Figure recaps the experimental setup that was implemented during the campaign. The 24 sound level meters (SLMs) surrounding the turbine were located every 15° at a distance of approximately one turbine tip height (135 m) from the turbine. Distance to the tower base was measured using a laser pointer and verified by comparing the GPS coordinates of the turbines and each SLM. The obtained values ranged from 132.5 to 139.4 m, which is consistent with the ±20 % and ±30 m tolerance criteria of the IEC standard . The angular difference between two successive SLMs was evaluated using their GPS coordinates and varied from 11.6 to 18.2°. The distance from the ground-based Windcube lidar to the turbine was also estimated based on its GPS coordinates and found to be roughly 330 m.

The site is very simple and flat, and the calculated terrain inclination angle ϕ (defined in the standard with the line joining the SLM and the turbine hub) for all positions varied between 29 and 31.5°, well within the 25–40° preconized range. The surrounding terrain mostly consists of wheat crops. In late March, at the time of the experiment, those crops reached a height of about 30 cm. In order to prevent any disturbance caused by the crops' wind-induced noise, they were cut within a diameter of roughly 3 m around each SLM position. Figure shows one SLM together with a controlled turbine in the background.

SCADA data for the misaligned turbine were collected during the test at 1 s resolution for the most important variables: active power, wind speed, vane angle, nacelle position, rotor and generator speed, and pitch angle. Almost all acoustics sensors were removed each night and reinstalled every morning at the same location. They were checked for time synchronization and calibration before new measurements were launched. Both the overall sound pressure levels and the 1/3-octave band spectra were recorded with a sampling period of 1 s. Lidar measurements were acquired at an identical temporal resolution.

In order to study the effect of yaw misalignment on wind turbine noise in similar atmospheric conditions, a specific measurement routine was designed for the campaign. The yaw set point parameter β is defined as the angle between the nacelle axis and the incoming main flow direction. The turbine was sequentially yawed from β=-20 to β=+20° in steps of 10°, staying in each position for 40 min. Between two successive positions, background noise and turbine noise measurements were also conducted with β=0°, each of them lasting 10 min. Finally, a period of 3 min was considered for each transition to give the turbine some time to move or restart and let the flow reach its equilibrium for the new position. The full routine, planned to last almost 4.5 h, can be found in Table .

In practice, this routine could not be programmed in the control software, and the turbine was manually switched between each state by an operator. The periods in each position were thus approximately followed but were maintained at least as long as indicated above. Overall, the fulfillment of one full round of measurement lasted slightly longer than originally planned. During the data post-processing, the SCADA 1 s time series of active power and nacelle position were visually inspected to precisely mark the exact timestamps of switching from one phase to another. In operation phases, the target turbine was settled to the full power mode, i.e., without any NRO mode implemented.

The two nearest turbines in the farm (WT10 and WT11, located 345 and 770 m northwest of WT12, respectively) were shut down at the beginning of each round of measurement and remained stopped for the full duration of the test to avoid disturbing the test and recording data and ensure a satisfactory signal to noise ratio. The closest neighboring turbine still in operation was located more than 1 km away. A person was also constantly present on site to keep a track record of noisy events (such as a plane or car passing by) so that they could be properly considered and filtered afterwards.

The experiment consisted of six rounds of measurements that were conducted over the 4 d: one on 25 March 2024 and on 26 March 2024 and two on 27 March 2024 and 28 March 2024. Rounds 2, 4, and 6 could not be conducted completely due to the appearance of rain in the afternoon of the 26th and 27th and strong and highly turbulent winds risking the endangerment of the turbine during yaw misalignment conditions in the late afternoon of the 28th. Considering that these above-rated conditions are of less importance to WFFC applications, these data would not have added much additional value. In total, a little more than 21 h of measurements was recorded over the 4 d (4.58 h on day 1, 2.35 h on day 2, 6.13 h on day 3, and 8.07 h on day 4).

