energy research center

´rieure ecole nationnale supe

´rieur institut supe

of the Netherlands

´ronautique et de l’espace de l’ae

´ronautique et de l’espace de l’ae

Wind energy: On the statistics of gusts and their propagation through a wind farm Emmanuel Branlard February 2009

ECN supervisor: Peter Eecen Supaero supervisor: Allan Bonnet

ECN-Wind-Memo-09-005

Contents

Introduction

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Notations

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I

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Wind analysis on ECN wind farm

1 The Energy research Center of the Netherlands 1.1 Petten site . . . . . . . . . . . . . . . . . . . . . . 1.2 ECN . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Mission of the ECN . . . . . . . . . . . . 1.2.2 History . . . . . . . . . . . . . . . . . . . 1.2.3 ECN units . . . . . . . . . . . . . . . . . . 1.3 EWTW site . . . . . . . . . . . . . . . . . . . . . 1.3.1 Presentation . . . . . . . . . . . . . . . . 1.3.2 Layout . . . . . . . . . . . . . . . . . . . . 1.3.3 The Nordex N80 wind turbine . . . . . . 1.3.4 The meteorological mast 3 (MM3) . . . .

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2 The wind, source of energy 2.1 From a natural resource to a source of energy 2.1.1 Origin of the wind . . . . . . . . . . . 2.1.2 Wind measurements . . . . . . . . . . 2.1.3 Power in the wind . . . . . . . . . . . 2.2 Wind models and classes . . . . . . . . . . . . 2.2.1 Vertical wind model . . . . . . . . . . 2.2.2 Qualifying the wind . . . . . . . . . . 2.2.3 Extreme wind speeds . . . . . . . . . . 2.3 Wind turbulence . . . . . . . . . . . . . . . . 2.3.1 Turbulence definition . . . . . . . . . . 2.3.2 Turbulence distribution . . . . . . . .

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13 13 13 13 14 14 14 15 17 18 18 18

II

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Gusts definitions and statistical analysis

3 Gusts description 3.1 Gust definitions . . . . . . . . . . . . . . . . . . . 3.1.1 Introduction . . . . . . . . . . . . . . . . 3.1.2 Example of gusts . . . . . . . . . . . . . . 3.1.3 Traditional definition and gust simulation i

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24 26 27 27 28 29 30 31 32 32 34

4 Gusts statistics 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 General statistics on gusts parameters . . . . . . . . . . . . . . . . . . . . 4.2.1 Density of probability of main parameters . . . . . . . . . . . . . . Rising and falling estimates HRR and HF R: . . . . . . . . . . . . Rising time dt: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Amplitude of the gust U : . . . . . . . . . . . . . . . . . . . . . . . Rise acceleration Acc: . . . . . . . . . . . . . . . . . . . . . . . . . Position: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gust amplitude U and relative amplitude DU : . . . . . . . . . . . 4.2.2 Gust amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Influence of the turbulence intensity . . . . . . . . . . . . . . . . . 4.2.4 Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.5 Acceleration of the gust . . . . . . . . . . . . . . . . . . . . . . . . 4.2.6 Duration of the gust . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Mean gust shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Theoretical mean gust shape based on isotropic turbulence theory 4.3.2 Validation with experimental data . . . . . . . . . . . . . . . . . . 4.3.3 Another way to tackle the mean gust shape problem . . . . . . . . 4.3.4 Gust vertical profile: wind speed and direction . . . . . . . . . . . 4.4 Summary of the gusts statistical study . . . . . . . . . . . . . . . . . . . .

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36 36 37 37 38 38 39 40 40 40 41 44 47 48 49 50 51 52 53 57 59

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3.1.4 IEC standard definitions . . . . . . . . . . . . . . . . . . . . . 3.1.5 Formalism associated with gusts . . . . . . . . . . . . . . . . Gusts detection methods . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Different methods, different results . . . . . . . . . . . . . . . 3.2.2 Peak-Peak procedure / velocity increment . . . . . . . . . . . 3.2.3 Peak-over-threshold procedure . . . . . . . . . . . . . . . . . 3.2.4 Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5 Velocity increment over threshold method . . . . . . . . . . . A suggestion of gust parameters definition and standardization . . . 3.3.1 General parameters . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Summary of gusts parameters - presentation of the database

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Gusts propagating through a wind farm

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5 Gusts propagation - overview of the method 5.1 Presentation of the wind farm . . . . . . . . . . . . . 5.1.1 The wind farm . . . . . . . . . . . . . . . . . 5.1.2 Data available and data used . . . . . . . . . 5.2 Hypothesis and method . . . . . . . . . . . . . . . . 5.2.1 First step: Gusts extraction . . . . . . . . . . 5.2.2 Selected gusts . . . . . . . . . . . . . . . . . . 5.2.3 Assessment of the wind field and propagation 5.2.4 Extraction of raw data . . . . . . . . . . . . .

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63 63 63 63 64 64 64 65 65

6 Gusts propagation results 6.1 Gust propagation speed . . . . . . . . . 6.1.1 Introduction . . . . . . . . . . . 6.1.2 Digression on the arrival time . . 6.1.3 Accurate position with the use of 6.2 Probability of detecting a gust . . . . .

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66 66 66 66 68 71

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6.3 6.4

IV

6.2.1 Restrictions and method . . . . . . . . . . . . . . . . . . . . 6.2.2 Longitudinal spread of a gust in a free stream . . . . . . . . 6.2.3 Lateral and vertical spread of a gust in a free stream . . . . 6.2.4 Longitudinal and lateral spread of a gust in a wake stream Example of gust propagation . . . . . . . . . . . . . . . . . . . . . Summary of the propagation results . . . . . . . . . . . . . . . . .

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On the relation between mechanical loads and gusts

7 Extreme loads 7.1 Introduction . . . . . . . . . . . . . . . . . . . . 7.2 Conventional method . . . . . . . . . . . . . . . 7.2.1 Overview and prospects . . . . . . . . . 7.2.2 Step by step description of the method .

71 72 72 75 78 81

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84 84 85 85 85

8 Load response to a gust 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Response below the rated wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Response above the rated wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Conclusion

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Acknowledgements

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Annexes

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A Examples of gusts propagation through a row of turbines

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B Determination of the wind spectrum

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C Digression on turbulence

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D Peaks and envelop detection

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E List of interesting gust events dates

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F An introduction to wind turbines

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G An introduction to blade design

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Index

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Bibliography

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List of Tables

1.1 1.2

Presentation of the companies located at Petten site . . . . . . . . . . . . . . . . . . . General information about the Nordex N80 wind turbine . . . . . . . . . . . . . . . . .

6 11

2.1 2.2

Typical surface roughness length useful for wind farm sites . . . . . . . . . . . . . . . Wind classes defining wind turbines classes . . . . . . . . . . . . . . . . . . . . . . . .

15 16

3.1 3.2

Wind classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gust parameters with their definitions for each algorithm and parameters stored in the database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4.1 4.2 4.3 4.4 4.5 4.6

Number of gusts detected per algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . Most probable values, and range of values that could be expected for some gust parameters Decreasing exponential regression coefficients for the density of probability of DU . . . Linear regression coefficients for the curves DU = f (W Smean ) . . . . . . . . . . . . . . Linear regression coefficients for the curves Acc = f (U ) . . . . . . . . . . . . . . . . . Linear regression coefficients for the curves τ = f (DU ) . . . . . . . . . . . . . . . . . .

37 38 41 44 49 50

6.1 6.2 6.3

Lateral and transversal spread of gusts for direction 2 . . . . . . . . . . . . . . . . . . Lateral and transversal spread of gusts for direction 3 . . . . . . . . . . . . . . . . . . Conditionnal probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73 75 77

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B.1 Number of 10 minute samples corresponding to each bin of wind speed for the year 2007.106 C.1 Number of occurrences of different bins of σ and U for 3 years of data at ECN test farm 112 C.2 Statistical moments m and s corresponding to the log normal distribution of the standard deviation σ for different bin of wind speed. . . . . . . . . . . . . . . . . . . . . . 113 E.1 Interesting events: IEC Correlation gusts, DU > 5 and Corr > 0.9 . . . . . . . . . . . 118 E.2 Interesting events: Velocity Increments gusts, DU > 6, T = 5 . . . . . . . . . . . . . . 119 E.3 Interesting events: POT A=6 gusts, DU > 7 . . . . . . . . . . . . . . . . . . . . . . . 120 G.1 Common operating conditions known before the blade design . . . . . . . . . . . . . . 125 G.2 Blade number and tip speed ratio, suggestions . . . . . . . . . . . . . . . . . . . . . . . 126

iv

List of Figures

1.1 1.2 1.3 1.4 1.5 1.6

View of Petten site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ECN turnover per unit in 2005 . . . . . . . . . . . . . . . . . . . . . . . . . . . Map of the Province Noord-Holland and a detailed map of test site EWTW polder of Wieringermeer[11] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Detailed map of the ECN Wind Turbine Test Station Wieringermeer[11] . . . . The five N80 wind turbines - Adaptation of a picture from Leo Machielse . . . The meteorological mast 3 - Adaptation of a picture from Erik Korterink . . .

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10 10 11 12

2.1 2.2 2.3

Wind direction convention with respect to the North . . . . . . . . . . . . . . . . . . . Wind direction distribution at ECN EWTW test site . . . . . . . . . . . . . . . . . . . Wind speed distribution, and cumulative distribution fitted with a Weibull function .

14 16 17

Two bad examples of gusts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . An example of gust fitting well the definition of the IEC Mexican-hat shape . . . . . Gusts that are far from the IEC definitions . . . . . . . . . . . . . . . . . . . . . . . . Gusts of particular shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A discrete gust event: a, amplitude; b, rise time; c, maximum gust variation; d, lapse time (inspired by [18]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Example of an extreme operating gust(a) and an extreme coherent gust (b) for Uhub = 25m/s, class IA , D = 80m, T = 10s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Definition of the velocity increment method for a moving window of length τ = 30s . . 3.8 Definition of the peak over threshold method for a threshold of 6 m/s . . . . . . . . . 3.9 Definition of the correlation method for τ = 20s and a correlation factor above 0.9 . . 3.10 Velocity increment over threshold method for τ = 10min and A =3 m/s . . . . . . . . 3.11 Illustration of the different HRR values - From left to right: HRR = 0.5, HRR > 0.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.12 Illustration of the different HFR values - From left to right: HF R = 0.5, HF R > 0.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22 22 23 23

4.1 4.2 4.3 4.4

39 40 42

3.1 3.2 3.3 3.4 3.5

4.5 4.6 4.7 4.8

Density of Probability of the gust absolute amplitude . . . . . . . . . . . . . . . . . . . Density of Probability of the gust relative amplitude . . . . . . . . . . . . . . . . . . . Strong correlation between the gust amplitude and the average wind speed . . . . . . Highlighting an affine relation between the relative gust amplitude and the average wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Turbulence intensity and average wind speed: influence of standard deviation on the gust relative amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Relative gust amplitude and turbulence intensity . . . . . . . . . . . . . . . . . . . . . The gust amplitude as function of the turbulence intensity . . . . . . . . . . . . . . . . Half Rise ratio and half fall ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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43 45 46 47 48

LIST OF FIGURES 4.9 4.10 4.11 4.12

Gust acceleration increasing with gust amplitude . . . . . . . . . . . . . . . . . . . . . Time spent over a threshold increasing with the wind speed . . . . . . . . . . . . . . . Theoretical mean gust shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mean gust shape - Comparison of theoretical results and experimental results for a bin of wind speed around 10m/s, and for two different amplitudes A = 3σ and A = 4σ . . Mean gust shape for different wind speed, comparison between theory and experiments Experimental mean gust shape - (U-Umean)/DU . . . . . . . . . . . . . . . . . . . . . Experimental mean gust shape - (U-Umean)/Umean . . . . . . . . . . . . . . . . . . . Experimental mean gust shape - (U-Umean)/sigma . . . . . . . . . . . . . . . . . . . . Mean shape of the wind speed at the three height locations 108m, 80m and 52m, when a gust is detected at height 80m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Logarithmic law fitting the vertical profile . . . . . . . . . . . . . . . . . . . . . . . . . Mean shape of the wind windection at the three height locations 108m, 80m and 52m, when a gust is detected at height 80m, so defining the mean “wind direction profile” of the gust. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49 50 51

5.1 5.2 5.3

Main dimensions and directions of the test wind farm . . . . . . . . . . . . . . . . . . Main direction of interest in the study of gust propagation . . . . . . . . . . . . . . . . Illustration of the plane wave hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . .

63 64 65

6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12

Pressure and velocity evolution through the actuator disk . . . . . . . . . . . . . . . . Determination of gust arrival time with the correlation method . . . . . . . . . . . . . Example of screen produced by our program to assess the propagation speed . . . . . Time obtained by correlation with comparison with estimated time . . . . . . . . . . . The test farm viewed from direction 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . Probability of seeing a gust in the lateral direction of the wind, 180m downwind . . . The test farm viewed from direction 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . Probability of seeing a gust in the longitudinal direction of the wind - exponential fit . Probability of detecting a gust - empirical function Pˆ . . . . . . . . . . . . . . . . . . . Example of gust propagation perpendicular to the row of turbines . . . . . . . . . . . Gust wind speed(left) and direction(right) at three different heights on MM3 . . . . . Gust wind speed at three different heights where a vertical delay is observed between each signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67 68 70 71 72 74 75 76 78 79 80

Annual wind speed distribution fitted with a 2 parameters Weibull distribution . . . . Conditional distribution of the wind standard deviation for a given wind speed U=5 m/s Cumulative distribution of the Flap moment - Influence of sigma - Bin of wind speed U=8.5 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cumulative distribution of the Flap moment - Influence of the wind speed - Sigma=1.25 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86 87

4.13 4.14 4.15 4.16 4.17 4.18 4.19

7.1 7.2 7.3 7.4

8.1 8.2 8.3

Evolution of the thrust with the wind speed[20] . . . . . . . . . . . . . . . . . . . . . . Response to a gust occuring below the rated wind speed . . . . . . . . . . . . . . . . . Response to a gust occuring above the rated wind speed . . . . . . . . . . . . . . . . .

A.1 A.2 A.3 A.4 A.5 A.6 A.7 A.8

Gust with a good lateral spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Good with a narrow lateral spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gusts propagating quite well through the row and turns off turbine 7 . . . . . . . . . Gusts propagating quite well through the raw and turns off turbine 7 - Power view . Gust propagating through the row of turbines, and turning off almost all turbines 7 Gust that turns off almost all turbines - Power output . . . . . . . . . . . . . . . . . A fast gust, well controlled by the pitch system . . . . . . . . . . . . . . . . . . . . . Pitch response to the wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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LIST OF FIGURES B.1 Power spectral density of the wind speed for different wind speed. . . . . . . . . . . . 107 B.2 Power spectral density of the wind speed for different heights : H=52m, H=80m, and H=108m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 B.3 Wind speed distribution at different heights: H=52m, H=80m, and H=108m . . . . . 108 C.1 p(uτ /σ) for different time scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 C.2 p(uτ ) for different time scales τ and different standard deviation values . . . . . . . . . 111 C.3 p(σ|u) for different bin of wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 D.1 Elementary mathematical functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 D.2 Mathematical operation defining an extreme above a threshold A . . . . . . . . . . . . 116 D.3 Example of a none smooth signal and different steps of the algorithm with a resolution of 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 F.1 F.2 F.3 F.4

Power curve - example of Turbine 6 . . . . . . . . . . Power coefficient - example of Turbine 6. . . . . . . . Definition of the 4 cross sections in the actuator disk Pressure and velocity evolution through the actuator

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122 122 123 123

G.1 3D representations of an ideal rotor without wake rotation . . . . . . . . . . . . . . . . 126

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Introduction

From wind turbines to gusts The design of wind turbine structures is determined by the nature of the wind field, and thus, knowledge of turbulent wind and its impact on loads is required. For pitch regulated turbines, the loads can be reduced by optimization of the regulation system after turbulence characteristics. Part of the turbulence, gusts are a relevant parameter to study the fatigue loading. According to the IEC 61400-1[29] standard, one of the design requirement for wind turbine is to resist to different extreme gusts. Extreme operating gust, or 50 year return period gust for instance are estimated to define the conditions the turbine have to satisfy. In order to perform loads simulation, an estimate of the mean gust shape[15] is needed. Nevertheless the turbulence is a sitespecific phenomenon, so that extreme gust or mean gust shape will also be dependent of the location of the wind farm. ECN test farm The Energy Research Center of the Netherlands is a dynamic environment for wind energy research, holding a strategic position between universities and industries. The Wind Energy unit has opened in 2003 an onshore test site for prototype wind turbines called ECN Wind turbine Test site Wieringermeer (EWTW). In addition to several prototypes, a row of five Nordex N80 wind turbines are equipped for experimental research and a 108m high meteorological mast has been built at proximity. The data measured by the turbine sensors combined with the meteorological mast, are validated and stored as “raw data”. An extensive validation and statistical treatment of these data is then peformed and stored in a database. In this study, the raw data will be manipulated with the use of the program R[7], [27], whereas the database data will be extracted using SQL statements. The results presented in this report come only from programs that have been written by the author, during the period of time assigned for the internship, separated in 200 R scripts, representing 10000 lines of code, with 15 Gb of results produced from the 100 Gb of “raw data”. Prospects and methods The focus of this study is the propagation of gusts through a row of wind turbines. To study this problem, it appeared necessary to clearly define the obscure notion of gusts. To study the propagation, some specific direction of the wind have to be selected. Instead of first selecting the wind direction, and then extract gust, it seems more relevant to first detect gusts in the wind, and then select interesting gusts. For this purpose, gusts detection algorithms have been developed to establish a database of gusts. The propagation results will be mainly obtained by a quantification of plots analyzed by eye by an operator. The difficulty of gusts detection in the wake of another turbine made difficult the ambition for further analysis such as the evolution of the gust amplitude as it propagates. Still, from the simple question of gust propagation, a lot of other analyses have been required and thus, were performed: turbulence spectrum by the mean of velocity increment method, wind speed spectrum, comparison between gusts detection algorithm, vertical profile of gusts, statistical analysis of gusts and their mean gust shape, etc. These site-specific results coming from the well equipped ECN test farm can be compared to other locations, increasing the knowledge of turbulent wind fields for the application in wind energy.

1

LIST OF FIGURES Contents This report is divided into 3 main parts. The first part entitled “wind analysis on ECN wind farm” will focus on the description of the wind farm, and will introduce the notions required for wind analysis. After this introduction, the “Gusts definitions and statistical analysis” part will try to gather all the different definitions that can be found in literature, and also suggest a standardization to unify these definitions, so allowing a study in parallel of different gusts detection algorithms.The algorithms being run through 3 years of “raw data”, a database of gusts is established, and statistical analysis can be performed. The results between theoretical mean gust shape and experimental shape will be compared. Once the definition of gusts is clear, their propagation through the ECN test farm is studied in part “Gusts propagating through a wind farm”. The gust propagation speed and the probability of detecting a gust is estimated. Eventually, the study of loads statistical methodology and load response to a gust is considered, even though the “Relation between mechanical loads and gusts” will be difficult.

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LIST OF FIGURES

Main notations and abbreviations

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X, Y, Z

System of axis attached to the wind

ρ D S P Cp z0 L Cl , Cd

Air density ≈ 1.225 kg/m3 Rotor diameter Rotor surface Power Power coefficient Surface roughness length Longitudinal length scale Aerodynamic coefficients

u v w u ˜ σ, W Sstd I W Dmean ¯ W Smean , U U , Umax DU A

Longitudinal wind speed Lateral wind speed Transversal wind speed Dimensionless wind speed Wind speed standard deviation (10 min sample) Turbulence intensity 10 minute average wind direction 10 minute average wind speed Gust absolute amplitude Gust relative amplitude Amplitude threshold

t0 tstart tend texpected tcorr τ Dt Acc 

Time of the maximum in the gust Gust detection starting time, for a given algorithm Gust detection ending time, for a given algorithm Estimate of gust arrival time Calculation by correlation of the gust arrival time Characteristic time parameter (of an algorithm) ¯ to U Estimated time required by the gust to rise from U Acceleration of the gust between tstart and t0 Relative error

EWTW IEC POT IECCorr VelocIncr HFR HRR WS WD T5 MM3

ECN Wind turbine Test site Wieringermeer International Electrotechnical Commission Peack Over Threshold method IEC Correlation method Velocity Increment method Half Fall Ratio Half Rise Ratio Wind speed Wind direction Turbine 5 Meteorological mast 3

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Part I Wind analysis on ECN wind farm

4

Contents

1

2

The Energy research Center of the Netherlands 1.1 Petten site . . . . . . . . . . . . . . . . . . . . . . . 1.2 ECN . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Mission of the ECN . . . . . . . . . . . . . 1.2.2 History . . . . . . . . . . . . . . . . . . . . 1.2.3 ECN units . . . . . . . . . . . . . . . . . . . 1.3 EWTW site . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Presentation . . . . . . . . . . . . . . . . . 1.3.2 Layout . . . . . . . . . . . . . . . . . . . . . 1.3.3 The Nordex N80 wind turbine . . . . . . . 1.3.4 The meteorological mast 3 (MM3) . . . . .

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The wind, source of energy 2.1 From a natural resource to a source of energy 2.1.1 Origin of the wind . . . . . . . . . . . 2.1.2 Wind measurements . . . . . . . . . . 2.1.3 Power in the wind . . . . . . . . . . . 2.2 Wind models and classes . . . . . . . . . . . . 2.2.1 Vertical wind model . . . . . . . . . . 2.2.2 Qualifying the wind . . . . . . . . . . 2.2.3 Extreme wind speeds . . . . . . . . . . 2.3 Wind turbulence . . . . . . . . . . . . . . . . 2.3.1 Turbulence definition . . . . . . . . . . 2.3.2 Turbulence distribution . . . . . . . .

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Chapter

1

The Energy research Center of the Netherlands 1.1

Petten site

This site is situated in the dunes near Petten, a village in the northern part of Holland. This location is shared between several firms as presented in table 1.1, and a view of the site is presented on figure 1.1 Table 1.1: Presentation of the companies located at Petten site The ECN is the largest research center in the Netherlands in the field of energy. At this moment ECN employs about 600 people on this sight.

The Nuclear Research and consultancy Group (NRG) is a daughter company of ECN, which deals with nuclear technology for energy, environment and health. It employs more than 300 people.

The Joint Research Centre (JRC) is a European institute. The JRC deals with various sciences topics, but focuses on the nuclear technology on this site, with the high flux reactor (HFR).

Covidien is the former Tyco Healthcare which separated from Tyco International. It is a $10 billion global healthcare products leader dedicated to innovation and long-term growth.

