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  • View in gallery

    Map of the wind farm, to scale.

  • View in gallery

    Wind resource characteristics of the site from 14 Sep 2011 to 12 Oct 2011, as measured at hub height by the met tower: (a) wind speed, (b) wind direction, and (c) turbulence intensity.

  • View in gallery

    Coordinate systems and variable definitions.

  • View in gallery

    Sketch of the velocity deficit profiles in the (a) near and (b) far wakes.

  • View in gallery

    Number of detected wakes vs downwind distance. The relatively low number of detected wakes close to the turbine (x ≤ 1.2D) is a consequence of the lidar’s limited FOV in that region.

  • View in gallery

    Velocity deficit vs downwind distance. The bold central lines indicate median values, whereas the symmetric shaded error bars represent the standard deviation of the measurements. (a) Overall results are shown, and velocity deficit measurements are further categorized by (b) ambient wind speed, (c) turbulence intensity, and (d) time of day.

  • View in gallery

    Estimate of the parameter φ vs downwind distance. The bold central lines indicate median values, whereas the symmetric shaded error bars represent the standard deviation of the measurements. (a) Overall results are shown, and measurements are further categorized by (b) turbulence intensity and (c) time of day.

  • View in gallery

    Wake centerline vs downwind distance. The bold central lines indicate median values, whereas the symmetric shaded error bars represent the standard deviation of the measurements. (a) Overall results are shown, and wake centerline measurements are further categorized by (b) turbulence intensity and (c) time of day.

  • View in gallery

    Wake width vs downwind distance. The bold central lines indicate median values, whereas the symmetric shaded error bars represent the standard deviation of the measurements. (a) Overall results are compared to the Park wake model, and wake width measurements are further categorized by (b) turbulence intensity and (c) time of day.

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Utility-Scale Wind Turbine Wake Characterization Using Nacelle-Based Long-Range Scanning Lidar

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  • 1 Department of Physics, University of Colorado Boulder, Boulder, Colorado
  • | 2 Department of Atmospheric and Oceanic Sciences, University of Colorado Boulder, Boulder, and National Renewable Energy Laboratory, Golden, Colorado
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Abstract

To facilitate the optimization of turbine spacing at modern wind farms, computational simulations of wake effects must be validated through comparison with full-scale field measurements of wakes from utility-scale turbines operating in the real atmosphere. Scanning remote sensors are particularly well suited for this objective, as they can sample wind fields over large areas at high temporal and spatial resolutions. Although ground-based systems are useful, the vantage point from the nacelle is favorable in that scans can more consistently transect the central part of the wake. To the best of the authors’ knowledge, the work described here represents the first analysis in the published literature of a utility-scale wind turbine wake using nacelle-based long-range scanning lidar.

The results presented are of a field experiment conducted in the fall of 2011 at a wind farm in the western United States, quantifying wake attributes such as the velocity deficit, centerline location, and wake width. Notable findings include a high average velocity deficit, decreasing from 60% at a downwind distance x of 1.8 rotor diameters (D) to 40% at x = 6D, resulting from a low average wind speed and therefore a high average turbine thrust coefficient. Moreover, the wake width was measured to expand from 1.5D at x = 1.8D to 2.5D at x = 6D. Both the wake growth rate and the amplitude of wake meandering were observed to be greater for high ambient turbulence intensity and daytime conditions as compared to low turbulence and nocturnal conditions.

Corresponding author address: Matthew Aitken, Department of Physics, University of Colorado Boulder, 390 UCB, Boulder, CO 80309-0390. E-mail: matthew.aitken@colorado.edu

Abstract

To facilitate the optimization of turbine spacing at modern wind farms, computational simulations of wake effects must be validated through comparison with full-scale field measurements of wakes from utility-scale turbines operating in the real atmosphere. Scanning remote sensors are particularly well suited for this objective, as they can sample wind fields over large areas at high temporal and spatial resolutions. Although ground-based systems are useful, the vantage point from the nacelle is favorable in that scans can more consistently transect the central part of the wake. To the best of the authors’ knowledge, the work described here represents the first analysis in the published literature of a utility-scale wind turbine wake using nacelle-based long-range scanning lidar.