The wind conditions observed during the campaign are represented in Fig. . Very different conditions were experienced each day: from low to medium wind speeds during the first 2 d to higher wind speeds on the last 2 d. The IEC standard requires a minimum number of 10 samples in each bin. As can be seen in Fig. in the representation of the raw capture matrix derived from the SCADA data recorded during the six rounds of the test, these criteria are fulfilled for a large number of wind speed bins and all yaw positions thanks to those very favorable wind conditions. Consequently, the minimum wind speed range recommended by the standard, 8 to 13.5 m s⁻¹ (corresponding to 0.8 to 1.3 times the wind speed at 85 % of the turbine rated power), was extended to 6–13.5 m s⁻¹ when analyzing the results.

The wind direction varied from the east on the first day to the southwest on the last day, meaning that the turbine was never affected by any wakes during the measurement. Turbulence and shear conditions were estimated using the ground-based Windcube lidar: the lidar measurement at hub height is considered for the turbulence, while the wind shear is estimated by fitting a power law to 14 planes of measurement ranging from 40 to 140 m (i.e., the span of the turbine rotor). Both were also very variable depending on the day, with high shear and low turbulence observed at the beginning of the week and, in contrast, a highly turbulent and low-sheared flow noticed at the end of the test.

A significant challenge for a field campaign utilizing as many sensors as this one is to maintain the availability of all of them during the periods of measurement. Figures and represent the availability of related wind and acoustic sensors, respectively, indicating that this challenge was practically met.

Most of the SLMs were also fully available during the test. Unfortunately, a few sensor defaults were observed when preprocessing the data. SLM no. 4 shows only a 10 % availability because it was only possible to record data every 10 s instead of 1 s due to a logger issue. SLM no. 7 reports reduced availability since it was not installed during the second day of measurement. The IEC standard also requires an analysis of 1/3-octave bands between 20 Hz and 10 kHz. A full dataset was obtained for 18 SLMs, but 1/3-octave information was missing for SLM nos. 9 and 18 and incomplete for nos. 4, 10, 16, 21, and 22.

Despite these small inconveniences, the quantity of data collected during the 4 d and six rounds of measurement can be considered satisfactory and ready to be processed for the derivation of the apparent sound power level, as is described in the next section.

The process described above must be performed on a cleaned dataset. Despite the effort made every day during the campaign to calibrate and check the time synchronization of each SLM before launching a new round of measurement, a few issues were noticed when the raw acoustics data were analyzed. Considering the large quantity of data to handle (more than 507 h when accounting for the 24 SLMs), specific post-processing techniques were designed to automatically filter and correct the dataset.

The data reduction procedure described in the IEC standard stipulates that the data must be binned by wind speed. The reference wind speed to be used for the binning is deduced from the active power signal by inverting the turbine power curve. The (adjusted) nacelle anemometer and external wind sensors are used as an alternative source of data when the power curve cannot be used (i.e., when the nominal power is reached or when the turbine is stopped for background measurement).

However, this methodology is only valid for a turbine that is aligned with the wind. Indeed, the performance of a steering turbine is reduced and no longer follows the expected power curve. Measurements from nacelle anemometers are also known to be unreliable when yaw misalignment is applied on a turbine . It was thus necessary to adapt the IEC methodology to account for the specificity of this test.

For this field campaign, the reference wind speed signal was calculated according to the following, in order of priority.

When the turbine was operating with no yaw misalignment and the wind speed was within the allowed range for interpolation prescribed by the standard, the active power signal and the power curve were used. These conditions represent approximately 9 % of the total dataset. The power curve considered for the interpolation was calculated thanks to the nacelle lidar data over 4 months of measurements from 7 February to 2 June 2024 and according to the procedure of the IEC 61400-12-1 standard .

