Results from a Wake Steering Experiment at a Commercial Wind Plant: Investigating the Wind Speed Dependence of Wake Steering Performance

Wake steering is a wind farm control strategy in which upstream wind turbines are misaligned with the wind to redirect their wakes away from downstream turbines, thereby increasing the net wind plant power production and reducing fatigue loads generated by wake turbulence. In this paper, we present results from a wake steering experiment at a commercial wind plant involving two wind turbines spaced 3.7 rotor diameters apart. During the three-month experiment period, we estimate that wake steering reduced wake losses by 5.7% for the wind direction sector investigated. After applying a long-term correction 5 based on the site wind rose, the reduction in wake losses increases to 9.8%. As a function of wind speed, we find large energy improvements near cut-in wind speed, where wake steering can prevent the downstream wind turbine from shutting down. Yet for wind speeds between 6–8 m/s, we observe little change in performance with wake steering. However, wake steering was found to improve energy production significantly for below-rated wind speeds from 8–12 m/s. By measuring the relationship between yaw misalignment and power production using a nacelle lidar, we attribute much of the improvement in wake 10 steering performance at higher wind speeds to a significant reduction in the power loss of the upstream turbine as wind speed increases. Additionally, we find higher wind direction variability at lower wind speeds, which contributes to poor performance in the 6–8-m/s wind speed bin because of slow yaw controller dynamics. Further, we compare the measured performance of wake steering to predictions using the FLORIS (FLOw Redirection and Induction in Steady State) wind farm control tool coupled with a wind direction variability model. Although the achieved yaw offsets at the upstream wind turbine fall short 15 of the intended yaw offsets, we find that they are predicted well by the wind direction variability model. When incorporating the predicted achieved yaw offsets, estimates of the energy improvement from wake steering using FLORIS closely match the experimental results.

the wind plant because of the higher wind speeds encountered by downstream wind turbines. Additionally, research suggests that wake steering can reduce fatigue loads on downstream turbines by redirecting high-turbulence wake flow away from the turbines and avoiding partial wake interactions which can cause asymmetric rotor loading (Kanev et al., 2018;López et al., 25 2020).
The potential for wake steering to improve wind plant power production has been demonstrated for stationary wind conditions using high-fidelity computational fluid dynamics (CFD) simulations, engineering models, and wind tunnel experiments.
Using the National Renewable Energy Laboratory's (NREL's) Simulator fOr Wind Farm Applications (SOWFA) large-eddy simulation (LES) tool, Gebraad et al. (2016) observed a 13% increase in power production for a 2 × 3 array of wind turbines 30 with 5-rotor-diameter (5D) spacing in neutral atmospheric conditions. Vollmer et al. (2016) used LES to investigate the impact of atmospheric stability on wake steering, finding that the ability to control the wake position strongly depends on stability; low-turbulence stable atmospheric conditions were shown to be more favorable for wake steering than unstable conditions with higher turbulence. Although high-fidelity CFD simulations are valuable for studying the physics of wake steering, computationally efficient engineering models are needed to optimize wake steering controllers and to estimate performance for a variety 35 of wind conditions. Gebraad et al. (2017) and King et al. (2021)

used NREL's FLOw Redirection and Induction in Steady State
(FLORIS) engineering wind farm control tool (NREL, 2021) to estimate annual energy production improvements of 3.8% for a 60-turbine wind plant and 2.8% for a wind plant with 38 wind turbines, respectively. Using scaled wind turbine models, wind tunnel experiments have been used to investigate the effectiveness of wake steering beyond simulation environments. For example, using two-turbine arrays, Adaramola and Krogstad (2011) and Campagnolo et al. (2016) achieved net power gains of 40 12% for a 3D turbine spacing and 21% for a 4D spacing, respectively. Similarly, Bastankhah and Porté-Agel (2019) measured a 17% increase in power production for a row of five model wind turbines spaced 5D apart.
To bridge the gap between simulations and wind tunnel experiments with static wind conditions and successful implementation of wake steering in the field, several recent studies have investigated the design of wake steering controllers for realistic dynamic wind conditions. Bossanyi (2018) used field measurements of wind conditions as inputs to a dynamic engineering estimate wind plant-level wind conditions, updating the yaw offsets accordingly. Using CFD simulations with time-varying mean wind directions across the wind plant, the authors demonstrated a 1.4% increase in energy production for a six-turbine array when updating the turbines' yaw positions every 20 seconds. 60 Following an early inconclusive test of wake steering discussed by Wagenaar et al. (2012), recently several wake steering experiments at commercial wind plants have been described in the literature.  implemented wake steering control on a single wind turbine in an offshore wind plant in China to benefit three turbines located 7D, 8.6D, and 14.3D downstream in different directions. The authors reported power gains as high as 29% for certain wind directions for the 7D spacing, but they highlighted large uncertainty in the results because of a lack of data. An extensive field campaign at a  validate wind measurements from the turbines and to identify the best references for assessing the ambient wind conditions.
Additionally, measurements from the WindCube lidar were used to estimate the turbulence intensity distribution at the site.  the nacelle orientation. It shows that even though some drifts were experienced at the end of 2019, a very stable offset was maintained for the full duration of the field experiment, February 17-May 25, 2020.
Before analyzing the data, all variables are downsampled to 1-minute average values. As will be discussed further in Section 3.2, 1-minute samples are intended to provide a balance between averaging small-scale turbulent variations and distinguishing between time-varying wind conditions. been averaged during a period of 12 hours to remove noise associated with the two signals. The vertical gray lines indicate periods when the turbine was intentionally misaligned for the wake steering experiment.