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CHAPTER 1. THE ENERGY RESEARCH CENTER OF THE NETHERLANDS

Figure 1.1: View of Petten site

1.2

ECN

The Energy research Center of the Netherlands is the biggest, independent, market oriented and innovative Dutch energy research institute. It investigates and develops technologies and products for a safe, efficient and environment-friendly energy supply. The ECN bridges the gap between research and real application, and is guided by the principle of a sustainable development.

1.2.1

Mission of the ECN

To develop high-level knowledge and technology for a sustainable energy system and transfers it to the market

1.2.2

History

• 1955: Started as RCN for nuclear research • 1975: Start of wind energy and coal research • 1978: RCN changed into ECN (general energy R&D) • 1985: Start of fuel cell research • 1990: Start of solar energy research • 1994: First biomass activities as part of coal research • 1995: Attention to building environment as part of solar research • 1998: NRG is founded for nuclear R&D As written in the ECN Annual Report 2007[1], the company has more than 600 employees on the Petten site and had a turnover of about 77.7 millions Euros in 2007 and a net result of about 2.5 millions Euros. It registered approximately five international patents each year. The research center maintains national and international strong co-operation with companies, universities and other research institutes. It publishes about six hundreds reports and other kind of publications each year.

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CHAPTER 1. THE ENERGY RESEARCH CENTER OF THE NETHERLANDS

Figure 1.2: ECN turnover per unit in 2005

This center targets various entities. The ECN concentrates on the knowledge and information demand of the government for policy preparation and evaluation, and for the realization of policy goals in the fields of energy, environment and technological innovations. It is partner of the business community for the development and implementation of products, processes and technologies, which are important for the transition to a sustainable energy supply.

1.2.3

ECN units

ECN Policy Studies offers public authorities, companies and civil society independent advice with respect to energy and environmental issues. Innovation in the field of policy studies focuses on the enhancement of the synergy between market forces and goals of sustainability. The multidisciplinary project teams provide consultancy services at the national, European and global level. Engineering & Services is the technical support and development group of ECN. This group of about 100 employees designs, engineers and realizes experimental installations, prototypes and high-tech components, conducts materials research, takes care of data acquisition, data processing and visualization and realizes scientific and technical software. Besides ECN, this group supports innovative institutes and companies. Energy Efficiency in Industry (EEI), one of the research units of ECN, concerns itself with the efficient use of energy, leading to energy savings, particularly in energy-intensive production processes. By focused knowledge and technological developments, EEI contributes to innovative solutions for the reduction of energy use and raw-materials use in industry. DEGO is the Dutch acronym for Renewable Energy in the Built Environment and constitutes one of the research areas within the Energy research Center of the Netherlands. DEGO studies the possibilities for application of renewable energy in buildings, both houses and utility buildings. ECN has performed research in the field of Intelligent Electricity Grids. With a group of approximately 15 specialists it has accumulated the knowledge required to achieve the transition to reliable, sustainable and cost-effective energy grids that are able to accommodate a large share (¿¿50%) of variable and decentralized sources. The Hydrogen and Clean Fossil Fuels unit develops visions and technologies for a future society which is partially hydrogen based, as well as for the transition to that society. The starting point is the largely fossil fuel based energy supply of today. The first point is to focus on technologies that will enable the reduction of the CO2-release caused by the use of fossil fuels which in combination with hydrogen will offer optimal performance. The Biomass, Coal & Environmental Research (BKM) unit focuses on two fields of study. Biomass and Coal contribute to a cleaner, less wasteful and more sustainable use of these two energy

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CHAPTER 1. THE ENERGY RESEARCH CENTER OF THE NETHERLANDS resources. Environment assesses the impact of human activities on air and soil quality and provides policy support. The Solar Energy unit offers a wide range of R&D activities on photovoltaic materials and processing technologies, as well as cell and module design. Its extensive facilities for solar cell processing and characterization are well suited to study almost all R&D issues currently relevant for the photovoltaic industry. Two main areas dominate current researches: crystalline silicon and thin-film photovoltaic technologies. The Wind Energy unit holds a strategic position between universities and industry covering all relevant wind energy disciplines. ECN’s research varies from long term and more fundamental research to high level consultancy for industry. The unit studies the theory and makes experiments in its various test sites. It has developed analytical tools such as wind farm and wind turbine design software. ECN and its strategic partner the Delft University share facilities such as blade fatigue testing rigs, experimental turbines to test advanced rotor concepts, wind tunnels, and mobile measurement sets for assessing local wind resources and for monitoring wind turbines. The work of this unit includes not only wind energy technique but also economic aspects and non-tangibles like environmental studies and training. This enables the unit to address all the development needs of participants in a comprehensive and integral way. The Wind Energy unit has opened in 2003 a test site for prototype wind turbines called ECN Wind turbine Test site Wieringermeer.

1.3

EWTW site

1.3.1

Presentation

The project will concern measurements of wind speed and direction from the ECN database. The studied wind turbines are in the ECN Wind Turbine test station Wieringermeer (EWTW )[11] . This test site has been created because the existing one in Petten was not equipped for the modern Mega Watt sized machines and local expansion at Petten is not possible. The EWTW is located in the North East of the Province Noord-Holland 35 km eastwards of ECN Petten (see fig.1.3). The test site is characterized by flat terrain, consisting of agricultural area, with single farmhouses and rows of trees. The lake Ijsselmeer is located at a distance of 2 km East of EWTW. The wind turbine test station consists of: • Four locations for prototype wind turbines with one 100m and one 108m high meteorological mast. • Five Nordex N80/2500 wind turbines; these wind turbines are equipped for experimental research including a third 108m high meteorological mast. • A measurement pavilion with offices and computer center for the measurements. • A scale wind farm with ten 10kW turbines and 14 meteo masts up to 19m height.

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Figure 1.3: Map of the Province Noord-Holland and a detailed map of test site EWTW in the polder of Wieringermeer[11]

1.3.2

Layout

The EWTW contains two rows of wind turbines; a row of five research Nordex N80 turbines and a row of four prototype turbines(see fig.1.4). In addition to these two rows some single wind turbines are also located near the research and prototype turbines. South of the row of prototype turbines a row of NEG Micon turbines is located. For wind measurements three meteorological masts are located at the EWTW; meteorological mast 3 (MM3 ) just south of the row of research turbines and meteorological masts 1 and 2 (MM1 and MM2) just south of the row of prototype turbines.

Figure 1.4: Detailed map of the ECN Wind Turbine Test Station Wieringermeer[11]

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CHAPTER 1. THE ENERGY RESEARCH CENTER OF THE NETHERLANDS The following study will concern the northern wind turbines, the Nordex N80, and the meteorological mast 3, further called MM3.

1.3.3

The Nordex N80 wind turbine

Figure 1.5: The five N80 wind turbines - Adaptation of a picture from Leo Machielse

The Nordex N80 wind turbine is a variable speed wind turbine. The principal information about the N80 is presented in the following table 1.2: Table 1.2: General information about the Nordex N80 wind turbine Type Power regulation Hub height Rotor diameter Rated power 2 Cut-in wind speed Wind speed for rated power Cut-out wind speed (10 min average)

1.3.4

3-blade rotor with horizontal axis pitch 80 m 80 m 500 kW 4 m/s 15 m/s 25 m/s

The meteorological mast 3 (MM3)

The third meteorological mast (MM3 ) has been erected in order to measure the wind conditions at hub height of the N80 wind turbines 5 and 6 at EWTW. Moreover, the mast is equipped to measure accurately numerous weather conditions and support the different research projects on the research turbines. Three triangular supports are installed in the mast at both 50.4m and 78.4m heights. Instrumentation was installed on those and at the top at 108m height. This meteorological mast has been functioning since October 2004. The sensors are connected to a data-acquisition system, where the signals are filtered, digitized and converted. An Ethernet connection allows the transportation of the data to a storage computer.

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CHAPTER 1. THE ENERGY RESEARCH CENTER OF THE NETHERLANDS

Figure 1.6: The meteorological mast 3 - Adaptation of a picture from Erik Korterink

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Chapter

2

The wind, source of energy A good understanding of the wind is required as it is obviously the main parameter influencing the power harvested by a wind turbine. Moreover, knowledge of the wind is required to define wind farm location and disposition, to assess the annual energy output and the structural loads that have to be supported by the whole system(blade, rotor, nacelle and tower).

2.1 2.1.1

From a natural resource to a source of energy Origin of the wind

Difference of heating in the atmosphere will cause difference of pressure. This gradient, will generate an air motion which will be influenced by gravitation, the inertia of air, and the friction with the earth surface. At the earth scale, the global motion of the wind follows this rule: the air rises at the equator and sinks at the poles. The part of the atmosphere where interactions with the earth surface have a strong influence is called the boundary layer. These interactions will have weaker influence as the height above ground increases. The wind is then mainly influenced by the rotation of the earth and large scale pressure gradients. This is called the geostrophic wind.

2.1.2

Wind measurements

The wind speed is generally measured with cups anemometers and the wind direction with vanes. Sonic anemometer are also used to determine the three components of the wind u,v,w. The average horizontal wind speed and direction(in degree) will be defined as follows: p W Sh = u2 + v 2 (2.1) 180 W Dh = atan(−u, −v) (2.2) π The Wind direction is by convention defined clockwise with respect to the north. Figure 2.1 illustrates a wind vector whose direction is 45◦ .

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CHAPTER 2. THE WIND, SOURCE OF ENERGY

Figure 2.1: Wind direction convention with respect to the North

2.1.3

Power in the wind

The main principle of wind turbines is to extract the kinetic energy from the air in order to convert it into mechanical energy. The Power present in a wind field of constant velocity U is: 1 1 P = mU ˙ 2 = ρSU 3 2 2

(2.3)

As we will further see, the maximum amount of power that can be extracted by a turbine from the wind, is around 59%, as defined by the Betz limit(cf. section F). In order to harvest more power, the air densityρ, the rotor surface S and the wind velocity U should be increased. • ρ: Commonly taken as 1.225 kg/m3 , ρ, decreases slightly with the height. Its small value compared to the density of the water, explained why the wind turbine are way bigger than hydro plants. This is the parameter which has the smallest influence on the power. • S: increasing the surface of the rotor is a relevant way to increase the power harvested by a turbine. Nevertheless, increasing the blade length will introduce structural constraints which will have a consequent cost for the manufacturer. • U : the cubic dependence of the power with respect to the wind speed, makes this parameter the most efficient to increase the power. Higher wind speed will be found at high altitudes, and at appropriate geographic areas.

2.2 2.2.1

Wind models and classes Vertical wind model

Logarithmic law The Shear stress τxz in the longitudinal direction, close to the earth surface can be expressed in two different ways (see [18], based on analysis of Wortman). In a first hypothesis, one can assume this stress is roughly constant near the surface: τxz = τ0 . This can be obtained by integrating the momentum equation: ∂τxz ∂p = (2.4) ∂x ∂z and later neglect the longitudinal pressure gradient. Another way to express this stress is by the use of the Prandtl mixing length theory, which provides a model to calculate the exchange of momentum in the flow, remembering that the turbulent shear stress in a turbulent flow is τxz = −ρu0¯w0 , where U = u + u0 and W = w + w0 are the longitudinal and vertical velocities. The mixing length l for a smooth surface can be written l = kz with k the von Karman’s constant. Prandtl mixing length theory then provides: ∂u ∂u , w0 = −l and thus: τxz = ρl2 u =l ∂z ∂z 0

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∂u ∂z

2 (2.5)

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CHAPTER 2. THE WIND, SOURCE OF ENERGY Equaling the two expressions of τxz , and integrating the velocity along z, yields the Logarithmic law : p   τ0 /ρ z (2.6) u(z) = ln k z0 p where z0 is the Surface roughness length. The ratio τ0 /ρ is called the Friction velocity, and is often noted u∗ A list of characteristic surface roughness length is provided in table 2.1. This theory has been applied to fit the wind speed found at three sensors, with different heights in the section 4.3.4.

Table 2.1: Typical surface roughness length useful for wind farm sites Type of terrain Calm open sea Blown sea Flat grassy plains Open farm land, few trees and building Small cities, forests

z0 (m) 0.0002 0.0005 0.01 0.03 0.7

Power law A convenient model for the vertical wind profile can be expressed with a Power law . Nevertheless, it is an empirical law in contrast with the previously described logarithmic law. In this model: u(z) ∝ z α (2.7) The power coefficient used is often α ≈ 0.16 onshore, and α ≈ 0.11 offshore, even though α is in practice highly variable and can depend on the reference wind speed and the surface roughness.

2.2.2

Qualifying the wind

Special care must be taken on the wind distribution before settling a wind farm. The wind speed distribution will largely determine the relevant locations for the turbines. The wind direction distribution will determined the disposition of the turbines to minimize the number of turbines operating in the wake of others. A turbine operating in the wake of another turbine will generally produce less energy due to the reduced wind speed and the increased turbulence. Figure 2.2 gives an example of wind distribution at the EWTW test site. Different conventions are used for the wind distributions. Usually bins of 30 degrees are used where the first sector, centered on 0, will be [−15◦ ; 15◦ ]. This is not the case on this figure.

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CHAPTER 2. THE WIND, SOURCE OF ENERGY

Figure 2.2: Wind direction distribution at ECN EWTW test site

Wind classes

Table 2.2 references the different wind classes defining the different class of turbines.

Table 2.2: Wind classes defining wind turbines classes Classes Reference wind speed Uref [m/s] Annual Average wind speed Uy [m/s]

I 50 10

II 42.5 8.5

III 37.5 7.5

IV 30 6

The Weibull distribution The wind speed distribution fluctuates during the year but also at a larger time scale. From one year to another the distribution can change, and this effects as to be taken into account for long-term power estimation. To qualify a wind distribution, the two parameters Weibull distribution is commonly used to fit the yearly data. Its cumulative distribution function F , and density of probability f are the defined as the following: “

−( U A)

k

”

F (U ) = 1 − e   k U k−1 −( U )k f (U ) = e A A A

(2.8) (2.9)

with k the shape factor usually between 1.4 for an inland location(e.g. Germany) and 3.5 for offshore. ¯ due to the value of the Γ A is the scale factor. We will always have A close to but smaller than U function and the values taken by k. For some specific test sites that don’t follow this distribution, a some of two weightened Weibull distribution is used. From the Weibull distribution we can analytically

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CHAPTER 2. THE WIND, SOURCE OF ENERGY ¯ ) and its standard deviation (σu ) by applying their definitions: get the average wind speed(U   Z ∞ 1 ¯ = U f (U )dU = A Γ 1 + U k 0      2 1 2 2 2 2 2 σu = E[U ] − E[U ] = A Γ 1 + −Γ 1+ k k

(2.10) (2.11)

¯ ≈ 0.89 A Due to the values of the gamma function and the range of values of k, the approximation U can be used. To fit an experimental distribution with the Weibull distribution, one can numerically solve the following system, or use the programming environment R[7] and its function f itdistr() :   1 ¯ U = AΓ 1+ (2.12) k
Γ 1 + k2 σu2
−1 = (2.13) ¯2 U Γ2 1 + k1 The experimental distribution and the Weibull distribution will then have the same statistical ¯ and σ, but not the same energy. The same method can be applied to obtain a fitted moments U R ¯ . Knowing the WS Weibull distribution of equal energy by using E = U 3 f (U )dU instead of U distribution will help to compare different wind farm sites, to assess the annual energy output(AEP), or determine statistically the extreme response over a certain return period (confer chapter 7). Figure 2.3 illustrates an annual wind speed distribution, using the data from the EWTW test site for the year 2007. A shape factor of 2 is quite common for the Netherlands. Note that the WS bins are 0.5 m/s bins, which is the convention for distribution curves.

Figure 2.3: Wind speed distribution, and cumulative distribution fitted with a Weibull function

2.2.3

Extreme wind speeds

A probability distribution of hourly mean wind speeds such as the Weibull distribution will yield estimates of the probability of exceeding any particular level of hourly mean wind speed. However, when used to estimate the probability of extreme winds, an accurate knowledge of the high wind February 2009

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CHAPTER 2. THE WIND, SOURCE OF ENERGY speed tail of the distribution is required, and this will not be very reliable since almost all of the data which were used to fit the parameters of the distribution will have been recorded at lower wind speeds. Extrapolating the distribution to higher wind speeds cannot be relied upon to give an accurate result. The extreme wind conditions may be characterized by a return time[6]: for example a 50 year gust is one which is so severe that it can be expected to occur on average only once every 50 years. It would be reasonable to expect a turbine to survive such a gust, provided there was no fault on the turbine. The extreme wind speeds and gusts may depend on the location of the wind farm, between flat grass land to mountain areas or offshore. The IEC(2005) standard[29], for example, specifies a reference wind speed Uref which is five times the annual mean wind speed. The 50 year extreme wind speed is then given by 1.4 times Uref at hub height. The annual extreme wind speed is taken as 75 percent of the 50 year value.

2.3 2.3.1

Wind turbulence Turbulence definition

Definition: Fast time-scale fluctuations of less than 10 minutes in the wind speed are associated with turbulence. The Reynolds number of the atmospheric wind speed is around Re ≈ 108 , which corresponds to a turbulent wind field. The wind speed can then be decomposed in a 10 minute averaged ¯10 and a turbulent fluctuation u ¯10 + u ˜, such that during a 10 minutes sample: u(t) = U ˜(t) velocity U Source of turbulence: The main causes of turbulence is the friction of the wind with the earth surface, and local fluctuations of temperature in the atmosphere. Thus, the turbulence will depend on the surface roughness z0 previously described (see 2.2.1). Model of turbulence: Various models of turbulence exist, taking into account the temperature, density, pressure and humidity of the air, and leading to differential equations that can be integrated numerically. Nevertheless, the space scale of such phenomena will lead to long calculation. Moreover, as it is difficult to model each parameter interdependence and to define initial and boundary conditions, statistical model of turbulence will be used. Turbulence intensity: To measure the level of turbulence, the Turbulence intensity factor I is used. It is generally defined for a time scale of 10 minutes. For an offshore wind farm one can expect a turbulence intensity around 12 %[9]. σu I= ¯ (2.14) U This definition can be applied to each component of the wind, defining: Iu , Iv and Iw . With the height, the effect due to the increase of wind speed is predominant so that the turbulence intensity decrease with the height.

2.3.2

Turbulence distribution

In order to assess the extreme loads the statistics of the wind amplitude and the wind turbulence should be known. Turbulent wind speed variations are often considered as Gaussian for easier applications. However, this approximation is not reliable for estimating the probability of a large gust within a certain period according to F. Boettcher and al.[13], and his previous work[12]. An analog study has been performed and the results are presented in annex C.

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Part II Gusts definitions and statistical analysis

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Contents

3

4

Gusts description 3.1 Gust definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Example of gusts . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Traditional definition and gust simulation . . . . . . . . . . . 3.1.4 IEC standard definitions . . . . . . . . . . . . . . . . . . . . . 3.1.5 Formalism associated with gusts . . . . . . . . . . . . . . . . 3.2 Gusts detection methods . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Different methods, different results . . . . . . . . . . . . . . . 3.2.2 Peak-Peak procedure / velocity increment . . . . . . . . . . . 3.2.3 Peak-over-threshold procedure . . . . . . . . . . . . . . . . . 3.2.4 Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5 Velocity increment over threshold method . . . . . . . . . . . 3.3 A suggestion of gust parameters definition and standardization . . . 3.3.1 General parameters . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Summary of gusts parameters - presentation of the database

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Gusts statistics 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 General statistics on gusts parameters . . . . . . . . . . . . . . . . . . . . 4.2.1 Density of probability of main parameters . . . . . . . . . . . . . . 4.2.2 Gust amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Influence of the turbulence intensity . . . . . . . . . . . . . . . . . 4.2.4 Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.5 Acceleration of the gust . . . . . . . . . . . . . . . . . . . . . . . . 4.2.6 Duration of the gust . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Mean gust shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Theoretical mean gust shape based on isotropic turbulence theory 4.3.2 Validation with experimental data . . . . . . . . . . . . . . . . . . 4.3.3 Another way to tackle the mean gust shape problem . . . . . . . . 4.3.4 Gust vertical profile: wind speed and direction . . . . . . . . . . . 4.4 Summary of the gusts statistical study . . . . . . . . . . . . . . . . . . . .

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21 21 21 22 23 24 26 27 27 28 29 30 31 32 32 34

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36 36 37 37 41 44 47 48 49 50 51 52 53 57 59

Chapter

3

Gusts description Why studying gusts ? The verification of the structural integrity of a wind turbine structure involves analyses of fatigue loading as well as extreme loading arising from the environmental wind climate. Due to their brutal and fast change in the wind speed, gusts have a predominant role in fatigue load assessments. With the trend of persistently growing turbines, the extreme loading is becoming relatively more important, and thus, complexes the blade design.

3.1 3.1.1

Gust definitions Introduction

Several approaches in the description of gusts lead to several definitions of a gust. The scope of this section will be to try to gather the common definitions found in standards and reference literature. Attention have to be paid because each definition will be associated with different parameters and will lead to different results. It is generally accepted that gusts and turbulence are observed over time intervals between 1s and 10 minutes. As a results of this, 10 minutes averaged data, commonly used in wind turbine study, cannot be taken into account. Smaller time scales must be used, and sometimes “raw data”, none averaged data, will be studied directly. In the case of the ECN test farm, data are sampled at various frequencies, the minimum, 4Hz, will be used. The most simple and maybe the only definition that should be given is the following: a Gust is a short-term wind speed variation within a turbulent wind field. From this, an extreme case of gust can be drawn where the wind speed suddenly goes up and down to reach the average wind speed again. A canonical example is the so-called “Mexican-hat” gust shape, as it is presented in figure 3.5. Nevertheless, we will see in the following chapter that analyses on the mean gust shape will provide us with different shapes. In other cases, one can focus on events where the wind speed goes up really fast. When the acceleration of the wind is important, leading to high wind speed in a short time, we qualify the gust as a “Front”. This can happen at a short time-scale, but also at a longer scale such as 5 to 10 minutes. Confusion is often made between these long-term events and gusts. But, as the “short-term” aspects is essential in the gust definition, long-term fronts and gusts will be studied and analyzed differently. The word Squall will then be preferred to qualify this long-term events. Such an example of long-term front is shown on figure 3.1. These phenomena can be very dangerous for the turbine. The wind is evolving too fast for the turbine to adapt to its environment. Eventually, attention is often centered on positive gusts as they are considered more dangerous, but fast Negative gust can also imply sharp increase of loads. As a result of this, the definitions that follow which will describe positive gusts, could be simply adapted to negative gusts.

21

CHAPTER 3. GUSTS DESCRIPTION

3.1.2

Example of gusts

(a)

(b)

Figure 3.1: Two bad examples of gusts. a)A front detected at ECN test farm on July 2007 which has a too large time-scale to be considered as a gust ; b) An interesting event, but of time length of 4 minutes which is also too long

Figure 3.2: An example of gust fitting well the definition of the IEC Mexican-hat shape

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(a)

(b)

Figure 3.3: Gusts that are far from the IEC definitions . a) A gust starting at high wind speed instead of the constant average wind speed. An interesting negative gust can be see on this plot ; b) A gust ending at high wind speed instead of the constant average wind speed.

