We propose a method for carrying out wind turbine load validation in wake conditions using measurements from forward-looking nacelle lidars. Two lidars, a pulsed- and a continuous-wave system, were installed on the nacelle of a 2.3 MW wind turbine operating in free-, partial-, and full-wake conditions. The turbine is placed within a straight row of turbines with a spacing of 5.2 rotor diameters, and wake disturbances are present for two opposite wind direction sectors. The wake flow fields are described by lidar-estimated wind field characteristics, which are commonly used as inputs for load simulations, without employing wake deficit models. These include mean wind speed, turbulence intensity, vertical and horizontal shear, yaw error, and turbulence-spectra parameters. We assess the uncertainty of lidar-based load predictions against wind turbine on-board sensors in wake conditions and compare it with the uncertainty of lidar-based load predictions against sensor data in free wind. Compared to the free-wind case, the simulations in wake conditions lead to increased relative errors (4 %–11 %). It is demonstrated that the mean wind speed, turbulence intensity, and turbulence length scale have a significant impact on the predictions. Finally, the experiences from this study indicate that characterizing turbulence inside the wake as well as defining a wind deficit model are the most challenging aspects of lidar-based load validation in wake conditions.

Wind turbines are designed according to reference wind conditions described in the IEC standards

Wake effects are responsible for wind speed reduction and turbulence level increase, generally resulting in reduced power productions and increased load levels

The comparison of fatigue loads predicted using the DWM model and the effective turbulence approach by the IEC showed a discrepancy of 20 %

The recent applications of lidars in the wind energy field demonstrate the feasibility of these systems to reconstruct inflow wind conditions including mean wind speed

Based on these findings, we extend the load validation procedure defined in

The paper is structured as follows. In Sect.

The design load cases and load validation procedure for wind turbines are described in the IEC standards. The IEC61400-1 requires the evaluation of fatigue and extreme loading conditions induced by wake effects originating from neighbouring wind turbines. The increase in loading due to wake effects can be accounted for by the use of an added turbulence model, or by using more detailed wake models (i.e. DWM). Load validation guidelines are described in IEC61400-13

The objective of this work is to carry out load validation of wind turbines operating in wake conditions using measurements from nacelle-mounted lidars only. The wake-induced effects are accounted for by lidar-estimated wind field characteristics, without employing wake deficit models. This implies that wake flow fields can be described by means of average flow characteristics commonly used as inputs for load simulations. We assess the viability of the suggested approach by carrying out a load validation study as follows:

one-to-one load comparison between measured and predicted load realizations using wind field characteristics derived from lidar measurements of the wake flow field;

uncertainty quantification in terms of the statistical properties of the ratios between measured and predicted load realizations;

comparison of lidar-based load prediction uncertainties in wakes against uncertainties of load predictions in free-wind conditions using lidar measurements.

We assume that the observed deviations in load predictions between those that are lidar-based under wake conditions and those that are lidar-based under free-wind conditions are solely due to the error in the wind field representation. This is a simplistic but conservative assumption, as the uncertainties of load predictions are a combination of uncertainty in the reconstructed wind profiles, aeroelastic model uncertainty, load measurement uncertainty, and statistical uncertainty

Wind and load measurements are collected from an experiment conducted at the Nørrekær Enge (NKE) wind farm during a period of 7 months between 2015 and 2016. The farm is located in the north-west of Denmark and consists of 13 Siemens 2.3 MW turbines, with a 93 m rotor diameter (

The wind turbine T04 was instrumented with sensors for load measurements at the roots of two blades, tower top, and tower bottom

This study uses wind measurements from the cup anemometers at 57.5 and 80 m, which are used to derive wind speed, turbulence, and shear as discussed in the following sections. According to the definition in IEC61400-12-1

The Nørrekær Enge wind farm in northern Denmark on a digital surface elevation model (UTM32 WGS84). The wind turbines are shown in circles, the turbine T04 with the nacelle lidars in red, and the mast as a triangle. The sectors used for the analysis are also shown; narrow direction sector: 97–109

Two forward-looking lidars were installed on the nacelle of T04: a pulsed lidar (PL) with a five-beam configuration and a continuous-wave (CW) system. The CW lidar by Zephir has a single beam, which scans conically with a cone angle of

The PL lidar provided by Avent technology has five fixed beams; a central beam oriented in the longitudinal direction at hub height and four beams oriented at the corner of a square pattern, as shown in Fig.

