Wind energy I. Lesson 3. Wind field characterization
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This document discusses wind field characterization for wind energy applications. It covers topics such as wind measurements, wind field characterization, wind turbines and blades, wind power calculations, and estimating annual energy production from wind speed distributions. In particular, it examines using a Weibull distribution to model the wind speed probability density and calculates energy production based on the wind speed distribution and power curve of a wind turbine.
![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](https://image.slidesharecdn.com/13rdlesson-111024033415-phpapp02/85/Wind-energy-I-Lesson-3-Wind-field-characterization-9-320.jpg)
![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](https://image.slidesharecdn.com/13rdlesson-111024033415-phpapp02/85/Wind-energy-I-Lesson-3-Wind-field-characterization-12-320.jpg)
![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](https://image.slidesharecdn.com/13rdlesson-111024033415-phpapp02/85/Wind-energy-I-Lesson-3-Wind-field-characterization-24-320.jpg)
![Wind Energy I Resource wind
Weibull distribution
u [m/s]
Michael Hölling, WS 2010/2011 slide 20](https://image.slidesharecdn.com/13rdlesson-111024033415-phpapp02/85/Wind-energy-I-Lesson-3-Wind-field-characterization-29-320.jpg)
Wind energy I. Lesson 3. Wind field characterization
- 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