Despite their potential as a valuable source of individual
turbine power performance and turbine array energy production optimization
information, nacelle-mounted anemometers have often been neglected because
complex flows around the blades and nacelle interfere with their
measurements. This work quantitatively explores the accuracy of and potential
corrections to nacelle anemometer measurements to determine the degree to
which they may be useful when corrected for these complex flows, particularly
for calculating annual energy production (AEP) in the absence of other
meteorological data. Using upwind meteorological tower measurements along
with nacelle-based measurements from a General Electric (GE) 1.5sle model, we
calculate empirical nacelle transfer functions (NTFs) and explore how they
are impacted by different atmospheric and turbulence parameters. This work
provides guidelines for the use of NTFs for deriving useful wind measurements
from nacelle-mounted anemometers. Corrections to the nacelle anemometer wind
speed measurements can be made with NTFs and used to calculate an AEP that
comes within 1 % of an AEP calculated with upwind measurements. We also
calculate unique NTFs for different atmospheric conditions defined by
temperature stratification as well as turbulence intensity, turbulence
kinetic energy, and wind shear. During periods of low stability as defined by
the Bulk Richardson number (

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Traditionally, each wind turbine has an anemometer and wind vane mounted on its nacelle, behind the hub (Fig. 1). Measurements collected from these instruments are used for yaw control and turbine cut-in and cut-out procedures. Nacelle measurements could also be used to help improve turbine or park efficiency. For example, power performance verifications for individual turbines can now be based on the nacelle anemometer with suitable nacelle transfer functions (NTFs) (International Electrotechnical Commission, 2013). Nacelle measurements can also provide critical input for wind farm production optimization (Fleming et al., 2016). With sufficiently accurate NTFs, these data can provide a valuable, extensive, and continuous source of turbine-specific performance information.

GE 1.5/77sle turbine at the National Wind Technology Center. Photo credit: Dennis Schroeder, NREL (image gallery number 29611).

Power performance validation has traditionally relied on hub-height wind speed observations from a meteorological (met) tower upwind of a turbine (Link and Santos, 2004; IEC, 2015). The IEC (2015) standards require a met tower to be placed at the turbine location prior to turbine erection (the so-called “site calibration” procedure) for a power performance test to be considered valid (of sufficiently low total uncertainty) in complex terrain. However, it is not feasible to erect site calibration met towers after the turbine has been erected. Furthermore, even if site calibration is not required because a site is in simple terrain, tower erection is time-consuming and unrealistic to complete for every turbine at a given park. These factors motivate exploration of the use of nacelle-mounted anemometers to provide wind speed data for power performance validation.

Several studies have found that nacelle anemometer measurements can be adjusted by the use of transfer functions between an upwind hub-height measurement and the nacelle-mounted anemometer measurement (Antoniou and Pedersen, 1997; Hunter et al., 2001, Smith et al., 2002; Smaïli and Masson, 2004). The IEC (2013) standard now allows the use of nacelle-mounted anemometers to verify power curves based on these transfer functions, or fitted functions of correction factors between upwind hub-height wind speed (UHWS) measurements and nacelle-mounted anemometer wind speed (NAWS) measurements. Quantifying these transfer functions requires that upwind measurements be available at some point post-construction. However, once transfer functions are calculated for a site, the tower can be taken down and the transfer functions used to correct the nacelle measurements for future performance testing.

An empirical NTF may not result in a linear relationship between the UHWS and
NAWS. In fact, Antoniou and Pedersen (1997) found that the transfer functions
fit well with a fifth-order polynomial curve. Hunter et al. (2001) similarly
found a nonlinear relationship and that a linear regression would
overestimate the wind speed between 6 and 11 m s

In previous work, the relationship between UHWS measurements and NAWS measurements has been found to depend on multiple factors, including rotor and turbine control settings such as blade pitch angle and inflow angle, the use of vortex generators, yaw error, terrain, flow induction, calibration of the anemometer, and nacelle height and position (Antoniou and Pedersen, 1997; Dahlberg et al., 1999; Smith et al., 2002; Smaïli and Masson, 2004; Frandsen et al., 2009; Zahle and Sørensen, 2011).

