Theoretical and Experimental Analysis of Aerodynamic Noise in Small Wind Turbines

: This paper presents an analysis of sound pressure levels through theoretical modeling and experimental validation in a 1 kW small wind turbine. The models used in the theoretical analysis are BPM (Brooks, Pope, and Marcolini) and BM (Brooks and Marcolini), where wind turbine blades are divided in sections, and each section has its own contribution with respect to the total emitted sound pressure level. The noise propagation study and its experimental validation were accomplished within the requirements of the standard IEC 61400-11 Ed.3 and the standard NOM-081-SEMARNAT-1994. The comparative study of theoretical and experimental results showed that the BPM and BM methods have a maximum error of 5.5% corresponding to the rated wind speed of 10 m/s. However, at low wind speeds, the theoretical models ﬁt well to experimental data, for example, in the range from 5 to 8 m/s. The experimental data showed that the rotor’s aerodynamic noise is more evident at low wind speed, because under these conditions, environmental noise is much less than wind turbine noise. Finally, to prevent possible negative effects on people’s health, there is a recommended minimum and suitable distance between small wind turbine installations and buildings.


Introduction
Wind energy has been the fastest expanding renewable energy in the world. Now in addition to observing them in the sea and large areas of land, you can see small wind turbines in rural communities, which have been used not only for power generation but also for water extraction. Some authors such as Schmidt and Klokker [1] maintain that people living near wind farms have serious health problems due to noise; Saab-Junior [2] evaluated several airfoils with the Qblade program and were able to minimize the noise with this evaluation.
One of the problems that small wind turbines present is the noise they emit; according to Ma et al. [3], the design of airfoils is fundamental to reduce noise and is achieved by trailing edge of the turbulence boundary layer and the turbine trailing edge noise, in part of his study, he found that in small wind turbines, the trailing edge noise is an important noise generation.
In Mexico, there are norms that establish the maximum permissible limits of noise to which people may be exposed, such as the Official Mexican Norm NOM-081- SEMARNAT-1994 [24] issued by the Ministry of the Environment and Natural Resources.
In this work, a study of the noise emitted by a wind turbine of 1 kW installed in the Isthmus of Tehuantepec, Oaxaca, Mexico, was carried out, in which the sound pressure levels produced by the detachment of the turbulent boundary layer at the trailing edge were determined using the semi-empirical method proposed by Brooks et al. [25] and the sound pressure levels due to the formation of vortexes at the tip of the blade generated by the rotation speeds of the wind turbine [17,26]. In order to validate the models' results, an experimental study was carried out using the recommendations of the IEC 61400-11 Standard [27]. Another study compared the noise emitted by the wind turbine for different distances from the wind turbine with the permissible values defined in the Mexican official standard NOM-081- SEMARNAT-1994 [24]. In this work, an analysis of the results of the emission values calculated with the prediction models will be carried out and then compared with the experimental data.
This work is based on an analysis of sound pressure levels through theoretical modeling and experimental validation in a small wind turbine of 1 kW. Section 1 presents the introduction of the models on which this study is based and the state of the art of the problem of noise in small wind turbines. Section 2 shows the BPM (Brooks, Pope, and Marcolini) and BM (Brooks and Marcolini) models used in this study. Section 3 presents the case study where the noise characteristics of the 1 kW wind turbine are analyzed. Section 4 presents the discussion and finally shows the conclusions of the study.