(a)

(b)

Figure 3.4: Gusts of particular shapes. a) A gust with two-spires ; b) A really fast front

3.1.3

Traditional definition and gust simulation

An extreme and canonical gust shape is the famous “Mexican hat” shape. Its sudden change in wind speed is likely to cause extreme change in loads. To characterize this kind of gust, one can measure the parameters described on figure 3.5, where notations were borrowed to J.F. Manwell et al. [18]. These parameters are: a, amplitude; b, rise time; c, maximum gust variation; d, lapse time. In this February 2009

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CHAPTER 3. GUSTS DESCRIPTION definition, the wind speed should go back at the end of the gust to the average speed.

Figure 3.5: A discrete gust event: a, amplitude; b, rise time; c, maximum gust variation; d, lapse time (inspired by [18])

An analytical function of a perfectly symmetric Mexican-hat can be the following wavelet function[17], used in [16] to asset critical wind speed:
2 1 ψ(t) = p 1 − t2 e(−t /2) Γ(5/2)

(3.1)

Simulation of gust Recalling our first definition, a Gust is a short-term wind speed variation within a turbulent wind field. This definition allows a lot of flexibility concerning the gust shape. Numerical gusts are simulated using an autocorrelation function of a theoretical spectrum, which defines a base for the mean gust shape[15]. Stochastic fluctuations are then added to this mean gust shape. This autocorrelation should be close to the one found in experimental wind. Still, other spectrum can be selected, and this will lead to different shapes of gusts. In this way, by simulation you can force a certain shape.

3.1.4

IEC standard definitions

Standardization of gust definition has been performed by IEC work groups. From the 2005 IEC standard [29] five extreme wind conditions are described: • Extreme operating gust (EOG): a decrease in speed, followed by a steep rise, a steep drop, and a rise back to the original value. The gust amplitude and duration vary with the return period. (see details below) • Extreme direction change (EDC): this is a sustained change in wind direction, following a cosineshaped curve. The amplitude and duration of the change once again depend on the return period. • Extreme coherent gust (ECG): this is a sustained change in wind speed, with a cosine-shaped curve but ending on a constant wind speed which corresponds to an increase of Ucg compared to the wind speed before the gust. The standard magnitude is Ucg = 15 m/s. (see details below)

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CHAPTER 3. GUSTS DESCRIPTION • Extreme coherent gust with direction change (ECD): simultaneous speed and direction transients similar to EDC and ECG. • Extreme wind shear (EWS): a transient variation in the horizontal and vertical wind gradient across the rotor. The gradient first increases and then falls back to the initial level, following a cosine-shaped curve. Extreme operating gust definition The extreme operating gust is an example of symmetric Mexican-hat like gust which should occur while the turbine is operating. An example of EOG is given on figure 3.6. The equation of an extreme operating gust is:      2πt U ¯ (z) − 0.37 Ugust sin 3πt 1 − cos for 0 ≤ t ≤ T (3.2) T T u(z, t) =  ¯ (z) U otherwise (3.3) where the hub height gust magnitude Ugust is defined as: (

σ1 1 + 0.1

Ugust = min 1.35 (Ue1 − Uhub ) ; 3.3 with: Ue1 (z)

=

Ue50 (z)

=

σ1

=

D Uref Iref

0.8 Ue50 (z) 1.4 Uref



z

!) (3.4)

D Λ1

the extreme wind speed with a recurrence period of 1 year

0.11

the extreme wind speed with a recurrence period of 50 years

zhub

Iref (0.75 Uhub + 5.6) Rotor diameter Reference wind speed at 15 m/s(see tab.3.1) Expected turbulence intensity at 15 m/s(see tab. 3.1)

And the turbulence scale parameter:  Λ1 =

0.7 z

z ≤ 60m

(3.5)

42m

z > 60m

(3.6)

Table 3.1: Wind classes Classes Annual Average wind speed Uy [m/s] Reference wind speed Uref = 5 Uy [m/s]

I 10 50

II 8.5 42.5

III 7.5 37.5

IV 6 30

(a) Reference wind speed

Categories of turbulence A(high) B(medium) C(low)

Turbulence intensity Iref [] 0.16 0.14 0.12

(b) Reference intensities at 15 m/s

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CHAPTER 3. GUSTS DESCRIPTION Extreme coherent gust definition Focusing on the sudden increase of wind speed, the extreme coherent gust is defined by the IEC with a cosine function. If Ucg defines the magnitude of the gust, then:  ¯ (z) U t U t0 /

u(t0 ) = max {u(t)} t∈IG

(3.23) (3.24)

tstart is the first instant where the wind speed exceeds the threshold, and tend the last one, such that IG = [tstart ; tend ]. t0 is the time of the maximum between tstart and tend

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Figure 3.8: Definition of the peak over threshold method for a threshold of 6 m/s

3.2.4

Correlation

The Correlation consists in correlating a reference signal with the data. In this study, gusts of the shape of the IEC extreme operating gust have been investigated. This method is independent of the amplitude of the reference signal. This is convenient because several relative amplitudes will be found. But on the other hand, a lot of gusts of small amplitude can then be detected. For this reason, only gusts of a relative amplitude above a certain threshold will be picked up. In this study, a threshold of 2m/s was chosen. As correlation can only be done between signals of the same size, only gusts of the size duration τ of the reference signal will be found. In this document, gusts with a correlation factor above 0.8 compared to the reference signal have been selected. tstart is the first instant where the wind speed exceeds the threshold, and tend the last one, such that IG = [tstart ; tend ]. t0 is the time when the correlation coefficient is maximum during the short time where the correlation coefficient is above the chosen threshold (for instance 0.8). tstart and tend are then respectively defined as t0 − τ /2 and t0 + τ /2. The correlation method is illustrated on figure 3.9

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Figure 3.9: Definition of the correlation method for τ = 20s and a correlation factor above 0.9

3.2.5

Velocity increment over threshold method

The velocity increment over threshold method, can be useful to detect fronts, because the detection starts as soon as an acceleration is over a certain threshold and stops as soon as the acceleration stops being above this threshold. In comparison with the velocity increment method, there is also a constraint on the time length of the window, but an other constraint is added concerning the amplitude of the window, so defining a acceleration threshold. By choosing a moving window of length 10 min and and an amplitude of 3 m/s, one can detect long time scale fronts. This is illustrated on figure 3.10.

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Figure 3.10: Velocity increment over threshold method for τ = 10min and A =3 m/s

3.3

A suggestion of gust parameters definition and standardization

In order to compare the gusts detected by the different algorithms, to store their parameters in a database, and to be able to perform statistics over the different gust parameters, standardization of gust parameters should be done. The notation introduced here will be in harmony with the previous one, and with all the following occurrences in this document.

3.3.1

General parameters

On the use of ten minutes statistics 10 minutes statistics are commonly used in wind energy, but most of the time, they are available in table form with data for consecutive 10 minutes samples. As the wind can have important fluctuation in 10 minutes, most of the time there will be a discontinuity between two values for two consecutive samples. For a gust occurring just at the end of a sample, say at 12:09, which of the two samples value is the more representative of the 10 minute average wind speed, 12:00-12:10 or 12:10-12:20? To solve this problem, a centered-10-minute-Moving-averaging method is used. Explicitly, given a time of occurrence of a gust t0 , the 10 minute sample used for the statistics data will be [t0 − 5min; t0 + 5min]. Wind speed and direction average and standard deviation are calculated for this 10 minute period and will be written: Average wind speed Wind speed standard deviation Average wind direction Wind direction standard deviation

¯ W Smean , U W Sstd , σ W Dmean W Dstd

Gust time labels, gust amplitude and acceleration Two different amplitudes are here defined, the gust absolute amplitude, and the gust relative amplitude. The gust relative amplitude is indeed an interesting parameter as it really illustrates the sudden increase of wind speed.

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CHAPTER 3. GUSTS DESCRIPTION Time of occurrence of the gust Time of starting detection of the gust Time of ending detection of the gust Gust absolute amplitude Gust relative amplitude Gust rise acceleration

t0 tstart tend U = u(t0 ) ¯ DU = U − U U −u(tstart) Acc = t0 −tstart

Gust rising time, HRR and HFR An interesting suggestion to assess the length of a gust, is to use the acceleration. In many algorithms, an estimate of the acceleration is made, without knowing exactly when the gust begins. Of course a reasonable amount of points is needed before the maximum of the gust to assess its rising acceleration. This problem will mostly be found for the POT algorithm, and a safe assessment method will be implemented. In this section, we will assess that a good estimate of the rise acceleration is known. • The Gust rising time Dt is defined as the time that it would take to the wind to go from the ¯ to the maximum of the gust U at a constant acceleration Acc. Which can average wind speed U be translated as: DU DU Dt = or Acc = (3.25) Acc Dt • The Half Rise Ratio is an estimate of how the gust is really following the constant rise acceleration. See figure 3.11 for an illustration. Its definition is: ¯ mean {u(t) / t ∈ [t0 − Dt; t0 ]} − U DU

(3.26)

• The Half Fall Ratio is an estimate of how the gust is really following the constant fall acceleration. See figure 3.12 for an illustration. Its definition is: ¯ mean {u(t) / t ∈ [t0 ; t0 + Dt]} − U DU Gust rising time Half Rise Ratio Half Fall Ratio

(3.27)

Dt HRR HF F

Even though it might appear anecdotal for the reader, these three definition are useful to select gust of a specific shape and specific length independently of the algorithm. The values of HRR are interesting if they are compared to the HF R. If the two values are close, the gust is likely to be symmetric. If HRR is close to zero or even negative, it means that the acceleration value has been underestimate. Thus, this gust have a high acceleration, and then represent a nice front. In the contrary, is HRR is close to one, the gust might not have a nice shape, and stayed probably a long time above the mean wind speed. Thus, this kind of gust are not likely to be compared with the Mexican hat shape. The HF R is even more interesting, because it qualifies what is happening after the maximum of the gust is reached. Close to 0.5, the wind speed will go down as fast as it rises. Close one and above, the wind speed is not likely to go down to the mean wind speed. And eventually, close to or under zero, the gusts is falling faster than it raised.

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Figure 3.11: Illustration of the different HRR values - From left to right: HRR = 0.5, HRR > 0.5

Figure 3.12: Illustration of the different HFR values - From left to right: HF R = 0.5, HF R > 0.5

3.3.2

Summary of gusts parameters - presentation of the database

In order to select easily gusts on different criteria, such as the average wind speed, the amplitude, or the algorithm chosen, a database has been created. The database has been created based on the 4Hz sampled data that are available at ECN. As each algorithm provides different kind of gusts, the standardization previously described was necessary. Table 3.2 lists the different parameters used in the database, and thus summarizes most of the parameters chosen to qualify gusts.

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CHAPTER 3. GUSTS DESCRIPTION Table 3.2: Gust parameters with their definitions for each algorithm and parameters stored in the database ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Abbr Y M D H m s W Smean W Dmean W Sstd W Dstd U Dt Acc DU HRR HF R Algo τ A wd id idstart idend Did

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Variable name Year Month Day Hours Minutes Seconds 10 min WS avg 10 min WD avg 10 min WS std 10 min WS std WS amplitude Rising time = DU/Acc S[tstart ] Acceleration = U −W t0 −tstart Amplitude = U − W Smean Half Rise Ratio Half Fall Ratio Algorithm ID Caract. time for Algo Caract. parameter for Algo avg wd during the gust Indice Starting indice Ending indice Caracteristic length

Units [years] [months] [days] [h] [min] [s] [m/s] [deg] [m/s] [m/s] [m/s] [s] [m/s/s] [m/s] [.] [.] [.] [s] [m/s] [deg] [.] [.] [.] [.]

35

POT t0 = tmax ” ” ” ” ” around t0 ” ” ” at t0

IEC Corr t0 = tcorr ” ” ” ” ” around t0 ” ” ” at t0

Veloc.Incr. t0 = tmax ” ” ” ” ” around t0 ” ” ” at t0

1 tstart − tend Threshold

2 τIEC Correlation

3 τ Threshold

idmax

idcorr

idend

idstart − idend

idstart − idend

idstart − idend

Emmanuel Branlard

Chapter

4

Gusts statistics 4.1

Introduction

Almost all algorithms presented in section 3.2, have been run through the raw data for the three available years 2006, 2007 and 2008, representing a total of 31 months of 4 Hz wind data. The different method will further be compared in order to point out the differences in the resulting gusts. Table 4.1 present the number of gusts detected and thus available in the database. For each gust, the parameters presented in table 3.2 are available, together with a sample of wind data of length 3 Dt and a time scaled sample, both centered on the maximum of the gust. The scaling method used for this last sample will be presented in this chapter. From the database, it will be easy to select specific gusts with parameters in a certain range. From the time-scaled samples, an averaging can lead to an assess of the mean gust shape. General statistics of different gusts parameters will first be presented in this chapter, and in a second time, the focus will be on the mean gust shape. It has to be mentioned that the functionality of the R language has been really useful for these statistical analysis, even if specific function have been written instead of using its useful statistic toolbox[23]. Method of bin To perform statistical analyses along all the data the Method of bins will be chosen. Assuming we want to plot a parameter Y with respect to another parameter X, the scatter of points with coordinates (xi , yi ) might be really dense and with a large spread due to the important amount of data. Intervals of same length δx are defined and so called bins. For each bin b, the point plotted (xb , y b ) will be the mean point of all the data available in this bin. If the bin considered is [xb0 − δx/2 ; xb0 + δx/2], this could be formalized as: n o xb = mean xi / xi ∈ [xb0 − δx/2 ; xb0 + δx/2] (4.1) n o y b = mean yi / xi ∈ [xb0 − δx/2 ; xb0 + δx/2] (4.2) Attention has to be paid on the fact that xb0 , which is the center of the bin, and xb , which is the representative abscissa point of the bin, are distinct, even though they should be really close for a large amount of data. Remark about the method In our case some bins might contain really large amount of data such as 20 000 points for instance. The scatter will be sometimes really dense and wide spread around the data obtained by the method of bin. As a result of this, one has to be careful before drawing any conclusions. Nevertheless, as a lot of data are still present around the mean, the binned value is still a good and reliable estimate. Moreover, as the results will always show the same trend for the different gusts found by the different algorithms, one can be more comforted to conclude. Most of the bins-plots will be printed for several methods, and attached with smaller plots showing the scatter of points. 36

CHAPTER 4. GUSTS STATISTICS Standard deviation The Standard deviation as an “error bar plot” can also be displayed. Once again, one have to be careful on its definition. In the program R and Octave(or Matlab), the standard deviation for a population xi is defined as: v uN uX t (xi − x ¯ )2 (4.3) i=1

whereas the probabilistic definition is: v u N u1 X t (xi − x ¯)2 N

(4.4)

i=1

But, as it not an unbiased estimator for the population variance σ 2 , the “bias-corrected” standard deviation[19] should be used: v u N u 1 X t (xi − x ¯)2 (4.5) N −1 i=1

Table 4.1: Number of gusts detected per algorithm Algorithm IECCorr T=5s T=10s T=20s T=30s T=60s Total VelocIncr T=5s T=10s T=20s T=30s Total POT A=2m/s A=4m/s A=6m/s Total

4.2 4.2.1

Gusts

Months

Gusts/Month

28734 52025 47419 40797 24840 193815

31.00 31.00 31.00 31.00 31.00 31.00

926.90 1678.23 1529.65 1316.03 801.29 6252.10

46686 48374 49413 49689 194162

12.00 12.00 12.00 12.00 12.00

3890.50 4031.17 4117.75 4140.75 16180.17

117324 20709 1306 139339

12.00 31.00 31.00 24.67

9777.00 668.03 42.13 5648.88

General statistics on gusts parameters Density of probability of main parameters

As gusts can take a lot of different forms, it is interesting to see what are the most probable values for each parameters. Some parameters will be presented here just for the reader to get accustomed with the different methods and also see in which way these parameters can be used to select specific gusts. Table 4.2 compares the different probability results obtained by the algorithms. The most probable value is referred as column max, and the interval in which the density of probability is over a certain February 2009

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CHAPTER 4. GUSTS STATISTICS threshold is referred as column I. The threshold chosen corresponds to 0.05% of the maximum density value.

Table 4.2: Most probable values, and range of values that could be expected for some gust parameters HRR max

HFR max

Rising time max I

U

Acc

Position I

max I max I IECCorr T=5 0.5 0.55 8 [4;22] 12 [6;24] 0.25 [0.05;0.95] 0.5 T=10 0.45 0.5 8 [4;22] 12 [6;24] 0.25 [0.05;0.75] 0.5 T=20 0.3 0.35 12− [6;25]− 12 [6;24] 0.18+ [0.05;0.5]+ 0.5 − − + + T=30 0.2 0.2 15 [10;38] 12 [6;24] 0.15 [0.05;0.35] 0.5 POT POT2 0.45 0.65 8 [4;28] 12 [6;26] 0.1 [0.05;1.2] [0.4 ; 0.6] POT4 0.45 0.68 8 [4;28] 18 [9;32] 0.1 [0.05;1.2] [0.4 ; 0.6] POT6 0.55 0.75 8 [4;28] 26 [12;38] 0.1 [0.05;1.2] [0.4 ; 0.6] VelocIncr T=5 0.55 0.8 4 [2;8] 7 [2;20] 0.35 [0.05;1.2] [0.9 ;1] T=10 0.5 0.75 5 [3;11] 7 [2;20] 0.2 [0.05;0.75] [0.9 ;1] T=20 0.35 0.65 8− [3;20]− 7 [2;20] 0.18+ [0.05;0.5]+ [0.9 ;1] − − + + T=30 0.35 0.55 13 [3;28] 7 [2;20] 0.08 [0.05;0.4] [0.9 ;1] max: value corresponding to the maximum of the Density of probability I: main interval (interval where the density of probability is above 1/20th of the maximum density)

Rising and falling estimates HRR and HF R: The Half Rise Ratio(HRR) is an estimate of how the gust is rising compared to a constant acceleration slope between tstart and tend . Its values are interesting if they are compared to the Half Fall Ratio(HF R). If the two values are close, the gust is likely to be symmetric. Moreover, if the HRR is close to 0.5, it means the estimated rising time corresponds well to the real rising time. If the HRR is smaller than 0.5, it means the rising time is in reality smaller and thus the acceleration bigger than estimated. From a quick view we can see that the gust is always falling slower than it is rising. For the correlation method where we force it to be symmetric, there are slight differences, but for the velocity increment method where nothing is specified after the maximum of the gust, the difference between the rise and the fall is clearly noticeable. We can notice that the longer the gust will last the sharper its rising shape will be in the sense that it would be closer to a front shape than a constant slope. This is the case for the algorithms IECCorr T=20s, T=30s, and VelocIncr T=20s and T=30s. As a result of this, the values of the acceleration and rising time for this algorithm should be interpreted carefully because they are different from the one expected and stored in the database. The gust is always falling slower than it is rising. The longer the gust will last the sharper its rising shape will be in the sense that it would be closer to a front shape than a constant slope. Rising time dt: Method comparison: The correlation method, executed for different τ , detects gusts of various Rising time with an overall range of [5s; 38s] bigger than the other methods. The correlation method selects gusts that have the same duration than the reference signal. As a result of this, the higher τ is chosen, the longer the gust will last, and thus, the longer it will take to rise till its maximum. The same kind February 2009

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CHAPTER 4. GUSTS STATISTICS of result is confirmed for the velocity increment method which is also an algorithm dependent on a time parameter. The gust rising time will then be close to τ /2. Moreover, the correlation method also specifies a certain shape and thus restricts the interval of values of the acceleration, which results in a restriction in the rising time also. In this sense the correlation method is more selective for the rising time. The POT method provides rising time mainly in the range [5s; 18s], and this, independently of the threshold chosen. As the velocity increment does not select gusts above a certain threshold, really sharp acceleration in the wind speed can be found, and thus, the gusts rising time can be really low. Global remarks: These results are reassuring in the sense that the different algorithms detect structures with a rather small duration. The correlation and the velocity increment method are selective due to their dependence on a time factor τ , whereas the POT method is likely to provides gust of a duration larger than 45s. In this sense the correlation method is more selective for the rising time than the POT method. Amplitude of the gust U : As no threshold has been imposed to the velocity increment method, really small gusts are detected so that the density of probability of the gust amplitude will be close to the distribution of the average wind speed, often represented by a Weibull distribution. By introducing a threshold condition, the other methods shift this distribution by focusing on amplitude values above the average wind speed(see figure 4.1). One has to remember that a threshold condition of 2m/s has been added to the IECCorr method, in order to avoid an important amount of small gusts. Interesting gusts with a high amplitude compared to the average wind speed will more likely occur at high wind speed. This is due to the relation between the relative amplitude and the average wind speed.(see fig. 4.2) For instance a lot of the gusts detected by the POT method for DU > 6 occur at the limit of the cut-out wind speed.

Figure 4.1: Density of Probability of the gust absolute amplitude

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CHAPTER 4. GUSTS STATISTICS Rise acceleration Acc: Time dependent methods will be more likely to provide high acceleration if the time constant chosen is small. Indeed, for small time constant the range of acceleration values is wider. For high time constants, high accelerations have a very low probability of occurring because gusts detected will most of the time have a small amplitude. On the other hand, the POT method which is not time dependent, allows a bigger range of acceleration. Position: These results are rather anecdotal and their needs came from the question of the mean gust shape. Indeed, in order to obtain a mean gust shape, gusts are most of the time centered on their maximum value so that the resulting mean gust shape is a nice peak. If this operation is not performed, and if the center used is the middle of the time interval where the gust is above a threshold, the POT method will give a mean gust shape that has two peaks centered around the middle.The velocity increment method will also provide different results for the mean gust shape as we will further see in section 4.3. Indeed, it is a method that only focuses on the wind speed rise. From the definition of tstart and tend given in section 3.2.2, it seems obvious that the maximum, between these two times defining in this case the rising interval, will be really close to tend . Gust amplitude U and relative amplitude DU : The previous table 4.2 presented the Absolute amplitude U of the gust and its density of probability is plotted on figure 4.1. Nevertheless, we saw that the Relative amplitude is also determinant for the qualification of gusts. Figure 4.2 present the density of probability of this parameter. The selection criteria of POT method, based on the relative gust amplitude can clearly be seen. Table 4.3 suggests regression coefficient for these curves, by fitting them with an negative exponential.

