Importance of Lidar Measurement Timing Accuracy for Wind Turbine Control* Fiona Dunne, Lucy Y. Pao, David Schlipf, and Andrew K. Scholbrock Abstract— A turbine-mounted lidar can measure wind speed ahead of a wind turbine, and this preview measurement can be used to improve turbine control performance by reducing structural loads and/or increasing power capture. Effective lidar-based control requires not only an accurate wind speed measurement, but also knowledge of the expected arrival time of the measured wind. Arrival time is the time it takes for the wind to travel from the measurement focus location to the turbine rotor. Typically, arrival time is assumed to be equal to the distance traveled divided by the average wind speed. Field test data show that this assumption can be improved on average through an induction zone correction. In addition, arrival time can temporarily deviate significantly above or below this average value. If we can anticipate how arrival time will change, we can improve control performance. In this study, we post-process turbine and lidar data to show how arrival time varies and to determine an upper limit on possible improvement as a result of accurately predicting arrival time. Results show that this upper limit is a 26% average increase in coherence bandwidth between the measured wind and the wind that arrives at the rotor. In above-rated wind speeds, for example, this corresponds to a 21% improvement in the performance cost reduction due to incorporating lidar into a blade pitch controller, where the performance cost is a combined measure of generator speed error and blade pitch actuation.
N OMENCLATURE vu (t) LPF(vu (t)) vr (t) td (t) Tv
Upstream estimate of the approaching rotor-effective wind speed Low-pass filtered vu (t) Estimated rotor-effective wind speed at the turbine rotor Time delay between LPF(vu (t)) and vr (t), found using time of peak cross-covariance Expected td (t) using Taylor’s hypothesis, various expressions replace v, see (3) I. I NTRODUCTION
Wind turbine control can be improved through the use of a turbine-mounted lidar, which measures the wind speed F. Dunne and L. Y. Pao are with the Dept. of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, CO, USA (e-mail:
[email protected]) D. Schlipf is with the Endowed Chair of Wind Energy, Institute of Aircraft Design, Universit¨at Stuttgart, Germany A. K. Scholbrock is with the National Renewable Energy Laboratory, CO, USA *This work was supported by the U.S. Department of Energy under Contract No. DE-AC36-08-GO28308 with the National Renewable Energy Laboratory. The authors thank Eric Simley for suggesting to analytically study induction zone effects on arrival time, and Paul Fleming and Alan Wright for their assistance in obtaining and understanding lidar measurements and turbine data.
LPF(vu (t)) Low-pass Filter
vu (t)
Variable Time Delay
Estimate Wind at Measurement Location (Ahead of Turbine) RotorEffective Wind Lidar Speed over Scan Delay and Pattern Evolution
Wind at Rotor Blade Pitch and/or Generator Combined Outputs Feedforward/ Torque Commands Wind Turbine Feedback Controller Wind Speed Estimator vr (t)
Fig. 1. Example block diagram of wind turbine control using a turbinemounted lidar. Physical devices and processes are shown in blue, and control system components are shown in green. It is likely that a different low-pass filter (sometimes called a prefilter) is also contained in the feedforward part of the Combined Feedforward/Feedback Controller.
at some chosen distance ahead of a wind turbine, giving advance notice of the approaching wind disturbance [1], [2], [3], [4], [5], [6], [7]. Fig. 1 shows an example block diagram of combined feedforward/feedback wind turbine control using a lidar. We use vu (t) to refer to the upstream estimate of the approaching rotor-effective wind speed. With the lidar system used in this study, we estimate the rotor-effective wind speed based on line-of-sight measurements distributed over a vertical plane upstream of and parallel to the turbine rotor plane by using a least-squares fit to a single uniform wind speed, while assuming that the turbine is perfectly aligned with the wind. We use vr (t) to refer to the wind experienced at the turbine rotor, as determined by a wind speed estimator, which essentially uses the turbine as an anemometer. The relationship between vu (t) and vr (t) can be characterized by their coherence (correlation as a function of frequency) and the time delay between them. This study focuses on the time delay between the two signals using data from field tests on a 600-kW wind turbine known as the twobladed Controls Advanced Research Turbine (CART2) at the National Renewable Energy Laboratory (NREL). Arrival time ta (t) is the time it takes for the wind to travel from the measurement location to the turbine rotor. Preview time tp (t) and time delay td (t) are closely related to ta (t), as shown visually in Fig. 2. Given one of these three timing signals, the others can be easily determined. Compared to the wind at the measurement location, the upstream vu (t) is delayed by one-half the time it takes to complete one scan
Wind at measurement location vu (t) Arrival time ta(t)
TABLE I DATA S ETS FROM 2012 CART2 F IELD T ESTS .