This sensor was favored over the ground-based lidar because its wind speed measurements were better correlated to the wind speed derived from the active power signal in step 1 above, as is shown in Table . Given that a transient period of 3 min was considered between each yaw category (see the toggle measurement routine in Table ), there were no direct transitions between the nacelle lidar measurement and the SCADA signals, thus avoiding the risk of introducing artifacts between the different sources.

The high-frequency measurement of such a lidar is only conducted along line of sights (LOSs) of the sensor. Data from the 4 LOSs must be averaged over a certain time period and combined to derive the hub height wind speed estimation . Unfortunately, it proved that the 10 s resolution was too short to properly achieve this reconstruction: the resulting wind speed signal was too noisy and did not correlate well with the SCADA data. While complex algorithms exist to assess the incoming wind field from high-frequency lidar measurements (; ; ), another solution was set up instead, for the sake of simplicity. For each day, a constant advection time was calculated using the mean wind speed observed during the recording period and the distance between the upstream lidar measurement range and the turbine. This advection time was used to temporally shift the lidar data and synchronize them with the rotor plane. Finally, wind speed measurements were averaged for every 10 s chunk considering a rolling window of 1 min.

In order to make sure this methodology provides the highest-quality signal for the rest of the study, the correlations of various lidar wind speed measurements are compared with the reference signal deduced from priority 1 above, in yaw-aligned conditions only. Table 2 recaps the calculated correlation coefficients. It is confirmed that the nacelle lidar gives a better correlation than the ground-based sensor since its measurement is made closer to the turbine but that considering a binning period of 10 s only introduces more noise and degrades the correlation with the reference signal. Conversely, the use of a rolling window with a constant advection time significantly improves the results: the obtained signal shows a correlation coefficient close to the one of the nacelle anemometer, considered as priority 2 in the IEC 61400-11-1 standard.

While wind direction is only considered in the IEC standard as a filtering variable, it is for this campaign a quantity of high interest. With the experimental setup being fully symmetric, the relative position of each SLM with respect to the turbine is determined based on the absolute wind direction. Like the nacelle anemometer, the turbine wind vane cannot be trusted under yaw misalignment . To ensure a consistent measure of wind direction during the full test, one of the lidars had to be used, and their correlations to the turbine data in yaw-aligned conditions were analyzed. The ground-based lidar proved to have the most consistent measure of wind direction, and its 10 min signal, averaged over all planes of measurement, was therefore selected.

Once noise data have been cleaned and reference wind conditions identified, both datasets can be combined and sorted into bins for both background and total noise to deduce the apparent sound power of the turbine. The diagram shown in Fig. summarizes the data processing methodology applied in this paper and underlines the differences from the current version of the IEC 61400-11-1 standard. For the sake of clarity, all variables and symbols used in this section are listed in Table .

The OASPLs of the estimated turbine noise are presented in Fig. for each observer position relative to the nacelle axis without yaw misalignment and across four wind speed bins. Since the turbine reaches rated power at 12 m s⁻¹, the selected wind speeds correspond to 52 % to 100 % of rated power. At all observed wind speeds, OASPL variations in the ground-based directivity pattern reach up to 4 dB(A). In each plot, a region of low noise levels is observed near the rotor plane, sometimes referred to as “noise dips” in the literature . Within these dips, sound levels are consistently 3.5 to 4.0 dB(A) lower than the maximum values in the corresponding directivity pattern. At lower speeds (7.5 and 9.5 m s⁻¹), the minimum noise levels occur at observer angles of θ=±90°. Interestingly, near rated power (11.5 and 13.5 m s⁻¹), the noise dips shift upstream, appearing at θ=±75°.