Methods
Aerodynamic noise is generated by the interaction of wind turbulence with wind turbine blades. The turbulence can be originated by the atmospheric boundary layer present in the inlet flow or by the viscous flow present in the boundary layer above the surface of the blades. Figure 1 shows the typical behavior of air flow around a wind turbine blade section. According to Brooks et al. [25] and Wagner et al. [6], there are several mechanisms of aerodynamic noise in wind turbines, namely: • Turbulent-Boundary-Layer-Trailing-Edge (TBL-TE) Noise. It is the noise that occurred due to the formation of turbulence and wakes around the trailing edge of the airfoil. Brooks et al. [25] and Wagner et al. [6] show in their works how this noise contribution is generated.
According to Lowson [28], there are three classes to classify the predictions methods in wind turbines. Class I models give simple estimates of the overall sound pressure level as a simple algebraic function of basic wind turbine parameters such as rotor diameter, power, and wind speed. Class II models estimate the noise based on separate consideration of the various mechanisms causing wind turbine noise. Class III models calculate the decibels produced by wind turbines using refined models describing the noise mechanism and relate them to a detailed description of the rotor geometry and aerodynamics.
Within the Class II model are the Brooks et al. BPM model [25], the Lowson model [29], and the Grosveld model [30]. For this study, the BPM model is used to determine the sound pressure levels produced by the detachment of the turbulent boundary layer at the trailing  [30] for vortex formation at the tip of the blade. We selected these two sources because the blade is from a small wind turbine, which is different from the ones usually analyzed; therefore, it is not affected by the turbulent incident flow [11,13].

Case of Study
As a case study, the RTO-1kW wind turbine with a diameter of 2 m and a nominal power of 1 kW was used. This wind turbine was manufactured by RTO Energy from México [33]. The study wind turbine is installed and operates in the Ejidal Bioclimatic Community Center located in the community of La Venta, Oaxaca, Mexico; see Figure 1. The low power wind turbine has a horizontal axis with a three-bladed rotor, the blades are 0.97 m long and were designed using the A18 aerodynamic airfoil, which presents the maximum coefficient relationship between the lift coefficient and drag coefficient respectively, ⁄ , for an optimal angle of attack (α) of = 2°.   Figure 2a shows a linear behavior of the rotation speed, with a minimum speed of 160 rpm for 3 m/s until reaching a maximum rotation speed of 750 rpm for 13.5 m/s. Figure 2b shows that the wind turbine begins to produce electricity at an input speed of 3 m/s, reaching a nominal power of 950 W at 13.5 m/s and an output speed is 17 m/s that is when the furling system is driven. The curves were provided by the builder RTO Energy [33].

Noise Caused by the Turbulent Boundary Layer at the Trailing Edge and by the Flow Detachment
The noise generated by the turbulent boundary layer at the trailing edge (TBL-TE) is caused by the formation of turbulence and wakes around the trailing edge of the aerodynamic profile. Aerodynamic noise is also generated when there is flow separation over the profile wall, which occurs when the angle of attack is increased.
In the BPM model, the wind turbine blade is divided into segments, each having its own chord, length, angle of attack, and relative speed. Therefore, each segment has its own contribution to the total sound pressure level emitted. The sound pressure levels of the different blade segments must be added up to produce the sound pressure levels of each of the noise sources.
A semi-empirical model proposed by Brooks et al. [25] was used to calculate the aerodynamic noise of the small wind turbine. This model was made based on wind tunnel experiments using a NACA0012 airfoil. The BPM model predicts the total noise spectrum in a 1/3-octave presentation, which is produced by the turbulent boundary layer at the trailing edge of the profile and at the flow detachment using the following parametric equations. SPL tot = 10· log 10 SPL α /10 + 10 SPL s /10 + 10 SPL p /10 (1) where SPL tot is the total Turbulent-Boundary-Layer-Trailing-Edge (TBL-TE) and separation noise, while the subscripts α, s, and p denote the pressure side of the aerodynamic profile, suction side of the aerodynamic profile, and the angle of attack, respectively. So, SPLp is the turbulent boundary layer trailing edge noise along the pressure side of the airfoil, SPLs is the turbulent boundary layer trailing edge noise along the suction side of the airfoil, and SPLα is the flow detachment noise at the leading edge of the airfoil. These are defined by Equations (2)-(4), respectively. Detailed descriptions of the functions and the parameters in Equations (1)- (13) are explained by Brooks et al. [25].
where r e is the observer distance, L is the span section, δ p * is the boundary layer displacement thickness based on the angle of attack and the Reynolds number, M is the Mach number, St p is the Strouhal number, St 1 is the Strouhal number based on the Mach number, K 1 and ∆K 1 are amplitude functions, A is an empirical function obtained from experimental tests, and D h and D l are high and low directivity functions.
where St 2 is the Strouhal number based on the effective aerodynamic angle of attack, K 2 is an amplitude function, and B is an empirical function obtained from experimental tests. Detailed descriptions of the functions and the parameters in Equations (1)-(13) are explained by Brooks et al. [25].
where U is the relative wind speed and c 0 is the speed of sound.
where f is the frequency. St 1 = 0.02M −0.6 (7) where α * is the effective aerodynamic angle of attack. The most relevant term in these equations is the argument of the logarithm. The numerical value it could take would be less than the unit (largely due to the Mach number), and therefore, the resulting logarithmic value of this term would have a negative sign. There is a value for the thickness of the boundary layer for each blade segment due to the variation in the length of the rope and the change in speed along the length of the blade; therefore, the Reynolds number varies in each segment.

