This study proposes two methodologies for improving the accuracy of wind
turbine load assessment under wake conditions by combining nacelle-mounted
lidar measurements with wake wind field reconstruction techniques. The first
approach consists of incorporating wind measurements of the wake flow field,
obtained from nacelle lidars, into random, homogeneous Gaussian turbulence
fields generated using the Mann spectral tensor model. The second approach
imposes wake deficit time series, which are derived by fitting a bivariate
Gaussian shape function to lidar observations of the wake field, on the Mann
turbulence fields. The two approaches are numerically evaluated using a
virtual lidar simulator, which scans the wake flow fields generated with the
dynamic wake meandering (DWM) model, i.e., the

Wind turbines operating under wake conditions experience higher loading and
lower power productions than those operating under wake-free conditions

To date, detailed predictions of wake-generated turbulence can be achieved
with large eddy simulation (LES); however, the computational cost is
prohibitive when large numbers of simulations are required. This makes
engineering wake models a practical alternative for certain applications. For
design load evaluation, the IEC 61400-1 standard

The DWM model considers wakes to act as passive tracers displaced in the
lateral and vertical directions by the large eddies of the atmospheric flow

There are three primary sources of uncertainty intrinsic of engineering wake
models that affect the accuracy in power and load predictions, which we here
denote as the measurement, modeling, and statistical uncertainty. The
measurement uncertainty includes deviations between the measured quantity of
interest (e.g., the ambient wind field's characteristics or the power and load
data) and its actual true values. The modeling uncertainty originates from
the simplistic flow-modeling assumptions adopted to describe wake flow
fields. This type of uncertainty can partly be reduced by improving the wake
model (e.g., by adding further physical effects)

The statistical uncertainty derives from the traditional method of performing aeroelastic simulations, for which the numerical wind fields are set to match the statistical properties (mean and variance) of the observed wind field on a 10

Alternative load verification procedures are being explored to potentially
reduce the statistical and modeling uncertainty in engineering wake models
and replace measurements from masts with those from Doppler lidars

In particular, nacelle-mounted lidars have the advantage of being aligned with
the rotor, which increases the number of validation data in contrast to a
fixed mast where only a small wind direction sector is valid. The feasibility
of nacelle-mounted lidar observations has been demonstrated for wake
characterization

The recent work of

Overall, developing lidar-based wake wind field reconstruction techniques that
reduce the modeling and statistical uncertainties in the inflow inherent of
low-order engineering wake models can improve loads and lifetime estimation
accuracy

The present work proposes two alternative approaches for wind turbine load
validation under wake conditions using nacelle-mounted lidar retrievals
combined with wake wind field reconstruction techniques. The first approach
builds on the work of

The second approach reconstructs wake deficit characteristics including wake meandering by fitting a bivariate Gaussian shape function to lidar retrievals and superimposes these deficits on a random realization of the Mann turbulence field. This approach intends to minimize errors in wake deficit representations and introduce the observed wake meandering path directly into the simulations. Both lidar-based wake field reconstruction techniques can potentially decrease the modeling and statistical uncertainty inherent to the DWM model, thus predicting accurate power productions and loads.

We evaluate these lidar-based wake field reconstruction techniques in a tailored designed numerical framework that simulates a nacelle-mounted lidar scanning the synthetic wake fields generated with the DWM model. The main objective of this study is to verify that nacelle-mounted lidar measurements incorporated into wake field reconstruction methods improve the accuracy of power and load predictions when compared to wake field reconstruction using engineering wake models alone.

The work is structured as follows. In Sect.

The design load cases (DLCs) and load verification procedure for wind turbines
operating in wakes are described in the IEC standards

An illustration of the numerical framework utilized to reconstruct wake fields through the DWM model and our proposed lidar-based wake field reconstruction techniques (i.e., the constrained simulations, CSs, and the wake deficit simulations, WDSs). Further, this framework allows quantifying the uncertainty in power and load predictions resulting from aeroelastic simulations with the DWM model-based and lidar-based wake fields. More details can be found in the text.

