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1. Wind Energy I
Wind field
characterization
Michael Hölling, WS 2010/2011 slide 1

2. Wind Energy I Class content
5 Wind turbines in
6 Wind - blades
general
2 Wind measurements interaction
7 Π-theorem
8 Wind turbine
characterization
3 Wind field 9 Control strategies
characterization
10 Generator
4 Wind power
11 Electrics / grid
Michael Hölling, WS 2010/2011 slide 2

3. Wind Energy I Motivation
Why should we know anything about the wind field ?
Atmospheric boundary layer (ABL)
Michael Hölling, WS 2010/2011 slide 3

4. Wind Energy I Motivation
Why should we know anything about the wind field ?
Atmospheric boundary layer (ABL)
Michael Hölling, WS 2010/2011 slide 3

5. Wind Energy I Motivation
Why should we know anything about the wind field ?
Atmospheric boundary layer (ABL)
Michael Hölling, WS 2010/2011 slide 3

6. Wind Energy I Motivation
Enercon E-126 BARD 5.0
http://www.wind-energy-the-facts.org http://www.ecogeneration.com.au
Michael Hölling, WS 2010/2011 slide 4

7. Wind Energy I Motivation
GROWIAN - Große Windkraftanlage (Big Wind energy converter)
Michael Hölling, WS 2010/2011 slide 5

8. Wind Energy I Resource wind
m 2 ρ·V ρ·A·x 2
Kinetic energy of wind: E = ·u = ·u =
2
·u
2 2 2
Corresponding power d ρ·A·x 2
for constant velocity u : Pair = ·u
dt 2
1 2 dx
= ·ρ·A·u ·
2 dt
1
= · ρ · A · u3
2
Wind energy converter can NOT convert 100% of that energy !
Consequently the power of the wind energy converter is also
smaller: 1
PW EC = cp · · ρ · A · u3 = cp · Pair
2
Michael Hölling, WS 2010/2011 slide 6

9. Wind Energy I Resource wind
Power curve of wind energy converter - theory
rated
2.0
P(u)
1.6
P(u) [MW]
1.2
cut out
0.8 cut in
0.4
0.0
0 10 20 30
u [m/s]
Michael Hölling, WS 2010/2011 slide 7

10. Wind Energy I Resource wind
Power curve of wind energy converter - reality
Michael Hölling, WS 2010/2011 slide 8

11. Wind Energy I Resource wind
Annual mean wind speed taken from wind atlas
Michael Hölling, WS 2010/2011 slide 9

12. Wind Energy I Resource wind
Estimation of Annual Energy Production (AEP) based on annual
mean wind speed from wind atlas:
2.0
P(u)
1.6
P(u) [MW]
1.2
0.8
500kW
0.4 u annual ≈ 7m/s
0.0
0 10 20 30
u [m/s]
Michael Hölling, WS 2010/2011 slide 10

13. Wind Energy I Resource wind
Is such a calculation realistic ? How does real wind behave ?
Wind velocity time series (20 days)
Michael Hölling, WS 2010/2011 slide 11

14. Wind Energy I Resource wind
Calculation of 10-minute averaged wind speed
Michael Hölling, WS 2010/2011 slide 12

15. Wind Energy I Resource wind
Calculation of 10-minute averaged wind speed
Michael Hölling, WS 2010/2011 slide 12

16. Wind Energy I Resource wind
Distribution of 10-minute averaged wind speeds
(u)
Michael Hölling, WS 2010/2011 slide 13

17. Wind Energy I Resource wind
Estimation of energy production based on wind distribution
(u)
Michael Hölling, WS 2010/2011 slide 14

18. Wind Energy I Resource wind
Estimation of energy production based on wind distribution
(u)
Michael Hölling, WS 2010/2011 slide 14

19. Wind Energy I Resource wind
Estimation of energy production based on wind distribution
E(u)
(u)
Michael Hölling, WS 2010/2011 slide 14

20. Wind Energy I Resource wind
Estimation of energy production based on wind distribution
E(u)
(u)
Michael Hölling, WS 2010/2011 slide 14

21. Wind Energy I Resource wind
Estimation of energy production based on wind distribution
E(u)
(u)
Michael Hölling, WS 2010/2011 slide 14

22. Wind Energy I Resource wind
Estimation of energy production based on wind distribution
E(u)
(u)
Michael Hölling, WS 2010/2011 slide 14