Noise Caused by Laminar Boundary Layer and Vortex Shedding (LBL-VS)
When there is a laminar boundary layer on most of at least one side of an aerodynamic profile, vortex shedding noise (SPL LBL-VS ) can occur. Vortex shedding is apparently coupled to acoustically excited feedback loops [25]. The noise spectrum LBL-VS in the 1/3 octave band is given by Equation (12).
where G 1 , G 2 , and G 3 are empirical runs, St is the Strouhal number based on δ p , St peak is the Strouhal number based on Re c , and y (Re c ) 0 is the reference Reynolds number that depends on the angle of attack.

Noise Caused by Vortexes at the Tip of the Blade
The prediction of noise caused by the formation of vortexes at the tip of the blade was calculated using the method proposed by Brooks and Marcolini [30]. The noise is associated with turbulence in the local flow separation region at the tip of the blade, where the vortex of the blade tip is formed. The mechanism of noise production is originated by the passage of this turbulence over the trailing edge of the profile, and it is detached toward the near wake of the rotor. The sound pressure level due to the vortex formation at the tip of the blade, SPL TIP , in the 1/3 octave spectrum, is determined using Equation (13).
where l tip is the length of the vortices at the tip of the blade; M max = U max /c 0 is the maximum Mach number. The second term on the right side of Equation (13), which gives the frequency dependence, is a parabolic fit about a peak Strouhal number of 0.5.

Propagation Model
Applying the spherical propagation method, the sound pressure level is reduced by 6 dB per doubling of distance. This simple model must be modified in the presence of reflective surfaces and other disruptive effects [31]. To predict the sound pressure level on a specific observer at a certain distance from the wind turbine, it is necessary to determine the sound power levels of reference (SWL ref ) of the wind turbine for different wind speeds, which is defined by Equation (14), based on a single sound source and a semispherical propagation model. SWL re f = GM − 10 log 10 r 2 re f + 11 (14) where GM is the geometric mean of the sound pressure level measurements, which is define as the n th root of the term product (Equation (15)), and r re f is the reference distance, in this case r re f = 1 m from the source. To calculate the sound power levels, the sound pressure levels of the wind turbine must be known. When the measurements are made at great distances from the wind turbine, the sources of noise from the wind turbine can be considered as a point. Then, from the geometric mean of the sound pressure level measurements, GM, a point value for the sound pressure level of the spectrum-frequency curve can be estimated for each wind speed. where xs are the measurements of the sound pressure level, and n is the number of measurements.
Finally, a simple model to determine sound propagation in a free field is the spherical propagation method (Equation (16)) considering only the attenuation of the noise caused by the geometric divergence. In this case, it is considered a point source, and the effects of the earth's surface, weather effects, and obstacles, among others, are disregarded. Details of sound propagation are discussed by Vers and Beranek [32].
where SPL is the estimated propagation sound pressure level r, and SWL re f is the sound power value obtained from Equation (14).

