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Magnitude (abs) To: blade pitch 0.05 0.045 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 10 −4 From: wind meas 10 −2 10 0 Bode Diagram 10 −4 Frequency (Hz) From: gen speed feedback only typical measurement perfect measurement Figure 152: Frequency responses of H2 optimal feedforward (From: wind meas) and feedback (From: gen speed) controllers for the NREL 5-MW turbine at a 13 m/s wind speed operating point, with 9 seconds of available preview time. perfect knowledge of the turbine model. 10.9 Summary This chapter presented an introduction to wind turbine control using lidar, primarily focusing on a frequency domain analysis of lidar measurement quality. Two control examples were included to highlight the challenges that accompany the design of feedforward controllers that use lidar measurements. A summary of the main results presented in this chapter is provided here. • With perfect preview measurements of wind speeds, a model-inverse feedforward controller can completely cancel the effect of the wind disturbance on a turbine variable of interest, assuming perfect turbine modeling. For imperfect preview measurements, a measurement filter can be introduced such that the mean square value of the turbine variable is minimized. • A feedforward control system requires not only measurements of the wind disturbance, but also a certain amount of preview time required for implementation. • For blade pitch control, the lidar system should be used to acquire an estimate of the “blade effective wind speed,” a weighted integral of wind speeds along the blade that describes the equivalent wind speed experienced by the blade. Furthermore, the longitudinal component of the wind is of interest because it has the greatest impact on the rotor aerodynamics. • The two main sources of lidar measurement error are geometry effects, or estimation of the longitudinal component using a line-of-sight measurement, and wind evolution, which represents the decorrelation of the turbulence as it travels downwind between the measurementlocationandtheturbine.Spatialaveraging,inherentinlidarmeasurements, appears to help with estimation of blade effective wind speed. • Windturbinecontrolsystemsareoftendefinedinthenon-rotatingframe,whereestimates of the collective, vertical shear, and horizontal shear wind components are required, as opposed to measurements of the wind speed at individual blades. 216 <strong>DTU</strong> Wind Energy-E-Report-0029(EN) 10 −2 10 0
• Measurement coherence, which can be calculated given a frequency domain wind field model, can be used to find the optimal lidar measurement configuration that minimizes the mean square value of a turbine variable of interest. • For a hub-mounted lidar, there is an optimal preview distance that minimizes measurement error. For shorter preview distances, geometry effects cause error to increase. Beyond the optimal preview distance, wind evolution becomes more severe, thus increasing measurement error. • A combined feedback/feedforward control system can be optimized given the measurement coherence. For perfect measurement coherence, the control system relies entirely on the feedforward controller. For measurements that are completely uncorrelated with the wind disturbance, the control system relies entirely on feedback. For imperfect measurements that have some correlation with the wind disturbance, the optimal control strategy utilizes both feedback and feedforward control. Notation 1P once per revolution CPSD Cross-Power Spectral Density CW continuous-wave CP(r) radially-dependent coefficient of power CQ(r) radially-dependent coefficient of torque d measurement preview distance DEL Damage Equivalent Load f frequency (Hz) F feedforward controller Fℓ lidar focus distance h hub height Hpre lidar measurement prefilter IEC International Electrotechnical Commission Ka state feedback gains for augmented states Kff state feedback gains for preview measurements Kx state feedback gains for turbine states ℓ lidar direction vector NREL National Renewable Energy Laboratory Ngb gear box ratio PSD Power Spectral Density Pa augmented dynamics Pt wind turbine dynamics r lidar scan radius R rotor radius Rℓ range along lidar beam RMS root mean square STD standard deviation Saa(f) power spectral density of signal a Sab(f) cross-power spectral density between signals a and b Ts sample period of control system Tywt transfer function from wind disturbance to output y TyβFF transfer function from feedforward blade pitch command to output y u longitudinal wind speed U mean wind speed ublade blade effective wind speed uhh hub height or collective wind speed component ûhh estimate of hub height wind speed component from lidar measurements urotor rotor effective wind speed uwt,los range weighted line-of-sight measurement û estimate of u component from lidar measurement uwt range weighted wind speed vector v transverse wind speed w vertical wind speed <strong>DTU</strong> Wind Energy-E-Report-0029(EN) 217
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Remote Sensing for Wind Energy DTU
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Author: Alfredo Peña, Charlotte B.