Wake Steering Controller
Because the wind turbine controller could not be accessed or modified for this experiment, the wake steering strategy was implemented following the same approach as in Fleming et al. (2020). A control box was installed to read the incoming relative wind direction signal from the nacelle wind vane installed on the turbine and to apply an offset before sending it to the turbine's existing yaw controller, thereby inducing the intended yaw offset. The control logic implemented in the control 145 box is illustrated in Fig. 5. As shown in Fig. 5, because the lookup table defining the offset angles is dependent on both wind speed and direction, the nacelle wind speed and yaw position are also used as inputs to the control box. The measured wind direction-formed by combining the absolute yaw position and the relative wind vane direction-and wind speed are passed through low-pass filters with a time constant of 60 seconds before they are used to determine the corresponding target yaw offset in the lookup table. Finally, a toggle allows the yaw offsets to alternate between the target offsets and zero offset to 150 analyze the effect of wake steering in wind conditions that are similar to the baseline yaw control case. Note that the unfiltered wind speed signal recorded through the control box is compared to the same signal measured by the 1-Hz SCADA system to remove any time lag between the two systems and to ensure that the two clocks are correctly synchronized.
The applied yaw offsets are represented by the offset schedule in Fig. 6 Figure 5. Yaw offset control architecture with hourly toggling between baseline and wake steering control. The output wind vane signal is input to the wind turbine's existing yaw controller. energy improvements from wake steering are expected for both positive and negative yaw offsets, research suggests that, overall, wake steering is more effective with positive yaw misalignment Nouri et al., 2020). Further, results from a field experiment investigating the impact of yaw misalignment on loads show a reduction in blade loads for positive yaw offsets but an increase in loads for negative offsets (Damiani et al., 2018). Adhering to an upper bound of 20 • , imposed to manage structural loads, SMV6 is misaligned by up to 20 • for full wake conditions (208°-216°), and then this angle 160 is linearly reduced throughout the partial wake sector until it reaches zero at a wind direction of 236 • . The yaw offset schedule for wind speeds below 10 m/s shown in Fig. 6 is a simplified form of the optimal yaw offsets for maximizing the combined power of SMV5 and SMV6 determined using FLORIS. The FLORIS model used when designing the controller was calibrated using data from a previous wake steering experiment performed on the same wind turbines. Additional considerations were included in the yaw offset schedule to provide some robustness to wind direction uncertainty, following the approach discussed 165 by Simley et al. (2020b); specifically, yaw offsets are applied for a wider sector of wind directions in the partial wake region than suggested using the original FLORIS model. Last, to further reduce the loading at higher wind speeds, the target offsets are reduced in four steps above 10 m/s until wake steering is stopped for wind speeds above 14 m/s. :::: Note :::: that ::: the ::::: target :::: yaw ::::: offsets ::: are :::::: binned ::: by ::::: wind ::::: speed :: in ::::: steps :: of :: 1 ::: m/s :::::: rather :::: than ::::::: specified ::: as : a :::::::::: continuous ::::::: function :: of ::::: wind ::::: speed :: to :::::: enable :: a ::::: simple :::::: lookup ::::: table ::::::::::::: implementation. :

Wind Conditions
The distributions of the wind directions, wind speeds, and turbulence intensities analyzed during the wake steering experiment for the baseline and the controlled periods are shown in Fig. 7 for the wind direction sector between 195 • and 241 • investigated in this paper. Specifically, Fig. 7 shows the number of 1-minute samples obtained for each wind direction, wind speed, and turbulence intensity bin. Note that the reference wind direction and wind speed measurements are obtained from nacelle-175 based wind turbine sensors, as will be discussed in Section 4. Turbulence intensity is estimated using measurements from the WindCube profiling lidar at the hub height of 80 m.
The wind direction histogram shown in Fig. 7a    in Fig. 2, the wind speed histogram provided in Fig. 7b indicates above-average wind speeds during the experiment period; 180 however, higher wind speeds are expected because most of the data were collected during the winter (in February and early March, as illustrated in Fig. 4), when the wind resource is strong at the site. Figure 7c shows that similar turbulence intensity distributions were sampled during the baseline and the controlled periods. Last, the joint distribution of wind direction and wind speed during the experiment period is shown in Fig. 8, considering the total amount of data analyzed for the baseline and the controlled periods. For almost the entire wind direction sector, data were collected for wind speeds from 4-13 :::: 3-13 m/s.