The direction of the maximum noise level is not aligned with the downstream flow axis but rather occurs at off-axis positions, either upstream or downstream of the turbine. Specifically, the peak noise levels are observed at θ=-150° at 7.5 m s⁻¹, θ=135° at 9.5 m s⁻¹, θ=45° at 11.5 m s⁻¹, and θ=120° at 13.5 m s⁻¹. These levels exceed the axial downstream measurement by 1.4, 0.7, 0.8, and 1.6 dB(A), respectively. This observation is not captured by most existing analytical and semi-empirical models , which typically predict symmetric directivity patterns with the maximum aligned along the main flow axis. In contrast, the directivity patterns shown in Fig. exhibit slight asymmetries with respect to not only the nacelle axis, but also the rotor plane. Since the observed differences in noise levels remain within the uncertainty bounds, a statistical paired t test was conducted to support this visual observation. The test is based on the level difference between two symmetrical positions ΔLV,θ=LV,θ-LV,θ′ for the same wind speed bin, where θ′ is chosen as

θ′=-θ to test the down-upstroke symmetry and

The set of available observation angle pairs (θ;θ′) is denoted as Θ and consists of 207 observations in both of the above-mentioned cases. The level difference ΔLV,θ is associated with a combined variance uθ2 such as 9uθ2=uc,θ2+uc,θ′2-2ρuc,θuc,θ′, where ρ is the correlation factor between the θ and θ′ series, which may be non-zero due to the previously identified noise dips. Following the approach in Eqs. ()–(), the weights are defined as the inverse of the combined variance wθ=1/uθ2, and the weighted average of the level difference is computed as 10ΔL‾V=∑θ∈ΘwθΔLV,θ∑θ∈Θwθ with the standard error 11σΔL=1∑θ∈Θwθ.

This enables us to use the test statistics t=ΔL‾V/σΔL, which are applied across the full set of available wind speed bins at once using a significance level of 5 % and assuming a normal distribution. On average, the OASPL value on the downstroke side is found to be 0.6 dB higher than on the upstroke side. The 95 % confidence interval is [0.5; 0.8] dB, associated with a p value p<10-6, indicating a highly significant left–right asymmetry in the directivity pattern. This result was found to be virtually independent of the correlation factor ρ within the range 0 to 0.5.

The same approach was applied to assess the symmetry between downwind and upwind directions. On average, the sound level measured on the downwind side was 0.4 dB higher than that on the upwind side at observer positions symmetric with respect to the rotor plane. The 95 % confidence interval for this difference is [0.3; 0.6] dB(A), associated with a p value p<10-8, again indicating a highly significant asymmetry.

From this analysis, it can be concluded that the directivity footprint of the turbine exhibits, on average, 0.6 dB(A) higher noise levels on the downstroke side compared to the upstroke side and 0.4 dB(A) higher levels on the downwind side compared to the upwind side. These slight asymmetries in the turbine’s noise radiation may result from the intrinsic directivity of elementary acoustic sources. Analytical models based on flat-plate assumptions (as for instance ) and (semi-)empirical models derived from symmetric airfoil measurements do not reproduce such asymmetries. However, camber has been shown to cause deviations of up to 1 dB(A) between the pressure and the suction side noise radiation of a nonsymmetrical airfoil . This behavior has also been captured in high-fidelity numerical simulations of cambered and loaded airfoils equipped with serrations . Thus, the turbine blade camber may be responsible for an asymmetric radiation on both sides of the airfoils. As the chord line is more or less contained in the rotation plane, it may result in an upstream–downstream asymmetry in noise levels at the turbine level. The left–right asymmetry is more likely to be linked to both the trailing-edge noise directivity and the acoustic amplification term as already proposed by .

Spectral directivity patterns at near-rated power (11.5 m s⁻¹) are presented in Fig. over a selected frequency range. At very low frequencies (e.g., 50 Hz), the pattern exhibits two distinct lobes oriented upstream and downstream, with higher levels on the downstream side. Pronounced noise dips are also observed, with sound levels up to 6 dB lower than at the axial downwind position, which corresponds to the direction of maximum noise emission at this frequency. As frequency increases, the directivity pattern becomes more complex, featuring several off-axis lobes. For instance, in the mid-frequency range of around 1000 Hz – where human hearing is most sensitive – a narrow lobe centered at θ=45° emerges, with noise levels approximately 4 dB higher than at adjacent directions. A secondary, less pronounced lobe appears on the descending blade side around θ=120°. These features are also reflected in the OASPL directivity patterns (lower-left part of Fig. ) at θ=45 and θ=135°. At higher frequencies (e.g., 5000 Hz), the pattern displays multiple lobes with significant local variations and increased uncertainty (±2.0 dB) compared to lower frequencies. This uncertainty increase is due to a higher data dispersion at 5 kHz than at lower frequencies (“type A” component).