The results presented are of a field experiment conducted in the fall of 2011 at a wind farm in the western United States, quantifying wake attributes such as the velocity deficit, centerline location, and wake width. Notable findings include a high average velocity deficit, decreasing from 60% at a downwind distance x of 1.8 rotor diameters (D) to 40% at x = 6D, resulting from a low average wind speed and therefore a high average turbine thrust coefficient. Moreover, the wake width was measured to expand from 1.5D at x = 1.8D to 2.5D at x = 6D. Both the wake growth rate and the amplitude of wake meandering were observed to be greater for high ambient turbulence intensity and daytime conditions as compared to low turbulence and nocturnal conditions.

Corresponding author address: Matthew Aitken, Department of Physics, University of Colorado Boulder, 390 UCB, Boulder, CO 80309-0390. E-mail: matthew.aitken@colorado.edu

1. Introduction

Because of the inherent limitations of conventional anemometry, high-resolution measurements of wind turbine wake dynamics are only possible with scanning remote sensors. Previously, ground-based long-range systems with maximum ranges of several kilometers have been used to study the wakes of utility-scale turbines (Käsler et al. 2010; Hirth et al. 2012; Hirth and Schroeder 2013; Iungo et al. 2013; Smalikho et al. 2013; Aitken et al. 2014), with hub heights ranging from 80 to 102 m and rotor diameters from 71 to 116 m. In addition, Bingöl et al. (2010) and Trujillo et al. (2011) collected wake measurements by mounting a continuous wave ZephIR lidar with a maximum range of 200 m on the nacelle of a stall-regulated 95-kW test turbine with a 29-m hub height and 19-m rotor diameter. Such nacelle-based systems are advantageous over ground-based ones in that scans can more closely transect the wake centerline. Yet, while scaled models are informative, a comprehensive understanding of wake losses at modern wind farms necessitates observations from pitch-regulated multimegawatt turbines. To the best of our knowledge, the work outlined here represents the first analysis in the published literature of a utility-scale wind turbine wake using nacelle-based long-range scanning lidar.

In particular, we present the results of a field experiment conducted in the fall of 2011 at a wind farm in the western United States, in which a Galion G4000 lidar with a maximum range of 4000 m was used to sample wakes from the nacelle of a utility-scale wind turbine. (Because of confidentiality requirements, certain details about the wind farm and turbine cannot be disclosed.) To quantify wake attributes—such as the velocity deficit (VD), centerline location, and wake width—we apply the procedure described in detail in Aitken et al. (2014). In what follows, section 2 provides an overview of the experimental setup and methodology. Results and a summary are presented in sections 3 and 4, respectively.

2. Data and methods

a. Instrumentation

Located in the western United States, the wind farm under consideration comprises turbines with rotor diameter D ≈ 100 m and hub height H ≈ 80 m, in addition to cut-in, rated, and cutout speeds of about 4, 13, and 25 m s−1, respectively. With strong winds typically channeled from the south-southwest, the wind farm is arranged in a series of rows spaced 15D along the prevailing wind direction (north–south) and 3D along the transverse direction (east–west), as seen in Fig. 1.

Fig. 1.
Fig. 1.

