Long-range Doppler wind lidars are applied more and more for high-resolution areal measurements in and around wind farms.
Proper alignment, or at least knowledge on how the systems are aligned, is of great relevance here. The paper describes in detail two methods that allow a very accurate alignment of a long-range scanning lidar without the use of extra equipment or sensors.
The well-known so-called
Scanning long-range Doppler wind lidar devices play an increasingly important role in the assessment of wind conditions
The wind field in the lowest part of the (marine) boundary layer is by nature inhomogeneous. Flow complexity is exacerbated around and inside wind farms. For wind energy applications the characterization of the wind conditions has to be performed with a spatial accuracy of some metres. Therefore, an exact positioning and orientation of the measuring device during a measurement campaign is very important. This is a major challenge for remote sensing devices, such as lidars, since even small inclination errors can lead to large deviations, e.g. in the resulting measurement height. To give an example, an error of 0.25
The position of a lidar device can be assessed with an internal GPS or by surveying methods with sufficient accuracy. However, the orientation of the system, which is more critical, is typically determined with two sensors with unknown (arguably insufficient) accuracy. The full orientation in three-dimensional space is given by three rotation angles, namely, bearing, pitch and roll. The bearing represents the deviation from north on the horizontal plane and is measured by a compass; as synonyms for this we also use the terms “northing” and “orientation” in this paper. Pitch and roll, which mainly affect the elevation of the laser beam, are measured by an internal inclinometer or a level spirit. To our knowledge, lidar manufacturers do not supply any calibration protocol of such sensors. Therefore, in a campaign they can only be used for rough levelling and must be complemented by more accurate measurements.
Doppler wind lidars are able to detect the backscatter of the laser beam from aerosols. Therefore, measurements against hard targets result in very high carrier-to-noise ratios (CNRs) in the detected signal. This phenomenon can be utilized to determine the distance of a hard target from the lidar and its direction with respect to the scanner orientation of the lidar, i.e. its line of sight.
An established technique to determine the positioning and the orientation of the device is the so-called hard targeting (HT). This technique can be applied onshore, as well as offshore. It uses existing hard targets with known positions like met masts, light houses or wind turbine towers for north orientation.
In an offshore wind farm setting it is difficult to get hard targets with a fixed height. From a lidar perspective, wind turbines experience a change in height due to the two main moving components, nacelle and rotor blades.
This makes scanning set-up and data analysis very difficult for the estimation of the levelling of the device.
To overcome this,
For HT no commonly used method has been established so far; in most cases researchers use individual estimations. The CNR mapper is not fully compatible with all lidar software programmes. Furthermore, at offshore sites often only wind turbines are available as hard targets, which do not provide a defined stationary object with a known height due to the rotor and yaw movements.
Knowing the levelling of the device becomes particularly relevant when a lidar is installed on a moving base, as discussed previously in
With the three concepts introduced, a framework for accurately assessing the northing and levelling of scanning lidar equipment installed on elevated offshore structures can be achieved.
Therefore, the goal of our work is to present the concepts, their implementation and validation in a real offshore wind farm environment. The paper is structured following the three objectives:
The first is the determination of the accurate northing and positioning of a lidar based on measurements with the device. This is achieved with the help of hard targeting (HT). This method is not limited to being used only offshore. The second is the precise measurement of the inclination of an offshore-installed lidar using sea surface levelling (SSL). This method and extension are explained so that device-specific parameters can be better considered.
The third is the estimation of the live roll and pitch angles of a lidar installed on the transition piece of a wind turbine based on operational measurements of the wind turbine using a platform tilt model (PTM).
The code and measurement data developed and used in this study are available for download in
The three methods of HT, SSL and the PTM involve several steps, outlined in Fig.
Overview of the procedure of the methods. In orange are the input devices. HT is shown in grey, SSL in blue and PTM in green. The variables are explained in the following sections.
The grey boxes represent the HT, which is described in more detail in Sect.
HT is a method to determine an accurate orientation and positioning of the lidar based on fixed objects in the vicinity whose positions are known. The method is outlined by the grey boxes in Fig.
The lidar measures information about the quality of the signal in the form of the CNR
Figure
Example of the measured CNR over the range for a hard target scan for a single beam (orange) compared to the median for all azimuth angles (blue). The black horizontal line presents the 5 dB threshold.
In a wind farm, it makes sense to use the towers of the other turbines as targets for the hard target scans, as we did in the case presented here. The turbine locations are given in a Cartesian coordinate system and are denoted by
If the resolution of the scan is high enough, a solid object, such as the tower of a wind turbine, is represented by a cluster of measurement points, which meet the criterion from Eq. (
In the next step, we are constructing an optimization which minimizes the distances of the identified hard targets to the known locations by adjusting the three parameters
The cost function is defined as follows:
The cost function calculates the quadratic Euclidean distances of the identified hard targets to all known locations of the turbines, chooses the turbine closest to the respective hard target and sums up all the squares of the closest distances.