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4 Introduction to continuous-wave D
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8 Nacelle-based lidar systems 157 8
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12 Complex terrain and lidars 231 1
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1 Remote sensing of wind Torben Mik
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Figure 2: Calibration, laboratory w
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Figure 3: Example of scatter plots
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1.2.3 Summary of sodars Most of tod
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1.3.3 Wind lidars Measuring wind wi
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Figure 6: CW wind lidars (ZephIRs)
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Further developments Furthermore, n
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2 The atmospheric boundary layer S
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Figure 9: Large spatial scale varia
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Du3 Dt Du1 Dt Du2 Dt The three mome
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Figure 13: Consensus relations betw
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ψ z L ∼ − 5 L . For unstable c
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Figure 15: Behavior of the turbulen
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Figure 17: Newly developed models t
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The value of q0 at the surface is d
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the spray is the source of icing on
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u∗2 u∗1 u1(h) = u∗1 k ln h
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Figure 26:Land-seabreeze system,whe
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Figure28:Three dimensionalpicture o
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sufficient information. Finally, we
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Mann, J. (1998) Wind field simulati
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(2010) and comparison under differe
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To get the velocity field from the
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τ(k) [Arbitrary units] 10 3 10 2 1
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(Koopmans, 1974; Bendat and Piersol
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anemometer was installed at each en
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and fSw(f) u 2 ∗ = 1.05n 1+5.3n 5
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and n = 0.468. This spectrum implie
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to be calculated. We do that on a m
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Notation A Charnock constant neutra
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Maxey M. R. (1982) Distortion of tu
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4.2 Basic principles of lidar opera
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4.2.5 Wind profiling in conical sca
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4.3.1 Behaviour of scattering parti
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the beam radius at the output lens.
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from which the value of VLOS is der
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the atmosphere. The SNR 4 for a win
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individual line-of-sight wind speed
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A general approach to mitigating th
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from ±VH sinδ (if the tilt is tow
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as a down draught (of the same abso
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Table 7: Combined results from 28 Z
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in Eastern Jutland between January
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Figure 56: Normalized power curves
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the concept. Developments include i
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References x horizontal position in
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Wagner R., Mikkelsen T., and Courtn
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5.2 End-to-end description of pulse
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Scanner Coherent lidar measure the
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Figure 62: Radial wind velocity ret
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transform in order to use data obta
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This wavelength is also the most fa
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Eq.(132)isadaptedforcollimatedsyste
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5.3.6 Existing systems and actual p
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(Gottshall et al., 2010; Albers et
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References Albers A., Janssen A. W.