Map of the wind farm, to scale.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00218.1

During the experiment, wind speed and direction data were collected at hub height with a Risø P2546A cup anemometer and Met One 020C wind vane mounted on a meteorological (met) tower located in the southernmost row of turbines. Wind speed was measured with an accuracy of 1% of reading and wind direction with an accuracy of 3°. As illustrated in Fig. 2a, most winds were fairly light during the experiment, with a median wind speed of about 5 m s−1, just above cut-in. The Weibull fit to the wind speed distribution (Justus et al. 1978) has scale parameter λ = 5.87 and shape parameter k = 1.70. The histogram in Fig. 2b shows a bimodal wind direction distribution, the fit to which is a finite von Mises mixture distribution (Masseran et al. 2013) with one mode at 17° and another, more prominent mode at 190°. In Fig. 2c, the turbulence intensity (TI) is defined as the ratio of the horizontal wind speed standard deviation to the mean horizontal wind speed, taken over a 10-min interval. The lognormal fit to the TI distribution (Larsen 2001) has location parameter μ = −2.34 and scale parameter σ = 0.51. The median TI during the experiment was 9.6%, similar to values measured in the midwestern United States (Elliott et al. 2009), where much of the nation’s wind power capacity is located. Turbulence intensity can be used as a measure of atmospheric stability, with lower (higher) values generally indicating stable (unstable) conditions (Wharton and Lundquist 2012), and the effect of stability on wake characteristics is examined in section 3.

Fig. 2.
Fig. 2.

Wind resource characteristics of the site from 14 Sep 2011 to 12 Oct 2011, as measured at hub height by the met tower: (a) wind speed, (b) wind direction, and (c) turbulence intensity.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00218.1

The Galion—a pulsed laser device for wind speed and direction measurement—was placed on the nacelle of one of the turbines adjacent to the met tower in the southernmost row. Pulsed lidar is advantageous in that multiple measurements can be taken simultaneously along a single line of sight (LOS). Moreover, pulsed systems are well suited for long-distance measurements, as the probe length is constant at all range gates. By comparison, continuous wave systems tend to be limited to ranges well below 1 km because the probe length scales as the square of the focus distance (Werner 2005). Lidar data were collected continuously from 14 September 2011 to 12 October 2011, up to a maximum range of 4000 m and with a velocity precision as great as 0.1 m s−1, depending on atmospheric conditions. The signal-to-noise ratio (SNR) of the lidar depends on various environmental factors, such as atmospheric extinction and aerosol concentration, which in turn affects the maximum range and velocity precision (Rye and Hardesty 1993; Aitken et al. 2012). Lidar data were recorded when the SNR exceeded a preset threshold of −20 dB. Plan position indicator (PPI) scans—in which the azimuth angle of the beam is swept while holding the elevation angle fixed—were used to sample the flow field in and around the wake, with measurements taken at 67 range gates r separated from one another by 60 m. In each scan, the azimuth was swept through an angle of 84°—symmetric about the longitudinal axis of the turbine—with azimuthal resolution Δθ = 3° while holding the elevation angle fixed at 0°. Each scan lasted approximately 4 min, which is long enough for meandering to influence the estimation of the wake characteristics, as discussed in section 3.

b. Wake detection procedure

The procedure used to determine wake parameters from the LOS velocity measurements uLOS is based on section 3d of Aitken et al. (2014). As depicted in Fig. 3, the ambient wind is modeled as having uniform speed u and uniform direction. An unprimed coordinate system is centered at the turbine and defined such that the x axis is aligned with the ambient wind direction. A second, primed coordinate system has the x′ axis (y′ axis) perpendicular (parallel) to the turbine rotor plane and is related to the unprimed system via a rotation matrix,
e1
to account for the possibility of yaw error. In this formulation, φ is an unknown parameter, whereby φ = 0 when the rotor plane is perpendicular to the flow and φ ≠ 0 in the case of yaw error. Nominally, the lidar beam should point along the x′ axis when the scanning head is in neutral position, that is, not rotated. LOS velocity measurements are taken at discrete points in the field, each of which is described by range gate r = (x′2 + y′2)1/2 and azimuth angle θ = arctan(y′/x′). For both θ and φ, counterclockwise (clockwise) rotations are defined to be positive (negative). Because the angle between the lidar beam and the vector describing the flow field at a given point is |θ + φ|, the measured LOS velocity is the actual wind speed multiplied by the function cos(θ + φ), which can be rewritten as
e2
Fig. 3.
Fig. 3.