The roles of inflow turbulence and atmospheric stability in NTFs have not yet been explored. However, previous work on power performance and annual energy production (AEP) does acknowledge the role of atmospheric stability, wind shear, and turbulence intensity (TI) in inducing deviations in power from the manufacturer power curve (MPC) (e.g., Sumner and Masson, 2006; Antoniou et al., 2009; Rareshide at el., 2009; Wagenaar and Eecen, 2011; Wharton and Lundquist, 2012; Vanderwende and Lundquist, 2012; St. Martin et al., 2016).

In this study, we quantify the effect of NTF-corrected nacelle anemometer measurements on the AEP and investigate the influence of different atmospheric stability and turbulence regimes on these NTFs. In Sect. 2, we briefly summarize our data set, which includes upwind and nacelle-based measurements, as well as our data analysis methods, which include filtering based on turbine operation, and definitions of the stability and turbulence regimes. We present results of AEP calculations together with results of separate NTFs for different stability and turbulence regimes in Sect. 3. In Sect. 4 we summarize conclusions about the effect of the NTF on the AEP in addition to the effects of atmospheric stability and inflow turbulence on the NTFs.

For this analysis, we use 2.5 months of data collected at the US Department
of Energy (DOE) National Wind Technology Center (NWTC) at the National
Renewable Energy Laboratory (NREL) during the winter
(29 November 2012 through 14 February 2013). We use 10 min-averaged turbine
supervisory control and data acquisition (SCADA) data
from a General Electric (GE) 1.5 MW turbine (GE 1.5/77sle; Fig. 1), with a
cut-in wind speed of 3.5 m s

Upwind data include 1 Hz measurements of wind speed and direction averaged to 10 min from a Renewable NRG Systems (NRG) Leosphere Windcube v1 vertically profiling Doppler lidar (2.7 rotor diameters (D) upwind; 208 m) and 10 and 30 min averages from a 135 m met tower (2.0 D upwind; 154 m). Volumetric-averaged wind speeds and directions are measured by the lidar every 20 m, from 40 m to 220 m. Comparison of the lidar wind profiles to those from the met tower suggest that the lidar data at this site suffered from inhomogeneities as a result of complex flows (Bingöl et al., 2009; Rhodes and Lundquist, 2013; Lundquist et al., 2015). Thus, the majority of this paper will focus on the results of the analysis using the tower data. On the met tower, cup anemometers placed at 3, 10, 30, 38, 55, 80, 87, 105, 122, and 130 m measure wind speed; vanes placed at 3, 10, 38, 87, and 122 m measure wind direction; and three-dimensional (3-D) sonic anemometers placed at 15, 41, 61, 74, 100, and 119 m measure all three components of the wind as well as sonic temperature, which is used to calculate momentum and heat fluxes (Table 1). Barometric pressure and precipitation amounts are measured at 3 m; temperature is measured at 3, 38, and 87 m; and dew point temperature is measured at 3, 38, 87, and 122 m (Table 1). See Fig. 2 in St. Martin et al. (2016) for a schematic of the tower.

Mounting heights of instruments on the 135 m met tower.

As discussed in St. Martin et al. (2016), meteorological and turbine data are
filtered for quality assurance. Data are only considered during time periods
when the turbine is operating and wind direction indicates the turbine is
located downwind of the lidar and met tower (235–315

Lastly, the nacelle-reported wind speeds used in this analysis have been subjected to a simple, linear-regression transfer function before the retrieval from the SCADA system around the DOE GE 1.5sle turbine. This linear regression function, built into the SCADA system by the turbine manufacturer, effectively translates the raw signal from the cup anemometer to wind speed and is not unlike a transfer function provided by an anemometer manufacturer. We see the uncertainty of this built-in transfer function as an advantage to our analysis as a typical wind plant operator would only have access to similar data.