Case of Study
As a case study, the RTO-1kW wind turbine with a diameter of 2 m and a nominal power of 1 kW was used. This wind turbine was manufactured by RTO Energy from México [33]. The study wind turbine is installed and operates in the Ejidal Bioclimatic Community Center located in the community of La Venta, Oaxaca, Mexico; see Figure 1. The low power wind turbine has a horizontal axis with a three-bladed rotor, the blades are 0.97 m long and were designed using the A18 aerodynamic airfoil, which presents the maximum coefficient relationship between the lift coefficient and drag coefficient respectively, C l /C d , for an optimal angle of attack (α) of α opt = 2 • . Figure 2 shows the curve of the rotation speed of the rotor in partial load and the output power of the wind turbine as a function of wind speed. Figure 2a shows a linear behavior of the rotation speed, with a minimum speed of 160 rpm for 3 m/s until reaching a maximum rotation speed of 750 rpm for 13.5 m/s. Figure 2b shows that the wind turbine begins to produce electricity at an input speed of 3 m/s, reaching a nominal power of 950 W at 13.5 m/s and an output speed is 17 m/s that is when the furling system is driven. The curves were provided by the builder RTO Energy [33]. Output power with respect to wind speed.

Field Measurements of Wind Turbine Noise
In the measurement of sound pressure levels, the area of study was characterized spatially and temporally, following the prescriptions described by Lee and Lee [23] and recommended by the IEC 61400-11 standard. The sound pressure level measurements were carried out during the day for several meteorological conditions. In all cases, significant variations in wind speed were observed at the time of measurement.
In a first instance, measurements of the noise emitted by the wind turbine were

Field Measurements of Wind Turbine Noise
In the measurement of sound pressure levels, the area of study was characterized spatially and temporally, following the prescriptions described by Lee and Lee [23] and recommended by the IEC 61400-11 standard. The sound pressure level measurements were carried out during the day for several meteorological conditions. In all cases, significant variations in wind speed were observed at the time of measurement.
In a first instance, measurements of the noise emitted by the wind turbine were made, including the background environmental noise [34]. In a second stage, the background noise was measured at the same site, under similar environmental conditions and with the wind turbine braked, Ω = 0 rpm.
In the first instance, and because we did not have class 1 measurement instruments, it was decided to use class 2 instruments such as the EXTECH EN300 sound level meter, with an Electret microphone from 1 2 ", measurement scale from 35 to 130 dB, automatic scale; resolution of 0.1 dB; response frequency from 3.5 to 8000 Hz. The accuracy of the sound level meter complies with the IEC 61400-2 Standard: A-weighting, fast response. Wind speed and temperature measurements were made with the UNI-T UT361/362 handheld anemometer.
The measurements were made according to the following steps: 1.
The appropriate measurement site was selected where the presence of obstacles was minimal.

2.
Then, the measuring instruments were installed at the distances recommended by the IEC 61400-11 standard [27]. It is important to mention that the place where the measurements were taken is well known for having sustained winds and almost unidirectional wind directions, from north to south [35,36].

3.
Subsequently, instantaneous data were captured every 5 min, namely: Background sound pressure level (SPL bg ) and sound pressure levels of the wind turbine in operation and the background (SPL wt,bg ); wind speed; temperature; pressure; relative humidity; and the time of measurement. These measurements were made during approximately one month in a daytime schedule. The measurements were made at a height of 3 meters and at 8 meters from the wind turbine.

4.
Finally, databases were generated with the information collected. As an example, Table 1 shows the field measured data of the background sound pressure level over a period of approximately three hours. Table 2 shows as an example the field measured data of the sound pressure level of the wind turbine in operation and the background.