Models
To help determine how accurately engineering wind farm control models represent wake steering in the field, the FLORIS tool and a probabilistic model of wind direction variability are used to predict realistic wake steering performance for the wind conditions observed during the experiment. In Section 3.1, we briefly describe the FLORIS model of the SMV wind plant, followed by a discussion in Section 3.2 of the model of wind direction variability.
Examples of the hub-height flow fields generated by FLORIS for the SMV wind plant are provided in Fig. 10 for a wind speed of 8 m/s. Figure 10a shows the flow field with a wind direction of 195 • , which is the southernmost wind direction 220 investigated in this study. Figure 10b highlights the impact of SMV6 operating with a 20 • yaw misalignment for a wind direction of 208 • , which is the first wind direction (moving clockwise) for which yaw offsets are implemented (see Fig. 6).
Finally, Fig. 10c shows the FLORIS flow field corresponding to the northernmost wind direction of 240 ::: 241 • investigated here. for the controlled turbine (discretized using 1 • × 1 • bins). First, the ideal PMF is established by assigning a probability of one to the intended yaw position corresponding to each wind direction using the yaw offset schedule. Next, the ideal PMF is convolved with a zero-mean joint PMF representing the uncertainty in the wind direction and yaw position (approximated as a bivariate normal distribution). Predicted ::: The :::::::: predicted : mean yaw offsets can then be calculated from the resulting PMF by 240 finding the expected value of the yaw position for a particular wind direction. Similarly, the predicted mean power production can be estimated ::::::::: determined : by calculating the expected ::::: value :: of ::: the : power from FLORIS across all possible yaw positions corresponding to the wind direction of interest.

Data Processing
Before assessing the performance of wake steering, the measured 1-minute data are filtered to remove periods with abnormal wind turbine operation or poor data quality, which will be discussed in Section 4.1. Next, the reference wind direction, wind speed, and power variables are derived using measurements from turbines SMV1, SMV2, SMV3, and SMV7, as will be explained in Section 4.2. Last, Section 4.3 describes the procedure used for quantifying uncertainty in the wake steering 275 performance metrics presented in Sections 5-7.

Reference Variables
The reference wind direction, wind speed, and power variables are derived from turbines SMV1, SMV2, SMV3, and SMV7.
The reference wind directions and wind speeds are used to represent the wind conditions encountered by the test turbines,

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whereas the reference power acts as an unbiased reference to which the power produced by the test turbines can be compared.
Measurements from SMV6 are not used to estimate the wind direction or the wind speed to avoid the potentially confounding effects of yaw misalignment on the estimated values. SMV4 is excluded from the set of reference wind turbines because of potential influences from wake steering, given its close proximity to the test turbines (see Fig. 1). Note that the WindCube ground-based lidar is not used to provide reference measurements either because of the impact of wakes on measurement 315 accuracy for southerly flow.
The reference wind direction is calculated as the mean wind direction measured by SMV1, SMV2, SMV3, and SMV7 using their nacelle position sensors and wind vanes. Measurements from multiple turbines are averaged to smooth small-scale wind direction variations that might be encountered at particular locations. The reference wind direction is calibrated to true north by first identifying the :::::::: measured wind direction where the ratio between the mean power produced by SMV5 and SMV6 ::::: during 320 ::::::: baseline :::::: periods : reaches a minimum, representing the direction where the wake losses suffered by SMV5 reach their peak.
Last, the reference power is formed by averaging the power production of SMV1, SMV2, SMV3, and SMV7. Following an approach similar to the reference wind speed derivation, a transfer function is applied to the average power produced by the four reference wind turbines to remove any bias from the power generated by SMV6 during baseline operation (e.g., caused 340 by differences in turbine performance, wake effects, or the impact of local terrain and surface roughness). Again, this transfer function is : a ::::: wind :::::::: direction ::: and ::::: wind :::::::::::::: speed-dependent :::::::: multiplier :::: that :: is : estimated by dividing the data into overlapping 3 • ::::::: reference : wind direction bins as well as 1-m/s ::::::: reference : wind speed bins, then calculating the ratio between the mean power produced by SMV6 and the mean uncorrected reference power for periods with baseline control.

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To quantify uncertainty in the wake steering metrics presented in Section 5 through Section 7, we provide 95% confidence intervals to accompany the estimates. Because many of the metrics require complicated calculations, analytic expressions for the confidence intervals are difficult to derive; therefore, we use bootstrapping, wherein the collection of 1-minute data samples used to derive a particular metric is randomly resampled with replacement many times to obtain a distribution of the estimates of the metric (Dekking et al., 2005). From this distribution, which we derive using at least 2000 bootstrap samples, 350 the confidence interval containing 95% of the estimates is used as a measure of uncertainty. Many of the results presented in Section 5 through Section 7 are derived for individual wind directionbins ::::: shown :: as : a :::::::: function :: of :::: wind :::::::: direction; for these cases, bootstrapping is performed using data from each wind direction bin individually. Similarly, for metrics based on data from both the baseline and the wake steering periods, the data corresponding to each control period are resampled independently before the final metric is calculated.