We use two sets of random turbulence field realizations, which we denote as
set A and set B. These turbulence fields are generated using
the model by

Hence, the result of a one-to-one comparison of load statistics between the
baseline and the target simulations is a direct measure of
the statistical uncertainty (i.e., load scatter) that originates from both the
random Mann-based turbulence realizations and the stochastic meandering
process inherent to the DWM model. In a traditional load validation analysis,
the target loads will be the measured loads, whereas the
baseline loads will be the loads resulting from aeroelastic
simulations using turbulence fields with the same properties as the measured
inflow conditions

To evaluate the lidar-based approaches, we use a virtual lidar simulator that
scans the target wake fields and, through our proposed wake field
reconstruction technique, incorporates these samples in a random turbulence
field realization from set B (see Fig.

Further, by incorporating lidar retrievals in the wind field reconstruction
technique, we expect to reduce the amount of statistical uncertainty as the
load time series resulting from this approach will have greater similarity
with the load time series based on the target turbulence
fields. Therefore, this procedure allows us to quantify the uncertainty in
load predictions that results from lidar-reconstructed wake fields (see the
red elements in Fig.

The load validation comprises a large number of simulations (we use 18
random turbulence field realizations for each individual 10

The bias (here defined as the mean ratio between simulated and target loads) obtained with the lidar-reconstructed CSs and WDSs is equal to that obtained with the baseline.

The statistical uncertainty (here defined as the standard deviation of the ratio between simulated and target loads) derived with the lidar-reconstructed CSs and WDSs is lower than that obtained with the baseline.

Provided that these criteria are satisfied, the proposed lidar-based wake field reconstruction techniques will produce (I) power and load predictions in wakes that are statistically unbiased compared to the DWM model results and (II) a reduced statistical uncertainty in power and load predictions compared to the DWM model results, which is achieved by reconstructing wake fields with stronger similarities to the actual inflow.

The time-domain aeroelastic simulations require input of a three-dimensional
turbulence field that mimics atmospheric turbulence

The model by

The DWM model is an engineering wake model that simulates wind field time
series and includes three components: a quasi-steady velocity deficit, the
wake-added turbulence, and the wake meandering

Qualitative representation of the three wake components predicted by the DWM
model, including an axisymmetric quasi-steady velocity deficit, which is
defined as the local wind speed

The velocity deficit definition is based on the work of

The wake-added turbulence originating from the breakdown of tip vortices and
from the shear of the velocity deficit is accounted for by a semi-empirical
turbulence scaling factor

The wake meandering is assumed to be governed by the atmospheric turbulent
structures of the order of two rotor diameters (

As a result, the wake field simulated by the DWM model can be seen as a
cascade of quasi-steady velocity deficits that meander in the lateral and
vertical directions and are advected downstream by the mean wind speed of the
inflow using Taylor's assumption. These wake features are superposed on
stochastic homogeneous turbulence field realizations to generate wake fields
time series that are then input into aeroelastic simulations (see
Fig.

Mathematically, a three-dimensional synthetic wake flow field compliant with
the DWM model formulation can be defined by a linear superposition of the
ambient wind field and two inhomogeneous turbulence terms as

We use the lidar simulator developed within the ViConDAR open-source numerical
framework to virtually replicate lidar measurements
(

The lidar simulator can mimic any arbitrary scanning pattern and includes a
time lag between each lidar-sampled measurement to resemble the scanning
frequency (see Fig.

An illustration of the virtual lidar simulator setup run for 175

To evaluate currently available nacelle lidars' ability to perform wake
characterization, we select a few standard scanning configurations and use
them to perform load validation within wakes. These are a four-beam lidar (4P)

Selected lidar scanning patterns for the load analysis. The red markers indicate the scanned locations, and the black dots in the background define the spatial resolution of the turbulence box. The rotor diameter is shown as a solid black line.

The lidar simulator is assumed to scan the selected patterns at the same
single range upwind of the rotor. Pulsed and continuous-wave (CW) lidar
technologies apply different approaches at scanning multiple ranges

Although we do not optimize the scanning patterns, we use scan radii (defined
as the radius between hub height and the location of the scanned points) of
about 70

A preview distance of

We assume a 2

Technical properties of the simulated lidar scanning configurations. Note that the Cone and SL measurements are binned according to the spatial resolution of the synthetic turbulence fields, thus leading to a reduction in the simulated scanning positions.