Implementation of Aeroacoustic Models
To carry out the aeroacoustic study, the sound pressure levels produced by the turbulent boundary layer at the trailing edge and the flow detachment were analyzed, as well as the noise generated by the laminar boundary layer at the trailing edge and the vortex detachment, as well as that caused by the formation of vortexes at the tip of the blade, which are described by the BPM and BM models, respectively, are shown in Table 3. The wind turbine rotor blade was divided into 15 sections, which are described in Table 3. The semi-empirical models for predicting the aerodynamic noise emitted by wind profiles were implemented in sections 9-15 of the wind turbine blade, the ones furthest from the center of the rotor, since their tangential speeds are higher, and therefore, their impact is more important in the generation of noise; see Figure 3.
gies 2021, 14, x FOR PEER REVIEW furthest from the center of the rotor, since their tangential speeds are fore, their impact is more important in the generation of noise; see Figu To apply the noise prediction models of an aerodynamic profile, cedure is applied: 1. First, the wind speeds to be evaluated are limited in this case to 5 to 2. The geometry is studied, and the blade is divided into segmen closest to the tip.
3. Depending on the length of the segment to be evaluated, the relati the wind-driven segment moves is calculated.
4. Given the relative speeds and length of rope of each segment, the R and Mach numbers are calculated.
5. Given this information, the thickness of the boundary layers on pressure side and their noise contribution are calculated.
6. By adding these boundary layers, the sound contribution of the s calculated.
7. Depending on the number of segments, they are added to when ev emission of the blade.
8. Finally, to know the sound emission of the wind turbine, the numb wind turbine are added together, so we know the sound emission a speeds. Figure 4 shows the sound pressure levels with respect to the ang airfoil, as shown in Equation (4), in a frequency spectrum from 20 to 16 15 and a wind speed range of 5-10 m/s. In the same figure, for higher w pressure levels above 40 dB are found, confirming that as wind sp sound contributions from the blade increase. To apply the noise prediction models of an aerodynamic profile, the following procedure is applied:

Turbulent Boundary Layer at the Trailing Edge and Flow Detach
First, the wind speeds to be evaluated are limited in this case to 5 to 10 m/s.

2.
The geometry is studied, and the blade is divided into segments, selecting those closest to the tip.

3.
Depending on the length of the segment to be evaluated, the relative speed at which the wind-driven segment moves is calculated.

4.
Given the relative speeds and length of rope of each segment, the Reynolds numbers and Mach numbers are calculated.

5.
Given this information, the thickness of the boundary layers on the suction and pressure side and their noise contribution are calculated. 6.
By adding these boundary layers, the sound contribution of the selected segment is calculated.

