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176 E. Anahua et al. D 1 L(u) 10 (a) 100 (b) 5 0 −5 −Φ D 1 L(u) −100 −200 0 2 P(L(u)) −10 1000 1500 2000 −300 1000 1500 2000 Elect. Power L(u) [kW]: = 14.6 [m/s] Elect. Power L(u) [kW]: = 14.6 [m/s] Fig. 31.2. (a) The deterministic dynamics D (1) (L) of the power for 〈u〉 = 14.6m s −1 .(b) The correspondent potential φD and the power distribution P (L(u)). The minima of φD are the fixed points, stable-states. Position 1 and 2 represents a fixed point and the simple average power, respectively Elec. Power Output [kW] 3000 2500 2000 1500 1000 500 0 0 5 10 15 20 25 30 35 Wind Speed [m/s] Fig. 31.3. Stationary power curve given by the fixed points for all wind velocity intervals, black line. The arrows represent the deterministic dynamical relaxation of the power output given by a two-dimensional analysis, D (1) (L, u) 31.5 Conclusion and Outlook A simple power output model has been described as a function of relaxation and noise. The stationary power curve has easily been derived by the fixed 1
31 Characterisation of the Power Curve for Wind Turbines 177 points method which does not depend any more on the average procedure, i.e. location specific with increased turbulence intensity. Heretofore the relaxation time is described analytically as linear and constant. A detailed analysis on the dynamical relaxation is actually researching together with the response model proposed by Rauh [6] for predicting power output. References 1. F. Boettcher, Ch. Renner, H.-P. Wald and J. Peinke, (2003) Bound.-Layer Meteorol. 108, 163–173 2. E. Anahua et al. (2004) Proceedings of EWEC conference, London, England 3. H. Risken, (1983) The Fokker-Plank Equation, Springer, Berlin Heidelberg New York, 1983 4. R. Friedrich, S. Siegert, J. Peinke, St. Lueck, M. Siefert, M. Lindemann, J. Raethjen, G. Deuschl and G. Pfister, (2000) Phys. Lett. A 271, 217–222 5. Tjareborg Wind Turbine Data (1992). Database on Wind Characteristic, www.winddata.com, Technical University of Denmark, Denmark 6. A. Rauh and J. Peinke, (2003) J. Wind Eng. Aerodyn. 92, 159–183
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Wind Energy Proceedings of the Euro
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Prof. Dr. Joachim Peinke Dr. Stepha
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VI Preface been presented, spanning
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VIII Contents 3.3 Stochastic Wind F
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X Contents 12.6 Subgrid Scale Turbu
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XII Contents 22 Stochastic Small-Sc
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XIV Contents 32 Handling Systems Dr
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XVI Contents 41 3D Numerical Simula
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XVIII Contents 51 Comparing WAsP an
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XX Contents 58.3 Ultra-High Perform
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XXII List of Contributors Lars Berg
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XXIV List of Contributors Renata Gn
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XXVI List of Contributors A. Kiss D
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XXVIII List of Contributors El˙zbi
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XXX List of Contributors Ivo Sláde
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1 Offshore Wind Power Meteorology B
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1 Offshore Wind Power Meteorology 3
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1 Offshore Wind Power Meteorology 5
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2 Wave Loads on Wind-Power Plants i
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Trubaduren 2 Wave Loads on Wind-Pow
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Base moment (10 6 Nm) 0.4 0.2 −0.
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2 Wave Loads on Wind-Power Plants i
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3 Time Domain Comparison of Simulat
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3 Time Domain Comparison Using Cons
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7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 3 T
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4 Mean Wind and Turbulence in the A
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5 Wind Speed Profiles above the Nor
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5 Wind Speed Profiles above the Nor
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Height [m] 100 90 80 70 60 50 40 30
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6 Fundamental Aspects of Fluid Flow
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f Suu(f, z) / σ 2 u(z) 10 0 10 −
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a) c) −0,375 6 Fluid Flow over Co
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7 Models for Computer Simulation of
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y/h 2.5 2 1.5 1 0.5 0 7 Models for
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8 Power Performance via Nacelle Ane
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9 Pollutant Dispersion in Flow Arou
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x1/B 0.3 0.5 0.8 1.0 9 Pollutant Di
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9 Pollutant Dispersion in Flow Arou
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10 On the Atmospheric Flow Modellin
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11 Comparison of Logarithmic Wind P
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Height above ground in m 100 90 80
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12 Turbulence Modelling and Numeric
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13 Gusts in Intermittent Wind Turbu
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Durations (s) 25 20 15 10 5 13 Gust
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14 Report on the Research Project O
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height z (m) 100 80 60 40 20 0 14 R
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14.6 Outlook 14 Report on the Resea
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15 Simulation of Turbulence, Gusts
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S(ƒ)(m/s) 2 /Hz 15 Simulation of T
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15 Simulation of Turbulence, Gusts
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16 Short Time Prediction of Wind Sp
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ms prediction error [m/s] 16 Short
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16 Short Time Prediction of Wind Sp
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17 Wind Extremes and Scales: Multif
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Log10 E(k)*k**(5/3) 6 4 2 0 5/3 cor
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17.3 Discussion and Conclusion 17 W
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18 Boundary-Layer Influence on Extr
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z/H (a) (b) 4 2 18 Boundary-Layer I
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18.6 Concluding Remarks 18 Boundary
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19 The Statistical Distribution of
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19 The Statistical Distribution of
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20 Superposition Model for Atmosphe
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h(u) 0.5 0.3 0.1 20 Superposition M
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21 Extreme Events Under Low-Frequen
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21 Extreme Events Under Low-Frequen
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22 Stochastic Small-Scale Modelling
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Page 159 and 160: 23 Quantitative Estimation of Drift
Page 165 and 166: 24 Scaling Turbulent Atmospheric St
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Page 169 and 170: 25 Wind Farm Power Fluctuations P.