A probe volume with an extension of 30

By defining the DWM model-based wake flow fields as the target
fields, the underlying assumptions on which we define the lidar-based wake
field reconstruction techniques are as follows:

The ambient wind conditions are known, including

The lidar-based wake fields are reconstructed by incorporating lidar observations (e.g., in the form of constraints or lidar-fitted velocity deficits) into a zero-mean, homogeneous, and random Gaussian turbulence field generated by the Mann spectral tensor model.

The induction effects on lidar measurements are neglected, and Taylor's frozen turbulence hypothesis is assumed.

Only the

The corresponding random turbulence field realizations from set A
(used for the target fields) and set B have similar spectral
properties; however, these fields only describe the turbulence structures of
the ambient wind field. The lidar measurements of the wake field, combined
with the wake field reconstruction approach, should recover all the
information regarding the wake characteristics, including velocity deficits,
wake-added turbulence, and meandering in lateral and vertical
directions. Further, the first assumption is no longer needed if a second
instrument is deployed at the site measuring the ambient conditions, for
example, using a mast or a nacelle-mounted lidar

The second and third assumptions are inherent in the modeling approach and
limitations of the DWM model and other analytical wake models; however, in
this study, the wake characteristics are extracted directly from the lidar
observations rather than from a physically based deficit formulation. Eventually,
wind turbine responses are mainly affected by the mean wind speed in the
longitudinal direction (

The algorithm for applying constraints on a zero-mean, homogeneous, and
isotropic Gaussian random field was developed in

Following the notation in

The objective of the algorithm is to define a turbulence field

The wake deficit superposition (WDS) approach assumes that velocity
deficits can be described by a bivariate Gaussian shape function, which is
fitted based on lidar measurements of the target wake flow
field. Several studies have demonstrated the viability and robustness of the
Gaussian curve fitting to track wake deficit displacements in the far-wake
region

In our study, the wake shape function not only tracks the wake meandering but also is used to quantify the depth and width of the wake at each
quasi-instantaneous scan performed by the lidar. Traditionally, the normalized
velocity deficit is defined as the difference between the ambient wind speed
and that inside the wake as

The optimal wake deficit parameters (

To compensate for these deviations and considering that the DWM model-based
wake fields can be defined as a linear summation of the ambient wind field

The results are divided into three parts. First, we assess the accuracy of
lidar-reconstructed wake fields against target fields in
Sect.

In this section, we evaluate the accuracy of the lidar-reconstructed fields
against the target fields. At first, we assess the accuracy of the
reconstructed

Spatial distribution of the error inherent to the CS- and WDS-reconstructed fields for selected scanning configurations. The top row refers to the RMSE normalized over the target velocity at each grid point (

Further, we compute the explained variance ratio across the turbulence box

Figure

As shown in Fig.

The errors introduced by the WDS fields are partly a consequence of
an inaccurate estimation of the wake deficit characteristics (i.e., due to the
limited spatial scanning configuration) and the small-scale turbulence
structures contained in the turbulence box. Finally, the results in
Fig.

Comparison between the target

In Fig.

Comparisons of the power spectra density (PSD) of the target

In addition, we compute the power spectral density (PSD) of the above-analyzed
time series of

The enhanced turbulent energy content of the target field within the high-frequency range (

The DTU 10

Following the load validation procedure illustrated in
Fig.

The analyzed wind turbine responses include mean power production levels

Furthermore, we quantify the accuracy of the reconstructed wake fields based
on estimates of the rotor-effective wind speed (

Load simulations are carried out using site-specific observations collected
from the FINO1 meteorological mast installed at the German offshore wind farm
Alpha Ventus. The wind farm is situated in the North Sea and about
45

In the present work, we only use wind speeds and turbulence intensities
measured under near-neutral conditions from a 90

For each 10

Note that the recorded turbulence estimates at Alpha Ventus are considerably lower (by approximately a factor of 3) than values recommended by the low-turbulence IEC class C. Here, we perform the load validation analysis on more realistic turbulence estimates characterizing offshore sites, since IEC class-C conditions would significantly attenuate the wake-induced effects, as higher ambient turbulence leads to a faster recovery of the wake deficit.

We use standard IEC-recommended turbulence parameters for the Mann model (i.e.,

Scatter plots of the 10

The target wake field characteristics as a function of the ambient wind
speed, which result from the 162 simulations, are shown in
Fig.