ds, Delay due to scan time dLPF, Delay due to low-pass filtering of vu(t)
LPF(vu (t))
Set
Date
1 2 3 4
2012-05-18 2012-06-11 2012-06-15 2012-06-15
Start Time 21:43:09 15:39:29 14:41:57 15:29:22
End Time 22:18:09 16:35:42 15:11:57 16:10:37
Length (mm:ss) 35:00 56:13 30:00 41:15
Mean Wind 9.5 m/s 7.7 m/s 7.1 m/s 6.5 m/s
Preview time tp(t)
II. L IDAR M EASUREMENTS , W IND T URBINE , AND W IND S PEED E STIMATOR
Time delay td (t) Wind at rotor vr (t)
dr, Delay due to rotor effective wind speed estimation
Fig. 2. Visual representation of possible introduced time delays and the naming conventions used in this paper. Delays in blue are constant in time, and red indicates functions of time that vary with the evolving wind field. In this paper, dLP F = dr = 0, and ds = 0.67s. We use the word “timing” to refer in general to all three signals ta (t), tp (t), and td (t).
pattern because vu (t) always depends on the most recent complete scan, which includes measurements taken one-half scan pattern ago on average. The most recent complete scan is used to provide a representation of the wind across the full rotor disk. There are mixed conclusions in the available literature on the importance of accurate timing predictions. One study involving a collective pitch feedforward controller [8] shows (in its Figure 9) that errors of more than 5 s are needed before the combined feedforward/feedback controller performance is worse than that of feedback alone. Another study [6] states that “lead or lag errors in the wind speed measurement, which is fed to the controller, severely reduce the performance of the controller.” The second study uses peak time of cross-covariance between vu (t) and vr (t) to predict timing, but it does not use real-world data for these signals. In this study, we analyze timing by using real-world data. We show how quickly timing can vary, and we show how helpful it would be to correctly predict it if that were possible, rather than assuming it stays constant for a constant average wind speed. In Section II, we describe the lidar measurements and how we obtain vu (t) and low-pass filter it into LPF(vu (t)). We also describe the wind turbine and the wind speed estimator used to obtain vr (t). In Section III, we describe taking windowed cross-covariances between LPF(vu (t)) and vr (t) to find td (t), the time delay between them. In Section IV, we pass the signal vu (t) through the varying time delay td (t), and show that this provides an improved preview measurement for use in a time-invariant controller. Finally, in Section V, we summarize conclusions.
