Abstract

High-spatial-and-temporal-resolution radial velocity measurements surrounding a single utility-scale wind turbine were collected using the Texas Tech University Ka-band mobile research radars. The measurements were synthesized to construct the first known dual-Doppler analyses of the mean structure and variability of a single turbine wake. The observations revealed a wake length that subjectively exceeded 20 rotor diameters, which far exceeds the typically employed turbine spacing of 7–10 rotor diameters. The mean horizontal wind speed deficits found within the turbine wake region relative to the free streamflow were related to potential reductions in the available power for a downwind turbine. Mean wind speed reductions of 17.4% (14.8%) were found at 7 (10) rotor diameters downwind, corresponding to a potential power output reduction of 43.6% (38.2%). The wind speed deficits found within the wake also exhibit large variability over short time intervals; this variability would have an appreciable impact on the inflow of a downstream turbine. The full understanding and application of these newly collected data have the potential to alter current wind-farm design and layout practices and to affect the cost of energy.

1. Introduction

Wind turbine wakes are partly responsible for what is commonly referred to as the “underperformance” of wind farms by 10%–20% (Barthelmie et al. 2007, 2009, 2010; Barthelmie and Jensen 2010; Schepers et al. 2012), in part attributed to shortcomings in the current power-output models to accurately replicate turbine wakes and modulated flow fields throughout a wind farm. Wakes represent an extraction of energy from the free streamflow that may become inflow for a downstream turbine, depending on the wind direction. In addition, enhanced turbulence contained within wakes can create increased fatigue loading on downstream turbines (Crespo et al. 1999; Vermeer et al. 2003; Troldborg et al. 2011). Reducing the cost of wind energy through the optimization of wind-farm layout and operations demands a full understanding of turbine wake behavior (Gonzalez et al. 2010; Kusiak and Song 2010; Knudsen et al. 2011; Meyers and Meneveau 2012; Chowdhury et al. 2012), including assessing overall wake length and meandering characteristics (Larsen et al. 2007, 2008; España et al. 2011) in a variety of atmospheric conditions. Typical turbine spacing for existing utility-scale wind-farm deployments spans 7–10 rotor diameters D (Barthelmie et al. 2010) coinciding with expected typical wake lengths. Although seemingly an extreme case, recent remote sensing observations have traced the length of a single turbine wake beyond 30D (Hirth et al. 2012). Although existing full-scale observations of turbine wakes are exceptionally limited, advances in remote sensing technologies provide optimism that the data required for model validation will soon be collected (Käsler et al. 2010; Bingöl et al. 2010; Trujillo et al. 2011; Hirth et al. 2012). The analyses presented in this study represent the first known effort to employ dual-Doppler (DD) syntheses to evaluate the structure of a turbine wake using mobile, research-grade Doppler radars. These results are expected to serve as a catalyst for future wake observations and simulation improvements, leading to optimized wind turbine layouts, refined design of control systems, and development of “smart” wind farms to help to reduce the cost of energy.

2. Experiment

a. TTUKa radar deployment

Texas Tech University maintains two research-grade mobile Ka-band Doppler radar systems (hereinafter called TTUKa). These systems provide excellent spatial resolution with a half-power beamwidth of 0.49° and an along-beam range resolution of 15 m. The TTUKa radars utilize a solid-state traveling wave tube transmitter that emits a coherent pulse. This coherency allows for the transmission of an engineered pulse using sophisticated pulse-compression techniques (Farnett and Stevens 1990; O’Hora and Bech 2007). Relatively long pulse widths can be used (12–30 μs), increasing sensitivity while retaining high along-beam spatial resolution.

On 27 October 2011, the TTUKa radars were deployed in the vicinity of a single utility-scale wind turbine (Hirth et al. 2012). The turbine possessed a hub height of 80 m and a rotor diameter of 86 m. A single turbine was selected (as opposed to a multiple-turbine wind farm) to serve as a benchmark study and to allow for a comprehensive investigation of the mean structure and evolution of a single wake. TTUKa1 was located 2.7 km upwind of the turbine while TTUKa2 was positioned 2.6 km west of the turbine (Fig. 1). Each radar scanned 10 elevation angles between 0.6° and 2.4° in 0.2° increments over a 30° sector. Each complete set of 10 scans, or volume, took ~45 s to complete. Both radars performed coordinated data collection over a 54-min period, yielding 72 consecutive volumes available for DD synthesis of the horizontal wind flow describing the turbine wake and surrounding free streamflow. Beyond the 54-min coordinated scanning period presented herein, each radar conducted additional independent scanning that is not conducive for DD synthesis.

Fig. 1.

Schematics of the TTUKa turbine deployment including (a) lower and upper beam heights originating from TTUKa1 at the location of the turbine and at 5-km range and (b) a plan view of the DD deployment and respective 30° scanning sectors from each radar. The DD domain is characterized by the overlapping sectors. The location of the turbine and the primary wind direction are also shown.