Yaw Offset Performance
In this section, we compare the yaw offsets achieved by the wake steering controller-measured using the nacelle wind vane as well as the WindCube Nacelle lidar-to the ideal yaw offsets determined from the yaw offset schedule and the predicted ::::::: expected : offsets based on the wind direction variability model. The overall mean achieved yaw offsets as a function of the reference wind direction are presented in Section 5.1, whereas Section 5.2 highlights the achieved ::: yaw : offsets for different 360 wind speed bins. Next, in Section 5.3, we directly compare the yaw offsets measured by the wind vane to those measured by the nacelle lidar. Based on this comparison, we suggest corrections to the nacelle wind vane measurements.
5.1 Achieved :::::: Overall : Yaw Offsets The ideal, predicted, and achieved ::::::: expected, :::: and :::::::: measured mean yaw offsets for all baseline and wake steering control periods are shown in Fig. 12 as a function of wind direction. As expected, the mean yaw offsets measured by the wind vane with 365 baseline control are close to zero. But the mean offsets measured by the nacelle lidar show a bias of 2 • -3 • during baseline periods, suggesting that the wind vane might be poorly calibrated (as will be explored in more detail in Section 5.3). During wake steering control periods, similar mean yaw offsets are measured by the wind vane and nacelle lidar. Whereas the achieved :::::::: measured yaw offsets fall short of the intended ::: ideal : offsets for wind directions between 209 • and 229 • , they are reasonably well represented by the predicted ::::::: expected yaw offsets using the wind direction variability model. Specifically, the wind 370 direction variability model predicts a reduction in the peak yaw offsets accompanied by the unintended yaw offsets outside of the target wake steering sector. Although the achieved :::::::: measured yaw offsets match this predicted trend, they exhibit a higher, more pronounced peak near the wind direction of 210 • . Differences between the predicted and achieved ::::::: expected :::: and :::::::: measured yaw offsets could be partly explained by biases in the wind vane measurements (see Section 5.3), which propagate to the estimated wind direction signal used by the wake steering controller.

Wind Speed Dependence of Achieved Yaw Offsets
Whereas Fig. 12 revealed the mean yaw offsets aggregated among all wind conditions, Fig. 13 highlights the wind speed dependence of the ideal, predicted, and achieved :::::::: expected, ::: and ::::::::: measured yaw offsets. The ideal yaw offsets reflect the yaw offset schedule shown in Fig. 6; for wind speeds above 10 m/s, the target yaw offsets are gradually phased out, until no offsets are applied when the wind speed reaches 14 m/s. The more spread out predicted ::::::: expected : yaw offsets show a similar reduction 380 for wind speeds above 10 m/s, but they also vary for lower wind speeds because of the impact of the wind speed-dependent yaw error on the wind direction variability model, as explained in Section 3.2. Namely, because the standard deviation of the wind direction uncertainty increases for low wind speeds, the predicted ::::::: expected : yaw offsets reach a lower peak offset and are spread out over a wider wind direction sector as wind speed decreases below 8 m/s.
Despite the large scatter and uncertainty in the achieved ::::::: measured : yaw offsets for certain wind speed bins-caused by the 385 relative lack of data for wind speeds below 8 m/s and above 12 m/s (see Fig. 7) as well as the greater wind direction variability for wind speeds below 8 m/s, potentially causing the reference wind direction measurements to poorly represent the wind conditions at SMV6- Fig. 13 reveals several trends. First, the positive wind vane bias observed during the baseline control :::::: periods, as measured by the nacelle lidar, is apparent for wind speeds below 10 m/s, but it disappears for higher wind speeds, suggesting wind speed-dependent vane error. Additionally, when wake steering control is active, the achieved yaw offsets Focusing on the wind speed dependence of the achieved and predicted :::::::: measured ::: and :::::::: expected : yaw offsets with wake steering control, Fig. 13 shows that the achieved :::::::: measured : offsets for wind speeds below 8 m/s generally agree with the 395 predicted ::::::: expected : offsets; because of the high wind direction variability at these wind speeds, the achieved :::::::: measured offsets are spread among a large wind direction sector. Uncertainty in the reference wind direction measurements stemming from wind direction variability could further contribute to the broadening of the achieved :::::::: measured offset curves. For wind speeds between 8-10 m/s, the achieved ::::::: measured : yaw offsets closely match the predicted ::::::: expected offsets. This wind speed bin is also favorable from a measurement perspective because of the large amount of data collected and the relatively low wind direction 400 variability. Within the 10-12-m/s wind speed bin, the achieved :::::::: measured yaw offsets tend to be higher than predicted, possibly because of lower wind direction variability or larger yaw offsets persisting from operation in lower wind speeds. Last, for wind speeds between 12-14 m/s, measurement uncertainty caused by the relative lack of data obscures the yaw offset trends. But, as expected, the achieved ::::::: measured : offsets are relatively low (the maximum target yaw offset for this wind speed bin is only 5 • ). yaw misalignments measured by the vane or lidar (see Fig. 1), only data corresponding to wind directions above 210 • are included in the analysis.
Specifically, we bin the measured yaw offsets by a separate reference yaw offset, given by the difference between the reference wind direction and the nacelle position of SMV6 (see Fig. 14a). With the random measurement errors significantly reduced, 425 the bin-averaged yaw offsets measured by the lidar and wind vane can then be compared to reveal biases in the wind vane measurements. An example of a linear regression applied to the bin-averaged yaw offsets for all wind speeds is provided in Fig. 14b, revealing an intercept of only 0.2 • but a slope of 0.9 ::::: ∼ 0.92, indicating the tendency for the wind vane to overestimate the magnitude of the yaw misalignment.
Scatter plots of the bin-averaged yaw offsets measured by the WindCube Nacelle lidar and the wind vane, along with the corresponding best-fit lines, are provided in Fig. 15 for different wind speed bins. Beginning with the wind vane bias when the measured yaw misalignment is zero, indicated by the intercept, a positive bias of ∼ 2 • is observed for wind speeds below 8 m/s.
For the 8-10-m/s wind speed bin, no significant bias : a :::: bias :: of :::: only :: 1 • : is observed; however, for wind speeds above 10 m/s, the wind vane measurement contains a negative bias of approximately −3 • . This wind speed dependence of the mean wind vane measurement error has been previously reported by Kragh and Hansen (2015). Despite the measurement bias for individual 435 wind speed bins, it is likely that the wind vane measurements are calibrated to achieve an average measurement bias close to zero, as indicated by the results in Fig. 14. In contrast to the intercepts, the slopes of the best-fit lines in Fig. 15 are nearly constant :::::: similar across different wind speeds; aside from an outlier in the 6-8-m/s wind speed bin, a slope of ∼ 0.9 is ::::: slopes ::::::: between :::: 0.84 ::: and :::: 0.92 ::: are : observed, suggesting that the wind vane measurements overestimate the true yaw misalignment by roughly 10%.