Lidar measurements were obtained from CART2 field tests [4] at NREL. The CART2 [9] is a 42.7-m diameter, 600-kW, two-bladed research wind turbine that is used to test advanced control algorithms. We use the four data sets shown in Table I, downsampled to a rate of 40 Hz. These are the four longest continuous data sets available from the 2012 CART2 field tests, excluding data taken before torque calibration, before hard target problems were solved, when lidar measurements were not available, and when the turbine was not operating in a region suitable for the wind speed estimator to produce accurate results. Set 1 had several periods of up to 4 s long of missing lidar measurements; we linearly interpolated to replace missing data. This did not cause any noticeable problems, and although we often plot data from Set 1 alone, we also provide a summary of results for each of the four data sets. The lidar used in the field tests is a modified Windcube [10], a pulsed lidar that scans a circular pattern at five focus distances, as shown in Fig. 3. Although the lidar can achieve other scan patterns, the circular pattern was chosen because it was expected to provide measurements well correlated to the wind experienced by the turbine. We chose to use data from the first focus distance of one rotor diameter (42.7 m) upwind of the lidar, because these measurements were best correlated to the turbine. The lidar was mounted on the wind turbine nacelle at a distance of 1.66 m downwind of the hub (rotor center). Thus the measurement location is 42.7 m−1.66 m = 41.0 m ahead of the rotor. Each circle of six measurement points was scanned in 1.33 s, yielding an average scan time delay (Fig. 2) of ds = 1.33 s/2 = 0.67 s. The lidar measures the wind component along its line of sight. Each measurement is adjusted using the lidar line-ofsight angle to find the wind speed in the x-direction (directly downwind toward the turbine), under the assumption that the y and z components of the wind are zero. A running average over the past six adjusted measurements was provided as an estimate of the x-component of the rotor-average wind speed. This is our vu (t), which is shown in Fig. 4. Fig. 4 also contains the low-pass filtered version of vu (t), LPF(vu (t)). This includes low-pass filtering with a cutoff frequency of 0.1432 Hz and notches at once-per-revolution (1P), twice-per-revolution (2P), and the drivetrain torsion frequency (0.695 Hz, 1.39 Hz, and 3.36 Hz, respectively). These particular low-pass and notch filters do not introduce any delays because zero-phase filtering (filtfilt() in MAT-
as follows: τr =
50 z (m)
40 30 20 10 −20
0 0
−20
−40
−60
0 20
−80
y (m)
x (m) Fig. 3. Lidar measurement configuration. The lidar is shown as a white square on the nacelle of the turbine. The black dots represent the locations of wind speed measurements used in this study. The white dots represent locations where wind speed measurements were also recorded.
v (t)
15
u
LPF(v (t)) u
Wind speed (m/s)
14
vr(t)
13 12 11 10 9 8 300
350
400
450 Time (s)
500
550
600
Fig. 4. Upstream measurement (vu (t)), low-pass filtered vu (t), and rotor estimate (vr (t)). Five-minute portion from Set 1 data.
LAB [11]) is used, which is possible because the filtering is not done in real time. Together these filters minimize the magnitude of vu (t) at frequencies at which it may be correlated to vr (t) because of tower and lidar motion rather than independent measurements of wind speed. The wind speed estimator uses the torque balance method, which assumes τr − τg = J Ω˙ (1) where τr is the torque applied by the wind to the rotor, τg is the torque applied at the generator (multiplied by the gearbox ratio), J is the drivetrain moment of inertia (as observed from the rotor side of the gearbox), and Ω˙ is the rotor acceleration. Wind speed estimators that neglect rotor acceleration may introduce a time delay because of the inertial response of the rotor. After τr is solved for using the above equation, a lookup table is used to determine the rotor-effective wind speed for the given τr , blade pitch angle β, and rotor speed Ω, with an adjustment for air density ρ. These variables are related
ρπR2 CP (λ, β)vr3 (t) 2Ω
(2)
where R is the rotor radius, CP is the power coefficient (fraction of wind power captured), and λ is the tip speed ratio (ΩR/vr (t)). Pitch, torque, and rotor speed signals are lowpass filtered and notch filtered (at 1P, 2P, and the drivetrain torsion frequency) using zero-phase filtering before being used in the estimator. The result of the lookup table is the rotor-effective wind speed vr (t) shown in Fig. 4. III. W INDOWED C ROSS -C OVARIANCES The time delay td (t) between LPF(vu (t)) and vr (t) can be estimated from the times of peak windowed crosscovariances between LPF(vu (t)) and vr (t). However, simply shifting a window across the data and recording each time of peak cross-covariance results in a td (t) that contains sudden jumps to unrealistic values. Three main steps can reduce these occurrences. First, we choose a Gaussian window with a large enough window size. Second, we detrend (subtract the best-fit line from) the data within each window before applying the cross-covariance function. Third, we enforce a rate limit on td (t), along with a lower limit of 0 s. These steps yield the blue td (t) curves shown in Fig. 5. We show results for three window sizes for comparison, with standard deviations of σ = 30 s, 15 s, and 60 s, and total window sizes of 180 s, 90 s, and 360 s, respectively. Throughout the remainder of this paper, we use only the td (t) resulting from the σ = 30 s window. This choice of window size is a trade-off because smaller sizes give better time resolution and tend to lead to the greatest increases in coherence bandwidth (when td (t) is used as described in Section IV); however smaller sizes are also more likely to produce non-physical results (which can be impossible to predict) and contain instances of near-zero preview times. A minimum of 1 s to 2 s of preview would be preferable if it were available in real time for control. Based on Taylor’s frozen turbulence hypothesis [12], [13], ta (t) is typically assumed to be equal to D/v, where D is the distance traveled from the measurement location to the rotor and v is the average wind speed. Fig. 5, in addition to showing td (t), also shows the expected td (t) computed as Tv = D/v − ds
(3)
where D = 41 m, ds = 0.67 s, T stands for Taylor, and the subscript v varies depending on what choice of v we use in the equation. We use either LPF(vu (t)) or vr (t) for v in Fig. 5. At approximately 2,000 s, there is a large spike in td (t). This corresponds to a data set portion when the lidar measurements are relatively inaccurate because of low wind speeds. In this portion, the wind speed as determined by the turbine-based estimator is below 6 m/s; whereas the lower limit of a possible lidar measurement is 6 m/s as a result of the technique used to eliminate data due to accidental lidar sensing of hard targets.