We conduct the load analysis using 10 min reference periods. The dataset is filtered so that we select only periods where the turbine is operational and load, mast, and lidar measurements are available. A total of 6198 10 min periods are available in the wide direction sector, which decreases to 1042 samples in the narrow sector. The majority of measurements within the wake sectors are from westerly directions 235–265

Top and front views of the CW lidar

Load simulations are carried out using the state-of-the-art aeroelastic HAWC2 software

In the present study, the HAWC2 turbine model is based on the structural and aerodynamic data of the Siemens SWT 2.3-93 turbine and is equipped with the original equipment manufacturer controller. The turbulence used in the simulations is generated using the Mann turbulence model

Wind field parameters serving as input for aeroelastic load simulations.

Wind field reconstruction (WFR) is defined as the process of retrieving wind field characteristics by combining measurements of the wind in multiple locations

We assume a linear variation in wind direction over the rotor diameter

Note that the wind flow inclination (tilt) is neglected. The orientation of the LOS velocity with respect to the reference coordinate system is defined by rotations about the

As lidars measure only the LOS velocity, the first row alone of

This formulation is suitable assuming lidar point-like measurements and homogeneous wind field, which implies that the three velocity component statistics do not change over the scanned area. By combining Eqs. (

The two-dimensional induction model assumes longitudinal and radial variation in the induced wind velocity. The resulting induction factor

The parameters

The CW and PL lidar-estimated mean wind speed in free wind, for the narrow direction sector (97–109

Comparison of 10 min lidar-estimated and mast-measured inflow characteristics. We show a

The wind field vector

The procedure to derive spectral parameters from the measured spectra of the three velocity components is described in

Turbulence characterization using lidars is subjected to several sources of uncertainty. The measurement volumes along the LOS lead to spatial averaging of turbulence, which reduces the LOS variance when compared to a point measurement

We implement two approaches to derive filtered and unfiltered turbulence based on the work of

The magnitude of

The effects of cross-contamination and flow direction are accounted for by means of matrix transformations including

The second approach avoids filtering effects by use of the ensemble-averaged Doppler radial velocity spectrum

By solving the variance operator and neglecting the resulting terms

We show the comparison between lidar-estimated and mast-measured

A wake detection algorithm is developed to determine whether the turbine is operating in free-, partial-, or full-wake situations. The algorithm relies on 10 min statistics of the lidar measurements and follows the approach of

At first, we fit the wake detection parameters to a probability distribution function (pdf) using data from the wake-free wide direction sector (97–220

Figure

Further, we attempt to distinguish situations where the mast is in wake or in free wind, based on 10 min mast data. Turbulence from the cup at 80 m and shear derived from the cups at 57.5 and 80 m are used as wake detection parameters (results are shown in Fig.

Improved wake detection can be obtained by establishing thresholds conditional to the ambient wind conditions (i.e. wind speed, turbulence, and atmospheric stability) and by assessing the detection parameters for shorter time periods

The results are presented in five parts. The wake-induced effects on the reconstructed wind field parameters are analysed in Sect.

Wind turbine wakes lead to a region characterized by reduced wind speed and increased turbulence. We observe these effects through the PL and CW lidar-estimated wind speed, turbulence, and shear exponent in Fig.

The influence of wakes on the lidar-estimated mean wind speed is shown in Fig.

We compare lidar-measured

The estimated shear exponent through the PL and CW lidar for free and wake conditions is shown in Fig.