Figure 4.2: Density of Probability of the gust relative amplitude

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Table 4.3: Decreasing exponential regression coefficients for the density of probability of DU Algorithm a b ln(b) IECCorr T=5s 22.18 0.25 -1.38629 POT A=2 m/s 19.38 0.27 -1.30933 POT A=4 m/s 103.6 0.32 -1.13943 POT A=6 m/s 247.13 0.39 -0.94161 VelocIncr T=10s 6.54 0.36 -1.02165 VelocIncr T=20s 8.81 0.34 -1.07881 P (DU > 2) = ea ln(b) R: correlation factor of the regression

4.2.2

R2 1 1 0.99 0.96 0.95 0.98

Gust amplitude

By binning the values of the gust amplitude with respect to the average wind speed, we obtain a straight line due to the fact that a lot of gusts have just a small amplitude above the average wind speed (see figure 4.3). As defined by the correlation and POT algorithms, the minimum threshold accepted for a gust is 2 m/s above the mean wind speed. As a result of this, most of the gusts found will have an amplitude just above this threshold as illustrated by the density of probability of DU (figure 4.2). This explains the parallel behavior observed with an offset of 2m/s, 4m/s and 6m/s, when ¯ . We will further use either the average wind the amplitude of the gust is binned with respect to U speed, either the gust amplitude for our plots, as these values are linearly related. An affine relationship close to identity exists between the average wind speed and the absolute amplitude of the gust

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(a)

(b)

Figure 4.3: Strong correlation between the gust amplitude and the average wind speed. Figures a) and b) have the exact same scales. Figure b) represents the scatter of points obtained with the IECCorr method, for a characteristic time T=5s (28680 gusts). The density of probability of each variable is represented against each axis.

It clearly is more relevant to study the relative gust amplitude with respect to the average wind speed. The binned results are plotted on figure 4.4 and a linear approximation of the curves is suggested in table 4.4. An interesting result is coming out from this plot. The relative amplitude of the gust seems to be well correlated with the average wind speed. All the methods based on selection of gusts above a certain threshold agree with a same slope for this correlation. Nevertheless the velocity increment method which includes really small rise in the wind present a different slope. The reason for this is once again related to the choice in the algorithm. The VelocIncr method as implemented in our study, and as used in most of the case for wind analysis, extract a maximum change of velocity of a 10 minute sample. If the sample has small fluctuations, which is the case for low wind speed, the maximum velocity increment for this sample will be very small. These small velocity increments are not taken into account by the different “threshold method”, as long as they are smaller than 2 m/s. But if the 10 minute sample has a higher average wind speed , it is of course more likely that the maximum velocity increment will be higher, say for instance equal to 4 m/s. This only value will be stored whereas a lot of other velocity increments with a value between 2 and 4 are present in the sample, and might be detected by the other algorithms. As a result of this, as the velocity increment method is taking only one maximum value per sample it is a good estimator of the average fluctuation one can expect at a certain wind speed. The gusts detected by the “threshold methods” at low wind speed are just the illustration that high fluctuations can occur at these low wind speed, but they are not representative of the average fluctuation because few examples of such gusts are present. As soon as the average wind speed is high enough to allow fluctuations that are often above the threshold chosen, the VelocIncr results contain less information than the POT method. To be convinced, one can have a look at the scatter presented on figure 4.4 b) and c). Few data are available for the VelocIncr method above 20 m/s, whereas a significant amount of them are still detected by the POT A=4m/s method. February 2009

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CHAPTER 4. GUSTS STATISTICS From this variety of results, one can hardly conclude on a perfect linear slope. A relation close from linearity surely exists between the average wind speed and the relative amplitude. The Velocity Increment method will provide the expected average fluctuation, whereas POT method with high threshold will directly and quickly select high relative amplitude gusts. By binning on the relative amplitude instead of the average wind speed, a linear relation is also drawn, but the slope coefficient suggested by the velocity increment,1/0.2 = 5, will be smaller, around three. A good assessment can ¯. be that the relation between those two parameters is of the following order: DU ≈ 0.25U An affine relationship exists between the average wind speed and the relative amplitude of the gust, but the results of the different algorithms have to be interpreted separately. As a reasonable approximation for quick assessment of the ¯ relative amplitude, one can use DU ≈ 0.25U

(b)

(a)

(c)

Figure 4.4: Highlighting an affine relation between the relative gust amplitude and the average wind speed. Figures a), b) and c) have the same scales. Figure b) represents the scatter of points obtained with the POT method, for a threshold A=4 m/s (12945 gusts). Figure c) is the scatter for the VelocIncr method, with T=10s(48374 gusts). The density of probability of each variable is represented against each axis.

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Table 4.4: Linear regression coefficients for the curves DU = f (W Smean ) Algorithm a b R2 IECCorr T=5s 0.06 2.1 0.95 POT A=2 m/s 0.08 2.1 0.89 POT A=4 m/s 0.05 4.31 0.84 POT A=6 m/s 0.02 6.87 0.32 VelocIncr T=10s 0.19 -0.05 0.96 VelocIncr T=20s 0.21 -0.11 0.96 ¯ ) = aU ¯ +b DU (U R: correlation factor of the regression

4.2.3

Influence of the turbulence intensity

As gusts are special turbulent structures, we expect a strong influence of the Turbulence intensity on the gust parameters. If the interest is turn toward gusts with high relative amplitude, it is expected that the value of turbulence might be high. Plotting the scatter of turbulence intensity with respect to the average wind speed, the large gusts will happen at high values of standard deviation. Even though this seems a natural result, one can be convinced by plotting iso-σ curves on the following figure. These curves ¯ . At a first approximation, one can see that the gusts of amplitude are “1/x” curves, as I = σ0 /U DU > 2 occur for σ0 > 1 and for DU > 6, the iso-σ curve that fit the results seem to be for σ0 ≈ 2. This is illustrated on figure 4.5 where, for a given wind speed, the higher the amplitude of the gust, the higher in the turbulence scatter it will occur. Gusts above a certain threshold follow an iso-σ curve

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(b)

(a)

(c)

Figure 4.5: Turbulence intensity and average wind speed: influence of standard deviation on the gust relative amplitude. Each algorithm follows a different iso − σ curve. Figures a), b) and c) have the exact same scales. Figure b) represents the scatter of points obtained with the POT method, for a threshold A=2 m/s. Figure c) is the scatter for the VelocIncr method, with T=10s. The density of probability of each variable is represented against each axis.

By studying the turbulence influence on the gust amplitude and relative amplitude, an influence of the turbulence intensity can be expected. But as we just have seen, the main parameter is more the standard deviation than the turbulence intensity. In the range of usual turbulence around 0.10, a lot of data, corresponding to a lot of different wind speed are available. As a result of this, the mean value in the range will not be characteristic of the overall scatter. On figure 4.6, the relative gust amplitude surprisingly seem independent of the turbulence intensity. All the algorithms give similar results. Nevertheless, one has to be careful before saying that the relative amplitude of the gust is independent of the turbulence intensity. The flatness of the plots clearly testify that this constant value is occurring a lot of times for different values of the turbulence intensity. But, due to the wide scatter of data in this range of turbulence intensity, it can be only concluded that the turbulence intensity is not a relevant parameter to study the gust relative amplitude. Average wind speed and standard deviation are the two parameters of real influence for the relative amplitude

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(b)

(a)

(c)

Figure 4.6: Relative gust amplitude and turbulence intensity. This plot does not highlight the expected influence of the turbulence intensity on the gust amplitude DU . All figures have the same scales. a) All algorithms. b) POT A=4 m/s scatter ; c) VelocIncr T=10s scatter

A contrario, the gust absolute amplitude , strongly linked to the average wind seed, have thus a dependence with the turbulence intensity. By plotting the gust amplitude with respect to the turbulence intensity, we expect to have a mirror plot of figure 4.5. Slight changes are observed due to the important amount of data for the bins of turbulence close to 10%. The gusts amplitude decrease from high values of 20 m/s at low turbulence to smaller values of 8 m/s at high turbulence intensity (figure 4.7), following the iso-σ curves which are defined as U ≈ σ0 /It + A, where A is an offset du to the algorithm. A=0 for the velocity Incr method, A=2 for the IECCorr method. At very low turbulence intensity, high standard deviation is not likely to occur. In this area, data are available for the algorithms Pot A=2 m/s, VelocIncr T=10s, IECCorr, but they don’t follow the iso-σ. The standard deviation in this area is really small, between 0.5 and 1. It illustrates the presence of anecdotical gusts that occur in a environment of low turbulence. These evenements keeps a small relative amplitude and thus are not too dangerous.

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(b)

(a)

(c)

Figure 4.7: The gust amplitude as function of the turbulence intensity. This plot is a mirror of the plot of the turbulence intensity as a function of the average wind speed. All figures have the same scales. a) All Algorithms ; Scatter of points for the method: b)POT A=2 m/s, c) Veloc Incr T=10s

4.2.4

Shape

To infirm or confirm the symmetric shape attributed to gusts, the plot of HF R = f (HRR) is drawn (see figure 4.8). The symmetry of the gust is characterize by an HFR equal to the HRR. But as it can be seen, it is far from being the case. For gusts rising faster than expected, the fall will be longer than the rise. And the opposite will occur for gusts rising slower than expected. Once again, the shape of the gusts detected from the VelocIncr method will be rather far from a symmetric shape. On the opposite side, the IEC correlation method, will tend to be the method which provides more symmetric gusts. The scatter of points is again very dense and hardly interpretable. But the fact that the density of probability are close to 0.5 for both the HRR and HFR are reassuring. The gust falling part lasts most of the time longer than the rising part

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(a)

(b)

Figure 4.8: Half Rise ratio and half fall ratio. Most of the time, the gust falls slower than it rises as its HF R is higher than its HRR. Figures a) and b) have the exact same scales. Figure b) represents the scatter of points obtained with the IECCorr method, for a characteristic time T=10s . The density of probability of each variable is represented against each axis.

4.2.5

Acceleration of the gust

The relative amplitude of the gust is an important parameter because it gives the sudden change in wind intensity a turbine should resists. But, the effects of such gust will be even stronger if it occurs in a short time. As a result of this, high relative amplitude gusts with high acceleration could be dangerous and disturb the control of the power. As the acceleration corresponds to the ratio DU/Dt, ¯ or U , we expect a relation of the following for and as DU is expected to be linear with respect to U the acceleration Acc = αU/Dt. The curves are presented on figure 4.5 and a linear approximation is given in table 4.9 where it seems like if the previous relation exists, then α ≈ 0.3.

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(b)

(a)

(c)

Figure 4.9: Gust acceleration increasing with gust amplitude. The acceleration depends on the gust duration. All figures have the same scales. a) Bin plot for all algorithm. Scatter of points for the method: b)POT A=4m/s; c) VelocIncr T=10s

Table 4.5: Linear regression coefficients for the curves Acc = f (U ) Algorithm IECCorr T=5s IECCorr T=10s IECCorr T=20s IECCorr T=30s POT A=2 m/s POT A=4 m/s VelocIncr T=5s VelocIncr T=10s VelocIncr T=20s VelocIncr T=30s

4.2.6

a 0.02 0.01 0.01 0.01 0.01 0.02 0.06 0.04 0.02 0.01

b 0.15 0.17 0.11 0.08 0.18 0.18 -0.01 -0.01 -0.01 0.01

R2 0.85 0.84 0.87 0.91 0.87 0.92 1 1 0.96 0.96

Duration of the gust

The peak over threshold method offers the advantage of being independent from the Duration of the gust comparatively to other methods. By calling τ the time spent over a threshold, a correlation between this parameter and the gust amplitude can be found. Indeed, the higher the value the wind speed will reach above the average wind speed, the longer the gust will last. This results are presented on figure 4.10, and a linear correlation on table 4.6. This results is expected because really fast fluctuations of very high amplitude have a low probability of occurring. The most reliable curve of the three is of course the POT A=2m/s one, because it should include all the other gusts. A gust February 2009

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CHAPTER 4. GUSTS STATISTICS such that DU = 7m/s is detected by the POT algorithm for the three threshold, A = 2, A = 4 and A = 6 m/s. The higher the relative amplitude of the gust is, the longer the gust lasts

(a)

(b)

Figure 4.10: Time spent over a threshold increasing with the wind speed. Figures a) and b) have the exact same scales. Figure b) represents the scatter of points obtained with the POT method, for a threshold A=2m/s.

Table 4.6: Linear regression coefficients for the curves τ = f (DU ) Algorithm Pot A=2 m/s Pot A=4 m/s

4.3

a 0.71 0.22

b 3.51 4.83

R2 0.98 0.79

Mean gust shape

As several definitions of a gust can exists, it seems difficult to provide a mean gust shape. Nevertheless it will be seen that the different algorithms tend to give the same trends and shape for the gusts, so the mean gust shape could eventually be a way to define gust. The theory presented here is based on an autocorrelation function, so on the spectrum of turbulence. It could be seen that this spectrum is the main parameter for the shape. So a good estimate of the turbulence spectrum is needed to provide stochastic gusts based on this theory. Reciprocally the experimental mean gust shape presented in this section, can be interpreted in term of autocorrelation function, and thus, turbulence spectrum. The work of G.Cr. Larsen, W. Bierbooms and K.S. Hansen [15] studies in detail the mean gust shape of

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CHAPTER 4. GUSTS STATISTICS simulated gusts. This kind of stochastic analysis has led to recent results concerning the determination of the specific gust shapes that leads to extreme response [4].

4.3.1

Theoretical mean gust shape based on isotropic turbulence theory

From the general method of Middleton, the mean gust shape can be determined in a Stochastic approach. A deep study of the parameter involved can be found in the following reference [15], and validation with gust simulation algorithms and experiments in [25]. The resulting mean Gust shape for an extreme between levels A and A + dA, with reference to the standard deviation, given by this theory is:   u ˜(τ ) r¨(τ ) A σ r(τ ) − (4.6) = r(τ ) − σ σ A r¨(0) Where, σ is the 10 minute standard deviation of the wind speed around the maxima, u ˜(τ )/σ is a ¯ , and r(τ ) is the normalized autocorrelation dimensionless wind speed such that u ˜(τ ) = u(τ ) − U function(ACF) that could be for instance written as: r(τ ) = 0.592 τ˜1/3 K1/3 (˜ τ)

(4.7)

K is the modified Bessel function of the second kind for a coefficient α = 1/3, and τ˜ is the dimensionless time: Vτ (4.8) τ˜ = 0.747 L ¯ stands for the 10 minute average wind speed and L is the longitudinal length scale. U The influence of wind speed and the amplitude ratio A/σ are respectively plotted on figures 4.11 a) and b) .

(a)

(b)

Figure 4.11: Theoretical mean gust shape. for different wind speed and an amplitude A/σ of 3.5 (fig. a). Theoretical mean gust shape for different amplitude ratio A/σ (fig. b)

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4.3.2

Validation with experimental data

Protocol In order to validate the analytical results of the previous section, the protocol described in [25] is followed, but with slight differences, for convenient reasons and in a prospect to be more accurate. • From a database of gusts corresponding to a gust detection method (like the POT method for ¯ and σ are extracted. It differs from a threshold of 4m/s), the 10 minute average statistics U the reference method in the sense that the data set used for averaging is centered around time corresponding to the gust ([t0 − 5min; t0 + 5min]). • The wind speed u(t) around the gust is then normalized using the following formula: ¯ u(t) − U u ˜= σ

(4.9)

• For each gust, datasets of 10s before and after the maximum of the gust are stored. • The average gust shape is obtained by averaging along all the datasets for each time value. ¯ between Results for a bin of wind speed By applying this protocol to gusts that occurred at U ¯ )/σ in the two following intervals 9.5 and 10.5 m/s and with a dimension less amplitude u ˜ = (U − U [2.5; 3.5] and [3.5; 4.5], two experimental mean gust shapes were calculated. The results are presented graphically on figure 4.12. It can be seen that good correlation with the theory is found for each amplitudes, if a length scale of 70 is chosen.

Figure 4.12: Mean gust shape - Comparison of theoretical results and experimental results for a bin of wind speed around 10m/s, and for two different amplitudes A = 3σ and A = 4σ

Results for two bins of wind speed For different wind speed and a same dimension less amplitude, the theory expects the mean gust shape to be more narrow in time for higher wind speed (see fig.4.11). This was drawn for the same length scale, exactly as found in [15]. Nevertheless, the experimental data does not seem to confirm this results. These results are plotted on figure 4.13. February 2009

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CHAPTER 4. GUSTS STATISTICS The theoretical gust shape suggested by the theory of Middleton and studied by Bierbooms et al, can be well fitted by the experimental data if an accurate length scale is found.

(a)

(b)

Figure 4.13: Mean gust shape for different wind speed, comparison between theory and experiments. a) Using a constant length scale, the results are not in agreement; b) By adapting the length scale parameter L, the theory can fit the experimental results.

4.3.3

Another way to tackle the mean gust shape problem

The protocol described in the last section (4.3.2) is based on extrema more than gusts. It takes into account the 10 or 20 seconds around a maximum does not seem to be characteristic of the whole gust structure which could last more than 20s. Time scaling As seen in the section 3.3 on standardization of gusts algorithm, a factor Dt has been defined to characterized the time spread of a gust. Dt is different for each gust. The main idea should then be to compare all gusts as if they had the same time spread Dt. For them to be comparable, the gusts should be transformed to signal of same time length. To perform this, the use of spline interpolation is chosen. Each gust of original size [−1.5Dt; 1.5Dt] around its maximum, will be transformed to a signal of arbitrary 401 points([-50s ; 50s]). Dimensionless wind speed Once each gust has the same time-scale, the wind speed should be dimensionless. Several formula can be used:

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u ˜(t) = u ˜(t) = u ˜(t) = u ˜(t) =

¯ u(t) − U σ ¯ u(t) − U DU ¯ u(t) − U ¯ U u(t) Umax

(4.10) (4.11) (4.12) (4.13)

For harmonization with the previous section and with literature, the first formula will be used. Nevertheless, results with a division per σ could be hard to interpret, so the second one, which clearly represent the shape of the gust above its mean speed will also be used IECCorr Results As imposed by the method, the shape of the IEC EOG can be recognize, but this, only for τ > 20s(written T on the figures). What does it mean ? Gusts correlated with the IEC gusts with a small τ , are really common in a turbulent wind field, and have most of the time a small relative amplitude, as it has been seen in the previous section. Moreover, as it is a short time scale event a lot of other short time scale events are occurring in the surrounding of the gust. As a result of this, thee gust event does not really have an amplitude higher than the local turbulence. By meaning all the gusts found with τ = 5, it is normal to find then even after the characteristic duration of the gust the average mean speed is not reached (fig 4.14). In contrast, as τ increases, the characteristic duration of the gusts DT also increases, and thus the shape specified by the IEC, is not that frequent if the time length is above 20s. As a result of this, gusts which are correlated with the reference IEC gusts will be isolated events. This explains why the surrounding of the gust is in average close to the average wind speed for τ > 20s. IEC EOGusts of long duration are isolated events so their mean shape for |τ | > Dt/2 will be close to the average wind speed It has been previously seen that the gust duration increases with the gust relative amplitude. Reciprocally , a long time event is more likely to happen at a higher relative amplitude. The longer the gust lasts, the more likely it will pull away from the average wind speed and also overcome the local ¯ (fig.4.15) are higher for longer turbulence. That explains why the ratio DU/σ(fig.4.16) and DU/U characteristic times(τ ≈ 30s) than the gusts corresponding to τ = 5s. VelocIncr Results The curves confirm the fact that this algorithm mainly focuses on front-like gusts. The consequence is that the tail of the gust ends in average at a higher amplitude. At small τ values, the front is more likely to have a straight line shape, whereas for longer τ , a more physical shape can be found, like an exponential. The velocity increments methods is a time dependent method as the IECCorr method. The same results is found: The longer the gust lasts, the more likely it will pull away from the average wind speed and also overcome the local turbulence. POT Results Gusts of a high relative amplitude are more likely to happen at high wind speed, and as the duration of the gust increases with the wind speed, they will have longer durations. Then, one can expect the same type of results as A increases for the POT method than when τ increases for a time dependent algorithm. This is what the three different figures tell us, and the results can seem intuitive: as the threshold A increases, the average relative amplitude DU increases, and thus the gust rise higher above the average wind speed and the overall standard deviation. Nevertheless, a more precise study has to be performed. Because, as DU (or A) increases, so does the standard February 2009

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CHAPTER 4. GUSTS STATISTICS deviation σ. By remembering the importance of the iso-σ curves of section 4.2.3, and mainly figure 4.5, one can recall the fact that POT A=6 corresponds to σ ≈ 2m/s, POT A=4 to σ ≈ 1.5m/s, and POT A=2 to σ ≈ 1m/s. By doing the math, the ratio DU/σ, is exactly the results obtained on figure 4.16 at t = 0. ¯ In the previous section 4.2.2, the relation DU ≈ 0.25 U ¯ has On the relation between DU and U been suggested. From figure 4.15 it can be seen that this assessment is reasonable. If a is the constant ¯ , the range of values for the different algorithms is [0.18;0.43]. such that DU ≈ a U Comparison of the algorithms On figure 4.14, it can be seen that the IECCorr and the POT method agree on a same exponential like shape of the gust. On the same figure, it can be noticed that the VelocIncr method detects gusts which rises along a straight line, in a front-like shape. It has been previously seen that the higher the threshold or the length of the gust, the more likely it can rise above the level of turbulence. Nevertheless, the three different algorithms provide different results for the mean gust shapes. The POT curves are above the IECCorr ones, which are above the VelocIncr ones. To be understood, we have to refer to the previous section, and remember again the iso-σ curves. The order between the algorithms is exactly the same than the order between their corresponding iso-σ curves. The fact that a lot of data are available at low standard deviation for certain algorithms shifts their amplitude DU/σ downward. The differences of amplitudes for the different algorithm is mainly due to the fact that each algorithm provides gusts of a certain class of standard deviation

Figure 4.14: Experimental mean gust shape - (U-Umean)/DU

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Figure 4.15: Experimental mean gust shape - (U-Umean)/Umean

Figure 4.16: Experimental mean gust shape - (U-Umean)/sigma

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4.3.4

Gust vertical profile: wind speed and direction

The gusts from MM3 were detected at height 80m. As wind speed and wind direction data are available at two other heights, 52m and 108m, it is interesting to see the vertical profile of the gust. Dimension less duration of the gust and wind speed have been used like in the previous section. To have a dimension less wind direction, a similar formula than the average wind speed was used: subtracting the mean direction W Dmean and dividing by the standard deviation of the direction W Dstd . The absolute value is taken: |W D − W Dmean | W˜D = (4.14) W Dstd The results of the wind speed profile are presented for two different algorithms on figure 4.17. The subfigure a) are results obtained with 40000 gusts detected by the IECCorr method for a characeristic time T=30s ; The sub-figure b) is obtained with 1306 gusts detected by the POT method for a threshold A=6 m/s. The results on the wind direction are presented on figure 4.19.

(a)

(b)

Figure 4.17: Mean shape of the wind speed at the three height locations 108m, 80m and 52m, when a gust is detected at height 80m. This qualifies the gust “vertical profile”. In average, the gusts seem to travel faster at higher heights. a) IECCorr method ; b) POT method.