Page 171 and 172: 25 Wind Farm Power Fluctuations 141
Page 173 and 174: d rc q rc V 0 q V 25 Wind Farm Powe
Page 175 and 176: References 25 Wind Farm Power Fluct
Page 177 and 178: 26 Network Perspective of Wind-Powe
Page 183 and 184: 27 Phenomenological Response Theory
Page 189 and 190: 28 Turbulence Correction for Power
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Page 193 and 194: 29 Online Modeling of Wind Farm Pow
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Page 197 and 198: 30 Uncertainty of Wind Energy Estim
Page 203 and 204: 31 Characterisation of the Power Cu
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Page 209 and 210: 32 Handling Systems Driven by Diffe
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Page 213 and 214: 33 Experimental Researches of Chara
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Page 217 and 218: 34 Methodical Failure Detection in
Page 219 and 220: 34 Methodical Failure Detection in
Page 221 and 222: 35 Modelling of the Transition Loca
Page 223 and 224: 35 Modelling an Airfoil with Surfac
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Page 227 and 228: 35 Modelling an Airfoil with Surfac
Page 229 and 230: 36 Helicopter Aerodynamics with Emp
Page 235 and 236: 37 Determination of Angle of Attack
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Page 239 and 240: Drag coefficient 0.5 0.4 0.3 0.2 0.
Page 241 and 242: 38 Unsteady Characteristics of Flow
Page 243 and 244: PSD PSD 38 Unsteady Characteristics
Page 245 and 246: 39 Aerodynamic Multi-Criteria Shape
Page 247 and 248: 39 Multi-Criteria Shape Optimizatio
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Page 251 and 252: 40 Rotation and Turbulence Effects
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Page 255 and 256: Standard deviation of Cp 0.7 0.6 0.
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41 3D Numerical Simulation and Eval
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41 3D-CFD-Simulation of a Wind Turb
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42 Performance of the Risø-B1 Airf
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42 Performance of the Risø-B1 Airf
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43 Aerodynamic Behaviour of a New T
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44 Numerical Simulation of Dynamic
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44 Numerical Simulation of Dynamic
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45 Modeling of the Far Wake behind
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8 6 uz 4 2 45 Modeling of the Far W
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46 Stability of the Tip Vortices in
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46 Stability of the Tip Vortices in
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47 Modelling Turbulence Intensities
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48 Numerical Computations of Wind T
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Z X Y 48 Numerical Computations of
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References 48 Numerical Computation
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49 Modelling Wind Turbine Wakes wit
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U mean / U ref 1 0.9 0.8 0.7 49 Mod
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49.5 Conclusion 49 Modelling Wind T
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50 Prediction of Wind Turbine Noise
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0.8 0.6 0.4 0.2 −0.2 −0.4 −0.
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51 Comparing WAsP and Fluent for Hi
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Table 51.1. Measurements and simula
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51 Comparing WAsP and Fluent for Hi
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52 Fatigue Assessment of Truss Join
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53 Advances in Offshore Wind Techno
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Simulation Measurement pitch angle
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53 Advances in Offshore Wind Techno
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54 Benefits of Fatigue Assessment w
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∆σN [N/mm²] 100 10 54 Benefits
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55 Extension of Life Time of Welded
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Transverse residual stresses [N/mm
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56 Damage Detection on Structures o
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56 Damage Detection on Structures o
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57 Influence of the Type and Size o
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[W/m 2 ] q t [W/m 5000 4000 3000 20
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58 High-cycle Fatigue of “Ultra-H
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(a) (b) 450 Load [kN] 400 350 300 2
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59 A Modular Concept for Integrated
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60 Solutions of Details Regarding F
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SR 1000 800 600 400 200 100 80 60 4
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60 Solutions of Details Regarding F
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61 On the Influence of Low-Level Je
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Relative Power and Loading [%] 61 O
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62 Reliability of Wind Turbines Exp
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62 Reliability of Wind Turbines 331
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