Turbulence levels within the wake region are nearly doubled at low wind speeds
compared to the ambient conditions, as shown in
Fig.

The uncertainties (

Comparison of bias

As a result, lower deficits are simulated or equivalently higher
rotor-effective wind speeds are predicted. Consequently, the power predictions
are overestimated (

The statistics of

The results from simulations with the SL, Grid, and Grid

Uncertainty indicators of the load validation analysis based on the constrained field simulations (CSs). Results are tabulated according to the load components and lidar scanning patterns. The color map reflects the amplitude of the error; thus dark blue identifies an overprediction while light green indicates an underprediction. A perfect statistical prediction leads to

Figure

The statistics of

The

We present the results relative to the WDSs in the same
fashion as for the CSs in Sect.

These findings suggest that more details on the wake characteristics are
better recovered by fitting a wake deficit function rather than by incorporating
lidar measurements directly into the turbulence boxes, when looking at
patterns where the inflow is scanned at few positions. Overall, simulations
with the 7P, SL, Grid, and Grid

Comparison of bias

Uncertainty indicators of the load validation analysis based on the wake deficit superposition simulations (WDSs). Results are tabulated according to the load components and lidar scanning patterns. The color map reflects the amplitude of the error; thus dark blue identifies an overprediction while light green indicates an underprediction. A perfect statistical prediction leads to

We quantify the statistics of

In this section, we investigate the accuracy of lidar-reconstructed load
time series against target observations. An illustrative example is
provided in Fig.

Comparison of predicted load time series based on aeroelastic simulations carried out with the target, baseline, and CS- and WDS-reconstructed fields. The lidar-based fields are reconstructed using the Grid pattern.

Average cross-correlation coefficient

In order to quantify the accuracy of the predicted load time series, we
evaluate the cross correlations

The correlation relative to MxTB drops to

We conduct a spectral analysis on the time series of MxBR,
MxTB, and MzTT, which are highly correlated with the
wake meandering

The spectral coherence analysis provides more insight into the accuracy of
reconstructed blade and tower loads. Here, we compute the coherence as

Spectral coherence analysis between the lidar-based load predictions and the target simulations for the

It is observed that both field reconstruction techniques lead to high
coherence in the proximity of the principal load frequencies, such as the
rotational frequency (1P for the blade and 3P for the tower; see
Fig.

By increasing the scanning pattern's temporal resolution and the number of
scanned points and by neglecting volume-averaging effects, the
CS approach could potentially reconstruct the whole spectrum of the
loads. With the WDS approach, we can only reconstruct turbulence
structures corresponding to the size of the wake deficit. Finally, given the
limitation of the reconstruction techniques to recover small-scale turbulence
structures, as discussed in Fig.

The load validation of Sect.

Figure

Influence of atmospheric turbulence conditions on the lidar-based load prediction accuracy, including

We investigate the influence of the atmospheric turbulence length scale on the
load prediction accuracy in Fig.

One of the main limitations of continuous-wave lidars is that the probe volume
size increases proportionally with the square of the focal distance

Influence of lidar scanning specifications on the lidar-based load prediction accuracy, including

Another limitation inherent in the pulsed lidar technology is the reduced
sampling frequency compared to continuous-wave lidars

One of the main elements used in the study is to regard as target
the wake flow fields generated by the DWM model. The DWM model is a simplified
engineering wake model subjected to modeling uncertainties. Although the mean
wind velocity and turbulence fields in the far-wake region can deviate from
high-fidelity simulations (e.g., computational fluid dynamics, CFD) or field
data, the calibration of the DWM model coefficients can considerably improve
the accuracy and provide wake fields in good agreement with lidar observations

The wake turbulence spectral properties are described, to the extent needed
for the load analysis, by an isotropic Mann-generated turbulence field with a
low length scale

Another limitation stems from the lidar simulator used in the study, which
replaces full-field lidar measurements. Real lidar data taken upstream of the
rotor should be corrected for induction

Characterizing the small-scale wake-added turbulence poses a challenge given
the limitations of the lidar's sampling frequency and probe volume size

We demonstrate that a high number of lidar-scanned positions of the inflow are required to ensure an acceptable level of accuracy in the reconstructed wake fields. The results reveal that the current commercially available nacelle-mounted lidars (e.g., the 4P, 7P, and Cone patterns) will not provide sufficient information to reconstruct the wake fields accurately for the load assessments. In contrast, the scanning requirements are fulfilled by the SpinnerLidar and any arbitrary lidar that can potentially scan a greater region of the rotor, e.g., a Grid-like configuration. Although we do not optimize the scanning strategies, it is inferred that the required number of positions scanned by the lidar depends on the size of the turbulence structures in the wake field.