A complementary perspective is provided in Fig. , which compares frequency spectra at selected observer positions. In Fig. a the maxima of the two OASPL lobes at 11.5 m s⁻¹ – located at θ=45 and θ=135° – are compared to the reference axial downstream position (θ=180°). At these two positions, the spectral content shows a pronounced mid-frequency component between 800 and 2000 Hz with increases of 5 and 3 dB, respectively, relative to the reference. At the very high frequency range (above 5000 Hz), further increases of +7 and +5 dB are observed. Conversely, a reduction in the low-frequency range (50–500 Hz) is noted, particularly at θ=45°, where levels are 7 dB(A) lower than at the reference.

Figure b presents two additional measurement points at the same wind speed, comparing positions in the rotor plane to the axial downwind reference. In the noise dip regions, the low-frequency content is significantly reduced – by up to 10 dB at 100 Hz. In contrast, an increase in the very high frequency range is observed, especially on the descending blade side (θ=90°). In summary, at this specific wind speed, the spectral analysis reveals a strong broadband component in the mid-frequency range at off-axis lobe maxima, as well as a spectral shift toward higher frequencies in the noise dip regions, relative to the axial downwind position.

Directivity patterns under intentional yaw misalignment are illustrated in Fig. at 9.5 and 11.5 m s⁻¹. The first row shows positive yaw misalignment angles (i.e., the ascending blade is oriented toward the incoming flow), while the second row presents negative yaw misalignment angles (i.e., the ascending blade is oriented away from the flow). A first observation is that yaw misalignment does not lead to dramatic changes in overall noise levels. The most prominent effect of steering the turbine away from the main flow direction is a rotation of the entire directivity pattern, which appears to remain aligned with the turbine orientation in all four cases – particularly around the recognizable noise dip regions. It is worth noting that the yaw angle sampling step Δβ=10° is not a multiple of the observer angle sampling step Δθ=15°, which explains why the noise dips may appear at similar positions for different yaw angles. Some regions appear to be more strongly influenced by the flow direction than by the turbine orientation and are amplified when a yaw misalignment is applied. This is particularly evident in the upwind-upstroke sector [0°; -45°] for β>0 and in the upwind-downstroke sector [0°; +45°] for β<0. In general, larger absolute yaw misalignment angles β tend to introduce greater complexity into the directivity pattern.

Spectral variations in the directivity patterns at v=11.5 m s⁻¹ are illustrated in Fig. . At the lowest frequencies (50 Hz), the rotation of the directivity pattern induced by the turbine misalignment is particularly visible. The most significant variations with respect to the yaw misalignment angle β are predominantly localized near the rotor plane (|θ|≃90°). However, the acoustic impact of yaw misalignment in the lowest frequency range (50 Hz) cannot be reduced to a rotation. The simple two-lobe pattern of the aligned case cannot be recognized at other yaw angles, showing a more complex structure. It may be the expression of a significant change in the prominent aeroacoustic sources at this frequency. Interestingly, this is not the case for most of the other plots at higher frequencies in Fig. . It is generally accepted that wind turbine aerodynamic noise is dominated by the turbulent boundary layer–trailing-edge noise (TBL-TE) in the higher-frequency range, typically above 800 Hz, and by the turbulent inflow (TI) noise at lower frequencies. If this holds for the current turbine, it would suggest that the yaw misalignment has a strong influence on the TI component and virtually not on the TBL-TE component, at least up to 5 kHz. TI noise is produced by the interaction between turbulent eddies in the atmosphere with the moving leading edge of the three blades. In yaw-aligned conditions, a scaling variable of TI noise models is the integral length scale of the atmospheric turbulence. The phase relationship between the relative normal wind velocity component encountered by different sections of a blade is indeed important, as it can reinforce or mitigate the noise production process. A typical signature of this relationship at the airfoil level is its noise directivity pattern. As the turbine is yawed, the blades pass through atmospheric turbulence with an angle. With the turbulence longitudinal correlation, this angle may increase the apparent length scale and reinforce the TI noise production process and alter its directivity trace on ground SLMs. Conversely, TBL-TE noise is produced by the interaction of a turbulent boundary layer (at the surface of the blade) and the trailing edge. The process is somewhat more local and may be less influenced by the yaw configuration.