Fig. 1.

Schematics of the TTUKa turbine deployment including (a) lower and upper beam heights originating from TTUKa1 at the location of the turbine and at 5-km range and (b) a plan view of the DD deployment and respective 30° scanning sectors from each radar. The DD domain is characterized by the overlapping sectors. The location of the turbine and the primary wind direction are also shown.

b. Dual-Doppler methods

Raw binary data collected by each TTUKa radar system were generated using the Sigmet, Inc., Radar Video Processor 9 signal processor. The Sigmet “IRIS” software package was used to convert raw data to so-called Universal Format (UF). The UF data were converted to Doppler Radar Data Exchange (DORADE) format using the “xltrsii” translator developed by the National Center for Atmospheric Research (NCAR). The DORADE sweep files were then edited using the NCAR “SOLOII” software package. For this study, minimal editing was necessary because of the high data quality and relatively low wind speeds (i.e., unfolding was not necessary). Complete volumes comprising multiple sweep files from both radars were interpolated from their native polar coordinate space to a Cartesian grid using the NCAR “REORDER” software package. The complete grid used for this study was 3 km × 3 km × 150 m, with 10-m grid spacing in both the horizontal and vertical directions. Data were interpolated using the Barnes (exponential) weighting scheme (Barnes 1964) with a radius of influence of 25 m in the horizontal plane and 15 m in the vertical direction. The REORDER Barnes weighting function was set to −2.3. Because the minimum (maximum) elevation scan used for both radars was 0.6° (2.4°), gridded data generally were not present below (above) 30 m (120 m) through relevant portions of the gridded domain. Final gridded data from REORDER were output in a binary format specifically prepared for the NCAR Unix-based Custom Editing and Display of Reduced Information in Cartesian Space (CEDRIC) software package in preparation for DD synthesis. CEDRIC was used to generate U and V horizontal wind velocity components for each grid point. Synthesized data were only considered to be valid at a given grid point if the beam-crossing angle was between 30° and 150°. The final synthesized output from CEDRIC was in the Network Common Data Form (NetCDF) format. An example of a single-volume DD synthesis is provided in Fig. 2.

Fig. 2.

An example of TTUKa DD-synthesized horizontal wind speed (m s−1) at (a) 40, (b) 60, (c) 80, and (d) 100 m AGL. Horizontal wind vectors are shown. The black dot represents the location of the turbine. The solid black line represents an algorithm-defined wake center to a distance of 15D.

Fig. 2.

An example of TTUKa DD-synthesized horizontal wind speed (m s−1) at (a) 40, (b) 60, (c) 80, and (d) 100 m AGL. Horizontal wind vectors are shown. The black dot represents the location of the turbine. The solid black line represents an algorithm-defined wake center to a distance of 15D.

c. Wake-tracking algorithm

Because of variations in wind direction, wake orientation, and spatial distribution (i.e., meandering), it was desirable to quantitatively define the wake center at incremental downwind distances from the turbine. Given that the wake evolves with downwind distance in both the horizontal and vertical dimensions, it was necessary to incorporate data from all vertical levels (as opposed to just considering hub height) across the rotor sweep. A domain-mean wind direction was calculated for each DD volume using all available volume grid points, and all wake cross sections were oriented normal to this value with a 100-m horizontal width (±50 m of the defined wake center) (Fig. 3). Because wake width varies with downwind distance, the defined cross section does not always transect the entire wake. Rather, the cross section is centered on the minimum wind speed assumed to be associated with the center of the wake. The first cross section at 0.25D was horizontally centered on the turbine at a downwind bearing equal to the domain-mean wind direction. For each successive cross section (every 0.25D), the DD horizontal wind speed was assessed across the width of the vertical slice at levels between 40 and 120 m (approximately the depth of the rotor sweep), where data were available. The horizontal (d distance) location of the minimum wind speed was tabulated for each height. The median horizontal location from all contributing vertical levels was set as the center point for the next incremental vertical cross section. For this study, it was found that the algorithm was able to detect the wake center to a downwind distance of 15D for all 72 volumes.

Fig. 3.

(a) An example constant horizontal plane of DD horizontal wind speed (m s−1) at 80 m with the wake-algorithm-derived wake centerline and vertical cross-section slices. (b) The DD horizontal wind speed cross-section slices at a downwind distance of 5D for the vertical levels between 40 and 110 m. The median location of the minimum horizontal wind speed for all contributing heights in this cross section was x = −10 m.

Fig. 3.