Coordinate systems and variable definitions.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00218.1

In the near wake—within a few rotor diameters downstream of the turbine—the horizontal cross section of the velocity deficit profile is expected to have a double-Gaussian shape; that is, the profile contains two local minima corresponding to the points of maximum lift along the blades. On the other hand, in the far wake, turbulent mixing causes the two troughs from the near wake to merge and forms a single local minimum, and the profile is Gaussian in shape (Magnusson 1999). The two profiles are sketched in Fig. 4. Accordingly, the wake is modeled as either a single-Gaussian or a symmetric double-Gaussian function subtracted from the uniform background flow, in an attempt to account for the difference between the shape of the VD profile in the near and far wake. For each sweep of the beam, and at each r, three models were fit to the LOS velocity data to identify the wake, if any: a wake-free model,
e3
a single-Gaussian wake model,
e4
and a double-Gaussian wake model,
e5
In both Eqs. (4) and (5), a denotes the amplitude of the Gaussian and sw is a parameter controlling the width of the wake. In Eq. (4), yc denotes the location of the wake center, whereas yl and yr are used to distinguish the locations of the left and right local minima, respectively, in Eq. (5). For a given range gate r, y′ is the only independent variable. All other variables appearing on the right-hand sides of Eqs. (3)(5) are parameters, whose best-fit values are obtained using nonlinear regression. An extra sum-of-squares F test is used to determine the simplest model (i.e., the model with the least number of parameters) to fit the data, in which the threshold p value is set to 0.05; that is, if the p value is less than 0.05, then the simpler model is rejected and the more complicated model is deemed to fit the data significantly better (Kleinbaum et al. 2007).
Fig. 4.
Fig. 4.

Sketch of the velocity deficit profiles in the (a) near and (b) far wakes.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00218.1

In addition to the extra sum-of-squares F test used to find the best-fit models, some models were rejected for having unusual parameter estimates. If, for a particular model fit, any parameter or confidence interval fell outside three standard deviations of the respective median value, the fit was deemed an outlier and disregarded. Moreover, model fits with unphysical parameter estimates were also eliminated from the analysis. Specifically, a wake is necessarily characterized by 0 < a < u because 0% < VD < 100% by definition. Because of unusually large ambient variability, undetected hard target strikes, or signal dropout, the algorithms could occasionally determine a to be outside of the valid range; such unphysical model fits were excluded from consideration.

For the single-Gaussian wake, the velocity deficit is given by
e6
and the wake width by
e7
following Aitken et al. (2014). For the double-Gaussian wake, the velocity deficit is given by
e8
where uwake is taken to be the minimum modeled wind speed inside the wake, and the wake width is calculated as
e9

Using the subscript “0” to denote initial coefficient estimates, seeding for the regression algorithm proceeded for each range gate as follows: φ0 was set to zero; u0 to the median-measured LOS velocity for the range gate of interest; a0 to the difference between u0 and the minimum measured LOS velocity; yc0 to zero; yl0 and yr0 to −0.25D and +0.25D, respectively (where lift and therefore the velocity deficit are expected to be maximum); and sw0 to 0.25D (a value corresponding to a wake width of one rotor diameter).