Estimates of the turbine's OASWL derived using Eqs. () and () are presented in Fig. for various yaw misalignment angles, both positive (left panel) and negative (right panel). All empirical sound power curves exhibit a consistent structure, characterized by a linear increase between 6 and 9 m s⁻¹, followed by a plateau at higher wind speeds, as expected for this turbine. For most wind speed bins, the aligned configuration β=0° is the less noisy configuration. In contrast, configurations with yaw misalignment tend to exhibit more elevated sound power levels. To evaluate the statistical significance of these observations, four inverse-variance-weighted paired t tests were conducted using Eqs. () and (). Each test compares the sound power curve for a misaligned configuration LWA,{v,β≠0°} against the reference aligned configuration LWA,{v,β=0°}. The results, summarized in Table , indicate that for yaw angles of β=-20, +10, 20°, the differences are statistically significant (p<0.05). These configurations exhibit a consistent increase in OASWL of approximately 0.5 to 0.7 dB(A). Accordingly, it can be concluded that these misaligned settings are slightly noisier than the baseline configuration, with an average increase in sound power of approximately 0.6 dB(A).

The slice summation described in Eq. () can be independently computed for each 1/3-octave band, yielding the turbine's sound power level spectra. These spectra are presented in Fig. for various yaw misalignment configurations. Consistent with the OASPL analysis, all yaw-misaligned configurations exhibit higher spectral levels compared to the baseline (aligned) case. The increase is particularly notable in the low- to mid-frequency range (200–1250 Hz), as well as in the high-frequency range (f>5 kHz). As previously discussed in the analysis of Fig. , this pattern suggests that the dominant noise generation mechanisms are differentially influenced by turbine yaw misalignment. At the wind farm level, the observed slight increase in TI noise levels under misaligned yaws may be compensated for by the fact that wake–turbine interactions are basically avoided in WFFC control strategies, a situation which typically produces large TI noise increases.

The results presented here may be compared with the extensive noise measurement campaign conducted at NREL by near a 77 m diameter 1.5 MW industrial wind turbine subjected to a yaw misalignment ranging from -18 to +25°. They reported a general decrease in SPL by 2 to 3 dB for intermediate yaw offsets (10 and 18°). At more extreme yaw misalignments of -18 and 25°, even larger noise decreases were observed, reaching up to -5 dB compared to the non-steered configuration. At first glance, this appears to contradict the present study, which reports a slight increase of +0.6 dB in noise power levels under yawed conditions. However, several aspects should be considered before drawing such a conclusion.

First, the turbines under investigation are from different manufacturers, and their designs differ significantly. The rated powers differ by 31 % and the diameters by 30 %, and the blade geometries are also dissimilar. For instance, suction side flow recirculation may occur for one blade design under yaw but not for another, with potentially significant consequences for noise emissions. To date, there is no general evidence supporting the assumption that the effect of wake steering on noise emissions is model independent. More specifically, the turbine controllers

Turbine controllers define the operating point (via torque and blade tip speed settings) as a function of the incoming wind speed. Their design details are typically not disclosed to wind farm operators.