Wind speed profile It is welcomed to see that the wind speed at height 108m is above the one at 80m, which is respectively above the one at 52m. The vertical wind profile is expected to follow an increasing logarithmic or power law(see section 2.2.1). By averaging the dimensioned wind speed, the following relation between height and wind speed can be found: 52m 80m 108m

9.2 m/s 9.6 m/s 10.7 m/s

Using the surface roughness  of ECN test site z0 = 0.05, a logarithmic law fitting these points is obtained: u(z) = 1.34 ln zz0 . Its representation is displayed on figure 4.18. Nevertheless, the amplitude of the gust is not following the vertical logarithmic law, for the following reasons: Gusts were detected at height 80m. The large amount of gusts detected, can lead to assumption that 80m height is in average the spatial center of the gust. An attenuation of amplitude is observed for heights February 2009

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CHAPTER 4. GUSTS STATISTICS far from the spatial center. As a result of this, the average wind speed of the gust at 80m will be higher than the average wind speed of the gust at 108m, which is far from the assumed spatial center. One shall thus not expect the gust amplitude to follow the logarithmic law. A statistical study of the probability of seeing a gust at the three different height will be performed in a following chapter. A good vertical spread of the gust can already be presumed, as the shape of the gust can be seen at each location. As the gusts were detected at 80m height, the gust amplitude will be in average higher there than for the other location. The same trends are found for the two different algorithms. On figure 4.17(a), it can be seen that the gust front arrive at 108m first, then at 80m, and eventually at 52m. This result seems coherent as the wind speed increases with the height. An illustration of this phenomenon can be seen on figure 6.12.On figure 4.17(b), one can notice again, that if no shape is imposed by the method, the gust will fall more slowly than it rises, and this at each height. The gust can be expected to travel faster at higher height, as the average wind speed profile follows a logarithmic law. Nevertheless, the amplitude of the gust is not following the vertical logarithmic law as its amplitude is in average, maximum at the height where it was detected and then attenuates with height.

Figure 4.18: Logarithmic law fitting the vertical profile

Wind direction profile Even though the focus of this study was not on wind direction change, it can be seen on the following picture, that in average all gusts come with a direction change. But in contrast with the extreme coherent gust with direction change (ECD), the mean shape seems to reveal a decrease before the direction change and then a decrease again to reach the previous wind direction. For this study, the 10 minute average wind direction has been taken. The fact that a lot of wind direction changes occur in 10 minute explain why the difference W D − W Dmean is not equal to zero. A clear direction change at each height is present in the average wind direction profile

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Figure 4.19: Mean shape of the wind windection at the three height locations 108m, 80m and 52m, when a gust is detected at height 80m, so defining the mean “wind direction profile” of the gust.

4.4

Summary of the gusts statistical study

This sections is not a stand alone section. It summaries the results presented during this chapter. The punctilious reader is invited to refer to the corresponding sub-section to have the detailed description leading to these results. Differences between the algorithms Each gusts detection methods provides different results and focuses on different aspects. A standardization of the notations has been done to unify all methods, and compare their parameters with same definitions. • The Peak Over Threshold method, is a fast method to detect high relative amplitude gusts, but the resulting shapes will be really different from the IEC definitions. • The velocity increment is not efficient to detect interesting gusts in the way it is often implemented. It is a good method to assess the maximum local turbulence though. Adding a threshold condition to this method, and allowing several gust extraction for a 10 minute sample, could provide interesting events, such as really fast front. • The correlation method, is one of the most time consuming methods. Its main advantage is to provide gusts with a specific shape, independently of the amplitude. As a result of this, a threshold has to be added to this method also, to avoid detecting low amplitude gusts, and a minimum correlation has to be defined. Nevertheless, strong and dangerous gusts can take a lot of different shapes, which are not likely to be close to the IEC definitions. Relation between gusts parameters • An affine relationship close to identity exists between the average wind speed and the absolute amplitude of the gust.

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CHAPTER 4. GUSTS STATISTICS • An affine relationship exists between the average wind speed and the relative amplitude of the gust, but the results of the different algorithms have to be interpreted separately. As a reasonable ¯. approximation for quick assessment of the relative amplitude, one can use DU ≈ 0.25U • The higher the relative amplitude of the gust is, the longer the gust lasts. • Gusts above a certain threshold follow an iso-σ curve • Average wind speed and standard deviation are the two parameters of real influence for the relative amplitude. It is more surprising that the turbulence intensity has a small influence. Indeed, for a given level of turbulence intensity, a lot of gusts of different amplitudes are found. No obvious correlation can be found. This is due to the fact that the relative gust amplitude depend with an affine relation on the average wind speed. As a result of this a given turbulence ¯ and σ, and thus a lot of different gust relative intensity, corresponds to a lot of values of U amplitudes. Mean gust shape Analysis on the mean gust shape, illustrates the differences between the different algorithms. Nevertheless it revealed some trends: • The gust falling part lasts most of the time longer than the rising part. • The longer the gust will last the sharper its rising shape will be in the sense that it would be closer to a front shape than a constant slope. • The differences of amplitudes between the different algorithms is mainly due to the fact that each algorithm provides gusts of a certain class of standard deviation • The theoretical shape suggested by the theory of Middleton and studied by Bierbooms et al, can be well fitted by the experimental data if an accurate length scale is found. In another way, the theoretical mean gust shape has to take into account the change of wind spectrum with the average wind speed. • The longer the gust lasts, the more likely it will pull away from the average wind speed and also overcome the local turbulence. Vertical profile It has been possible to study the “lateral profile” of the gust by studying three different heights. Following this study, it has been seen that: • The gusts detected were in average detected 80% of the time at the three different heights, representing a spread of at least 60m vertically. • As the wind speed is higher at high heights, the gust might arrive earlier at higher heights, and later at lower heights than at the reference detection height. • The amplitude of the gust is not following the vertical logarithmic law as its amplitude is in average maximum at the height where it was detected and then attenuates with the distance from this point. • The mean direction profile corresponding to the wind speed gusts, seem to reveal the presence of a direction change in average. This means that in average, a gust detected with an method based on its amplitude, is likely to include a direction change.

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Part III Gusts propagating through a wind farm

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Contents

5

6

Gusts propagation - overview of the method 5.1 Presentation of the wind farm . . . . . . . . . . . . . 5.1.1 The wind farm . . . . . . . . . . . . . . . . . 5.1.2 Data available and data used . . . . . . . . . 5.2 Hypothesis and method . . . . . . . . . . . . . . . . 5.2.1 First step: Gusts extraction . . . . . . . . . . 5.2.2 Selected gusts . . . . . . . . . . . . . . . . . . 5.2.3 Assessment of the wind field and propagation 5.2.4 Extraction of raw data . . . . . . . . . . . . .

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Gusts propagation results 6.1 Gust propagation speed . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Digression on the arrival time . . . . . . . . . . . . . . . . . 6.1.3 Accurate position with the use of correlation . . . . . . . . 6.2 Probability of detecting a gust . . . . . . . . . . . . . . . . . . . . 6.2.1 Restrictions and method . . . . . . . . . . . . . . . . . . . . 6.2.2 Longitudinal spread of a gust in a free stream . . . . . . . . 6.2.3 Lateral and vertical spread of a gust in a free stream . . . . 6.2.4 Longitudinal and lateral spread of a gust in a wake stream 6.3 Example of gust propagation . . . . . . . . . . . . . . . . . . . . . 6.4 Summary of the propagation results . . . . . . . . . . . . . . . . .

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Chapter

5

Gusts propagation - overview of the method 5.1 5.1.1

Presentation of the wind farm The wind farm

The part of the ECN test farm(EWTW ) studied, is composed of 5 turbines with hub height at 80m and diameter of 80m, and a meteorological mast with sensors at 52, 80 and 108 meters. The five turbines are labeled from T5 to T9, and the meteorological mast: MM3 . Distances and angles with respect to the North are presented on figure 5.1, where D stands for the turbine diameter.

Figure 5.1: Main dimensions and directions of the test wind farm

5.1.2

Data available and data used

Data from years 2006 to 2008 (end of August) are used. For each turbine, data qualifying the wind and the loads are measured by ECN[22] with a frequency above 4Hz. ECN meteorological mast provides pressure, temperature, wind speed and wind directions at different heights, with a rate also above 4Hz. The main signals used are produced by cup anemometers and vanes at 80m, even though other sensors, like sonic anemometers, at other heights will be sometimes used. Description of ECN mast sensors is well described in the following reference [11]. Except for certain loads, most of the data were extracted from “raw data”, which correspond to the direct output of the sensors. Several steps of validation have been applied on these data. Some loads were also directly taken from ECN database(LVTM), idem for all 10 minute average statistics used.

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5.2

Hypothesis and method

The following protocol will be applied and is further detailed: • Detect gust from MM3 data • Select interesting gusts, depending on the wind direction and/or the relative amplitude • Assess the distanced covered, and the propagation time with the plane-wave hypothesis • Extract the raw data for a relevant time interval • Treatment of the signals for analysis

5.2.1

First step: Gusts extraction

In this approach, we will consider gusts detected at mast 3, at the height 80m on the boom oriented at 240 degrees with respect to the North. This direction is indeed close to the main wind direction of the test site and provides undisturbed wind data for the directions selected (see section 5.2.2). Gusts from both IECCorr method and POT method are used. The IECCorr gusts have a specific shape and this can help the detection by eye of the gust.

5.2.2

Selected gusts

In the following study several directions for the wind will be selected. These direction are represented on figure 5.2. • Direction 1 [201◦ ; 221◦ ]: Turbine 6 is directly behind Mast 3. This direction is relevant to determine gust propagation speed (see section 6.1). • Direction 2 [175◦ ; 195◦ ]: In this interval the wind is perpendicular to the row of turbines and thus, lateral spread of gusts can be studied (see section 6.2.3). • Direction 3 [265◦ ; 285◦ ]: This direction will be used to study the propagation of a gust trough the row of turbines (see section 6.2.4).

Figure 5.2: Main direction of interest in the study of gust propagation

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5.2.3

Assessment of the wind field and propagation time

We will only use the wind data from the mast to assess the wind field. The data of two or three other masts parallel to the row of turbines could have provided good informations concerning the incoming wind field. In spite of this lack of data, we will assess that the wind seen on mast 3 is a Plane wave. This means that on a line perpendicular to the wind direction and going through mast 3, the wind will have the same amplitude and direction, and this direction will stay constant, as illustrated on figure 5.3. The choice of the wind direction and speed used to define this plane-wave will be, W Smean and wd, the 10 minute average wind speed and the average wind direction of the gust around the time of the gust t0 . From this hypothesis, by a simple projection, the distance covered by this hypothetical constant wind to arrive on the turbines can easily be assessed. Once the distance is known, the time of propagation can be calculated using different wind speed, in order to predict the “arrival time” of the gust on each turbine.

Figure 5.3: Illustration of the plane wave hypothesis

5.2.4

Extraction of raw data

For each interesting gust, a relevant time interval is defined. This interval should include the “arrival time” of each turbine, with a certain error-margin in case the estimate of the time propagation is wrong. In order to render the plots clearly interpretable, the time of the gust detected at MM3 t0 , is defined as the origin t = 0.

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Chapter

6

Gusts propagation results 6.1 6.1.1

Gust propagation speed Introduction

To be able to study the Propagation of gusts through a row a wind turbines, it is first needed to know at which speed the gust is expected to travel to see if the gust is present at the expected time or not. In this section we will look at the propagation speed of a gust in a free wind field. Gusts will be detected at mast 3. Most of the time these gusts will be present at Turbine 6 with 10 seconds delay. The distance between turbine 6 and mast 3 is of dcovered = 2.5 D = 201m. Nevertheless, the wind direction of the gusts will not be exactly 211◦ , so in the hypothesis of the plane-wave, the projection of the wind direction can imply small fluctuations of the distance covered, between 198 and 201 meters. These fluctuations could have been neglected as they only imply a maximum error on the expected time of 0.5s. The expected time, texpected , is calculated in function of the 10 minute average wind ¯ : texpected = dcovered /U ¯ . The prospect of this section is to prove that this speed around the gust U approximation is sufficient so that the maximum of the gust can be expected to travel at a speed close to the average wind speed.

6.1.2

Digression on the arrival time

MM3 is the reference location for the gust. As it is upstream the conservation of momentum[18] implies a loss of velocity associated with the induction factor a (see figure 6.1). We will assume that the loss of velocity starts at MM3, at a distance from turbine 6 of L1 = 2.5D. a=

U1 − U2 UM M 3 − UT 6 ≈ U1 UM M 3

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(6.1)

CHAPTER 6. GUSTS PROPAGATION RESULTS

Figure 6.1: Pressure and velocity evolution through the actuator disk

This loss of velocity depends on the upstream velocity U∞ ≈ UM M 3 . The assessment of the traveling time from MM3 to turbine 6 should be done by integration. We will write V˜u∞ the function defining the shape of the change of velocity which takes values between −1 and 1, such that: L1

Z tint = 0

dl 1 = Vu∞ L1

1

Z 0

dx V˜u∞

(6.2)

The continuous values of V (or V˜ ) can be obtained by numerical integration. Thanks to the details provided in [21], integration of the analytical model is performed. If the result is known for a different distance of propagation (i.e. a different rotor diameter): L2

Z Iu∞ = 0

dl 1 = Vu∞ L2

Z 0

1

dx ˜ Vu∞

(6.3)

The two last equations provide us with the expected time: tint =

L2 Iu L1 ∞

(6.4)

With these hypotheses, taking texpected = 2.5D/U∞ instead of tint introduce an relative error  = (tint −texpected ) of: tint  = 0.10 for U∞ = 15 m/s and with I15 = 0.322

(6.5)

 = 0.04 for U∞ = 24 m/s and with I24 = 0.188

(6.6) (6.7)

This means that for a wind speed of 24 m/s at MM3, the time of arrival of the gust on turbine 6 estimated with this integration method would be 0.3 second higher than texpected . For a wind speed of 15 m/s, the difference would be of 1.5s. Due to these small influences, the effect of the loss of velocity will not be taken into account in the estimation of the arrival timey. The influence of the fall in speed due to the presence of the turbine can be neglected in the estimation of the propagation time between MM3 and T6

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6.1.3

Accurate position with the use of correlation

Most of the time, the gust detected on mast 3 is visible on turbine 6(see section 6.2.2). A solution could then be to measure manually the time where the gust is seen on turbine 6. This method is fastidious and can leads to errors, specially when a lot of fluctuations are present in the turbine anemometer signal. As the wind speed captor of the turbine is in the wake of the rotor, the complex turbulent structure in the wake can make the assessment of the gust equivalent position by eye difficult. A correlation between the original gust at mm3 and the signal at turbine 6 is then used to find a more accurate time position. The correlation is performed for time between texpected − 1.5 Dt and texpected + 1.5 Dt. The time corresponding to the maximum correlation coefficient is saved, and will be further called tcorr . If for each gust we define a function CorrGust such that: CorrGust(τ ) = corr ({u(t) | t ∈ [−1.5 Dt; 1.5 Dt]} , {uT 6 (t) | t ∈ [τ − 1.5 Dt; τ + 1.5 Dt]})

(6.8)

Then the definition of tcorr is: CorrGust(tcorr ) = max {CorrGust(τ ) /τ ∈ [texpected − 1.5 Dt ; texpected + 1.5 Dt]}

(6.9)

Figure 6.2 illustrates the correlation method to determine the gust arrival time in a accurate way.

Figure 6.2: Determination of gust arrival time with the correlation method

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CHAPTER 6. GUSTS PROPAGATION RESULTS A typical screen generated by the program written with R is shown on figure 6.3. In this figure, the solid(purple) vertical line represents texpected , while the dotted(green) vertical line represents tcorr . The other long-dashed(orange) line, corresponds to the arrival time if the gust was traveling at its maximum speed. It can be seen that in this case the time obtained by correlation corresponds exactly to the arrival time of the gust on the turbine. Moreover, one can notice that tcorr is really close to texpected . This will indeed be observed most of the time. Nevertheless, there are some exceptions where the correlation method reaches its maximum at a time which is irrelevant. It could be due to the presence of two similar phenomenas close to one another, or simply due to the fact that the gust did not propagate well. The correlation method can most of the time detect arrival time better than a human operator, but the automatic process will provide bad results in the case of a bad gust propagation. Plotting tcorr with respect to texpected , one will obtain a scatter around the line Y=X (figure 6.4). On this figure, the data were not validated, so that the algorithm has sometimes(≈ 10%, see section6.2.2) provided irrelevant data as explained previously. The fact that tcorr is around texpected , is provoked by the algorithm because for each gust the condition tcorr ∈ [texpected − 1.5 Dt; texpected + 1.5 Dt] is fulfilled. This is needed to avoid the algorithm to find correlation times too far from the reality. One can then claim that the result is forced. But still, a lot of correlated times are close to texpected , and moreover, if the gust was traveling significantly slower or faster, the binned values would be above or under the line Y=X, which is clearly not the case here. Looking in details to the screen produced by the program, one can see that the gust is almost always traveling slower than the maximum speed of the gust. The gust is traveling sometimes faster, but sometimes slower than the average wind speed. As a result of all this, in the prospect of this study where an estimate of the arrival time of a gust on each turbine is needed: The gusts will be reasonably considered to travel at the 10 minute average wind speed around the gust.

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Figure 6.3: Example of screen produced by our program to assess the propagation speed. It can be seen that the correlation method provides an accurate position. Top left: the original gust detected at MM3. Top right: wind speed at T6. The perpendicular lines represent: the expected time (solid/purple), the time obtained by correlation (small dashed/green), and the time obtained using the gust maximum speed(long-dashed/orange). Middle left: superposition of the two wind speed signals for comparison. Middle right: correlation coefficient between the two signals for different delays. Bottom left: overview of the turbine disposition, wind direction and incoming wind plane wave. Bottom right: wind direction at MM3.

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CHAPTER 6. GUSTS PROPAGATION RESULTS

Figure 6.4: Time obtained by correlation with comparison with estimated time

6.2 6.2.1

Probability of detecting a gust Restrictions and method

In this section, a “hand on” method has been used to assess the probability of propagation of a gust, longitudinally, laterally and transversally . From a gust detected at a certain location and answering to certain criteria the aim was to look whether this gust can be found anywhere else in the wind farm. The locations used to detect gusts were MM3 and T5. The criteria the selected gusts have to fulfill are a high amplitude and an average wind direction in a certain range (cf 5.2.2). It is needed to use high amplitude gusts, otherwise the gust structure might dissipate and mix with other turbulent structures preventing its detection by eye or even by numerical method like correlation. Moreover, as the data from the turbine correspond to sensor located behind the rotor, their measure are really disturbed. A moving averaging of these signal is performed to smoothen the signal, but the chance of seeing a gust can be reduced by the perturbation introduced by the rotation of the turbine. The validation of the results is only done by eye, with a little computational help of course to plot the wind fields and suggest an expected time of arrival of the gust. An assessment of the propagation speed and thus, the expected arrival time, has been done in the previous section(see 6.1). For each direction studied, the following system of axes will be used:

To qualify the propagation, one has to be sure that the structure seen at location two has from origin the previously upstream detected one, at location one. Thus, binary probabilities were used. If the operator thinks the gust seen at location two is the result of the propagation of the detected gust February 2009

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CHAPTER 6. GUSTS PROPAGATION RESULTS at location one, then, the value one is attributed. If there is a doubt, the value zero is attributed. The probability of seeing a gust at location two, knowing that this gust is detected at location one is obtained by meaning these values entered by the operator. The propagation results can also be interpreted as spatial spreading. By looking at two different locations aligned with the wind direction, one can obtain the longitudinal spread. By looking at three locations forming an isosceles triangle perpendicular to the wind direction and pointing toward the wind direction, one can obtain the lateral spread of the gust. Eventually, looking at the data at three different heights, 52, 80 and 108 m, one can obtain the transversal spread of the gust. For this last step, the operator will provide a discrete value corresponding to the proportion of signals where the gust is clearly visible. 1/3, if the gusts is only seen at 80m high. 2/3, if it is visible at 80m and 52m, or 108m and 80m. Eventually, 1 if it is visible on each sensor.