7.
Depending on the number of segments, they are added to when evaluating the sound emission of the blade. 8.
Finally, to know the sound emission of the wind turbine, the number of blades of the wind turbine are added together, so we know the sound emission at the selected wind speeds. Figure 4 shows the sound pressure levels with respect to the angle of attack of the airfoil, as shown in Equation (4), in a frequency spectrum from 20 to 16,000 Hz for section 15 and a wind speed range of 5-10 m/s. In the same figure, for higher wind speeds, sound pressure levels above 40 dB are found, confirming that as wind speed increases, the sound contributions from the blade increase. Figure 4 shows the sound pressure levels emitted by the angle of attack of the A18 aerodynamic profile in a frequency spectrum from 20 to 16000 Hz and a speed range from 5 to 10 m/s of incident wind speed. From the segment of position 15 of Table 3 and calculated with Equation (4) of the BPM model, it can be seen that in the wind speeds of greater magnitude and at low frequency values, there are sound pressure levels of 46.6 dB, confirming that the wind that drives the wind turbine to blow faster, and at frequencies below 1000 Hz, the sound contributions of the blade increase. Figure 5 shows the contribution in the sound pressure level emitted by the pressure side of the aerodynamic profile, Equation (2), for section 15 and a wind speed range of 5−10 m/s. In the same figure, it is observed that the sound pressure levels have a very uniform behavior, being noticed that they are higher in the low frequency zone reaching 47 dB for speeds of 10 m/s.    Table 3 and calculated with Equation (4) of the BPM model, it can be seen that in the wind speeds of greater magnitude and at low frequency values, there are sound pressure levels of 46.6 dB, confirming that the wind that drives the wind turbine to blow faster, and at frequencies below 1000 Hz, the sound contributions of the blade increase. Figure 5 shows the contribution in the sound pressure level emitted by the pressure side of the aerodynamic profile, Equation (2), for section 15 and a wind speed range of 5−10 m/s. In the same figure, it is observed that the sound pressure levels have a very uniform behavior, being noticed that they are higher in the low frequency zone reaching 47 dB for speeds of 10 m/s.     Figure 6 shows the contribution in the sound pressure level emitted by the suction side of the aerodynamic profile, as shown in Equation (3), for section 15, and a wind speed range of 5−10 m/s. This phenomenon occurs because the boundary layer of the wind along the longest zone of the airfoil creates a low-pressure zone where aerodynamic lift is developed. Therefore, when the boundary layer breaks away from the trailing edge of the airfoil, it emits pressure disturbances or sound pressure levels.  Figure 6 shows the contribution in the sound pressure level emitted by the suction side of the aerodynamic profile, as shown in Equation (3), for section 15, and a wind speed range of 5−10 m/s. This phenomenon occurs because the boundary layer of the wind along the longest zone of the airfoil creates a low-pressure zone where aerodynamic lift is developed. Therefore, when the boundary layer breaks away from the trailing edge of the airfoil, it emits pressure disturbances or sound pressure levels. Once data are obtained on the sound pressure levels emitted by the suction side, pressure side, and leading edge in section 15, the total sound pressure levels, as shown Equation (1)   Once data are obtained on the sound pressure levels emitted by the suction side, pressure side, and leading edge in section 15, the total sound pressure levels, as shown Equation (1)   Subsequently, the total sound pressure levels emitted by the other sections that make up the blade were determined, for example, sections 9-15 of the wind turbine blade, in Table 3, for a wind speed range that varies between 5 and 10 m/s. Figure 8 shows the sound pressure levels of each segment of the blade study at different wind speeds and frequencies, where the sound pressure level presents high values in the low-frequency ranges and showing a decrease as the frequency increases, but it also increases as the wind speed of the selected segment increases. Subsequently, the total sound pressure levels emitted by the other sections that make up the blade were determined, for example, sections 9-15 of the wind turbine blade, in Table 3, for a wind speed range that varies between 5 and 10 m/s. Figure 8 shows the sound pressure levels of each segment of the blade study at different wind speeds and frequencies, where the sound pressure level presents high values in the low-frequency ranges and showing a decrease as the frequency increases, but it also increases as the wind speed of the selected segment increases.

Turbulent Boundary Layer at the Trailing Edge and Flow Detachment
for a wind speed range that varies between 5 and 10 m/s. Figure 8 shows the sound pressure levels of each segment of the blade study at different wind speeds and frequencies, where the sound pressure level presents high values in the low-frequency ranges and showing a decrease as the frequency increases, but it also increases as the wind speed of the selected segment increases. The contribution of the emission of the total sound pressure levels of the rotor of the wind turbine under study can be seen in Figure 9, where it is observed that for a high-speed range, the total sound pressure values are above 60 dB. The contribution of the emission of the total sound pressure levels of the rotor of the wind turbine under study can be seen in Figure 9, where it is observed that for a high-speed range, the total sound pressure values are above 60 dB. To adjust the frequency range of the sound pressure levels to the frequency response of the human ear, the A-weighting is used. This is a central tendency measure that is convenient to use when a dataset has a corresponding value with respect to the other data. By including the A-weighted values in the data of Figure 9, the results of the A-weighted wind turbine sound pressure levels are obtained, which are shown in Figure  10.  To adjust the frequency range of the sound pressure levels to the frequency response of the human ear, the A-weighting is used. This is a central tendency measure that is convenient to use when a dataset has a corresponding value with respect to the other data. By including the A-weighted values in the data of Figure 9, the results of the A-weighted wind turbine sound pressure levels are obtained, which are shown in Figure 10. To adjust the frequency range of the sound pressure levels to the frequency response of the human ear, the A-weighting is used. This is a central tendency measure that is convenient to use when a dataset has a corresponding value with respect to the other data. By including the A-weighted values in the data of Figure 9, the results of the A-weighted wind turbine sound pressure levels are obtained, which are shown in Figure  10.