TABLE II M EAN VALUES OF td (t) AND Tv : E ITHER U NCORRECTED OR C ORRECTED FOR I NDUCTION Z ONE
25 Time of peak cross covariance (td(t)) σ=30 s Time of peak cross covariance (td(t)) σ=15 s 20
Time of peak cross covariance (td(t)) σ=60 s Expected td(t) (TLPF(v (t))) u
Set
Mean td (t) [s]
1* 2 3 4
4.2 5.3 6.2 7.4
Expected td(t) (Tv (t)) r
Time (s)
15
10
Mean TLPF(vu (t)) [s] Uncorrected Corrected 3.7 4.2 4.8 5.5 5.3 6.0 5.6 6.4
Mean Tvr (t) [s] Uncorrected Corrected 3.6 4.3 5.0 5.9 5.4 6.4 6.6 7.8
*Final 110 s excluded 5
500
1000 1500 Window center time (s)
2000
2500
Fig. 5. Time (td (t)) of peaks of windowed cross-covariances of LPF(vu (t)) with vr (t). σ describes Gaussian window size; td (t) with σ = 30s is used throughout this paper and can be assumed when not specified; plots using the other two sizes are presented here for comparison. This plot also includes two versions of Tv as in (3). Set 1 data used.
In the remaining data in Fig. 5, td (t) on average matches its expected value Tv relatively well, as shown in Table II. It is likely that induction zone effects (slowing of wind as it approaches the rotor) are responsible for td (t) being longer than expected on average. Theoretically, the induction zone velocity U is characterized by −1 U∞ = 1 − a[1 + ξ(1 + ξ 2 )−1/2 ] (4) U where U∞ is the undisturbed velocity and ξ = x/R, where x is the distance from the rotor (negative upwind) and R is the rotor radius [14]. The axial induction factor a is approximately the optimal 1/3 in below-rated wind speeds because the turbine is extracting as much power as possible from the wind. This is when we expect the induction-zone slowdown effect to be strongest. As wind speed increases above rated, the axial induction factor decreases, and the slowdown effect diminishes. The CART2 has a rated wind speed of approximately 13 m/s, and we have little data above this speed. Integrating (4) with respect to ξ and then multiplying by U/U∞ /ξ gives the arrival time multipliers M shown in Fig. 6. To calculate theoretical arrival time ta (t) that accounts for the induction zone, use ta (t)T aylor,corrected = (D/v)M
(5)
where D is the measurement distance and v is the wind speed at the measurement location. Our measurement distance results in x/R = −1.92, and we assume a = 1/3, corresponding to an M of 1.12. This means ta (t) should be 12% greater than the value we calculated without accounting for the induction zone. Table II shows the uncorrected and corrected versions of TLPF(vu (t)) , where the corrected
Arrival Time Multiplier M
0 0
1.25
1.2
a=1/6 a=1/3 a=1/2
1.15
1.1
1.05
1 −8
−6
−4 x/R
−2
0
Fig. 6. Arrival time multipliers M for use in (5). x is the measurement distance from the rotor (positive downwind), R is the rotor radius, and a is the axial induction factor.