3. Results

a. Wake detection

A total of 11 323 PPI scans were taken over the course of the experiment. Periods for which the turbine was not operating were excluded from the analysis, as determined from the turbine power data. Figure 5 shows, as a function of distance downstream of the turbine x, the percentage of scans for which a wake was determined to be statistically significant in comparison to the background flow. For a wake to be detected, both the entire width of the wake w and an adequate number of points in the ambient flow outside the wake must be sampled. In the case of an 84° sector, the arc length is just 1.8D for r = 120 m = 1.2D, and yet w is expected to be about 1.4D at this distance behind the turbine, based on Eq. (2) in Aitken et al. (2014). The relatively low number of detected wakes at the first two range gates suggests that, close to the turbine, the lidar field of view (FOV) was not wide enough for both the full w and a sufficient portion of the background flow outside the wake to be seen in the scanned velocity profile. However, as the FOV increases, so does the overall number of detected wakes until x = 3D, after which wakes are detected with diminishing frequency because 1) the amplitude of the velocity deficit decreases and therefore scales increasingly with the variability in the ambient flow and 2) velocity measurements become less precise, with lidar SNR falling off as 1/r2 (Fujii and Fukuchi 2005). Although a better distinction between the single- and double-Gaussian profiles could likely be made by employing finer azimuthal resolution—Δθ = 3° seems to be too coarse—the fraction of double-Gaussian wakes does decrease with downwind distance past x = 1.8D, in accordance with expectations.

Fig. 5.
Fig. 5.

Number of detected wakes vs downwind distance. The relatively low number of detected wakes close to the turbine (x ≤ 1.2D) is a consequence of the lidar’s limited FOV in that region.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00218.1

Related to the FOV issue in the near wake, the lateral spacing of the turbines influences the maximum distance to which the wake from an individual machine can be reliably discerned. As turbulent mixing causes the wake to expand with downstream distance, the wakes from lateral-neighbor turbines will eventually merge at some point. Based on average wake expansion rates (Aitken et al. 2014) and the lateral spacing of 3D at this particular wind farm, we estimate that the wake boundaries from lateral neighbors should intersect at about x ≈ 8D. But, similar to the near wake, a sufficient portion of the background flow must also be sampled in the far wake for the wake to be reliably distinguished. Accordingly, we were able to detect wakes on average out to x = 6D in this particular arrangement. Interestingly, our wake detection rate at intermediate range gates—about 40% on average—agrees quite well with the rejection rate of 60% noted in España et al. (2011), in which instantaneous wakes from porous disks in a wind tunnel were identified using particle image velocimetry.

b. Velocity deficit

In Fig. 6, VD is shown to decrease with x, as faster-moving ambient air is entrained within the wake. From basic one-dimensional momentum theory, the maximum velocity deficit is expected to be 67% at the Betz limit, whereby the turbine operates at peak efficiency (Manwell et al. 2010). On average, then, the initial velocity deficit was quite high, presumably because the average wind speed was just above cut-in, meaning that the turbine was often operating at or near maximum thrust. Notably, a substantial velocity deficit of about 40% was apparent as far as 6D behind the turbine. As in Aitken et al. (2014), wind speed had the most pronounced effect on the magnitude of the velocity deficit, with a consistent difference of about 20%, on average, between region 2 (below rated power; 4 < u < 13 m s−1) and region 3 (at rated power; 13 m s−1 < u < 25 m s−1) of the power curve. In Fig. 6c, low TI corresponds to TI < 7.5% and high TI corresponds to TI > 12.5%; the categories were chosen to divide the data roughly into thirds and to provide a buffer zone about the median value of 10%. In Fig. 6d, “day” (“night”) corresponds to 1000–1600 (2100 to 0600) local daylight time, with the intention of capturing periods with unstable (stable) stratification in lieu of detailed temperature profiles that could provide more accurate stability metrics, such as the bulk Richardson number (Friedrich et al. 2012). The average velocity deficit was modestly lower for high TI and daytime conditions, presumably because of more effective mixing between the wake and ambient flow. We note here that there are two competing influences when it comes to turbulence: higher turbulence levels should cause the wind speed inside the wake to recover more quickly but also preclude the detection of smaller velocity deficits. These two effects seem to more or less cancel out here, and more data will need to be collected in future experiments to reliably discern the influence of turbulence on the wake decay rate.

Fig. 6.
Fig. 6.