Sound Pressure Levels Due to Vortex Formation at the Tip of the Blade
In Figure 11, we can see the sound pressure levels due to the vortex formation at the tip of the blade for different tangential speeds of the blade tip, which were obtained using the data in Table 3, and the operating parameters of the wind turbine studied. In this figure, it is observed that as the speed at the blade tip increases, the sound contribution increases until reaching a maximum of 83 dB.

Sound Pressure Levels Due to Vortex Formation at the Tip of the Blade
In Figure 11, we can see the sound pressure levels due to the vortex formation at the tip of the blade for different tangential speeds of the blade tip, which were obtained using the data in Table 3, and the operating parameters of the wind turbine studied. In this figure, it is observed that as the speed at the blade tip increases, the sound contribution increases until reaching a maximum of 83 dB. To estimate the sound pressure level in a specific receiver located at a certain distance from the wind turbine, a detailed analysis of the sound pressure levels in the 1/3 octave bands was carried out [28,10], with the groups of parameters (independent variables) proposed by the BPM and BM models. The sound power levels for wind speeds recommended by the IEC 61400-11 standard were calculated based on it. The results can be seen in Table 4.

Discussion
Taking as an example the data obtained with the experimental measurements, as shown in Table 1, from which only wind speeds varying in a range of 1 to 8 m/s were obtained, we decided to calculate the trend of the sound emission by means of a Pearson linear extrapolation model up to the wind speed of 10 m/s (wind speed range recommended by IEC 61400-11). It is important to mention that for these measurements, the To estimate the sound pressure level in a specific receiver located at a certain distance from the wind turbine, a detailed analysis of the sound pressure levels in the 1/3 octave bands was carried out [10,28], with the groups of parameters (independent variables) proposed by the BPM and BM models. The sound power levels for wind speeds recommended by the IEC 61400-11 standard were calculated based on it. The results can be seen in Table 4.

Discussion
Taking as an example the data obtained with the experimental measurements, as shown in Table 1, from which only wind speeds varying in a range of 1 to 8 m/s were obtained, we decided to calculate the trend of the sound emission by means of a Pearson linear extrapolation model up to the wind speed of 10 m/s (wind speed range recommended by IEC 61400-11). It is important to mention that for these measurements, the wind turbine was kept in a stationary position, so the sound pressure levels measured were the background noise; see Figure 12.
Energies 2021, 14, x FOR PEER REVIEW wind turbine was kept in a stationary position, so the sound pressure levels me were the background noise; see Figure 12.   Table 2 as an example. The table shows that only wind speeds varyin range of 1.5 to 8.5 m/s were obtained, so we decided to calculate the sound e trend by Pearson linear extrapolation up to a wind speed of 10 m/s (wind spee recommended by IEC 61400-11).  Table 5 shows the sound pressure levels of the wind turbine calculated by th and BM models and propagated according to the spherical propagation model, as in Equation (16), at 8, 10, and 20 m distance from the wind turbine.   Table 2 as an example. The table shows that only wind speeds varying in the range of 1.5 to 8.5 m/s were obtained, so we decided to calculate the sound emission trend by Pearson linear extrapolation up to a wind speed of 10 m/s (wind speed range recommended by IEC 61400-11).
Energies 2021, 14, x FOR PEER REVIEW wind turbine was kept in a stationary position, so the sound pressure levels me were the background noise; see Figure 12.   Table 2 as an example. The table shows that only wind speeds varying range of 1.5 to 8.5 m/s were obtained, so we decided to calculate the sound em trend by Pearson linear extrapolation up to a wind speed of 10 m/s (wind speed recommended by IEC 61400-11).  Table 5 shows the sound pressure levels of the wind turbine calculated by th and BM models and propagated according to the spherical propagation model, as in Equation (16), at 8, 10, and 20 m distance from the wind turbine.  Table 5 shows the sound pressure levels of the wind turbine calculated by the BPM and BM models and propagated according to the spherical propagation model, as shown in Equation (16), at 8, 10, and 20 m distance from the wind turbine. When the emission values calculated with the prediction models were available, it was decided to compare them with the experimental data, since the values of only the wind turbine in operation were not available, as it was not possible to cancel the background sound pressure levels. It was decided to subtract the measured values of the background sound pressure levels ( Figure 12) from the values of the sound pressure levels of the wind turbine in operation and the background ( Figure 13) by means of a decibel subtraction, thus obtaining the values of the sound pressure levels of only the wind turbine in operation. Figure 14 shows the data obtained from the experimental measurements of the sound pressure levels of the wind turbine in operation at the corresponding distance established by the IEC 61400-11 standard, which is 8 m, as well as the sound pressure levels of the BPM and BM models, which were propagated to 8 m.  When the emission values calculated with the prediction models were available, it was decided to compare them with the experimental data, since the values of only the wind turbine in operation were not available, as it was not possible to cancel the background sound pressure levels. It was decided to subtract the measured values of the background sound pressure levels ( Figure 12) from the values of the sound pressure levels of the wind turbine in operation and the background ( Figure 13) by means of a decibel subtraction, thus obtaining the values of the sound pressure levels of only the wind turbine in operation. Figure 14 shows the data obtained from the experimental measurements of the sound pressure levels of the wind turbine in operation at the corresponding distance established by the IEC 61400-11 standard, which is 8 m, as well as the sound pressure levels of the BPM and BM models, which were propagated to 8 m.  Table 6 shows the regression and linear extrapolation values obtained from the measurements and compares them with the calculated values of the sound pressure levels emitted by a wind turbine, as shown in Figure 14. We can see in this table the relative error between the values, where the error does not exceed 3.8%, with the largest error corresponding to a wind speed of 6 m/s.  Table 6 shows the regression and linear extrapolation values obtained from the measurements and compares them with the calculated values of the sound pressure levels emitted by a wind turbine, as shown in Figure 14. We can see in this table the relative error between the values, where the error does not exceed 3.8%, with the largest error corresponding to a wind speed of 6 m/s.