version is (D/v)M − ds . It also shows the uncorrected and corrected versions of Tvr (t) , where the corrected version is (D/v)M ∗ − ds , where M ∗ results from integrating (4) with respect to ξ and then multiplying by 1/ξ. The multiplication factor U/U∞ is not included in M ∗ because vr (t) is assumed to be a delayed estimate of U∞ instead of U . In both cases, the induction zone correction improves the match with td (t). On shorter time scales, td (t) often differs from its expected value Tv by several seconds, as shown in Fig. 5. Timing does not stay constant for a constant average wind speed. This may be in part because of the evolution of the wind field, and also the 3D nature of the wind field in which the wind speed at a given location does not always match the speed of travel of the turbulent airflow structure carrying that wind speed. The timing may also be affected by wind shear and wind components in the y and z directions, which exist although we assume them to be zero. In this paper, our goal is not to improve the modeling to predict timing, but to use the time lag found in post-processing to estimate how much room for improvement exists in the current model. IV. F ILTERING L IDAR M EASUREMENTS U SING A VARIABLE T IME D ELAY A controller incorporating lidar measurements, for example the controller used in the field testing [4], can be designed for some given preview time and some given correlation or transfer function estimate. The controller may be adapted
16 LPF(vu(t)) LPF(vu(t)) w/ variable time delay
15
vr(t)
Wind speed (m/s)
14 13 12 11 10 9 8 300
350
400
450 Time (s)
500
550
600
Fig. 7. Low-pass filtered upstream measurement LPF(vu (t)), LPF(vu (t)) stretched and shrunk by filtering using the variable time delay td (t) plotted in Fig. 5, and rotor estimate (vr (t)). Five-minute portion from Set 1 data. mscohere( vr(t) , vu(t) w/ variable time delay according to: ) 1 0.9 0.8 0.7 Magnitude
as arrival time and correlation change, but so far this has been done on a timescale of a few minutes. Fig. 5 shows td (t) (σ = 30 s) jumping from 3 s to 6 s in only 68 s, for example. One way to address varying arrival time is to delay the measured signal vu (t) by varying amounts before sending it to the controller. This essentially uses interpolation to stretch and shrink various parts of vu (t) in time. The amount of varying delay that should be used on vu (t) is equal to the preview time tp (t) minus the constant amount of preview expected by the controller. For this method to be successful, two requirements must be met by the preview time tp (t). First, tp (t) must always be greater than or equal to the amount of preview required by the controller. This is required for real-time operation because it is impossible to use negative delay. Second, the slope ∆tp (t)/∆t (and thus ∆ta (t)/∆t and ∆td (t)/∆t as well) must always be greater than −1. If ∆tp (t)/∆t = −1, two different wind speeds would be expected to arrive at the same time, and below a slope of −1, wind speeds would be expected to arrive in a swapped order than when they were measured. In situations when arrival time has a slope ≤ −1, a possible solution is to overwrite the older measurement with the more recently measured wind speed, which is arriving at the same time or sooner. Without zooming in, td (t) in Fig. 5 appears to meet the requirement of ∆td (t)/∆t > −1. However, upon zooming in, we see that the time of peak cross-covariance is discretized at the sample rate (40 Hz). This results in steep steps, many with slope equal to −1. To solve this problem, we filter this data with a boxcar filter of 11 samples in length, which, for this data, provides just enough smoothing to keep ∆td (t)/∆t > −1. The boxcar filter is centered so that no time delay is introduced. After smoothing the data, Fig. 7 was created by stretching and shrinking LPF(vu (t)) from Fig. 4 according to td (t) from Fig. 5. Because of this, it sometimes lags and sometimes leads the original LPF(vu (t)), and this results in a better correlation at low frequencies to vr (t). We are most interested in improving low-frequency correlation because the low frequencies contain the most power in the wind and have the most effect on the turbine. Fig. 8 shows coherence (correlation as a function of frequency) using three methods of variable time delay. TLP F0.003 (vu (t)) means that the wind speed v used in (3) is the lidar measurement filtered with a first-order low-pass filter with a cutoff of 0.003 Hz. This is most similar to the method used in the field tests: the time delay is updated slowly, on the order of minutes, based on a filtered version of the measured wind speed. Using Tvu (t) , the time delay is updated instantaneously, with no filter on the measured wind speed. Surprisingly, this improves coherence compared to TLP F0.003 (vu (t)) , even though by using a time delay with such high frequency variations, we are subjecting the signal to a swapped order of data points due to slopes being below −1 as previously described. Fig. 9 shows that there is a general trend toward improved coherence bandwidth as lowpass filtering cutoff frequency is increased. However, some filtering should be employed to ensure availability of a mini-
0.6 0.5 0.4 0.3 0.2
TLPF
0.1
Tv (t) u
(v (t))
0.003
u
td(t) 0 0
0.05
0.1 Frequency (Hz)
0.15
0.2
Fig. 8. Magnitude squared coherence between turbine estimate vr (t) and lidar measurement vu (t) with each of the three different methods of variable time delay listed in the legend. Set 1 data.