(a) An example constant horizontal plane of DD horizontal wind speed (m s−1) at 80 m with the wake-algorithm-derived wake centerline and vertical cross-section slices. (b) The DD horizontal wind speed cross-section slices at a downwind distance of 5D for the vertical levels between 40 and 110 m. The median location of the minimum horizontal wind speed for all contributing heights in this cross section was x = −10 m.

3. Wake analyses

During the 54-min data collection period, the DD-derived domain-mean wind speed and direction varied considerably. At hub height (80 m), the domain-averaged wind speed evaluated for each DD volume ranged from 8.5 to 11.3 m s−1, corresponding to region 2 on the power curve of this particular turbine (i.e., where power output depends on wind speed and is below the rated power for the turbine). The domain mean wind direction veered from 16° to 62°, resulting in a large variability in wake orientation (Fig. 4). The discernible length of the wake also varied on short time scales. At times, the wake visually (subjectively) appeared to extend beyond the DD analysis domain to a length greater than 20D (Fig. 4b). In general, beyond 15D the visual character of the wake began to scale with the free-stream boundary layer wind speed heterogeneity (e.g., Fig. 4a) associated with atmospheric boundary layer rolls or streaks (Young et al. 2002; Drobinski and Foster 2003) that represent local areas of atmospheric mixing. The interaction of these boundary layer features with an existing wake is evident in these analyses; the role that these coherent features play in modulating wake structure remains to be further studied, however.

Fig. 4.

TTUKa DD-synthesized horizontal wind speed (m s−1) on 27 Oct 2011 at 80 m AGL at (a) 1233, (b) 1241, (c) 1304, and (d) 1317 UTC. Horizontal wind vectors are shown. The black dot represents the location of the turbine. The algorithm-defined wake center to a distance of 15D is denoted by the solid black line.

Fig. 4.

TTUKa DD-synthesized horizontal wind speed (m s−1) on 27 Oct 2011 at 80 m AGL at (a) 1233, (b) 1241, (c) 1304, and (d) 1317 UTC. Horizontal wind vectors are shown. The black dot represents the location of the turbine. The algorithm-defined wake center to a distance of 15D is denoted by the solid black line.

A mean free-stream wind profile is developed for each DD volume by averaging a 1 km × 1 km section of the DD domain not impacted by the turbine wake. Algorithm-constructed wake vertical cross sections from all 72 DD volumes are then composited at each downwind increment. Each composited cross section is presented as a percent reduction from the derived free-stream wind profile (Fig. 5). Using the grid points contained within the wake-relevant rotor sweep (black circle), the mean and maximum wind speed deficit are assessed for each downwind composite cross section. The mean (maximum) wind speed deficit within the wake at D is 27.7% (38.5%), at 7D it is 17.4% (23.5%), at 10D it is 14.8% (19.1%), and at 15D it is 11.5% (15.5%). For the first 10D of downwind distance, the difference between the maximum and mean wind speed deficit converges with increasing distance; it is 10.8% at D, 6.1% at 7D, and 4.3% at 10D. For downwind distances beyond 10D, this difference changes little and is 4.0% at 15D (Fig. 6) as mixing and entrainment reduce the peak wake deficits. The higher wind speed reductions associated with the wake are stretched upward in the gridded data fields, particularly where reductions are the most significant (e.g., Figs. 3a,b). Because of a lack of data above 120 m, larger deficit values are interpolated upward during the coordinate-space conversion process. This effect is estimated to induce a positive bias in the mean wind speed reduction behind the rotor sweep of no more than 0.5%.

Fig. 5.

Vertical slices of the reduction (%) in horizontal wind speed within the wake composited from 72 DD volumes at (a) D, (b) 2D, (c) 5D, (d) 7D, (e) 10D, and (f) 12D downwind. Domain grid points are shown, and magenta grid points represent those contained by the rotor sweep (solid black circle). The black plus sign represents the center of the turbine hub. The maximum and mean reduction values from the contributing rotor-sweep grid points are annotated.

Fig. 5.

Vertical slices of the reduction (%) in horizontal wind speed within the wake composited from 72 DD volumes at (a) D, (b) 2D, (c) 5D, (d) 7D, (e) 10D, and (f) 12D downwind. Domain grid points are shown, and magenta grid points represent those contained by the rotor sweep (solid black circle). The black plus sign represents the center of the turbine hub. The maximum and mean reduction values from the contributing rotor-sweep grid points are annotated.

Fig. 6.

Horizontal wind speed reductions (%) within the wake at various downwind distances from the turbine relative to the free-streamflow field. Thin lines represent individual volume maximum and mean values. Thick lines indicate maximum and mean reduction composites from all 72 contributing DD volumes.

Fig. 6.

Horizontal wind speed reductions (%) within the wake at various downwind distances from the turbine relative to the free-streamflow field. Thin lines represent individual volume maximum and mean values. Thick lines indicate maximum and mean reduction composites from all 72 contributing DD volumes.