Comparison of the slope of a linear regression model between lidar-estimated and mast-measured inflow characteristics including mean wind speed

In addition to the wake-induced effects on the average flow properties, turbulence spectral properties are also affected in wake regions. Earlier work on this subject showed a shift of the wake spectrum towards low length scales, compared to the free-wind spectrum, in both wind tunnel and field experiments

Based on these findings, we extract the turbulence spectra parameters of the Mann model, with focus on the length scale

The 10 min time series of radial velocity are classified into free-, partial-, and full-wake situations and the spectra are ensemble-averaged over all conditions within each class. Then, the parameter

The small-scale turbulence generated within wake flows generally leads to a significantly larger broadening of the Doppler spectrum compared to that in the ambient flow

We select around 500 10 min samples for each of the free-, partial-, and full-wake scenarios, which are distributed within the wind speed range 4–14 m s

The comparison of the reconstructed wind field characteristics in partial-wake conditions using PL and CW lidar measurements from all ranges is presented in Fig.

Comparison of the CW and PL lidar 10 min reconstructed wind speed

Same as Fig.

The load validation analysis is conducted on the dataset described in Sect.

coefficient of determination

uncertainty

bias

The

The rain flow counting algorithm is used to compute the 1 Hz damage-equivalent fatigue loads with a Wöhler exponent of

We provide detailed scatter plots of measured and predicted load sensors used in the analysis in Figs.

List of accuracy and uncertainty values for power and extreme load validation procedures. The marker

List of accuracy and uncertainty values for fatigue load validation procedures. The marker

Power production levels are overestimated in the partial wake but underestimated in the full wake by approximately 4 % compared to the free-wind case. Larger

The extreme loads (

The biases of fatigue load predictions in the partial wake, using unfiltered turbulence statistics and

Fatigue loads are found to correlate significantly better when a synthetic turbulent field characterized by small length scales is used (i.e.

We use a first-order polynomial response surface for evaluating the sensitivity of the predictions with respect to input wind variables. We consider

The obtained linear regression coefficients for Power

Regression coefficients of a linear response surface model identifying the sensitivity of wind field parameters to

We analyse the bias and uncertainty of Power

The power prediction uncertainties with respect to mean wind speed in free-, partial-, and full-wake situations are plotted in Fig.

Comparison of bias (solid line) and uncertainty (error band) of

Wind field parameters used as inputs for aeroelastic simulations are derived from PL and CW lidar measurements of the wake field behind an operating wind turbine. Although the two lidars follow different scanning patterns and the wake flow field is strongly inhomogeneous, we find a very good agreement between the PL and CW lidar-estimated horizontal wind speed and filtered turbulence in partial- and full-wake situations. The estimation of the wind veer, yaw error, and shear exponent using nacelle-mounted lidars is prone to a high level of uncertainty and is affected by the scanning patterns. This is demonstrated by the larger scatter between the estimated parameters by the PL and CW lidars in wake compared to free-wind conditions (not shown). However, we demonstrate that the influence of these parameters on the loads and power predictions is minor compared to mean wind speed, turbulence intensity, and length scale.

Although the present work does not focus on details of the performance of the two lidar systems, the findings indicate that the main sources of uncertainty in load predictions are related to flow modelling assumptions. The wind velocity gradient in the wake is characterized by the combined effect of the atmospheric shear and the wake deficit. The former can be explained by a power-law profile, while the latter is often approximated in the far wake by a bivariate Gaussian shape function, whose depth and width depend on ambient conditions and turbine operation regimes

It is well-established that fatigue loads are dominated by turbulence levels. However, to extract turbulence parameters by combining a turbulence model with a model of the spatial radial velocity, averaging of the lidars introduces significant uncertainty under wake conditions. Indeed, filtered turbulence estimates in wakes are 6 %–10 % higher than unfiltered turbulence measures, derived from the Doppler radial velocity spectrum, as shown in Figs.