6.2.2

Longitudinal spread of a gust in a free stream

The presence of wakes in wind farms really disturb the incoming flow. To compare the result of propagation in this situation, it is needed to first know the propagation of the gusts in an unperturbed flow. This situation where all the turbines receive an undisturbed flow will be qualified here as a Free stream. Two directions were exploited in order to assess the probability of seeing a gust detected in a free stream at a turbine. Gusts were detected at MM3. Direction 1 [201◦ ; 221◦ ] For this direction turbine 6 is directly behind mast 3, the longitudinal spread of the gust can be studied. Using gusts detected by the POT algorithm at MM3, for a threshold of 6 m/s: Out of 109 gusts detected at MM3, 92 were clearly visible on T6, and thus propagated well, leading to the following probability: P (T 6 | M M 3)P OT 6 = 84% (6.10) This can also be translated as: For a gust detected at a meteorological mast located 200m behind a turbine, the probability of seeing this same gust at the turbine is 84%. P (∆X = 200m, ∆Y = 0) = 84%

(6.11)

Figure 6.5: The test farm viewed from direction 2

6.2.3

Lateral and vertical spread of a gust in a free stream

Direction 2 [175◦ ; 195◦ ] This direction is really close to the previous one, but has the advantage of being perpendicular to the row of turbines. The lateral space spread of the gust can be studied. Assuming the wind is a plane wave, the gust should arrive nearly at the same time on each turbine. The signals from the three turbines closest to the mast were studied. Two algorithms were used for gusts extraction: the peak over threshold with a relative amplitude of 6 m/s, and the IEC correlation method with a relative amplitude above 5 m/s. The results are presented in table 6.1. A plan view of the test farm through direction 2 is drawn on figure 6.5. February 2009

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CHAPTER 6. GUSTS PROPAGATION RESULTS Table 6.1: Lateral and transversal spread of gusts for direction 2

Condition Number of gusts Amplitude U [m/s] Duration Dt [s] Relative amplitude DU [m/s] P (T 5 | M M 3) P (T 6 | M M 3) P (T 7 | M M 3) P (H = 52, H = 80, H = 108)

POT 21 25.63 38.56 6.61 0.35 0.90 0.45 0.72

100 20.89 18.67 5.62 0.38 0.68 0.33 0.92

IEC Corr DZ¡56 DZ¿56 23 77 19.85 21.20 12.22 20.60 5.66 5.61 0.43 0.36 0.65 0.69 0.30 0.34 0.64 1

(a) Influence of vertical spread

Condition Number of gusts Amplitude U [m/s] Duration Dt [s] Relative amplitude DU [m/s] P (T 5 | M M 3) P (T 6 | M M 3) P (T 7 | M M 3) P (H = 52, H = 80, H = 108)

100 20.89 18.67 5.61 0.38 0.68 0.33 0.92

IEC Corr DY¿500 DY¿250 14 29 20.66 21.3 15.77 14.11 5.5 5.66 1 0.48 1 1 1 0.52 0.875 0.89

100¡DY¡300 25 20.89 24.97 5.52 0 1 0 0.89

(b) Influence of lateral spread

These probabilities can be interpreted in terms of spatial propagation, as we know the position of each turbine. This would results in the following interpretations: P (T 5 | M M 3) P (T 6 | M M 3) P (T 7 | M M 3) P (H = 52m, H = 80m, H = 108m)

≈ ≈ ≈ ≈

P (∆X = 180m, ∆Y = 215m) P (∆X = 180m, ∆Y = −90m) P (∆X = 180m, ∆Y = −390m) P (∆Z = 56m)

= = = =

0.38 0.68 0.33 0.92

The POT results are not that far away from the results obtained with the IECCorr method, but they won’t be taken into account due to the small amount of gusts available. Influence of the vertical spread ∆Z: Most of the gusts detected at the mast can be seen at the three different sensor heights. The lateral spread of the gusts does not seem to be affected by the vertical spread of the gust. Indeed, the probability of seeing the gust on the different turbines is the same for gusts with a wide vertical spread and a small vertical spread. Nevertheless, one can notice that: Gusts of wide vertical spread seem to last longer than the ones with a small ∆Z. The lateral spread of the gusts does not seem to be affected by the vertical spread of the gust Influence of the longitudinal spread: By splitting the gusts into different categories, the samples will have a small population in each category, so one should be careful of the conclusion that could be drawn. The categories provided by the turbine disposition are: DY > 500, DY > 250, 100 < DY < February 2009

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CHAPTER 6. GUSTS PROPAGATION RESULTS 200. They respectively correspond to gusts that were seen on every turbine, on only two turbines, and eventually, only on T6. The problem is that most of the time the spatial center of the gust is not at MM3. It is then hard to really assess the spatial spread of the gusts. We will rely on the category DY > 500 where it is known for sure that the lateral spread of the gust is wide, and the third category where the lateral spread is relatively narrow. At a first glance one can see the confirmation of the previous result, the vertical spread of a gust does not seem to affect its longitudinal spread. Indeed the probability of ∆Z > 56 is constant and roughly equal to 0.9 for the different samples. One can expect a result correlating the duration of the gust and it spatial spread. For instance, short gust would have a large spatial spread, and long gusts a wider spatial spread. The previous table seem to follow this trend, even though more data and a better assessment of the gust duration are needed to confirm this interesting result. Gusts of narrow lateral spread seem to last longer than the ones with a wide ∆Y . Digression on the lateral spread: Looking at the test farm through direction 2 (see fig.6.5) we can see the different location where the gusts are detected/seen. If it is assumed that, over all the gusts observed, the mean lateral center of the gust is MM3, then, one can try to fit the probability of seeing a gust obtained at these three locations with a curve centered on 0. This would provide us with a continuous function that express the probability of seeing a gust perpendicularly to the wind, knowing that the gust center is at a certain location. A fourth point is added, by approximation of the result from the longitudinal spread P (∆X = 180m, ∆Y = 0) ≈ P (∆X = 200m, ∆Y = 0) = 84%. Gaussian fit Exponential fit

1 δy P (∆X = 180m, ∆Y = δy) = a| : e− 2 ( σ ) P (∆X = 180m, ∆Y = δy) = a e−|δy|/ly

2

a = 0.79, σ = −204m a = 0.87, ly = 265m

 = 11%  = 8.9%

Figure 6.6: Probability of seeing a gust in the lateral direction of the wind, 180m downwind

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CHAPTER 6. GUSTS PROPAGATION RESULTS

6.2.4

Longitudinal and lateral spread of a gust in a wake stream

Direction 3 [265◦ ; 285◦ ] When the wind comes from this direction, all the turbines are in the wake of turbine 5. This situation will be qualified here as a Wake stream. As a result of this, if a gust is detected at T5, it could be expected to see it propagating through the row of turbine. Due to the disposition of the turbines, three different locations can be used for the gust detection: MM3, T5 or T9. T9 could be used for wind direction around 95◦ , but this direction is not frequent as it can be seen on the wind direction distribution (fig.2.2). Detecting gusts at MM3, over the advantage of having a free stream, less fluctuations, and a good sensor set. Nevertheless, the row of turbines is at a distance of 180m laterally, so it reduces the chance of seeing the gusts almost by a factor two (cf fig.6.6). The following results were performed with gusts detected at T5. A plan view of the test farm through direction 3 is drawn on figure 6.7. The results for the direction 3 are presented in table 6.2. As expected, the probability of seeing a gust decrease as the distance traveled in the wake increase. Further analysis will be done in the following paragraphs.

Figure 6.7: The test farm viewed from direction 3

Table 6.2: Lateral and transversal spread of gusts for direction 3 Condition Number of gusts Amplitude U [m/s] Average duration Dt [s] Relative amplitude DU [m/s] P (T 5 | T 5) P (T 6 | T 5) P (T 7 | T 5) P (T 8 | T 5) P (T 9 | T 5) P (M M 3 | T 5)

153 20.66 21.66 4.90 1.00 0.79 0.68 0.56 0.46 0.33

U ∈ [12; 18[ 46 15.64 27.28 4.35 1.00 0.80 0.61 0.49 0.33 0.37

U ∈ [18; 24[ 75 20.63 19.56 4.83 1.00 0.83 0.75 0.65 0.56 0.37

U ∈ [24; 34[ 32 27.94 18.13 5.84 1.00 0.69 0.59 0.47 0.41 0.19

In this case it will be also suggested to interpret the results in terms of spatial propagation. In contrast with the free stream, the wake stream propagation will be written ∆X w .: P (T 6 | T 5) P (T 7 | T 5) P (T 8 | T 5) P (T 9 | T 5) P (M M 3 | T 5)

≈ ≈ ≈ ≈ ≈

P (∆X w P (∆X w P (∆X w P (∆X w P (∆X w

= 300m, ∆Y = 0m) = 600m, ∆Y = 0m) = 900m, ∆Y = 0m) = 1200m, ∆Y = 0m) = 390m, ∆Y = 180m)

= = = = =

0.79 0.68 0.56 0.46 0.33

Influence of the gust amplitude on the longitudinal and lateral spread On the influence of the gust amplitude, a previous result concerning the gust relative amplitude is found. The increase of amplitude U (strongly correlated to the average wind speed), implies an increase of the gust relative amplitude DU . The values found in a previous section(see fig.4.4) for an algorithm with a threshold of 5m/s(which is the case here), are really close to the one found in table 6.2. February 2009

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CHAPTER 6. GUSTS PROPAGATION RESULTS By concentrating on Turbine 6, the range of probabilities found is [0.69; 0.83] for the different wind speeds, with a mean at 0.79. These results are reasonably close to, but lower than the result obtained for a longitudinal spread in a free stream which was 84%. This can be expected as the flow is more turbulent in the wake and thus, the turbulent origin of the gust might mix with other structures, or be desintegrated by the motion of the rotor. The probability of longitudinal propagation of a gust is lower in a wake stream than in a free stream. A surprising result is that all the probabilities found at high wind speed are lower than the other ones. At these wind speed, the pitch control is working permanently, and thus add some more fluctuations to the wind. The gusts are then even harder to detect. Digression on the longitudinal spread As it has been previously suggested for the lateral spread, one can try to fit the probability of seeing a gust obtained at the five turbine locations. This would provide a continuous function that express the probability of propagation of a gust in the longitudinal direction, knowing that the gust center is at a certain location. Linear fit Exponential fit

P (∆X w = δx, ∆Y = 0) = a δx + 1 P (∆X w = δx, ∆Y = 0) = e−δx/lx

a = −475m−1 lx = 1545m

 = 5.1%  = 2%

Figure 6.8: Probability of seeing a gust in the longitudinal direction of the wind - exponential fit

A more detailed study of the longitudinal spread By focusing only on the gusts that manage to propagate through one, two, three four or five turbines, one can try to reveal general rules of propagation in a wake stream. The probabilities presented in bold in table 6.3 can be interpreted in this way:

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CHAPTER 6. GUSTS PROPAGATION RESULTS P (T 7 | T 5&T 6) P (T 8 | T 5&T 6&T 7) P (T 9 | T 5&T 6&T 7&T 8)

≈ ≈ ≈

P (∆X w = 300m, ∆Y = 0m|...) P (∆X w = 300m, ∆Y = 0m|...) P (∆X w = 300m, ∆Y = 0m|...)

= = =

0.85 0.77 0.76

In a rigorous sense, all these probabilities are conditioned on something: “—...”. This has not been explicited in purpose, because in the prospect of this study, one can neglect these conditions. Assuming this, the three probabilities are in a way comparable, and thus, one can be satisfied that they are of the same order. The results figured on the last line and on the first column of table 6.3 are slightly different. The results in the first column represent propagation probability, without specifying if the gust has been seen on each turbine. Indeed, it can occur that a gust is seen on T5, T6, T8, but not on T7. To have the probability of detecting a gust, knowing that the gust has been detected on each turbine before, one has to use the last row of the table. A decreased exponential can also fit these data by using lx = 1300m instead of 1545m. The longitudinal probability of detecting a gust that have been previously detected at each location is: P (∆X w = [0; δx], ∆Y = 0) = e−δx/lx with lx = 1300m

(6.12)

The function • → N (•) gives the number of gust that are concerned by the condition •. For instance, the condition T5 & T6, means, gusts that were detected at T5 AND T6. With this definition, one can easily express the function • → P (•|T 5) = NN(T(•)5) Table 6.3: Conditionnal probability • P(T5— • ) P(T6— • ) P(T7— • ) P(T8— • ) P(T9— • ) N( • ) P( • —T5)

T5 1.00 0.79 0.68 0.56 0.46 153 1.00

T5 & T6 1.00 1.00 0.85 0.70 0.58 121 0.79

T5 & T6 & T7 1.00 1.00 1.00 0.77 0.63 103 0.67

T5 & T6 & T7 & T8 1.00 1.00 1.00 1.00 0.76 79 0.52

T5 & T6 & T7 & T8 & T9 1.00 1.00 1.00 1.00 1.00 60 0.39

Digression on the lateral and longitudinal digressions From the different results obtained with direction 2 and direction 3, one can expect the lateral spread of the gust to follow a same trend. The following results were found: P (M M 3 | T 5) P (T 5 | M M 3)

≈ ≈

P (∆X w = 390m, ∆Y = 180m) P (∆X = 180m, ∆Y = 215m)

= =

0.33 0.38

Even though the values are close, these data do not seem to be comparable at a first glance, but as they are the only ones available for the lateral spread of the gust, it could be interesting to see if they are coherent. For this it will be useful to have a continuous function of the lateral and longitudinal propagation probability. From the two empirical functions suggested before: P (∆X w = δx, ∆Y = 0) P (∆X = 180m, ∆Y = δy)

= =

e−δx/1545 0.87 e−δy/265

By extrapolating, an empirical function that combines the lateral and longitudinal probabilities of detection can be obtained. Noting it Pˆ , the function suggested is: δx

− Pˆ (∆X = δx, ∆Y = δy) = e− lx e

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|δy| ly

(6.13)

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CHAPTER 6. GUSTS PROPAGATION RESULTS where lx = 1545m and ly = 265m are two characteristic lengths that might depend on several gust parameters, like the amplitude or the duration, and geographical parameters like the surface roughness. A colored map of this probability function is drawn on figure 6.9. From this function we get Pˆ (∆X = 180m, ∆Y = 215m) = 0.4 and Pˆ (∆X = 390m, ∆Y = 180m) = 0.39.

Figure 6.9: Probability of detecting a gust - empirical function Pˆ

6.3

Example of gust propagation

Other examples of gust propagation can be found in annexes. The six upper plots represent the wind speed at the 6 locations from the meteorological mast to the 5 turbines. Bottom left: overview of the turbines disposition. Bottom right: wind direction at MM3.

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Figure 6.10: Example of gust propagation perpendicular to the row of turbines. The gust is clearly seen on T6 T5 and T7. Its recognition on T8 and T9 is less obvious.

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Figure 6.11: Gust wind speed(left) and direction(right) at three different heights on MM3. Top: 108m ; Middle: 80m ; Bottom: 52m.

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Figure 6.12: Gust wind speed at three different heights where a vertical delay is observed between each signal. The gust travels faster at higher wind speed, following a logarithmic law.

6.4

Summary of the propagation results

This sections is not a stand alone section. It summaries the results presented during this chapter. The punctilious reader is again invited to refer to the corresponding sub-section to have the detailed description leading to these results. Based on a correlation method, it has been proved that in a good approximation, the gust can be expected to travel at the average wind speed. Given this result, it has been possible to look into the raw data to describe the propagation of gusts. Probability of detecting a gusts • For a gust detected at a meteorological mast located 200m behind a turbine, the probability of seeing this same gust at the turbine is 84%. P (∆X = 200m, ∆Y = 0) = 84%

(6.14)

• The longitudinal probability of detecting a gust that have been previously detected at each location is: (6.15) P (∆X w = [0; δx], ∆Y = 0) = e−δx/lx with lx = 1300m • Still, The probability of longitudinal propagation of a gust is lower in a wake stream than in a free stream. By extrapolating the results obtained for several directions, we tried to interpret them in terms of longitudinal, lateral and vertical spread. The results were fitted with decreasing exponential, which seem to be the best fitting function. The empirical function suggested is of the form ;Pˆ (∆X = δx, ∆Y = δy) = δx

−

|δy|

e− lx e ly . It provides the probability of detecting a gust at a position downstream the location where the gust was detected. lx = 1545m and ly = 265m are two characteristic lengths that might depend on several gust parameters. Spread of the gust Even though the attenuation in amplitude of the gust has not been studied in this report, we strongly expect that the amplitude of the gust follows the same kind of mathematical shape than the empirical probability function above. Some trends have been noticed that require further investigation. For instance: • Gusts of narrow lateral spread seem to last longer than the ones with a wide ∆Y . • Gusts of wide vertical spread seem to last longer than the ones with a small ∆Z. • The lateral spread of the gusts does not seem to be affected by the vertical spread of the gust

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Part IV On the relation between gusts and mechanical loads

82

Contents

7

8

Extreme loads 7.1 Introduction . . . . . . . . . . . . . . . . . . . . 7.2 Conventional method . . . . . . . . . . . . . . . 7.2.1 Overview and prospects . . . . . . . . . 7.2.2 Step by step description of the method .

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84 84 85 85 85

Load response to a gust 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Response below the rated wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Response above the rated wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . .

90 90 91 91

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Conclusion

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Acknowledgements

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Chapter

7

Extreme loads 7.1

Introduction

In the design phase, one of the condition a wind turbine should fulfill is the resistance to an Extreme case. This extreme condition is generally based on a probabilistic estimation of the Extreme load that can occur with a Return period of 50 or 100 year. This should be indeed the worst case a wind turbine can encounter during its working life. The standard definition of extreme wind has been presented in the previous section 2.2.3. In this chapter, the focus is on extreme loads, and the traditionnal method using conditionnal probability is presented. Extreme case : Extreme gust, extreme response or extreme load? Different notions are gathered in the term extreme case. One can for instance look at extreme wind conditions or extreme loads conditions. A strong gust will not always imply a severe load response, especially for pitch regulated turbines(see chapter 8 and figure 8.1). Then the response of a turbine from a 50 year gust might not be the worst load case that can occur in 50 year. Even during strong storms, when the turbine is stand still, the loads on the turbine are smaller than during its operationnal mode. This is due to the importance of the aerodynamic forces, which are maximum at the rated wind speed. This is why the traditionnal study of extreme loads is not based on extreme wind conditions. Nevertheless, the IEC standards define a list of load cases(see [29], table 2) that sould be considered for the design of the turbine. These load cases are not only extreme cases, normal conditions are also found. It takes into account turbulence, gusts events and wind shear that can occur during the whole life of the turbine, from transport to operation. In this list the Extreme Operating Gust and the Extreme Direction Change can be found. From this list, the manufacturer will study the effects of each event on the loads. Each event is called a Design load case. For ultimate strength analysis, the assessment of the 50 year extreme load is required. 50 year extreme load If l stands for a load value(e.g. flap moment, in-plane moment, tower bending moment, etc.), and F is the cumulative density function of the load variable L, from the definition: we define F¯ as: F (L) = P (l ≤ L) (7.1) F¯ (L) = P (l > L) = 1 − P (l ≤ L) F¯ (L) then corresponds to the probability of exceeding a certain load value L.

84

(7.2)

CHAPTER 7. EXTREME LOADS

7.2

Conventional method

7.2.1

Overview and prospects

The conventional method to assess the extreme load is based on 10 minute average data, because these are the most common data available for wind turbines. Unfortunately a database of wind and load data over 50 year does not exist for obvious reason. Estimating the probability of exceeding a medium load is easy because a lot of data are available. The problem lies for high loads. These loads will determine the “tail” of the distribution. A good estimation of the tail is important to assess a 50 or even 100 year load. To compensate the lack of data, and mostly the lack of load data, simulations are performed using a stochastic model of the wind and model of the turbine response to a certain wind. As simulation has a certain time cost, the idea is to perform a sufficient but not too large number of simulations to provide a good estimate of the 50 year extreme load. The use of conditional probability is helpful to reduce the number of simulations. In the following, the results presented correspond to experimental data over 3 years. This can be used to validate results obtained with simulation methods. Other methods are currently developed for wind turbine design to determine the extreme response. The method that would be further described here, can be easily changed to add several observed/simulated extreme for each sample, by changing F (L|U, σ) by F (L|U, σ)E(n|U,σ) where E(n|U, σ) is the expected number of local maxima in the observation time period [28]. The method can also be easily improved by adding other conditions. For the design of an offshore turbine the zero up-crossing period Tz , and the wave height Hs can be added as condition for the load probability. This implies four successive integration instead or two, and a more complex joined probability density function [30]. To save simulation time, stochastic gusts for a given amplitude and standard deviation can be directly generated (P-W. Cheng [5] and W. Bierbooms [26], [3]). The condition added to the following method is then the gust amplitude, ad the join probability of gust amplitude for a given standard deviation and wind speed should be known. Eventually, the method of constrained simulation by means of wavelets [16] can also be used.

7.2.2

Step by step description of the method

Conditional distribution Conditioning the load on the wind speed (U ) and wind speed standard deviation(σ), the cumulative density function of the load is then defined as: Z Z F (L) = F (L|U, σ)f (U, σ)dσdU (7.3) U

σ

or in term of the probability to exceed a load value L: Z Z ¯ F (L) = F¯ (L|U, σ)f (u, σ)dσdU U

(7.4)

σ

Where f (U, σ) is the joined probability density function of σ and U defined by: f (U, σ) = f (U )f (σ|U )

(7.5)

Wind occurrence As the interest is focused on extreme values, the maximum from 10 minute load time series is extracted for different wind speed (U ) and wind speed standard deviation(σ). The number of 10 minute samples fulfilling the conditions of a certain wind speed bin and standard deviation bin,NUi σj ,is stored in a table:

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An example of this table can be found in annex C on table C.1. This table obtained with wind statistics data is a starting point to know how many simulation should be performed for each bin. Wind speed PDF The probability density function of the wind speed is commonly assumed to be a 2 parameters Weibull distribution, differing from on site to the other. The fitted distribution will be further written as f W (U ). The distribution at ECN test farm is plotted on figure 7.1.   k U k−1 −( U )k W f (U ) = e A (7.6) A A

Figure 7.1: Annual wind speed distribution fitted with a 2 parameters Weibull distribution

σ conditional PDF For the different values of the wind speed, the experimental conditional PDF of sigma is fitted with a log-normal distribution f ln (σ|Ui ). An example is given on figure 7.2. The general expression of the log normal probability density function of a positive variable x is : f ln (x) =

1 √

xs 2π

e−

(ln x−m)2 2s2

(7.7)

where m and s are the mean and standard deviation of the variable’s logarithm. Applying this definition it yields : (ln σ−m(Ui ))2 1 − ln 2s(Ui )2 √ f (σ|Ui ) = e (7.8) σs(Ui ) 2π February 2009

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CHAPTER 7. EXTREME LOADS For each bin of wind speed Ui , the distributions and values of m(Ui ) and s(Ui ) for ECN test farm are presented in annex C, on table C.2 and figure C.3.

Figure 7.2: Conditional distribution of the wind standard deviation for a given wind speed U=5 m/s

Load cumulative distribution For each bin {Ui , σj }, Nij 10 minutes samples are available. The maximum load value of each sample is extracted. These Nij load values are fitted with a 2 parameters Weibull distribution using the maximum likelihood method. A three parameters Weibull distribution would give better results. The Weibull cumulative density function of the load for the bin {Ui , σj } is written F W (L|Ui , σj ). The influence of U and σ on the flap moment distribution is shown on figure 7.3 and 7.4

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Figure 7.3: Cumulative distribution of the Flap moment - Influence of sigma - Bin of wind speed U=8.5 m/s

Figure 7.4: Cumulative distribution of the Flap moment - Influence of the wind speed - Sigma=1.25 m/s

Integration The final step of this method is to integrate the different conditional distributions in order to obtain the probability of exceeding a certain load L. XX F¯ W (L|Ui , σj )f W (Ui )f ln (σj |Ui )∆σ∆U (7.9) F¯ (L) = Ui

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CHAPTER 7. EXTREME LOADS This probability can be plotted with a logarithmic y-axis for better details on the tail of the distribution. Equalling F¯ (L) with the 50-year probability, one obtain an equation (solved graphically) that provides the extreme load for a return period of 50 years. The 50-year probability corresponds to the number of samples in 50 years. This yields the following equation to solve : F¯ (L) =

1 50 × 365 × 24 × 6

(7.10)

The number ’6’ in the previous fraction corresponds to the fact that six 10-minutes samples per hour are used to extract maximum loads. If several maximum loads are extracted by 10-minutes sample, this value should be changed.

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Chapter

8

Load response to a gust 8.1

Introduction

Method Gust propagation has been studied previously with the use of statistics. The term “propagation” was interpreted in the sense of “probability of detecting” a gust. Nevertheless, instead of looking at the position of the gust, it is also interesting to see what are the consequences of the gust propagation on the turbine loads. This task is a delicate one, and unfortunatly not enough time have been spent on this topic. Preliminary results are presented in this chapter. The method used consisted in detecting gusts at the meteorological mast MM3 where the wind direction was such that the gusts was expected to propagate to Turbine 6. From the ECN database, validated loads and turbine parameters for the corresponding gust event were extracted. This operation takes a long time. This procedure has been repeated for 8 different gusts events. The problem was to find appropriate gusts below the rated wind speed. Indeed, gusts occuring at low wind speed have low relative amplitude, and thus, they will not propagate well. Gusts of high relative amplitude occuring below the rated wind speed and with a wind direction corresponding to the direction MM3-T6 are rare. An example of such event is studied in this chapter, and then, a gust occuring above the rated wind speed is studied. Turbine response The Nordex turbines studied are pitch regulated turbines. In a previous study[20] of these turbines the relation between the thrust and the incoming wind speed has been studied. An illustration of this relation is plotted on figure 8.1.