Velocity deficit vs downwind distance. The bold central lines indicate median values, whereas the symmetric shaded error bars represent the standard deviation of the measurements. (a) Overall results are shown, and velocity deficit measurements are further categorized by (b) ambient wind speed, (c) turbulence intensity, and (d) time of day.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00218.1

c. Wake meandering and yaw error

In addition to yaw error, the estimate of the parameter φ is influenced by other factors, such as wake meandering and variations in the ambient wind direction. Moreover, misalignment of the lidar beam, which should nominally point perpendicular to the rotor plane when the scanning head is not rotated, also induces systematic error in the estimate of φ. For range gates nearer to the turbine, φ should closely approximate the yaw error. As r increases, however, the estimate of φ may gradually diverge somewhat from the actual yaw error because of decreasing correlation between the ambient wind direction at r and that at the turbine. In the case of no yaw error, the effect of meandering is such that the estimate of φ should be zero on average and the variability in φ should be greater when the flow is unstable—that is, more turbulent— because wake oscillations are random and governed by scales of atmospheric turbulence on the order of the dimension of the wake (España et al. 2011).

As depicted in Fig. 7a, the median estimate of φ was found to be slightly negative, presumably because the measured yaw error α—defined here to be the difference between the turbine yaw angle and the hub height wind direction measured by the met tower—had a median value of −0.3° taken over the entire experiment. The median estimate of φ is more negative for low TI and nighttime conditions because the median-measured yaw error was −0.5° during these periods, whereas the median α was almost zero for high TI and daytime conditions. Although there is a small discrepancy between the median values of α and φ at the range gates closest to the turbine—likely explained by the effects of meandering, ambient variability, calibration errors, and lidar misalignment—the wake detection procedure seems capable of quantifying yaw error with reasonable accuracy. Because the standard deviation of α was about 10° during both the day and night, we can attribute the greater variability in φ for high TI and daytime conditions to the larger turbulent structures—and therefore the larger amplitude of wake meandering—experienced during these periods.

Fig. 7.
Fig. 7.

Estimate of the parameter φ vs downwind distance. The bold central lines indicate median values, whereas the symmetric shaded error bars represent the standard deviation of the measurements. (a) Overall results are shown, and measurements are further categorized by (b) turbulence intensity and (c) time of day.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00218.1

We note here that the yaw error is a function of wind direction variability, which in turn depends on both wind speed and atmospheric stability, as noted in Mahrt (2011). Wind direction variability decreases with increasing wind speed because submesoscale motions (on scales of minutes or tens of minutes) significantly enhance wind direction variability for low winds, but cause only small changes of the wind direction for high winds. Moreover, for a given wind speed, wind direction variability is generally larger during the day because of wind direction changes associated with large convective eddies. Mahrt (2011) found greater wind direction variability at night, with the effect of weaker nocturnal winds overwhelming that of daytime convective eddies. Similarly, in our experiment, the median wind speed measured by the met tower was 7.5 and 5.4 m s−1 during the day and night, respectively. Thus, weaker nocturnal winds are likely responsible for greater wind direction variability, and therefore the larger yaw error observed at night.

The estimate of the horizontal location of the wake centerline yc is related to the yaw error and the parameter φ. Given the definitions in section 2b, the force imparted by the turbine on the flow has a component in the +y direction when the yaw error is negative. The median trajectory of the centerline shown in Fig. 8a corresponds to a yaw error of about −1°, which agrees fairly well with the median-measured value of −0.3°. Similar to φ, the median estimate of yc trends away from zero for low TI and nighttime conditions because of nonzero yaw error during these periods. Moreover, the variability in yc is relatively lower for these conditions because the turbulence length scale and, therefore the amplitude of the wake oscillations, is reduced in magnitude.

Fig. 8.
Fig. 8.