mum preview time for control. Using td (t) for the time delay gives the best coherence bandwidth. Although creating the signal td (t) in real time is not possible, this method estimates an upper limit of coherence bandwidth improvement that is possible to achieve through improved knowledge of arrival time. Table III shows the results from these three methods on the four data sets in terms of coherence bandwidth. We define coherence bandwidth as the pole location of the firstorder low-pass filter whose magnitude squared best fits the magnitude squared coherence. On average across all four data sets, our results show a 26% increase in coherence bandwidth when going from using TLP F0.003 (vu (t)) to td (t), and a 13% increase in coherence bandwidth when going from using Tvu (t) to td (t). These
0.09
A method for accurate real-time prediction of these quick variations in arrival time is outside the scope of this paper. Instead, we used post-processing to obtain these variations in arrival time from CART2 field test data. Knowing these variations in advance, compared to a method of predicting arrival time similar to that used in the field tests, would have increased coherence bandwidth between measured and rotor-estimated wind by 26% on average, and therefore could have improved control performance. In above-rated wind speeds, for example, this translates to an approximately 21% improvement in the performance cost reduction due to incorporating lidar into a blade pitch controller. This work sets an upper limit of possible performance improvement because real-time prediction at best will be no more accurate than what can be achieved in post-processing.
coherence bandwidth (Hz)
0.08
0.07
0.06
0.05
0.04 Set 1 data Set 2 data Set 3 data Set 4 data
0.03
0.02 −5 10
−4
10
−3
−2
−1
10 10 10 LPF cutoff frequency (Hz)
0
1
10
10
Fig. 9. Coherence bandwidth between turbine estimate vr (t) and lidar measurement vu (t) with variable time delay using TLP Fx-axis (vu (t)) (the wind speed v used in (3) is the lidar measurement filtered with a first-order low-pass filter with cutoff frequency shown on the x-axis). The dashed lines represent no filtering (infinite cutoff frequency). TABLE III C OHERENCE BANDWIDTHS [H Z ]
Set 1 2 3 4 Mean
1. TLP F0.003 (vu (t)) 0.0814 0.0740 0.0757 0.0381 0.0673
2. Tvu (t) 0.0846 0.0993 0.0726 0.0431 0.0749
3. td (t) 0.0996 0.1065 0.0838 0.0486 0.0846
%∆ 1→3 22 44 11 28 26
%∆ 2→3 18 7 15 13 13
Coherence bandwidths [Hz] between turbine estimate vr (t) and lidar measurement vu (t) with three methods of variable time delay.
increases, for example, would allow a pitch controller to provide an improvement in its combined goal of generator speed regulation and minimal pitch actuation: Each 1% improvement in coherence bandwidth allows an approximately 0.8% improvement in the cost reduction due to using lidar [15], when the cost function is defined as minimizing Jc = r ∗ σ 2 (blade pitch) + q ∗ σ 2 (generator speed)
(6)
where [15] describes the ratio between q and r. V. C ONCLUSIONS Using data from field tests on NREL’s CART2 wind turbine, we have shown how the arrival time of the lidar measurements varies, we have filtered the measured wind speed signal using a variable time delay, and we have found an upper limit on the improvement that can be obtained through better prediction of arrival time. The data show that we can improve the prediction of average arrival time by using an induction zone correction when using Taylor’s frozen turbulence hypothesis. This allows a good prediction of average arrival time, but arrival time can temporarily deviate significantly above or below this average value.