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To estimate p P using Eq. 3, we measure the yaw misalignment, γ, using the nacelle lidar. Rather than treating the reference power defined in Section 4.2 as P 0 , we use the power given by the theoretical power curve shown in Fig. 3  the lidar-measured wind speed. Using this nacelle lidar-based reference power helps ensure that the P 0 estimates represent the wind conditions local to SMV6. The exponent p P is then estimated by fitting the function cos (γ − α) p P to the ratio between the mean power produced by SMV6 and the mean value of P 0 binned by γ using nonlinear least-squares optimization. Note Best-fit cosine power law curves are provided along with the best-fit cosine exponents and wind direction offsets, with accompanying 95% confidence intervals. Shaded regions indicate the 95% confidence intervals of the energy ratios for individual yaw offset bins (blue) and the best-fit cosine power law curves (red). is maximized. As explained in Section 5.3, data corresponding to reference wind directions from 210 • -270 • are used in this analysis.
The ratios between the mean power produced by SMV6 and the mean value of the lidar-estimated P 0 , along with the best-fit cos (γ − α) p P curves, are shown in Fig. 16 for different wind speed bins. The highest cosine exponent of p P ≈ 2.5 is :: p P :::::: cosine :::::::: exponents :: of ::::::: 2.2-2.3 ::: are : estimated for wind speeds from 4-8 m/s. Region 2 of the wind turbine's power curve, in which the controller tracks the optimal tip-speed ratio to maximize power production, roughly spans wind speeds from 5-8 m/s; therefore, the maximum value of p P is expected in this wind speed range. As wind speed increases above 8 m/s, the estimated value of p P decreases from ∼1.15-1.3 :: 1.3 : for wind speeds between 8-12-m :::: 8-12 :: m/s to p P = 0.35 :::::::: p P = 0.36 : for the 12-14-m/s wind speed bin. Once the wind turbine reaches rated power in the 14-16-m/s wind speed bin, the estimated p P is close to zero, 475 with power showing almost no dependence on yaw misalignment (albeit based on limited data). The reduction of the cosine exponent p P as the wind speed increases above Region 2 of the power curve agrees with the shape of the power curve, shown in Fig. 3. As the wind speed increases, the slope of the power curve decreases; thus, reductions in the effective rotor-averaged wind speed caused by yaw misalignment should result in a smaller change in power. Note that by modeling the relationship between the power and the yaw misalignment via the effective wind speed (see Eq. 1), FLORIS captures the trend of the 480 observed wind speed dependence of p P , if not necessarily the exact relationship. The large reduction in p P as wind speed increases above Region 2 could have significant implications for wake steering strategies; in some situations, wake steering might be most effective at higher wind speeds where less power is lost from yaw misalignment. Finally, despite the observed trends in the p P values, we note that the estimation uncertainty is high. For example, in the 6-8-m/s wind speed bin, the 95% confidence interval of the estimated cosine exponent of p P ≈ 2.5 :::::::: p P = 2.3 ranges from roughly 2-3 :::::: 1.8-2.8.