To simulate a scenario in which a wind plant operator only has nacelle-based
measurements and no upwind tower or remote-sensing measurements, we calculate
an AEP (as described in Sect. 9.3 of IEC 61400-12-2, 2013) using only nacelle
winds to compare to an AEP calculated with upwind met tower 80 m winds. We
then correct the nacelle-based measurements with NTFs and calculate AEP based
on these results for comparison as well. Although data for this analysis only
span 2.5 months in the wintertime at the NWTC during the 2012–2013 season,
we calculate AEPs using the total number of hours in an entire year to show
values close to a representative AEP value. A sample wind distribution using
Weibull distribution parameters representative of the data set (scale
parameter:

We calculate Bulk Richardson numbers (

Using near-surface flux measurements at 15 m (within the surface layer) as
well as surface temperature and humidity measurements linearly interpolated
to 15 m, we calculate 30 min values of

Using horizontal wind speeds as measured by cup anemometers at 38 and 122 m
(lower tip and upper tip of the rotor disk), we calculate 10 min values of

Though some previous studies combine metrics to define stability (Vanderwende
and Lundquist, 2012), the three atmospheric stability metrics discussed here
are treated separately with regard to the NTFs because of slight differences
between their definitions of unstable and stable conditions (see Fig. 11 in
St. Martin et al., 2016). These differences may be attributed to distinctions
between each approach in defining atmospheric stability, a difference in
averaging period, heights of the measurements used in the calculations, or
how

Comparison of upwind wind speeds with nacelle anemometer wind
speeds:

Furthermore, we calculate TI and turbulence kinetic energy (TKE) to provide
turbulence metrics and estimate the effect of hub-height inflow turbulence on
the NTFs. Using 80 m wind speed measurements from the met tower, we
calculate 10 min values of TI, or the standard deviation of the horizontal
wind speed normalized by the average horizontal wind speed at hub height.
Using 74 m wind measurements from a 3-D sonic anemometer on the tower, we
calculate 30 min values of TKE per unit mass, or the sum of the variances of
the components of the wind divided by 2. Note that after filtering out
spikes in the raw 74 m sonic anemometer data, only about 367 30 min TKE
values remain (183.5 h) and the fewer number of data points likely affects
the statistical significance of the NTFs for different TKE regimes. Regimes
of TI, TKE, and

Defined stability and turbulence regimes.

To explore the variability in the NTF, we calculate specific NTFs filtered by atmospheric stability metrics, TI, and TKE. We investigate filters that have either previously been found to affect the transfer function or are suspected to have an effect on the transfer functions based on power curve studies (e.g., St. Martin et al., 2016). Additionally, we explore the effects of yaw error and wind veer and distributions of these variables, but, as in St. Martin et al. (2016), yaw error and wind veer do not seem to impact either the power curves or the NTFs at this site and are therefore not shown.

A general NTF (Fig. 2a) compares the tower 80 m wind speed to the
nacelle-reported wind speed using all data that pass the wind speed, wind
direction, and normal operation criteria defined in Sect. 2.1 and in more
detail in Sect. 3.2 and 3.3 in St. Martin et al. (2016). As a fifth-order
polynomial fit was found to be suitable for power curve assessment in
previous work by Antoniou and Pedersen (1997) and Hunter et al. (2001), we
also apply this type of fit to the wind speeds in this work to estimate an
empirical transfer function between 80 m tower wind speed measurements and
nacelle-mounted anemometer wind speed measurements (Fig. 2a). The

Based on the small coefficients of the third, fourth, and fifth orders of
the fit in Fig. 2a, a fifth-order polynomial may be unnecessarily complex.
Therefore, a second-order polynomial fit is also calculated to estimate an
empirical transfer function. The

Both transfer functions for this data set (Figs. 2a, 3a) are close to
linear at low wind speeds but nonlinear just before rated speed
(14 m s

Comparison of upwind wind speeds with nacelle anemometer wind
speeds. The red line in panel

Comparison of the NTF developed from the upwind tower measurements and the NTF developed from the upwind lidar measurements (Fig. 4a) emphasizes that the lidar measurements exhibit greater variability ranging over all relevant wind speeds. The variability in the lidar measurements caused by the inhomogeneity of the flow suggests that the tower measurements are more reliable for calculating power curves and transfer functions at this particular site, which is known to experience complex and inhomogeneous flow (Aitken et al., 2014). Despite the larger variability in the lidar data set for both the transfer function (Fig. 4a) and deviations between the corrected nacelle wind speed and the upwind wind speeds (Fig. 4b), both transfer functions in Fig. 4a show linearity at lower wind speeds and nonlinearity at higher wind speeds.