Figure 8.1: Evolution of the thrust with the wind speed[20]

From the previous picture one can expect that the effect of a gust below the rated wind speed will be to increase the thrust. On the opposite, above the rated wind speed, the loads will decrease. In this sense, negative gusts would represent a sudden increase of the loads. The dynamic response of the controller will be quickly studied. Comparison with stall regulated turbines would have been interesting. Indeed, the previous figure would have been different for this kind of turbines as the thrust

90

CHAPTER 8. LOAD RESPONSE TO A GUST is always increasing with the wind speed. Gusts are more dangerous phenomena for stall regulated turbines than pitch regulated ones.

8.2

Response below the rated wind

The example presented on figure 8.2 is studied. The gust detected at MM3 propagates well to T6 as it can still be detected 10s after at Turbine 6. Below 12 m/s the pitch controller is not active. The increase of the wind speed due to the arrival of the gust imply a small increase of the loads, but at t=11s the controller is active, and start pitching the turbine. The load then quickly drops down. As soon as the wind speed starts dropping again, the load increases till it reach its value before the gust. As expected in the introduction of this chapter, the turbine is not affected by the gust. The pitch controller quickly damps the loads if the wind speed increases above the rated wind speed. There is of course a small delay before the attenuation of the load where the load increase. Nevertheless, this increase is not dangerous for the turbine.

(a)

(b)

Figure 8.2: Response to a gust occuring below the rated wind speed. The pitch control system activates the pitching of the blades to reduce the loads. Fig. a) corresponds to the gusts detected at MM3. Fig. b) represents the outplane load and the wind speed at turbine 6.

8.3

Response above the rated wind speed

The example presented on figure 8.3 is studied. Above 12 m/s the pitch controller is always active and perfom a permanent control on the load. February 2009

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(a)

(b)

Figure 8.3: Response to a gust occuring above the rated wind speed. The controler is active and performs a permanent control on the load. Fig. a) corresponds to the gusts detected at MM3. Fig. b) represents the outplane load and the wind speed at turbine 6.

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Conclusion

From turbulence to gust definition Wind turbulence has been studied world wide during the past fifty years. Among all the notions related to turbulence, the notion of gusts which corresponds to a short-term fluctuation of the wind field has been studied. As this definition is not accurate, and as a lot a different definitions of gusts are used by wind experts, an overview of all definitions has been presented. From this, some general trends can be underlined. Gust duration is below 2 minutes. Above this, the origin of the fluctuations are associated with large scale phenomena in the atmosphere, that might not be associated with turbulence. Low amplitude fluctuations do not keep their structure for a long time as it dissipates, so that, to differentiate a gust event from the local turbulence a minimum amplitude should be given. In this report, the relative amplitude of 2 m/s has been used for several algorithms. Indeed, the relative amplitude, which is the difference between the average wind speed and the gust amplitude is a relevant parameter for gust descriptions. The IEC standards define extreme gusts that can be used for the design of wind turbines. These extreme events are based on experimental data and have been idealized in a mathematical form. Gust detection algorithms After the different definitions of gusts were presented, several detection methods were described, and implemented. Each method provides different results and focus on different aspects. A standardization of the notations has been done to unify all methods, and compare their parameters with same definitions. The comparison of the method led to the following conclusions. The Peak over threshold method is a fast method to detect high relative amplitude gusts, but the resulting shapes will be really different from the IEC definitions. The velocity increment is not efficient to detect interesting gusts in the way it is often implemented. It is a good method to assess the maximum local turbulence though. Adding a threshold condition to this method, and allowing several gust extractions for a 10 minute sample, could provide interesting events, such as really fast fronts. The correlation method is one of the most time consuming method. Its main advantage is to provide gusts with a specific shape, independently of the amplitude. As a result of this, a threshold has to be added to this method also, to avoid detecting low amplitude gusts, and a minimum correlation has to be defined. Nevertheless, strong and dangerous gusts can take a lot of different shapes, which are not likely to be close to the IEC definitions. Mean gust shape and gusts statistics Analysis on the mean gust shape, illustrates the differences between the different algorithms. Nevertheless it revealed some trends such that, for instance, the fall of the gust takes more time than its rising. The standard deviation of the wind sample is of course determinant in the amplitude of the gust, and in a sense, has more influence than the local turbulence intensity. The fact that the standard deviation determines the gust relative amplitude is obvious. Nevertheless, it is more surprising that the turbulence intensity has a small influences on the relative amplitude of the gust. Indeed, for a given level of turbulence intensity, a lot of gusts of different amplitudes are found. No obvious correlation can be found. This is due to the fact that the relative gust amplitude depend with an affine relation on the average wind speed. As a result of this a given turbulence intensity, corresponds to a lot of values of Umean and σ, and thus a lot of different 93

CHAPTER 8. LOAD RESPONSE TO A GUST gust relative amplitudes. Vertical profile ECN test site EWTW is implemented with a really rich set of sensors. It has been possible to study the “lateral profile” of the gust by studying three different heights. Following this study, it has been seen that the gusts detected were in average detected 80% of the time at the three different heights, representing a spread of at least 60m vertically. The average profile along all gusts suggested that, as the wind speed is higher at high heights, the gust might arrive earlier at higher heights, and later at lower heights than at the reference detection height. Nevertheless, even though the gust can be seen at the three heights, its amplitude is not following the vertical logarithmic law for the reason that follows. Gusts were detected at 80m height. The large amount of gusts detected, can lead to the assumption that 80m height is in average the spatial center of the gust. An attenuation of amplitude is observed for heights far from the spatial center. As a result of this, the average wind speed of the gust at 80m will be higher than the average wind speed of the gust at 108m, which is far from the assumed spatial center. One shall thus not expect the gust amplitude to follow the logarithmic law. The IEC refers also to wind direction change. Eventhough it has not been a complete part of our study, the mean direction profile corresponding to the wind speed gusts, seems to reveal the presence of an average direction change. This means that in average, a gust detected with an method based on its amplitude, is likely to include a direction change. Nevertheless the wind direction change with height is a complex phenomenon that was not part of the prospect of this report. Gust propagation Based on a correlation method, it has been proven that in a good approximation, the gust can be expected to travel at the average wind speed. Given this result, it has been possible to look into the raw data to describe the propagation of gusts. By extrapolating the results obtained for several directions, we tried to interpret them in terms of longitudinal, lateral and vertical spread. The results were fitted with decreasing exponential, which seem to be the best fitting function. The |δy| δx − empirical function suggested is of the form:Pˆ (∆X = δx, ∆Y = δy) = e− lx e ly . It provides the probability of detecting a gust at a position downstream the location where the gust was detected. Even though the attenuation in amplitude of the gust has not been studied in this report, we strongly expect that the amplitude of the gust follows the same kind of mathematical shape. Some trends have been noticed that require further investigation. For instance it has been noticed that the gusts of narrow lateral spread seem to last longer than the ones with a large ∆Y . Further on A row of onshore turbines, characterized by flat terrain, has been studied. The gusts parameters are site-specific, so that, comparison with other locations is required to complete this work. Even though ECN test farm is well equipped the presence of several additional meteorological mast would have made easier the detection of gusts during their propagation. A correlation method to detect their spatial propagation could be then implemented. The attenuation of amplitude of gust with the distance was hard to analyze in this case as the wind speed sensors of the turbines were in the wake of the rotor, and thus, not representative of the average wake wind speed. Further work can be performed for typical offshore wind parks for instance, or other parks that have a different layout than a row. Gusts simulation have now to take into account the difference of spectrum of the wind with the average wind speed to correct the analytical spectrum used, which does not seem to reflect the experimental results for the mean gusts shape. The knowledge of gust propagation can also be used to optimize the production of power by introducing a communication between all the pitch controllers of a wind park. The influence of small gusts on loads can be neglected for pitch regulated turbines. Nevertheless, the upcoming of new generation offshore 2/3 blades stall regulated turbines can be expected in the following years as this technology can significantly reduce the operation and maintenance cost. It would then require careful analyses on stress and constrains due to gusts and vertical shears they can imply.

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Acknowledgements

I would like to thank Peter Eecen, first because he offered me the possibility of doing my internship in the wind department of ECN, but mainly because, as a supervisor, he really made this work enjoyable: regularly guiding and advising me, but also offering me the freedom to inquire and spend some time in other directions if I was curious about it. One can only appreciates how he contributes to provide to the trainee more than knowledge by encouraging to set up contacts, participate to team projects and colloquium, and travel to meet people from the wind energy or visit a wind farm, or assist to a wind-car race! From the housing accommodation to the office comfort, ECN makes the daily life of interns really easy. I have been sharing my office with Lucas Pascal and Vincent Grebille, two friends who really participated by their joy and support in bringing a human dimension to this project: supporting me to face the different problems, and distracting me to make the work place a comfortable and delightful environment. I would also like to thank Wim Bierbooms, whose expertise in gusts and their simulation contributed to guide me into my research. Meeting him was a chance, and a pleasure. Eventually, I would like to thank all the personnel from ECN I met. If it was for scientific or administrative purpose, or if it was in spare time, they all welcomed me with attention. They all participate in making this project a rich adventure.

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Appendix

A

Examples of gusts propagation through a row of turbines Two types of figures will be presented in this annex. Figures consisting of 8 different plots have the following disposition: • Top left: the original gust detected at MM3. • The five other red time plots represent the wind speed at each turbine. The solid(purple) vertical line represents texpected , while the dotted(green) vertical line represents tcorr . The other longdashed(orange) line, corresponds to the arrival time if the gust was traveling at its maximum speed. • Bottom left: overview of the turbine disposition, wind direction and incoming wind plane wave. • Bottom right: wind direction at MM3. Figures with 10 plots have on the left side the wind speed at each turbine, and on the right time plot of a parameter such as the power or the pitch angle.

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Free stream propagation

Figure A.1: Gust with a good lateral spread. The gust detected at MM3 can be seen on T5, T6 and T7

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Figure A.2: Good with a narrow lateral spread. The gust detected at MM3 is visible on Turbine 6 but nowhere else

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Propagation through a row of turbines Good propagation - example 1

Figure A.3: Gusts propagating quite well through the row and turns off turbine 7. The Power output of the turbines is presented on figure A.4

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Figure A.4: Gusts propagating quite well through the raw and turns off turbine 7 - Power view

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Good propagation - example 2

Figure A.5: Gust propagating through the row of turbines, and turning off almost all turbines 7. The Power output of the turbines is presented on the next figure A.6

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APPENDIX A. EXAMPLES OF GUSTS PROPAGATION THROUGH A ROW OF TURBINES

Figure A.6: Gust that turns off almost all turbines - Power output

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APPENDIX A. EXAMPLES OF GUSTS PROPAGATION THROUGH A ROW OF TURBINES

Good propagation - example 3

Figure A.7: A fast gust, well controlled by the pitch system. To see the pitch response to the gust refer to figure A.8

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Figure A.8: Pitch response to the wind speed. The pitch controller is fast enough to quickly reply to the gust.

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Appendix

B

Determination of the wind spectrum Theory The wind spectrum of the measured turbulence is required to provide an estimate of the mean gust shape. Indeed, knowing the power spectral density of the wind S(f ), the Wiener-Khinchin theorem relates it to the autocorrelation function R(τ ) via the Fourier transform: Z ∞ R(τ ) = S(f ) e2πjf τ df (B.1) −∞

The autocorrelation function can then be used to estimate the mean gust shape using the theoretical analysis described previously in section 4.3.1. The power spectral density can be obtained numerically using the fast Fourier transform. If y(t) is a signal, and Y (f ) = fft (y(t)) its Fourier transformation, the power spectrum is: S(f ) = Y (f ).Y (f )∗ (B.2) Protocol The determination of the spectrum, is performed for different bins of wind speed as differences in their spectra are expected. Bins of 1 m/s centered on the integer values are used. The spectrum has been determined using one year of data: 2007. For each day, each 10 minute sample is extracted, its average wind speed is calculated, and then it is saved with a unique name corresponding to its time and average wind speed. Once this extraction has been done for each day, all the samples corresponding to one bin of wind speed are concatenated to form one long sample. A spectral analysis is performed on this long sample, to extract the spectrum of the corresponding bin of wind speed. u [m/s] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

H=52m 566 1839 4064 6236 6979 6907 5896 4684 3748 2709 2081 1679 1235 801 620

H=80m 499 1576 3811 5097 5558 5948 5763 5179 4090 3128 2388 1913 1578 1107 778

H=108m 580 1433 2890 4136 4583 5321 5269 4879 4393 3754 2705 2328 1860 1414 949

u [m/s] 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

H=52m 341 215 183 118 54 29 17 13 8 13 10 14 4 1 0

H=80m 591 331 183 187 150 77 27 18 19 12 8 10 10 10 2

H=108m 595 463 362 192 178 138 96 42 14 12 14 9 11 6 12

Table B.1: Number of 10 minute samples corresponding to each bin of wind speed for the year 2007.

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APPENDIX B. DETERMINATION OF THE WIND SPECTRUM

Figure B.1: Power spectral density of the wind speed for different wind speed.

(a)

(b)

Figure B.2: Power spectral density of the wind speed for different heights : H=52m, H=80m, and H=108m. Slight differences are found between the spectrum at different height for a same sensor type. Nevertheless, the type of sensor has a strong influence on the shape of the spectrum at high frequencies. Fig. a) Use of cup anemometers, except for H=108m. Fig. b) Use of sonic anemometers. The data at height 80m and 52m for the sonic anemometers are unvalidated data

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APPENDIX B. DETERMINATION OF THE WIND SPECTRUM

Figure B.3: Wind speed distribution at different heights: H=52m, H=80m, and H=108m

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Appendix

C

Digression on turbulence In this annex, results concerning the turbulence and related probability density functions(PDF) at ECN test farm are presented. A precise statistical description of the occurrences of gusts is important for many applications and thus requires the knowledge of the intermittency of small-scale turbulence, which corresponds to an unexpected high probability of large velocity fluctuations[12]. Two studies were performed and their results will be presented below : • PDF of velocity differences for different time scales • PDF of the standard deviation σ for different wind speeds

PDF of velocity differences for different time scale A velocity increment algorithm has been run through one month of raw data for several characteristic times τ ∈ {0.5s; 2.5s; 25s; 250s; 4000s}. At each time position t of the studied month, the velocity increment uτ (t) = u(t + τ ) − u(t) is calculated for each τ , and so is the standard deviation of the 10 minute samples centered around t. u(τ ) and σ are rounded to the closest bin value. Bins of 0.1m/s are used for σ, and 0.05m/s for uτ . The three informations uτ , σ,τ determine a position in the tridimensional matrix containing the number of occurrence of each parameter value. The value of the matrix at this position is incremented by one. When this procedure has been performed for each time t, the matrix contain the number of occurrence in one month of each event defined by a set of three values {uτ ; σ; τ } . From this matrix of occurrences, the probability density functions is immediate. A model introduced by B. Castaing[2] and recently studied in Germany[14], suggests the following PDF by the use of Gaussian conditional probabilities p(uτ |σ) and a log-normal distribution of σ : Z ∞ p(uτ ) = p(uτ |σ) f (σ) dσ (C.1) 0     Z ∞ 1 u2 1 ln2 (σ/σ0 ) √ exp − τ2 √ exp − = (C.2) 2σ 2λ2 σ 2π σλ 2π 0 Adjustment of the two parameters σ0 and λ has been performed in [14]. In our study no time was available for this comparison. The number of occurrences of uτ /σ for different τ is plotted in figure C.1 The influence of the standard deviation σ on the number of occurrence of the amplitude values uτ (noted A in the plot) for different time scale τ is studied in figure C.2.

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(a)

(b)

Figure C.1: p(uτ /σ) for different time scales. A wide range of increments are found with a high time scale. Fig. a) with a normal scale, Fig. b) with a semi-logarithmic scale

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Figure C.2: p(uτ ) for different time-scale τ and different standard deviation values. As expected, for higher σ values(dashed lines), the increments have a higher amplitude. Nevertheless the time scale is still the parameter which has the main influence on the shape of the PDF. February 2009

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PDF of the standard deviation for different wind speed In the assessment of extreme loads, conditional distribution can be used. The method using conditions on the wind speed U and its standard deviation σ has been developed in chapter 7. The number of samples available for each bin of wind speed and standard deviation is presented on table C.1. In this method the log-normal distribution is used to determine the probability density function of the standard deviation σ, given a certain wind speed Ui . Let’s recall the general expression of the log normal probability density function of a positive variable x is : f ln (x) =

1 √

xs 2π

e−

(ln x−m)2 2s2

(C.3)

where m and s are the mean and standard deviation of the variable’s logarithm. For bin of each wind speed Ui , the distributions and values of m(Ui ) and s(Ui ) for ECN test farm are presented on table C.2 and figure C.3. Table C.1: Number of occurrences of different bins of σ and U for 3 years of data at ECN test farm σ: U : 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5 23.5 24.5 Sum

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0.25 5115 7379 7115 6939 5701 4392 2300 1087 460 227 131 116 49 2 0 0 0 0 0 0 0 0 0 41013

0.75 1454 5114 6275 7028 8100 8534 7585 5603 3272 1837 873 360 165 38 2 0 0 0 0 0 0 0 0 56240

1.25 46 390 1352 2035 2252 2645 3084 3516 3596 3434 2816 2051 1327 553 246 63 17 2 2 0 0 0 0 29427

1.75 5 12 54 207 389 534 595 666 665 723 840 865 866 836 678 463 250 164 70 29 10 1 1 8923

112

2.25 3 3 6 12 41 50 94 105 110 115 136 95 118 160 138 155 134 149 122 55 39 15 2 1857

2.75 1 1 5 1 5 4 11 30 12 21 23 22 13 15 21 24 23 22 22 21 18 9 7 331

3.25 2 0 0 0 2 1 4 9 9 10 5 5 8 8 3 2 6 4 5 4 2 2 2 93

3.75 1 0 0 0 0 0 1 3 0 3 1 2 3 1 0 1 0 1 0 1 1 1 1 21

Sum 6627 12899 14807 16222 16490 16160 13674 11019 8124 6370 4825 3516 2549 1613 1088 708 430 342 221 110 70 28 13 137905

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APPENDIX C. DIGRESSION ON TURBULENCE Table C.2: Statistical moments m and s corresponding to the log normal distribution of the standard deviation σ for different bin of wind speed. U 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5 23.5 24.5

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m -1.28 -0.91 -0.75 -0.66 -0.54 -0.44 -0.28 -0.14 -0.02 0.09 0.18 0.23 0.32 0.46 0.53 0.60 0.66 0.71 0.75 0.80 0.85 0.91 0.98

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sd 0.71 0.64 0.63 0.62 0.58 0.54 0.49 0.44 0.40 0.36 0.35 0.36 0.32 0.22 0.17 0.16 0.16 0.15 0.15 0.16 0.13 0.14 0.16

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APPENDIX C. DIGRESSION ON TURBULENCE

Figure C.3: p(σ|u) for different bin of wind speed February 2009

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Appendix

D

Peaks and envelop detection Peaks Detection The problem of peaks detections is of course present in gust detection method, but we also encountered it for detecting the main frequencies of a Fourier spectrum or for estimating the number of resonance phenomenon occurring in a meteorological mast. Different approaches are possible, depending on the regularity/smoothness of the signal.

A mathematical approach - Extremes above a threshold Local maxima correspond to the points where the derivative of a function is equal to zero, given the fact that our function is differentiable. To obtain a theoretical expression of a mean gusts shape, using stationary stochastic process statistics, the method of Middleton can be used. Further explanation of this method can be found in the section 4.3.1 and in the work of Gunner Chr. Larsen [15] We will here extract extrema of a signal, for data above a certain threshold A, and represent them by positive and negative Diracs. An elegant mathematical way to define this process, uses the following elementary operation functions g, e , δ, define as in figure D.1. g(x)

Rectifier

e(x) =

d dx g(x)

Step function

δ(x) =

d dx e(x)

Delta function

Figure D.1: Elementary mathematical functions We can then easily formalize the process of extreme above a threshold A detection by the following: Diracs(t) = −¨ u δ (u(t)) ˙ e (u(t) − A)

(D.1)

It is chosen to define minima as negative Diracs equal to −1. This instinctive process is described in figure D.2, borrowed in the mentioned above reference [15].

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APPENDIX D. PEAKS AND ENVELOP DETECTION

Figure D.2: Mathematical operation defining an extreme above a threshold A

Discrete signals A discrete signal cannot be defined as differentiable because on each point it’s left derivative and its right derivative are most of the time different. Then, an extremum will be defined as a change of sign in the discrete derivative of the signal. One can be satisfied by this result if studying a smooth signal or if each of the small extrema matters. An example of smooth signal is the mast acceleration envelop. An example of a none smooth signal is given in figure D.3.

Figure D.3: Example of a none smooth signal and different steps of the algorithm with a resolution of 3

In order to detect only main peaks, we introduce an algorithm which depends on a resolution parameter. This resolution defines the minimum length of the interval on which a extrema can be defined. The algorithm will consist in going through the signal vector. At each current position, we February 2009

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APPENDIX D. PEAKS AND ENVELOP DETECTION look at the position of the minimum and maximum in a vector of length resolution starting from the current position. We register these positions in a vector R, by adding or subtracting 1 in this vector. At the end of this, positions of R where the values equals ±resolution, are the positions of the wanted extrema. 1

2 3 4 5 6 7 8 9

FUNCTION f i n d M a x i m a A c c o r d i n g T o R e s o l u t i o n ( Resolution : Integer , S : Vector ) NEW R : Vector , size of S , filled with zeros . FOR i =0 to length of S T = S ( i : i + resolution ) imax = Position of max ( T ) in T imin = Position of min ( T ) in T R ( i + imax ) = R ( i + imax ) +1; R ( i + imin ) = R ( i + imin ) -1; ENDFOR

’Punctilious reader can see that this algorithm is not valid at the end of S. This is solved by adding at the end of S, resolution zeros. Figures D.3 illustrate the behavior of algorithm.

Envelop Detection Envelop detection is performed by multiplying a signal S by itself, and filter the resulting signal into an ideal filter that keeps only the low frequency. An appropriate cut-out frequency has to be chosen.