Energy Improvement from Wake Steering
To assess the impact of wake steering on the performance of the test turbines SMV5 and SMV6, we measure the change in energy production between the baseline and the wake steering control periods as a function of wind direction. Specifically, after dividing the measurement data into 2 • -wide wind direction bins, we quantify the ratio between the energy produced by 525 the test turbines and the reference turbines for the baseline and the wake steering control periods using the balanced energy ratio method introduced by . For each wind direction bin, the energy ratio is calculated as: where P Test,i and P Ref,i are the mean test and reference powers, respectively, in wind speed bin i, and the weighting factor w i is defined as the total number of samples in wind speed bin i for the baseline and the controlled periods combined : , ::: and ::::: N WS 530 ::::::: indicates ::: the ::::::: number :: of :::::::::: 1-m/s-wide :::: wind ::::: speed :::: bins ::::: used :: in ::: the ::::::::: calculation. The test power P Test can be the power produced by the downstream turbine SMV5, the power of the upstream turbine SMV6, or the average power produced by SMV5 and SMV6. P Ref is given by the reference power defined in Section 4.2. The weights w i ensure that the energy ratio is based on the observed distribution of the wind speeds while providing a fair comparison between the measurements from the baseline and the controlled periods. Normalization by the reference power is performed to attempt to control for factors beyond wake 535 steering that could cause performance to change, such as wind shear or turbulence intensity, assuming the test and reference turbines are affected equivalently.
In Section 7.1, we present the overall energy ratios for the baseline and the controlled periods as well as the change in the energy ratio with wake steering for the downstream turbine, SMV5, the upstream controlled turbine, SMV6, and the two turbines combined. In Section 7.2, the energy ratios and the changes in energy ratio with wake steering are shown for individual 540 wind speed bins, highlighting wind speeds where wake steering is most effective. Finally, in Section 7.3, we estimate the longterm change in energy production from wake steering for the combined turbines using the long-term wind rose for the site, shown in Fig. 2. For all scenarios, the measured energy ratios and changes in energy production are compared to estimates using the FLORIS model. The overall energy ratios and the change in energy ratio for the baseline and the wake steering control periods for the downstream turbine, SMV5, are plotted in Fig. 17 as a function of wind direction, along with 95% confidence intervals. The measured energy ratios and the change in energy ratio with wake steering are compared to the same metrics based on FLORIS simulations using :: the : three different FLORIS modeling assumptions :::::::: discussed :: in ::::::: Section ::: 3.2. First, FLORIS estimates of power production are calculated for the observed distribution of wind directions, wind speeds, and yaw offsets measured using 550 SMV6's nacelle wind vane (labeled "FLORIS"in Fig. 17 :::::::: Measured ::::::: Offsets"). Next, the ideal FLORIS estimates are calculated using the intended yaw offsets for SMV6 as a function of ::: the observed wind direction and wind speed according to the yaw offset schedule shown in Fig. 6 ::::::: (labeled ::::: "Ideal :::::::: Offsets"). Last, the realistic predicted ::::::: expected energy ratios based on FLORIS are calculated by combining the intended :::: ideal yaw offsets for SMV6 with the wind direction variability model discussed in Section 3.2 ::::::: (labeled ::::::::: "Expected :::::::: Offsets").
Shaded regions indicate the 95% confidence intervals of the energy ratios for individual wind direction bins. The gray dashed lines encompass the intended wake steering sector.
To reveal the net impact of wake steering on energy production as a function of wind direction, the energy ratios for the baseline and the controlled periods along with the change in energy ratio for the average power produced by SMV5 and SMV6 are provided in Fig. 19. Despite the energy loss at SMV6 from the yaw misalignment, a net increase in energy production 580 of up to 3%-5% of the energy produced by the unwaked reference turbines is measured for wind directions from 205 • -225 • . The increases in energy production in this sector are generally greater than both the predicted ::: the ::::::: FLORIS ::::: gains ::::: using :::: both ::: the ::::::: expected : and the ideal FLORIS gains :::: yaw :::::: offsets. As predicted using FLORIS combined with the :: by :::::::: FLORIS ::::: using :: the :::::::: expected :::: yaw :::::: offsets ::::: based ::: on :  . Energy ratios for the baseline and the controlled periods and the change in the energy ratio for turbines SMV5 and SMV6 combined. Energy ratios are derived from field observations as well as from FLORIS calculations using 1) observed ::::::: measured yaw offsets, 2) ideal (intended) yaw offsets :::: given :: by ::: the ::: yaw ::::: offset :::::: schedule, and 3) predicted :::::: expected : yaw offsets using the wind direction variability model. Shaded regions indicate the 95% confidence intervals of the energy ratios for individual wind direction bins. The gray dashed lines encompass the intended wake steering sector.
unintentional wrong-way steering-and above 225 • . In the latter case, a minor loss in energy is predicted by FLORIS because 585 the gains at SMV5 are not large enough to outweigh the loss in energy from the yaw misalignment at SMV6.
Because increases in energy production are observed for the combined upstream and downstream turbines for most wind directions, as shown in Fig. 19, but losses are measured as well, we assess the net impact of wake steering on energy production over the entire wind direction sector from 195 • -240 :::: -241 • . We quantify the net impact by estimating the percentage of wake losses in the sector that are reduced by wake steering, as discussed by Fleming et al. (2020). Wake losses are calculated for