Wake centerline vs downwind distance. The bold central lines indicate median values, whereas the symmetric shaded error bars represent the standard deviation of the measurements. (a) Overall results are shown, and wake centerline measurements are further categorized by (b) turbulence intensity and (c) time of day.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00218.1

d. Wake width

Figure 9 illustrates the increase in wake width with downwind distance from 1.5D at x = 1.8D to 2.5D at x = 6D. We note here that, as in Aitken et al. (2014), the industry-standard Park model (Barthelmie et al. 2006)—with the typical onshore value for the wake decay constant k = 0.075—underestimates the extent of the wake boundary in comparison to our median results. The expansion rate is greater under more turbulent conditions, as represented by TI and time of day in Figs. 9b and 9c, respectively, because of more effective mixing between the wake and ambient flow. The standard deviation of the wake width is a result of 1) inherent variability, 2) measurement uncertainty, and 3) wake meandering. For more turbulent conditions and regions in the far wake, the wake boundary is more diffuse and its detection is therefore less precise. In addition, because each scan takes several minutes to complete, the wake width estimate is somewhat influenced by the meandering of the wake. Accordingly, the standard deviation of the wake width is greater for high TI and daytime conditions and increases with x.

Fig. 9.
Fig. 9.

Wake width vs downwind distance. The bold central lines indicate median values, whereas the symmetric shaded error bars represent the standard deviation of the measurements. (a) Overall results are compared to the Park wake model, and wake width measurements are further categorized by (b) turbulence intensity and (c) time of day.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00218.1

4. Summary and conclusions

A nacelle-mounted long-range scanning lidar was used to measure wakes from a utility-scale wind turbine, and wake characteristics from the resulting dataset were quantified with the statistical model developed in Aitken et al. (2014). To the best of our knowledge, this effort represents the first such dataset in the published literature. The wake velocity deficit was observed to depend on ambient wind speed, with the deficit differing by about 20% between regions 2 and 3 of the power curve. The average deficit was large—decreasing from 60% at x = 1.8D to 40% at x = 6D—as a result of a low average wind speed and therefore high average turbine thrust coefficient. Moreover, the wake width was measured to expand from 1.5D at x = 1.8D to 2.5D at x = 6D. Both the wake growth rate and the amplitude of wake meandering were observed to be greater for high ambient turbulence intensity and daytime (unstable) conditions. The model is capable of tracking the wake centerline and capturing the yaw error of the turbine with reasonable accuracy.

Up to now, wind farm wake simulations, and hence turbine layout optimization, have suffered from an unacceptable degree of uncertainty, largely because of a lack of adequate experimental data for model verification. To expand upon the results here, additional measurements will need to be taken for a variety of locations and turbine models. Nacelle-based remote sensors are particularly well suited for such experiments because scans can more closely transect the wake centerline as compared to ground-based systems. For future studies involving nacelle-mounted systems, we recommend distinct scanning strategies in which the sensor field of view is varied depending on the range of interest: the scanned sector should be wider when sampling the near wake, such that the entire extent of the wake can be seen against the background flow, while a relatively narrower sector can be used for scans of the intermediate and far wakes. Similarly, the azimuthal resolution ought to be finer for scans of the near wake to facilitate the detection of the velocity deficit profile in that region, while coarser resolution may be more appropriate for scans of the far wake. In addition, faster scan rates would allow for more instantaneous representations of the flow. For studies of the far wake, the turbine of interest should also be relatively isolated, to avoid interference from the wakes of neighboring turbines or other obstacles. Range–height indicator (RHI) scans conducted from the nacelle would provide insight as to the vertical structure of the wake. Methods for quantifying atmospheric stability, such as measurements of both wind speed and temperature at two distinct vertical levels to calculate the Richardson number, would be valuable for categorizing wake characteristics based on stability conditions. The procedure developed in Aitken et al. (2014) and applied here should prove useful in the analysis of wind turbine wakes in future field campaigns.

Acknowledgments

We thank the wind farm operator for generously collecting and sharing the data and for the many helpful discussions during the analysis. We also appreciate the insights and suggestions of three anonymous reviewers, which helped to improve the paper. NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

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