R EFERENCES [1] M. Harris, M. Hand, and A. Wright, “Lidar for turbine control.” National Renewable Energy Laboratory, Golden, CO, Tech. Rep., NREL/TP-500-39154, Jan. 2006. [2] K. A. Kragh and M. H. Hansen, “Individual pitch control based on local and upstream inflow measurements.” in Proc. AIAA Aerospace Sciences Meeting, Nashville, TN, Jan. 2012. [3] F. Dunne, D. Schlipf, L. Y. Pao, A. D. Wright, B. Jonkman, N. Kelley, and E. Simley, “Comparison of two independent lidar-based pitch control designs,” in Proc. AIAA Aerospace Sciences Meeting, Nashville, TN, Jan. 2012. [4] D. Schlipf, P. Fleming, F. Haizmann, A. K. Scholbrock, M. Hofs¨aß, A. Wright, and P. W. Cheng, “Field testing of feedforward collective pitch control on the CART2 using a nacelle-based lidar scanner,” in The Science of Making Torque from Wind, Oldenburg, 2012. [5] A. K. Scholbrock, P. A. Fleming, L. J. Fingersh, A. D. Wright, D. Schlipf, F. Haizmann, and F. Belen, “Field testing LIDAR based feed-forward controls on the NREL controls advanced research turbine,” in Proc. AIAA Aerospace Sciences Meeting, Grapevine, TX, Jan. 2013. [6] M. Mirzaei, M. Soltani, N. Poulsen, and H. Niemann, “Model predictive control of wind turbines using uncertain LIDAR measurements,” in Proc. American Control Conference, Washington, D.C., 2013. [7] J. Laks, E. Simley, and L. Pao, “A spectral model for evaluating the effect of wind evolution on wind turbine preview control,” in Proc. American Control Conference, Washington D.C., 2013. [8] D. Schlipf and M. K¨uhn, “Prospects of a collective pitch control by means of predictive disturbance compensation assisted by wind speed measurements,” in Proc. German Wind Energy Conference DEWEK, Bremen, Nov. 2008. [9] E. Bossanyi, A. Wright, and P. Fleming, “Controller field tests on the NREL CART2 turbine.” National Renewable Energy Laboratory, Golden, CO, Tech. Rep., NREL/TP-5000-49085, December 2010. [10] A. Rettenmeier, O. Bischoff, M. Hofs¨aß, D. Schlipf, J. J. Trujillo, and M. K¨uhn, “Wind field analyses using a nacelle-based lidar system,” in Proc. European Wind Energy Conference, Warsaw, Poland, 2010. [11] Matlab, Simulation and Model-Design Software Package. Natick, MA: The MathWorks, Inc. [Online]. Available: http://www.mathworks.com [12] G. I. Taylor, “The spectrum of turbulence,” in Proc. Royal Society of London, Series A, Mathematical and Physical Sciences, vol. 164, no. 919, 1938, pp. 476–490. [13] D. Schlipf, D. Trabucchi, O. Bischoff, M. Hofs¨aß, J. Mann, T. Mikkelsen, A. Rettenmeier, J. Trujillo, and M. K¨uhn, “Testing of frozen turbulence hypothesis for wind turbine applications with a scanning lidar system,” in International Society of Acoustic Remote Sensing Symposium, Paris, France, 2010. ˚ Dahlberg, and P. H. Alfredsson, “The [14] D. Medici, S. Ivanell, J.-A. upstream flow of a wind turbine: Blockage effect,” Wind Energy, vol. 14, no. 5, pp. 691–697, 2011. [15] F. Dunne and L. Y. Pao, “Benefit of wind turbine preview control as a function of measurement coherence and preview time,” in Proc. American Control Conference, Washington, D.C., 2013.