Wind Speed Dependence of Energy Gain
The changes in the energy ratios with wake steering for wind turbines SMV5 and SMV6 combined for different wind speed bins are provided in Fig. 20, followed by the wind speed-dependent energy ratio changes for the downstream turbine, SMV5, and upstream turbine, SMV6, separately, in Figs. 21 and 22, respectively. For reference, the energy ratios for the combined 600 upstream and downstream wind turbines during the baseline and the controlled periods are provided in Fig. A1 in Appendix A.
Note that because fewer data samples comprise the energy ratios for the individual wind speed bins, the uncertainty is larger than that of the overall energy ratios shown in Section 7.1. Nevertheless, trends in wake steering performance as a function of wind speed can be observed.
Mixed wake steering performance is observed for wind speeds below 8 m/s, as shown in Fig. 20. For the 4-6-m/s wind 605 speed bin, significantly larger increases in energy production are achieved with wake steering than predicted by FLORIS, with energy ratios increasing by as much as 0.1-0.3 for wind directions from 195 • -233 • . The large energy gains for wind speeds below 6 m/s are potentially caused by wake steering preventing SMV5 from shutting down by allowing higher velocity inflow to interact with the rotor, as discussed by Howland et al. (2019). As shown in Figs. 21 and 22, however, significant energy improvements are observed for the upstream wind turbine, SMV6, in addition to SMV5 for the 4-6-m/s wind speed bin; 610 therefore, additional sources of the apparent energy improvement for this wind speed bin might exist. For wind speeds between 6-8 m/s, wake steering appears to cause little net change in energy production for the combined wind turbines despite the large energy gains predicted using FLORIS ::: with ::: all :::: three :::: yaw ::::: offset :::::::::: calculation ::::::: methods. Specifically, as illustrated in Figs. 21 and 22, lower-than-predicted energy gains at SMV5 are roughly cancelled by losses at SMV6. Poor wake steering performance for wind speeds between 6-8 m/s is likely related to relatively high wind direction variability, as explained in Section 3.2.
Last, the performance of wake steering for the 12-14-m/s wind speed bin is unclear based on the data collected. Figure 20 suggests that energy ratio increases of up to 0.1 are achieved for wind directions between 213 • -221 • . But these gains appear to . Change in energy ratios for the baseline and the controlled periods for the upstream turbine, SMV6, binned by wind speed. Energy ratios are derived from field observations as well as from FLORIS calculations using 1) observed ::::::: measured yaw offsets, 2) ideal (intended) yaw offsets :::: given :: by ::: the :::: yaw :::: offset ::::::: schedule, and 3) predicted ::::::: expected yaw offsets using the wind direction variability model. Shaded regions indicate the 95% confidence intervals of the energy ratios for individual wind direction bins. The gray dashed lines encompass the intended wake steering sector.

Long-Term Corrected Energy Gain
As discussed in Section 2.3, above-average wind speeds were observed during the experiment period because of the typically stronger wind resource at the site in the winter. To estimate the expected impact of wake steering on energy production during 0.7 0.8 0.9  and SMV6 combined. Energy ratios are derived from field observations combined with the long-term wind rose shown in Fig. 2 as well as from FLORIS calculations using 1) observed ::::::: measured : yaw offsets, 2) ideal (intended) yaw offsets :::: given :: by ::: the :::: yaw :::: offset ::::::: schedule, and 3) predicted ::::::: expected yaw offsets using the wind direction variability model. Shaded regions indicate the 95% confidence intervals of the energy ratios for individual wind direction bins. The gray dashed lines encompass the intended wake steering sector.
a typical year, we compute long-term corrected energy ratios for the baseline and the wake steering periods based on the long-635 term wind rose frequencies shown in Fig. 2. The long-term corrected energy ratio calculation requires only a slight modification to the energy ratio definition in Eq. 4; instead of weighting the mean power for the test and reference turbines in a particular :::::::: 2 • ×1-m/s : wind direction and wind speed bin by the total number of samples measured in that bin, we weight the mean power by the long-term frequency of occurrence of the wind conditions represented by :::::: within the bin.
Using the modified energy ratio calculations, the long-term corrected energy ratios for the baseline and the wake steering 640 periods together with the change in energy ratio with wake steering for SMV5 and SMV6 combined are provided in Fig. 23.
Energy gains of up to 3%-5% of freestream energy production are measured for wind directions between 207-225 • , generally matching the predicted energy improvements using FLORIS ::: with ::: the :::::::: expected :::: yaw :::::: offsets. Slight losses in energy production are observed for wind directions below 207 • and above 225 • , as also predicted by FLORIS :::: using ::: the :::::::: expected ::::: offsets. Overall, the long-term corrected change in energy ratio from wake steering follows the same trends as the change in energy ratio for the experiment period shown in Fig. 19; however, the peak gains and losses are less extreme when the long-term corrected wind rose is applied.