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derived from fluctuations of the wi
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Acoustic received echo (ARE) method
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Figure 71: Sample time-height cross
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A gradient minimum is characterized
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Figure73:Bragg-relatedacoustic(belo
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stability (inversion strength) can
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Figure 76: Combined soundingwith a
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Figure 79: Favorite regions (shaded
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Direct detection of MLH from acoust
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Engelbart D.A.M.and Bange J. (2002)
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7 What can remote sensing contribut
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uyms 9.0 8.5 8.0 7.5 7.0 120 140 16
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Bottom of rotor Φ rotation r w u
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Height Height Hub 1.6 1.4 1.2 1.0 0
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PP rated PP rated 1.0 0.8 0.6 0.4 0
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KEprofileKEhub 1.2 1.1 1.0 0.9 0.8
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PP rated WS Lidarms 1.0 0.8 0.6 0.4
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8 Nacelle-based lidar systems Andre
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• Flexibletrajectories.Dependingo
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Figure 104: Sketch of simultaneous
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The normal wind direction vector nw
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Page 169 and 170: Notation C number of sent photons C
Page 171 and 172: 9 Lidars and wind turbine control -
Page 173 and 174: for three unknowns, it is impossibl
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Page 177 and 178: |GRL| [-] 1 0.8 0.6 0.4 0.2 10 k [r
Page 179 and 180: PSD(Ωg) [(rpm) 2 /Hz] PSD(Ωg) [
Page 181 and 182: 0.04 0.03 ˆk [ rad m ] 0.02 0.63 0
Page 183 and 184: [%] 10 0 −10 −20 −30 MyT Moop
Page 185 and 186: PSD(θ1) [rad 2 /Hz] PSD(Moop1) [Nm
Page 187 and 188: Pel/Pel,max [-] 1 0.98 0.96 0.94 0.
Page 189 and 190: fL weighting function GRL transfer
Page 191 and 192: E. Hau, Windkraftanlagen, 4th ed. S
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Page 195 and 196: vertical (m) 150 100 50 R d 0
Page 197 and 198: With feedback only, on the other ha
Page 199 and 200: Figure 136: Estimated preview requi
Page 201 and 202: Normalized C r = C r P Q 2 W (r) b
Page 203 and 204: Normalized C r = C r P Q 2 W (r) b
Page 205 and 206: Coherence 1 0.8 0.6 0.4 0.2 0 10
Page 207 and 208: Coherence 1 0.8 0.6 0.4 0.2 0 10
Page 209 and 210: Magnitude Squared 10 8 10 7 10 6 10
Page 211 and 212: Figure 148: During simulation, FAST
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Page 215: Magnitude (abs) blade pitch gen spe
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Page 221 and 222: 11 Lidars and wind profiles Alfredo
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Page 225 and 226: z [−] zo 1 κ ln 40 38 36 34 32 3
Page 227 and 228: z [m] z [m] 1000 900 800 700 600 50
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Page 233 and 234: Figure 158: The ZephIR models which
Page 235 and 236: Uconst wΑx l h Φ h.tanΦ Figure 1
Page 237 and 238: Figure 162: Lavrio: The scatter plo
Page 239 and 240: Figure 163: Panahaiko: The scatter
Page 241 and 242: References Albers A. and Janssen A.
Page 243 and 244: Wexler (1968), where the limitation
Page 245 and 246: 13.2.1 Systematic turbulence errors
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Page 249 and 250: The theoretical systematic errors a
Page 251 and 252: Height (m) 160 140 120 100 80 60 40
Page 253 and 254: Height (m) Height (m) 160 140 120 1
Page 255 and 256: RMSPE (%) 70 60 50 40 30 20 10 0 vu
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Page 259 and 260: Lindelöw P. (2007) Fibre Based Coh
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with rain are shown in Fig. 179. A
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This method gives a good accuracy (
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Figure 183: A recent maintenance in
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Figure 185: Temperature profiles in
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References s point in space Sν(s)
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Also the Doppler Centroid anomaly c
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Christiansen et al., 2006). The res
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educe speckle noise, a random noise
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Figure 188: Envisat ASAR wind field
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Figure 190: Envisat ASAR wind field
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Satellites in sun-synchronous polar
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500 overlapping scenes for wind res
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(with the fewest samples). The unce
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Badger M., Hasager C. B., Thompson
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Ren Y. Z., Lehner S., Brusch S., Li
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tracking, climate studies, air-sea
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The modified logarithmic wind profi
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sea ice mask was applied and σ0 me
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QuikSCAT 25 20 15 10 5 Horns Rev Fi
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Figure 203:Example of an ASCAT coas
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References Bourassa M.A., Legler D.
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DTU Wind Energy Technical Universit
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