4. Relationship to power output

The analyzed mean wind speed deficits within the wake-relevant rotor sweep are linked to the potential power deficits that a downwind turbine located within the wake might experience. Within region 2 of a power curve, power output is proportional to the inflow mean wind speed cubed (Hansen 2000). Note that the coefficient of power for the turbine studied was not available for use. All calculated power reductions are considered to be estimates that assume a constant coefficient of power across the range of documented wind speeds but are still believed to provide meaningful perspective. At a downwind distance of 2D, the composite mean wind speed reduction behind the rotor sweep is 27.3% relative to the free streamflow. This reduction corresponds to a potential power reduction for a turbine centered within this wake of 61.6% relative to the power output from a turbine experiencing the free streamflow. Similarly, at a downwind distance of 7D, a 17.4% mean wind speed reduction relates to a 43.6% decrease in potential power output. At 10D and 15D downwind, 14.8% and 11.5% mean wind speed reductions correspond to potential power output decreases of 38.2% and 30.6%, respectively. Note that the turbulent character of the wake can vary significantly with downwind distance (Vermeer et al. 2003; Sanderse et al. 2011), which can affect the relationship between wind speed and power output.

These initial results agree well with independent analyses using Supervisory Control and Data Acquisition (SCADA) data collected at the Middelgrunden offshore wind farm in Denmark (Barthelmie et al. 2007). This study compared data collected from the nacelles of a leading turbine and another turbine located 2.4D downwind. For a well-aligned wind direction, the SCADA data showed a wind speed reduction within the wake center of roughly 30% at the location of the downwind turbine. Similar analysis from SCADA data at the Horns Rev offshore wind farm in Denmark showed a decrease in normalized power output of roughly 38% between a leading-row turbine and a turbine that was located 7D downwind for a well-aligned wind direction (Barthelmie et al. 2009). Meteorological tower data collected over a 5-yr period at the Energy Research Center of the Netherlands Wind Turbine Test Site in Wieringermeer showed maximum velocity deficits within a wake to be 45% at 2.5D and 35% at 3.5D (Schepers et al. 2012). Maximum power loss between the first turbine and the second turbine (separated by 3.8D) reached 67%. Although there are differences in turbine specifications, surface roughness, and atmospheric conditions associated with data collected from these previous studies and the single turbine examined herein, similar findings are shown using vastly different analysis methods.

The collected data also reveal considerable variability between individual DD horizontal wind speed deficits within the wake (Fig. 6). Maximum wind speed reductions in the wake within 4D of the turbine exceeded 50% on several occasions during the collection period. At 2D, the range in mean wind speed reduction behind the rotor sweep over the 72 contributing volumes is 32%. The spread reduces at 6D to 20% and increases to 31% at 14D—a result that can be likely attributed to wake meandering. The mean wind speed deficit range for all calculated downwind distances from D to 15D is 26%. The net result to a downwind turbine could be a large variability in potential power output on very short time scales (within minutes).

5. Conclusions

Data collected by the TTUKa mobile research radars were utilized to construct DD-synthesized horizontal wind analyses of the wake downstream of a single utility-scale wind turbine. The analyses revealed considerable temporal variability in free-stream wind speed and direction over the 54-min data-collection period. Large variability in wake length was documented, and at times the wake was found to subjectively extend out of the analysis domain—a distance of greater than 20D. Large variability was found in maximum wind speed deficits measured within the wake as compared with the free-stream wind speed at hub height. These maximum wind speed deficits were observed over multiple volumes to exceed 50% within a distance of 4D. Mean wake wind speed deficits encompassed by the rotor sweep were also related to potential reductions in power output. Composite analyses showed 17.4% and 14.8% wind speed reductions at 7D and 10D, respectively, proportional to decreases in potential power output of 43.6% and 38.2% for a turbine centered in the wake at 7D and 10D versus a turbine experiencing the free streamflow.

6. Future work

This study lays the framework for utilizing the TTUKa technology and DD methods in a full wind-farm deployment. It has been shown here that for a well-aligned wind direction significant turbine-to-turbine interaction must occur given the current turbine spacing nominally utilized in wind farms. Given the mobile nature of the TTUKa systems, this interaction can be comprehensively observed within a variety of wind farms utilizing diverse turbine configurations for varying wind speed and direction regimes. In addition, a more broad representation of the horizontal wind speed deficits downstream of several rows of turbines can be assessed to investigate the impact of multiple turbines on the available energy within a large wind-farm deployment.

Acknowledgments

The authors thank Scott Gunter for assisting with the data-collection effort and Jerry Guynes for leading the design and providing technical support for the TTUKa radar systems. Funding for this study was provided by the U.S. Department of Energy Congressionally Directed Project grant known as Great Plains Wind Power Test Facility (Award DE-FG-06-GO86092).

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