Conclusions
In this paper, we analyzed the performance of wake steering control for two wind turbines spaced 3.7D apart at a commercial wind plant by examining the change in energy production from wake steering as well as the achieved yaw offsets during the 3-month experiment period. To highlight the wind speed dependence of wake steering performance, we presented results in aggregate as well as for individual wind speed bins between 4-14 m/s. The overall improvement in energy production was 665 quantified by estimating the percentage of wake losses reduced by wake steering, both during the experiment period and extended to represent the long-term wind resource for the site. To help validate the use of the FLORIS engineering wind farm control tool for wake steering controller design, we compared the measured energy production to the FLORIS predictions based on the achieved ::::::: measured : yaw offsets, the ideal offsets, and the predicted :::::::: expected yaw offsets using a model of wind direction variability. We also compared the achieved ::::::: measured : yaw offsets to the predicted ::::::: expected : offsets based on the wind direction 670 variability model. Finally, we used measurements from a WindCube Nacelle lidar to determine the accuracy of the nacelle wind vane used to implement wake steering as well as to better understand the power loss caused by the yaw misalignment.
Further, yaw misalignment measurements from the nacelle lidar revealed a wind speed-dependent bias in the wind vane measurements as well as the tendency for the wind vane to overestimate the true yaw misalignment. Although we found that the resulting wind vane measurement error was typically within a few degrees, we suggest that sensors used to measure yaw 700 misalignment as part of a wake steering control strategy be carefully calibrated to maximize the effectiveness of wake steering.
When combined with the ::::::: expected :::: yaw :::::: offsets ::::: using ::: the wind direction variability model, we found that FLORIS predicts the impact of wake steering on energy production reasonably well. But for the combined upstream and downstream wind turbines, the observed energy gains were generally higher than those predicted by FLORIS. Note that we used a relatively high turbulence intensity of 11% in the FLORIS model to match the measured baseline wake losses. The energy gain predictions 705 from FLORIS could be improved by using a lower turbulence intensity value (the effectiveness of wake steering improves as turbulence intensity decreases), suggesting that further work is needed to reconcile the wake deficit and wake deflection models in FLORIS, at least for relatively short turbine separations such as the 3.7D spacing investigated here. The wind direction variability model was found to relatively closely predict the trend of the ::::::: measured : yaw offsets achieved by the wake steering controller. Specifically, because of imperfect yaw tracking in variable wind conditions, the achieved :::::::: measured yaw 710 offsets were found to be lower than the target offsets in the intended wake steering region, with undesired yaw offsets persisting outside of the intended sector. As reflected by the measured impact on energy production, these unintended yaw offsets appear to cause slight reductions in energy for wind directions outside of the intended wake steering sector. Overall, the wind direction variability model offers a simple way of accounting for unintentional yaw misalignment when optimizing robust wake steering control strategies.

715
Despite the increase in energy production observed in this study, there are several opportunities to improve the performance and field validation of wake steering. First, a conservative yaw offset schedule was employed in this experiment to limit the impact of yaw misalignment on structural loads. After performing a detailed load assessment for the specific wind turbine used, the effectiveness of wake steering could be increased by allowing larger yaw offsets for a wider range of wind speeds in addition to leveraging both positive and negative yaw offsets. Further, whereas this experiment showed that the effectiveness of wake 720 steering depends on wind speed, the energy gains achieved through wake steering strongly depend on atmospheric stability as well, as shown by Fleming et al. ( , 2020. Thus, if relevant measurements are available, yaw offsets could be optimized and scheduled as a function of stability-or other variables related to stability such as turbulence intensity, as described by Doekemeijer et al. (2021)-in addition to wind speed and direction. Additionally, whereas we used an indirect wake steering control strategy based on modifying the input to the wind turbine's existing yaw controller, more advanced controllers, such as 725 those discussed in Section 1, could improve performance by directly controlling the yaw position and responding more quickly to changing wind conditions. Opportunities also exist to increase the accuracy of the inputs to the wake steering controller.
For example, the consensus control strategy described by Annoni et al. (2019) uses information sharing between neighboring wind turbines to improve local wind direction estimates. Finally, the energy gains estimated in this study are accompanied by a significant amount of uncertainty. In addition to extending the duration of wake steering experiments, we expect uncertainty 730 can be greatly reduced by increasing the number of wind turbines used to validate the overall impact of wake steering. ENGIE and NREL aim to incorporate some of these improvements by collaborating on a larger-scale wake steering campaign as part of the upcoming AWAKEN experiment in the United States .

Appendix A: Wind Speed Dependence of Energy Ratios for Combined Downstream and Upstream Turbines
Code availability. The FLORIS code used to model wake steering performance and calculate the energy ratios in this paper is available at https://github.com/NREL/floris (NREL, 2021).
Author contributions. NG, TD, and PF envisioned the wake steering experiment, which was designed by TD, PF, and ES. ES, PF, EG, and TD analyzed the data and interpreted the results. ES performed the modeling steps, with significant contributions from EG. NG supervised and managed the project for ENGIE. LA contributed immensely to the implementation of the wake steering controller and data recording hardware. TD organized and monitored the field experiment. ES prepared the manuscript, with major contributions from TD and input from Fleming, P., Annoni, J., Shah, J. J., Wang, L., Ananthan, S., Zhang, Z., Hutchings, K., Wang, P., Chen, W., and Chen, L.: Field test of wake