Conclusions
This article presents a theoretical and experimental study of the noise generated by a 1 kW small horizontal axis wind turbine during its operation. The theoretical model used for the noise analysis was shown to be a good tool to estimate the aerodynamic noise of a rotor thanks to its simplicity of implementation and its good approximation compared to the measured data. The comparative study of theoretical and experimental results showed that the BPM and BM methods have a maximum error of 3.8% corresponding to the rated wind speed of 6 m/s. However, at low wind speeds, theoretical models fit well to experimental data-for example, in the range from 5 to 8 m/s. Furthermore, results showed that the largest aerodynamic noise contribution comes from the blade tip vortices.
On the other hand, experimental data showed that the rotor's aerodynamic noise is more evident at low wind speed, because under these conditions, environmental noise is much less than wind turbine noise. By contrast, at high wind speeds, aerodynamic noise and environmental noise have similar noise pressure levels.
Based on the performed analysis, installing and design rules can be proposed to avoid exposure to high noise pressure levels when a small wind turbine is in operation; for example, it is recommended to install small wind turbines at a minimum distance of 20 m from the receptor; it is also important to carry out the labeling of the sound pressure levels of the small wind turbines as essential technical data before its installation in residential areas. Additionally, a theoretical model can be applied in the early blade design step to consider the aerodynamic noise mitigation. Furthermore, the rotational speed can be limited by active or passive systems to avoid aerodynamic noise for very high wind speed.
The methodology implemented to estimate sound pressure levels can be used in the design of the wind rotor by companies in the low power wind sector (RTO Energy Mexico) to develop wind turbines that operate with the parameters established by the IEC 61400-11 standard. This can encourage the use of low-power wind turbines in urban areas.
As a result of the research obtained in this work, this research group is currently collaborating with the company RTO Energy in the design of wind turbine rotors with capacities from 1 to 10 kW.
At the Universidad del Istmo, a small wind turbine test station is being prepared with all the class I equipment and instruments recommended by the IEC 61400-11 Standard, where the study developed in this work will be implemented, and thus certify the small wind turbines to be installed in residential areas. In addition, the possibility of determining the approximations for predicting noise by considering the 2D and 3D equations is considered, as well as determining the uncertainties of the results.