Conditional Probability for Turbulence Intensity
Lognormal Distributions
Plot from Hansen and Larsen, J. Wind Engineering, 2005