To try to quantitatively explain this change in the transfer function from linear to nonlinear and to connect with possible flow blockage behind the rotor and along the nacelle, the non-dimensional Froude number (Stull, 1988) for flow around the nacelle is calculated. Froude numbers are investigated during stable conditions using measurements from the tower at the surface and around hub height and using a range of length scales from 1 to 10 m to represent the length and width of the nacelle. However, distinctions between these two wind speed regions could not be seen in these calculations as Froude numbers were found to be positive and increase with increasing wind speed.

Additionally, because the transfer functions become nonlinear between cut-in wind speed and rated speed, the transfer function may be impacted by turbine operations in that region of the power curve, possibly because of root vortices (Whale et al., 2000). Just below rated speed, the blades begin to pitch forward to maintain rated generator speed, thus allowing power production to remain near rated power (Fig. 5). This “feathering” of the blades changes the flow around the blades and therefore the wind that affects the nacelle-mounted anemometer measurement. Though this hypothesis cannot be further investigated within this campaign as higher-resolution data from the SCADA system are unavailable, this does make a compelling argument for installing 3-D sonic anemometers on nacelles so that vertical velocity can be measured to further understand the 3-D wind structures behind the rotor and along the nacelle and how these flow structures change as inflow wind speed increases.

Scatter power curve using 80 m tower winds after filtering for wind
speeds between 3.5 and 25 m s

It is important to understand the characteristics of the NTF and how it changes with wind speed, as this under-estimation of the ambient wind speed, especially at wind speeds in which the growth in power production with wind speed is the most significant, could result in a significant overestimation of AEP in power performance verification.

With no NTF correction applied (aside from the transfer function that is built into the SCADA system by the manufacturer), the AEP calculated with nacelle winds (AEP_nacelle) overestimates the AEP calculated with 80 m tower winds (AEP_upwind) by 5.96 % (Table 3). This overestimation of AEP is expected as the nacelle anemometer consistently underestimates the upwind wind speed, which leads to the misrepresentation of higher power output at lower wind speeds, effectively shifting the entire power curve to the left, and therefore leading to a higher AEP.

Top row shows Annual energy production (AEP) in megawatt hours per year calculated using upwind tower measurements (AEP_upwind), nacelle winds (AEP_nacelle), corrected nacelle winds using the NTF calculated with a fifth-order polynomial (AEP_NTF5th), and corrected nacelle winds using the NTF calculated with a second-order polynomial (AEP_NTF2nd). Bottom row shows AEP in percentage calculated as a percentage of AEP_upwind.

The use of the NTF to correct the nacelle anemometer measurements reduces the AEP error significantly (Table 3). With the application of the fifth-order polynomial NTF (AEP_NTF5th), AEP_NTF5th underestimates AEP_upwind by only 0.003 %, whereas with the application of the second-order polynomial NTF (AEP_NTF2nd), AEP_NTF2nd underestimates AEP_upwind by 0.18 %. Therefore, using either the fifth-order polynomial or the second-order polynomial for the NTF results in an AEP similar to that of an AEP calculated with upwind hub-height winds, though both lead to a slight underestimation.

The value of atmospheric-stability segregation for NTFs seems to depend on
how stability is defined. Some statistically significant distinctions in the
NTFs for

Coefficients for fifth-order polynomial NTFs for stability metrics.

Coefficients for fifth-order polynomial NTFs for the shear exponent.

Tower 80 m NTFs calculated using fifth-order polynomial fits with
turbulence regimes based on

Coefficients for fifth-order polynomial NTFs for turbulence metrics.

We apply the NTFs to the nacelle anemometer measurements to evaluate the deviations from the upwind met tower data (Figs. 6b, 7b, and 8b); however, the results show no consistency or systematic distinctions between stability metrics, stability classes, or wind speed.

The hypothesis that convectively driven mixing and turbulence causes
underestimation by the nacelle-mounted anemometer is further supported in the
NTFs segregated by TI (Fig. 9a, Table 6) and TKE classes (Fig. 9b, Table 6).
Distinctions between unstable and stable cases in the transfer functions for
wind speeds between 5.5 and 12 m s

Corrections to the nacelle wind speeds using NTFs based on atmospheric turbulence show lower deviations from the ambient wind speed below rated speed and larger deviations from the ambient wind speed after rated speed for high TI cases. However, similar to the results in Figs. 6b, 7b, and 8b, Fig. 9c, d also show inconsistencies between deviations from the upwind speed for the different turbulence metrics and regimes.