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Appendix

E

List of interesting gust events dates In this annex interesting events detected by the three algorithms are listed. They have been selected on their relative amplitude DU . The date, average wind speed and average direction are detailed on the following tables. The events detected with the IEC correlation method are on table E.1, the events detected by the Peak Over Threshold methods on table E.2, and for the velocity increment on table E.3. Table E.1: Interesting events: IEC Correlation gusts, DU > 5 and Corr > 0.9 19/05/2006 07/10/2006 01/11/2006 01/11/2006 01/11/2006 12/11/2006 04/12/2006 30/12/2006 31/12/2006 09/01/2007 11/01/2007 18/01/2007 18/01/2007 20/01/2007 21/03/2007 14/08/2007 10/09/2007 10/09/2007 10/09/2007 27/09/2007 09/11/2007 09/11/2007

-

Date 13:13:50 01:39:57 01:31:44 02:59:32 07:22:26 04:13:56 06:32:19 21:10:08 20:52:59 08:51:48 12:21:08 12:37:42 12:45:28 08:54:52 12:00:50 17:57:57 15:50:33 17:13:03 17:59:15 23:10:08 04:50:51 06:30:28

WS 18.6 13.1 18.9 18.8 20.9 11.5 9.9 22.6 15.9 20.1 24.7 28.4 27.2 21.4 11.0 11.6 9.5 11.2 9.0 10.7 13.4 13.7

WD 243 258 322 319 339 325 216 220 206 224 230 238 240 230 41 195 314 323 323 37 328 322

09/11/2007 09/11/2007 25/11/2007 25/11/2007 25/11/2007 18/01/2008 30/01/2008 31/01/2008 26/02/2008 01/03/2008 10/03/2008 12/03/2008 12/03/2008 12/03/2008 16/08/2006 16/08/2006 12/11/2006 25/11/2007 22/02/2008 01/03/2008 01/03/2008

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Date 09:45:11 12:13:03 11:15:43 20:01:40 22:56:02 23:29:00 05:56:16 13:35:14 07:07:01 00:32:29 13:30:58 08:20:03 10:34:34 15:50:49 16:13:10 16:13:11 02:30:25 12:48:55 12:58:22 09:55:52 09:55:53

WS 17.1 16.1 10.4 9.3 14.0 20.8 7.3 23.7 19.5 22.0 18.3 19.2 21.6 21.1 10.7 10.7 16.1 8.0 17.4 22.4 22.4

WD 327 340 313 305 328 242 324 203 230 241 165 241 257 280 273 272 303 314 236 306 306

APPENDIX E. LIST OF INTERESTING GUST EVENTS DATES

Table E.2: Interesting events: Velocity Increments gusts, DU > 6, T = 5 03/01/2007 04/01/2007 04/01/2007 04/01/2007 04/01/2007 07/01/2007 08/01/2007 09/01/2007 10/01/2007 10/01/2007 10/01/2007 10/01/2007 10/01/2007 11/01/2007 11/01/2007 11/01/2007 11/01/2007 11/01/2007 11/01/2007 11/01/2007 11/01/2007 11/01/2007 11/01/2007 13/01/2007 13/01/2007 17/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007

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Date 21:20:34 01:23:22 01:55:47 02:50:39 05:45:36 10:52:29 06:23:48 13:06:32 08:28:31 09:41:29 12:46:41 14:17:29 14:30:48 06:15:59 06:47:07 06:59:03 09:27:49 10:06:13 12:20:15 12:35:34 18:53:06 20:24:01 20:31:39 23:32:50 23:49:00 03:44:04 08:40:46 09:29:36 09:57:45 12:20:45 13:36:20 13:56:01 15:04:43 15:42:04 16:04:57 16:12:58 17:15:18 17:29:31 17:36:59 19:23:11 19:34:10

WS 17.9 19.5 18.3 18.9 14.9 16.9 13.5 22.4 20.0 20.0 18.8 17.6 17.3 18.6 19.6 20.6 23.2 22.7 24.8 24.3 19.9 20.6 20.0 18.6 19.7 13.2 23.3 26.8 27.0 27.5 24.2 20.3 19.1 21.0 22.2 26.2 25.4 28.7 31.6 25.5 26.8

WD 220 221 225 218 243 225 208 227 221 224 225 225 261 218 218 221 222 225 228 227 269 278 280 244 277 219 218 233 230 235 277 287 262 269 262 267 265 262 271 275 281

20/01/2007 20/01/2007 20/01/2007 28/01/2007 03/03/2007 18/03/2007 18/03/2007 21/03/2007 21/03/2007 05/05/2007 08/05/2007 08/05/2007 14/05/2007 26/06/2007 16/07/2007 24/07/2007 26/07/2007 10/09/2007 10/09/2007 24/09/2007 25/09/2007 28/09/2007 06/11/2007 06/11/2007 09/11/2007 09/11/2007 09/11/2007 09/11/2007 09/11/2007 09/11/2007 09/11/2007 09/11/2007 09/11/2007 09/11/2007 11/11/2007 11/11/2007 14/11/2007 25/11/2007 01/12/2007 02/12/2007 02/12/2007

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Date 07:47:00 08:27:28 09:12:33 14:34:17 08:26:37 05:42:29 06:48:14 00:34:47 12:30:25 00:10:52 15:39:33 16:50:09 09:21:39 11:18:33 17:50:26 07:50:32 20:16:55 16:11:13 17:13:03 10:41:48 03:18:00 06:05:16 05:49:48 07:25:11 00:16:09 02:28:14 04:50:05 05:12:28 10:01:27 12:12:30 15:37:49 17:20:28 18:21:44 22:04:35 14:40:22 20:22:37 02:10:58 11:15:39 06:46:02 03:09:48 14:03:45

WS 20.6 21.4 21.6 16.2 10.6 19.1 19.6 7.6 11.3 6.3 15.4 15.7 12.9 18.2 11.6 18.8 13.9 11.4 11.2 11.4 8.9 12.7 11.8 12.5 12.4 17.5 13.4 14.8 20.6 15.7 15.4 11.6 13.3 9.7 10.9 8.9 5.7 10.4 19.8 15.9 16.9

WD 228 226 234 291 74 246 273 19 16 21 244 275 226 308 273 339 233 332 323 193 247 49 327 337 312 313 339 312 332 328 320 310 330 309 328 324 40 306 256 271 202

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APPENDIX E. LIST OF INTERESTING GUST EVENTS DATES

Table E.3: Interesting events: POT A=6 gusts, DU > 7 19/05/2006 31/10/2006 01/11/2006 01/11/2006 01/11/2006 01/11/2006 01/11/2006 01/11/2006 11/11/2006 12/11/2006 30/12/2006 30/12/2006 04/01/2007 04/01/2007 09/01/2007 10/01/2007 10/01/2007 11/01/2007 11/01/2007 11/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007

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-

Date 13:18:20 22:23:49 00:56:00 02:37:04 02:57:13 04:01:36 06:08:30 07:33:25 17:46:35 11:34:47 20:19:17 21:52:35 01:23:22 01:48:03 11:26:30 08:41:30 14:17:29 06:15:59 10:09:05 12:20:32 08:52:58 09:36:24 09:39:47 09:41:46 10:56:43 11:29:57 12:10:03 12:24:37 12:27:54 12:38:13 13:25:07 13:56:01 15:50:40 15:57:41

WS 18.3 14.8 15.4 14.4 18.4 18.6 20.4 20.9 18.8 13.5 20.9 22.9 19.5 18.7 20.9 19.1 17.6 18.6 23.2 24.7 24.2 28.2 28.5 28.1 29.2 28.3 27.0 28.6 28.2 28.1 25.3 20.3 21.8 23.9

WD 237 315 313 322 323 321 326 342 302 316 216 236 221 224 223 218 224 218 219 228 229 230 226 229 232 233 230 233 234 240 279 286 262 264

18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/01/2007 18/03/2007 18/03/2007 21/03/2007 06/11/2007 06/11/2007 09/11/2007 09/11/2007 09/11/2007 07/01/2008 21/01/2008 31/01/2008 01/02/2008 29/02/2008 29/02/2008 01/03/2008 01/03/2008 01/03/2008 01/03/2008 01/03/2008 20/03/2008 30/03/2008

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Date 16:04:57 16:45:23 17:06:24 17:07:35 17:29:31 17:43:51 18:05:26 18:33:43 19:34:10 19:34:46 19:39:03 19:44:13 20:25:34 05:42:02 06:48:14 00:33:37 05:49:32 07:26:29 10:33:26 10:34:03 17:20:28 12:42:33 16:25:23 12:49:58 18:33:05 20:27:22 23:26:35 00:14:19 00:49:52 06:14:05 06:48:20 08:08:43 21:19:41 07:27:27

WS 22.2 23.8 24.2 24.2 28.7 32.0 27.7 28.0 26.8 27.1 26.3 26.3 27.9 19.3 19.6 7.3 11.6 13.2 12.8 13.0 11.6 18.7 19.3 21.5 15.4 21.4 21.7 21.3 21.4 23.4 23.3 23.0 17.9 16.6

WD 262 260 262 260 262 271 275 280 281 278 278 283 285 241 274 9 328 341 326 327 312 250 226 198 261 232 237 241 243 284 284 286 294 186

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Appendix

F

An introduction to wind turbines Why wind turbines ? After the oil crisis of 1973, governments started to see great interest in wind turbines. This was the first stimulus. After the oil crisis, wind energy tend to be a little bit forgotten, but now, it is more and more popular because of its low emission of C02 by considering the entire life of a turbine: manufacturing, installation, operation and maintenance, and eventually its de-comissionning. Rentability of wind turbine: the energy invested into the manufacturing and installation of a wind turbine is recovered within it’s first year of operation. For a customer the wind turbines is reimbursed within 7 years.

Generality about wind turbines One can differentiate the different turbines by their rotational speed regulation method: • Pitch control turbine: Adjusting the pitch can augment or reduce the incidence α. Reducing the incidence reduce the lift Cl . The rotational speed will then decrease, and so will the in-plane and axial loads. • Stall control turbine: While the wind speed increases, the incidence keeps increasing as well. As a result of this, stall will occur, which will reduce the rotational speed but not the axial loads.

Wind turbine performance The power coefficient represents the amount of energy that can be harvested from the wind to convert it into mechanical energy. The power coefficient reach it’s maximum for a unique tip speed ratio. Rotor designers focus on increasing the range of operating wind speed that will correspond to this maximum. Nevertheless, the main parameters that can significantly increase the output power, are the wind speed and the swept area. The following equations define general parameters involved in wind turbine performance. Power: P (U ) = Generator efficiency: η = Power Coefficient: Cp = Tip-speed ratio: λ =

1 ρSCp ηU 3 2 Generator Power Rotor Power Rotor Power Protor = 1 3 Dynamic Power 2 ρSU Blade tip speed ΩR = Wind speed U

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(F.1) (F.2) (F.3) (F.4)

APPENDIX F. AN INTRODUCTION TO WIND TURBINES

Figure F.1: Power curve - example of Turbine 6

(a)

(b)

Figure F.2: Power coefficient - example of Turbine 6. Cp as a function of: a)the wind speed ; b) the tip speed ratio.

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APPENDIX F. AN INTRODUCTION TO WIND TURBINES

Introduction to wind turbines aerodynamics: the actuator disk theory The actuator disk is a physical “trick” to represent the pressure drop as the rotor plan. Figure F.3 presents the different plane used in the Blade elementum theory (BEM) in order to obtain theoretical loss of velocity and thus, the theoretical maximum power that can be harvested from the wind, known as the Betz limit. Figure F.4 provides the shape of the velocity and pressure curves as the wind get through the turbine. The actuator disk concept, introduce a gap of pressure through the disk, whereas the the velocity is continuous.

Figure F.3: Definition of the 4 cross sections in the actuator disk method(inspired by [24])

Figure F.4: Pressure and velocity evolution through the actuator disk (inspired by [24])

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APPENDIX F. AN INTRODUCTION TO WIND TURBINES The steps leading to the establishment of the Betz results will be briefly presented. Curious reader can refer to [18] for further explanations. The figure above simply illustrates the mass rate definition: m ˙ = ρSU 2 . Conditions: U2 = U3 (continuity)

(F.5)

p1 = p4 (= p∞) (equilibrum)

(F.6)

Bernouilli’s equations: 1 p1 + ρU12 = p2 + 2 1 p3 + ρU32 = p4 + 2

1 2 ρU 2 2 1 2 ρU 2 4

(F.7) (F.8) (F.9)

The Thrust T is expressed by difference of momentum: 1 T = U1 m ˙ 1 − U4 m ˙ 4 = ρS(U12 − U42 ) 2

(F.10)

but also corresponds to the pressure drop through the disk: T = S(p2 − p3 )

(F.11)

We introduce a, called the Induction factor a=

U1 − U2 such that U2 = U1 (1 − a) U1

(F.12)

By equaling the thrust expression, and after some algebra: U2 =

U1 + U4 2

(F.13)

a=

U1 + U4 2

(F.14)

And:   1 ρSU13 4a(1 − a)2 2 1 T = ρSU13 [4a(1 − a)] 2 Cp = 4a(1 − a)2 P

(F.15)

=

(F.16) (F.17)

To get the maximum power that can be harvested, Cp is differenciated with respect to a: a =

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Cpmax

=

CT

=

1 3 16 ≈ 0.593 27 8 ≈ 0.889 9

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(F.18) (F.19)

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Appendix

G

An introduction to blade design Introduction The blade design is an important phase of the development of a wind turbine, which is generally done by a specific company. Aerodynamicist and structure engineers will work together to fulfill the requirement of the manufacturer. Most of the time the informations explicited in table G.1 are provided by the manufacturer to define the operating conditions of the turbine.

Table G.1: Common operating conditions known before the blade design Parameter P Urated Ucutin Ucutout Φrotor Φhub 1 2ρ Cprated λmax Wind class

The ratio

P SR otor

=

P

π Φ 4 R

Example 2.5 MW 13 m/s 4 m/s 25 m/s 90 m 9m 0.645 > 0.45 70 m/s 1

is 450 for a Class 1 turbine, and 300 for class 3.

3 Srotor Cp we obtain Urated that we can compare with the one From the Power equation: P = 12 ρUrated given by the manufacturer. We can then obtain λrated : λmax λrated = (G.1) Urated λdesign λrated

is usually around 1.2 , 1.25

Then, λdesign can give the φ = 23 arctan





1 λdesign r/R

Blade shape for ideal rotor without wake rotation Basics formula used in the pre-design phase come from the optimization of the rotor which takes into account the rotation in the wake[18]. This theory ignores the drag and tip losses. The optimization is

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APPENDIX G. AN INTRODUCTION TO BLADE DESIGN obtained by differentiation of the power coefficient Cp with respect to φ, where φ is the angle of the relative wind. The algebra is described in the previous reference. The results used are:   2 −1 ) (G.2) φ = tan 3λr 8πr(1 − cos(φ)) c = (G.3) BCl Where c(r) is the chord of the blade at the radius r. B, the number of blade, and λr is the local tip speed ratio: s Ωr a(1 − a) r λr = =λ = (G.4) U R a0 (1 + a0 ) The simple use of these formula combined with the equation of a thick profile (e.g. NACA64418) and the choice of blade number suggested by table G.2, can provide an idea of the ideal shape of the rotor. By using a mesh, one can easily plot a 3D turbine with Matlab. The result of the small Matlab program written during this internship is plotted on figure G.1.

(a)

(b)

Figure G.1: 3D representations of an ideal rotor without wake rotation. a) λ = 10, B = 3 ; b)λ = 2, B=7

Table G.2: Blade number and tip speed ratio, suggestions λ 1 2 3 4 >4

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B 8-24 6-12 3-6 3-4 1-3

Torque Good torque ” ” Convenient for electric power ”

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Airfoil Curved plates is enough ” ” Aerodynamic design required ”

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APPENDIX G. AN INTRODUCTION TO BLADE DESIGN

General design rotor procedure • U : Knowing the region where the turbine will be implemented gives the main wind speed at this area. • P :The Power needed at this main wind speed is chosen. • R: From the power equation, with an estimation of the Cp , the blade radius is calculated. • λ: The tip-speed ratio is chosen, depending of the use of the turbine and the noise specification (see table G.2) • B: The number of blade is chosen according to λ (see table G.2. • Airfoil: An airfoil is chosen (for the predesign, only one airfoil is enough) • α: α and Cl are chosen such that ∀r ∈ [0; R], CCdl is minimum • φi , ci : For each element i of the blade, the optimum rotor theory provides the twist angle and the chord. φi = θp,i + αdesign,i

(G.5)

θT,i = θp,i − θp,0

(G.6)

• Shape: Linearizing the chord and the twist angle provides a smoother shape • Performance a,a0 : For each element the performance are determined. • Cp : Numerical integration provides the Cp . General rules and remarks: • A more slender design is always better for extreme loads. • The higher the λdesign , the lower are the extreme loads. • The maximum tip speed ratio for a turbine design is specified by the maximum noise. • Number of blades: with two blades, the rotational speed has to be higher. as a result of this, the turbine will be noisier. This will be the main limitation, at least for onshore turbines. • Predesign: For the predesign, no specific optimised profile is chosen. Calculations are based on standard values such as: Cl ∈ [0.9; 1]

(G.7)

α ∈ [6.5; 7]

(G.8)

In order to use real data, one can for instance use the NACA421 profile which has an average thickness. • The aerodynamist would of course like to have a thin profile(thickness around 12%) all along the profile, but this is structurally impossible. • From equation G.3, the table of the chord c with respect to r/R can be filled. The values we obtained are bigger at the hub and the tip than the expected one though. The use of BOT, an ECN software optimizing the aerodynamic design of wind turbine blades, in a later process, will generally render the blade more slender by 80%.

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APPENDIX G. AN INTRODUCTION TO BLADE DESIGN • It is generally good to keep the value γ∆r = dΓ dr ∆r more or less constant all along the blade to avoid increasing turbulent in the wake. This condition is almost the same than keeping a constant. The optimal would be to keep γ constant, but this will only give good performance for the rated conditions and the turbine needs to keep efficient off design conditions. .

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Index

Betz limit, 14, 123 Blade elementum theory, 123

Middleton, 51 MM3, 10, 11, 63 Moving window, 28 Moving-averaging method, 32

Correlation, 30 Correlation method, 28

Negative gust, 21 Nordex, 9

database, 34 Design load case, 84 Duration of the gust, 49 Durst, 27

Peak over threshold, 27 Peak-peak procedure, 27 Pitch control turbine, 121 Plane wave, 65 Power, 14 Power law, 15 Prandtl mixing length theory, 14 Propagation of gusts, 66

Absolute amplitude, 40

EWTW, Extreme Extreme Extreme Extreme Extreme Extreme Extreme

9, 63 case, 84 coherent gust, 24 coherent gust with direction change, 25 direction change, 24 load, 84 operating gust, 24 wind shear, 25

Free stream, 72 Friction velocity, 15 Front, 21 Gust factor, 26 Gust peak factor, 27 Gust rising time, 33 Gust shape, 51 Gusts extraction, 64 Half Fall Ratio, 33, 38 Half Rise Ratio, 33, 38 IEC, 24 Induction factor, 124 log-normal distribution, 86 Logarithmic law, 15

Relative amplitude, 40 Return period, 84 Rising time, 38 Shear stress, 14 Squall, 21 Stall control turbine, 121 Standard deviation, 37 Stochastic, 51 Surface roughness length, 15 Turbulence intensity, 18, 44 Velocity increment method, 27 Velocity increment over threshold, 28 Wake stream, 75 Weibull distribution, 16, 86 Wieringa, 27 Wind classes, 25 Wind direction, 13

Method of bins, 36 Mexican-hat, 21 129

Bibliography

[1] ECN annual report. ECN, 2007. [2] E.J. Hopfinger B. Castaing, Y. Gagne. Physica D 46,177, 1990. [3] W. Bierbooms. A gust model for wind turbine design. JSME International Journal, Series B, Vol.47, No.2, 2004. [4] W. Bierbooms. Specific gust shapes leading to extreme response of pitch-regulated wind turbines. Journal of physics : Conference series 75, 2007. [5] Po Wen Cheng. A reliability based methodology for extreme responses of offshore wind turbines. DU Wind, Delft University wind Energy Research Institute, 2002. [6] European Commission. European wind turbine standards II. ECN-C–99-073. [7] CRAN. The R project - http://www.r-project.org/. [8] Lidija Cvitan. Determining wind gusts using mean hourly wind speed. Geofizika Vol.20 - UDC 551.509.52, August 2003. [9] P.J. Eecen. Turbulence intensity ewtw according to iec 61400-1. ECN report. [10] P.J. Eecen and S.A.M. Barhorst. Extreme wind conditions - Measurements at 50m Meteorological Mast at ECN, Petten. ECN-C–04-019, February 2004. [11] P.J. Eecen and J.P. Verhoef. EWTW Meteorological database. Description June 2003 - May 2006. ECN-E–06-004, September 2006. [12] H.-P. Waldl F. Boettcher, Ch. Renner and J. Peinke. On the statistics of wind gusts. Boundary layer meteorology, Vol. 108, August 2002. [13] St. Barth F. Boettcher and J. Peinke. Smale and large scale fluctuations in atmospheric wind speed. June 2005. [14] St. Barth F. Bottcher and J. Peinke. Small and large scale fluctuations in atmospheric wind speeds. 2006. [15] W. Bierbooms G.Cr. Larsen and K.S. Hansen. Mean Gust Shapes. Ris-R-1133(EN) - Ris National Laboratory, Roskilde, Denmark, December 2003. [16] Kurt S. Hansen Gunner Chr. Larsen and Bo Juul Pedersen. Constrained simulation of critical wind speed gusts by means of wavelets. [17] S. Mallat. A wavelet tour of signal processing. Academic Press, 1998.

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BIBLIOGRAPHY [18] J.F. Manwell, J.G. McGowan, and A.L. Rogers. Wind Energy Explained. J. Wiley and Sons, LTD, August 2003. [19] Mathworld. http://www.mathworld.wolfram.com/Variance.html. Wolfram. [20] T.S. Obdam. Using Operational Experience for Optimizing O&M of Offshore Wind Farms. ECNWind Memo-07-034, 2007. [21] L. Pascal. Mexico project data analysis. ECN, February 2008. [22] H. Braam P.J. Eecen, L.A.H. Machielse and J.P. Verhoef. EWTW statistics. ECN-CX–05-084 Confidential, September 2005. [23] E. Gilleland qand R. W. Katz. Extremes Toolkit : weather and climate applications of ectreme values statistics. 2005. [24] Nick Jenkins Tony Burton, David Sharpe and Ervin Bossanyi. Wind Energy Handbook. J. Wiley & Sons, 2001. [25] J. B. Dragt W. Bierbooms and H. Cleijne. Verification of the mean shape of extreme gusts. Wind Energy, 2, 137-150, August 1999. [26] Po-Wen Cheng W. Bierbooms. Stochastic gust model for design calculation of wind turbines. Journal of wind energineering and industrial aerodynamics, Vol.90 Pages 1237-1251, 2002. [27] D. M. Smith W. N. Venables and the R Development Core Team. An Introduction to R : A Programming Environment for Data Analysis and Graphics. 2008-10-20. [28] TC88 WG1. IEC 61400-1 Annex F : Statistical extrapolation of loads for ultimate strength analysis. 2005. [29] TC88 WG1. IEC 61400-1 Wind turbines : Design requirements. 2005. [30] TC88 WG3. IEC 61400-3 Annex G : Characteristic offshore wind turbine loads for ultimate strength analysis. 2005. [31] Y. Zhou and A. Kareem. Definition of wind profiles. J. Struct. Eng. - ASCE, 128, 1082-1086, 2002. .

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