23. Wind Energy I Resource wind
Estimation of energy production based on wind distribution
E(u)
(u)
energy production:
N N
E= E(ui ) = counts(ui )/6 · P (ui )
i=1 i=1
Michael Hölling, WS 2010/2011 slide 14

24. Wind Energy I Resource wind
Comparison of energy production for mean wind speed and 10-
minute averaged wind speed distribution (example based on
data of 20 days):
u = 6.3m/s 244 kW
E = counts(< u >)[h] · P (< u >)
= 24 · 20 · 244 = 117120kW h
Michael Hölling, WS 2010/2011 slide 15

25. Wind Energy I Resource wind
E(u)
N N
E= E(ui ) = counts(ui )/6 · P (ui ) = 166, 920kWh
i=1 i=1
Michael Hölling, WS 2010/2011 slide 16

26. Wind Energy I Resource wind
Description of wind speed distribution
(u)
Michael Hölling, WS 2010/2011 slide 17

27. Wind Energy I Resource wind
Convert to probability density by normalization
Michael Hölling, WS 2010/2011 slide 18

28. Wind Energy I Resource wind
Distribution can be fitted by Weibull distribution
A = scaling parameter
k = form parameter
A=7
k = 2.59
Michael Hölling, WS 2010/2011 slide 19

29. Wind Energy I Resource wind
Weibull distribution
u [m/s]
Michael Hölling, WS 2010/2011 slide 20

30. Wind Energy I Resource wind
Wind speed variation with height
Atmospheric boundary layer (ABL)
Michael Hölling, WS 2010/2011 slide 21

31. Wind Energy I Wind field characterization
Meteorological approach:
logarithmic profile
roughness length for topographical effects
thermal effects
International Electrotechnical Commission (IEC) approach:
power law profile
standard for site assessment
Alternative approach:
stochastic analysis
high frequency data for better understanding
Michael Hölling, WS 2010/2011 slide 22

32. Wind Energy I Meteorological approach
Wind speed u (mean values) as a function of height z:
Logarithmic profile:
u* = friction velocity (typically between
0.1m/s and 0.5m/s)
k = von Karman constant, about 0.4
z0 = surface roughness length
Michael Hölling, WS 2010/2011 slide 23

33. Wind Energy I Meteorological approach
classes
3
2
1
0
Michael Hölling, WS 2010/2011 slide 24

34. Wind Energy I Meteorological approach
classes
3
2
1
0
Michael Hölling, WS 2010/2011 slide 25

35. Wind Energy I Meteorological approach
Influence of friction velocity u* on profile
Michael Hölling, WS 2010/2011 slide 26

36. Wind Energy I Meteorological approach
Influence of friction velocity u* on profile
Michael Hölling, WS 2010/2011 slide 27

37. Wind Energy I Meteorological approach
Thermal effects make ABL stable, neutral or unstable
Monin Obukhov
length
Michael Hölling, WS 2010/2011 slide 28

38. Wind Energy I IEC approach
Wind speed u (mean values) as a function of height z:
Power law profile:
z2
α needs to be fitted from data !
Velocity at height z can be determined by:
α
z z1
u(z) = u(z1 ) ·
z1
Commonly used for wind energy applications !
Michael Hölling, WS 2010/2011 slide 29

39. Wind Energy I Wind profile
What is the difference between the two approaches ?
Michael Hölling, WS 2010/2011 slide 30

40. Wind Energy I Wind profile
What is the difference between the two approaches ?
u(z2)
u(z1)
Michael Hölling, WS 2010/2011 slide 30

41. Wind Energy I Wind profile
What is the difference between the two approaches ?
u(z2)
u(z1)
Michael Hölling, WS 2010/2011 slide 31

42. Wind Energy I Site characterization / assessment
IEC demands information for site characterization:
annual mean wind velocity
parameters for Weibull distribution of 10-min averaged wind
speeds
annual mean wind profile
σ<u>10min
turbulence intensity Ti =
< u >10min
Michael Hölling, WS 2010/2011 slide 32

43. Wind Energy I Alternative approach
What happens in reality ?
Michael Hölling, WS 2010/2011 slide 33

44. Wind Energy I Alternative approach
What happens in reality ?
Michael Hölling, WS 2010/2011 slide 34