Incorporating a sufficient number of lidar measurements directly in the
turbulence fields leads to more accurate load predictions than assuming a wake
deficit's generic shape function. The CS algorithm can also be
extended to reconstruct the

On the other hand, the accuracy of the WDS-predicted loads is
conditional on the selected shape function's capability to represent velocity
deficits. The wake deficit can deviate from a Gaussian shape as the atmosphere
becomes more unstable

The fitting procedure of the WDS approach is relatively fast and can
provide real-time spatial and temporal characteristics of the wake flow field,
which are useful for power and load predictions, wind farm monitoring, and
control strategies. The computational cost of the CS algorithm
considerably increases with the number of constraints simulated and the
dimension of the turbulence boxes. For reference, a single wind field with
27 900 constraints (i.e., using the SL configuration) and a turbulence box
with a grid size of

This study proposed two alternative wind turbine load validation procedures under wake conditions that reconstruct synthetic wake fields from time series of lidar retrievals. The first approach consisted of incorporating nacelle lidar measurements of the wake as constraints into random Mann turbulence field realizations. The second approach relied on the superposition of lidar-fitted bivariate Gaussian wake deficit time series on the Mann turbulence fields. The two approaches were numerically evaluated, adopting a tailored designed framework that uses a virtual lidar simulator to scan three-dimensional wake fields simulated by the DWM model (i.e., the target fields).

We demonstrated that lidar-reconstructed wake fields recovered the main wake flow features affecting wind turbine power and load predictions, such as the spatial distribution of the velocity deficit and its meandering dynamics. However, the accuracy of power and load estimates was highly conditional on the number of scanned points by the lidar, the probe volume size, and the ambient turbulence intensity that in turn affected the wake evolution.

The load validation analysis showed that the current commercially available nacelle-mounted lidars would not provide sufficient spatial resolution to characterize wakes for power and load assessments, whereas research lidars, e.g., the SpinnerLidar and the Grid-like configuration, fulfilled these requirements.

Provided that a sufficient number of wind measurements were taken upwind of
the rotor (e.g., using the SpinnerLidar or the Grid), incorporating them as
constraints into turbulence fields was the most robust and accurate procedure
for reconstructing wake fields and predicting power and loads. The
lidar-reconstructed wake fields produced power and load time series that were
highly correlated with the target turbine responses; thus, reducing
the statistical uncertainty (realization-to-realization) by a factor of 1.2–5
when compared to the traditional load validation procedure (i.e., using the
DWM model). Although unbiased power productions were predicted, the SpinnerLidar- and
Grid-based reconstructed wake fields underpredicted fatigue load estimates by
1

Further investigations should evaluate the effects of rotor induction and turbulence evolution on the accuracy of lidar-reconstructed wake fields. Besides, the proposed wake field reconstruction techniques should be validated using full-field data collected in operating wind farms.

Figure

Compared to the rotating blades, the PSD of the tower loads MxTB
and MzTT exhibits the largest energy content at higher frequencies
of up to 3P (

Power spectral density (PSD) of the

The ViConDAR framework can be accessed at

DC, VP, ND, and AP participated in the conception and design of the work. VP developed the ViConDAR framework. ND developed the constrained simulation framework. DC developed the numerical framework that gets ViConDAR to scan wake-generated fields and use virtual lidar measurements as inputs to reconstruct wake field via CS and WDS approaches. DC also carried out aeroelastic simulations and wrote the draft manuscript. VP, ND, and AP provided key elements of the programming code, supported the overall analysis, and critically revised the manuscript.

The authors declare that they have no conflict of interest.

Vasilis Pettas is partially funded by the German Federal Ministry for Economic Affairs and Energy (BMWi) in the framework of the national joint research project RAVE – OWP Control (ref. 0324131B).

This paper was edited by Raúl Bayoán Cal and reviewed by two anonymous referees.