We demonstrate that improved fatigue load predictions are obtained using unfiltered turbulence measures from the Doppler radial velocity spectrum. However, the estimation of

The influence of wake effects on power and load levels depends on the wind farm layout, ambient wind speed and turbulence, and atmospheric stratification, among others. The current state-of-the-art approach to predict wake flows and their influence on wind turbine operations relies on engineering-like wake models

We demonstrated a procedure for carrying out load validation in partial- and full-wake conditions using measurements from two types of forward-looking nacelle lidars: a pulsed- and continuous-wave system. The suggested procedure characterized wake-induced effects by means of lidar-reconstructed wind field parameters commonly used as input for load simulations, without applying wake deficit models.

We considered the uncertainty of lidar-based load predictions against wind turbine on-board sensors in free-wind conditions as the reference case. Hence, we quantified the uncertainty of lidar-based load predictions against sensor data in wake conditions, and we compared it to uncertainty of the free-wind case. The reconstructed mean wind speed, turbulence intensity, and turbulence length scale in wake conditions were found to be the most influential parameters on the predictions.

Power production levels under wake conditions were strongly driven by the reconstructed wind speed at hub height, whereas turbulence intensity as well as turbulence length scales had negligible effects on those levels. Power predictions were overestimated in partial-wake conditions but underestimated in full-wake conditions by approximately 4 % compared to on-board sensors, while free-wind conditions were unbiased.

Fatigue loads were affected by turbulence characteristics inside the wake. The use of a spectral velocity tensor model to derive turbulence parameters introduced significant uncertainty under wake conditions. The tower-bottom and blade-root bending moment predictions were overestimated by 21 % in full-wake conditions using filtered turbulence measures and turbulence length scales typical of free-wind conditions. The bias was reduced to 11 % using unfiltered turbulence measures derived from the ensemble-average Doppler radial velocity spectrum.

Overall, the measured and predicted fatigue and extreme loads were found to correlate significantly better when a synthetic turbulent field characterized by a low turbulence length scale was used. Furthermore, simulations with low turbulence length scales led to an underestimation of blade-root fatigue load predictions by 4 % compared to on-board sensors, while free-wind situations were unbiased. However, estimating turbulence characteristics under wake conditions using measurements from nacelle-mounted lidars was prone to a high level of uncertainty due to probe volume effects and flow modelling assumptions.

The present work demonstrated the applicability of nacelle-mounted lidar measurements to extend load and power validations under wake conditions and highlighted the main challenges. Further investigation is necessary to verify that the observed uncertainty of predictions is comparable with results using state-of-the-art wake models recommended by the IEC standard. Future research should apply a wind deficit model that accounts for the combined effect of atmospheric shear and wake deficit and quantify the uncertainty of resulting power and load predictions.

Schematic view of the measurement patterns of nacelle-mounted lidars: CW lidar

The wake detection algorithm (see Sect.

Scatter plots of the normalized measured and predicted power mean realizations used in the analysis.

Scatter plots of the normalized measured and predicted extreme fore–aft tower bottom bending moment realizations used in the analysis.

Scatter plots of the normalized measured and predicted extreme flapwise bending moment at the blade-root realizations used in the analysis.

Scatter plots of the normalized measured and predicted fatigue fore–aft tower bottom bending moment realizations used in the analysis.

Scatter plots of the normalized measured and predicted fatigue flapwise bending moment at the blade-root realizations used in the analysis.

Turbine data are not publicly available because there is a non-disclosure agreement between the partners in the UniTTe project. Lidar and mast data can be requested from Rozenn Wagner at DTU Wind Energy (rozn@dtu.dk).

DC, ND, and AP participated in the conception and design of the work. DC conducted the data analysis, carried out aeroelastic simulations, and wrote the draft manuscript. ND and AP contributed with the acquisition of the dataset, 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.

This article is part of the special issue “Wind Energy Science Conference 2019”. It is a result of the Wind Energy Science Conference 2019, Cork, Ireland, 17–20 June 2019.

Special thanks to Rozenn Wagner for making the NKE dataset available for our study. Thanks to the lidar manufacturers from Avent and Zephir for providing their systems. Thanks to Vattenfall and Siemens Gamesa Renewable Energy for providing the site and turbine to conduct the measurement campaign.

This paper was edited by Julie Lundquist and reviewed by two anonymous referees.