We speculate that at wind speeds below rated, mixing in the atmosphere during more convective conditions, as well as the turbine interaction with these turbulent eddies, may result in additional motion that exaggerates blockage effects by the rotor and nacelle and causes underestimation by the nacelle-mounted anemometer. We suspect that rotor response is lagging in more convective and turbulent conditions as the turbine responds more quickly to drops in wind speed. Therefore, during more turbulent conditions, it is possible that lower rotor efficiency influences flow induction and thus the wind speeds measured on the back of the nacelle. If turbine and rotor efficiencies are lower during periods with convective and more turbulent conditions, it may then be surmised that less momentum passes through the rotor and along the nacelle. In addition, power curve results from the same data set discussed here (St. Martin et al., 2016) show that during less stable and more turbulent conditions at wind speeds within the ramp-up region of the power curve, more power is produced than during periods of more stable and less turbulent conditions. Power production will also affect the flow induction (Frandsen et al., 2009) and thus the wind speed directly behind the rotor disk: if more energy is extracted by the rotor, the nacelle-mounted anemometer will likely measure lower winds.

Over 2 months of data from both upwind instruments and nacelle-based instruments are used to quantify general nacelle transfer functions (NTFs) as well as NTFs that vary with atmospheric stability and turbulence parameters. We show that correcting nacelle winds using these NTFs results in more accurate annual energy production (AEP) estimates that are similar to estimates obtained using upwind meteorological (met) tower-based wind speeds. Furthermore, multiple factors have been investigated for their influence on NTFs, including both parameters known to influence wind power production and parameters never before investigated in the context of transfer functions.

We find that fitting the data to a fifth-order polynomial to estimate the
NTF results in a slightly higher

At wind speeds below 9 m s

The use of NTFs in AEP calculations results in a difference of less than 1 % from the AEP calculated with the upwind met tower wind speed. AEP calculations reveal that an AEP calculated using a fifth-order polynomial correction to the nacelle winds results in a 0.003 % underestimation of the AEP calculated with the upwind wind speed, whereas an AEP calculated using a second-order polynomial correction results in a 0.18 % underestimation of the AEP calculated with the upwind wind speed. Both are sizeable improvements over using the uncorrected nacelle wind speed, which leads to a 5.96 % overestimation when compared to the AEP calculated with the upwind wind speed.

Statistically significant distinctions emerge in the transfer functions for
unstable and stable cases as defined by the Bulk Richardson number
(

Distinctions in power curves (Sumner and Masson, 2006; Antoniou et al., 2009; Vanderwende and Lundquist, 2012; Dörenkämper et al., 2014; St. Martin et al., 2016) can lead to a correlation between these distinctions and distinctions in NTFs as well as the idea of validating power performance data with similar atmospheric and operational characteristics with their corresponding power curve in an effort to decrease the amount of uncertainty in power performance testing.

NTFs have recently been accepted for power curve validation under certain circumstances (IEC, 2013). They can also enable the use of nacelle-mounted anemometers for AEP estimates, turbine performance analysis, and data assimilation for improved forecasting (Draxl, 2012; Delle Monache et al., 2013).

Further work could explore how turbine controls and characteristics such as thrust affect the transfer functions. Simulations of flow around the nacelle such as those of Keck (2012) could be expanded to account for variations in atmospheric stability and could be coupled with control software simulators. As Bibor and Masson (2007) suggest, a single transfer function should not be used for every wind plant site and for every atmospheric and operating condition. Several atmospheric and operational conditions and how they affect the transfer functions should be investigated and perhaps combined to provide an algorithm for manufacturers and wind plant operators to use in power performance validation.

Data from the M5 tower are available for download at

The authors declare that they have no conflict of interest.

The authors express appreciation to the Center for Research and Education in Wind for supporting this work, to Thomas Fischetti and Peter Gregg at GE Renewable Energy for their assistance in turbine data collection and interpretation, and to the reviewers of a previous version of this work. This work was supported by the US Department of Energy under contract no. DE-AC36-08GO28308 with the National Renewable Energy Laboratory. Funding for the work was provided by the DOE Office of Energy Efficiency and Renewable Energy, Wind and Water Power Technologies Office. Edited by: H. Hangan Reviewed by: two anonymous referees