We can now formulate the optimization problem as follows:
This optimization can be solved numerically quite easily. We used the Nelder–Mead algorithm
SSL is a method that uses the water surface to estimate the levelling of the lidar. An overview is given in Fig.
For the SSL we measure the distance from the scanner head to the sea surface for different azimuth angles by the use of a PPI scan with a negative elevation. In our case we set the elevation to
Schematic representation of the sea surface levelling scan from the transition piece platform of a turbine at the Global Tech I wind farm.
We assume that the sea surface is a flat and horizontal area, neglecting the curvature of the earth, and we interpret waves as measurement noise.
The shape of the intersection between this scan and the sea surface is a conic section with an azimuthal range of less than 360
At the point where the laser hits the sea surface, the water absorbs the infrared light and the CNR signal drops significantly. This drop does not occur in the form of a step since the lidar cumulates measurements over a probe volume; i.e. the measurement for a certain target range consists of a weighted average of measurements around the target distance due to the length and shape of the laser pulses.
Figure
Example of a measured CNR over the range for one azimuth angle. The black graph is an inverse sigmoid function fitted to the CNR values, and the vertical blue line is in the sigmoid's midpoint, representing the estimated distance to the sea surface.
The figure also shows an inverse sigmoid function, which was fitted to the CNR values, in black, and the midpoint of the sigmoid function is shown by the vertical line in blue, which is our estimate for the sea surface distance. For the sigmoid function we use a logistic function given by
This function is defined over the range
For the estimation of the distance to the sea surface we have chosen this value because at this distance the signal is partially weakened, which represents a partial absorption of the probe volume. This assumption is considered reasonable since the height of the lidar device above the still water level calculated by trigonometrical relations corresponds well with the actual height above the sea surface. Depending on the lidar instrument used and the settings, it is possible that the shape of the CNR curve will look different. In our study, the inverse sigmoid fit was found to give a robust estimate of the distance to the water surface; for other systems it may be possible that the fit function needs to be adjusted.
We only considered scans in which the CNR value exceeded a defined threshold. If the maximum CNR value for a single beam was below
To estimate the levelling of the lidar with respect to the sea surface, we built a model to calculate the distances for every azimuth angle to the surface plane for given roll and pitch angles and a height above the surface.
Figure
Coordinate system of the lidar with the clockwise rotations around the axes and a compass rose.
Now we can define the building blocks for modelling the laser beam of the lidar.
Without any rotations the laser beam
We define the pitch
Modelled distances to the sea surface for an example set of parameters (
In addition, we can add the displacement vector
We want to estimate the range
When we include the non-trivial displacement
Given the set of parameters
Figure
To estimate the levelling of the lidar from the measured sea surface levelling scan, we have to first determine the ranges
To do this we build an optimization problem, which minimizes the deviation of the model to the measurement data. For the cost-function we used the maximum likelihood method by utilizing the Lorentz distribution.
The Lorentz distribution does not weight outliers as strongly as the commonly used Gaussian distribution, i.e. the least-squares method.
The cost function is
The set
Analogous to the previous optimization problem, we again used the Nelder–Mead method
The PTM estimates the correlation between the turbine operation and the bending of the transition piece platform. The procedure is summarized in the green boxes in Fig.
We observed that the platform with the lidar was tilted, depending on the turbine operation. To consider this we assume in accordance with the elastic bending of a cantilever beam a linear rotational spring stiffness
Combining Eqs. (
For most wind turbines the thrust and power coefficient can be approximated as constant in the variable operational speed range which corresponds to the lower to medium partial load range. Beyond and especially above the rated wind speed the dependency on the wind speed has to be considered since the thrust loading is reduced, while the rated power is maintained.
In the following we consider only the variable operational speed range, typically extending between 3.5 and 9 to 11 m s
To define the tilt of the platform we are using the rotational matrices we defined in Sect.
The negative tilt angle
The matrix
The operator
Again, we solved this optimization with the Nelder–Mead algorithm
In the last step we want to utilize the obtained parameters
The objective is to solve for
This can be reformulated to
Now we can derive the dynamic roll and pitch angles from the SCADA data.
The three methods presented in this paper refer to a measurement campaign which was carried out from August 2018 until June 2019 in the German North Sea with a scanning lidar positioned on the platform of the transition piece of a wind turbine in the offshore wind farm Global Tech I (GT I). A more detailed description of the measurement campaign is given in
The offshore wind farm GT I consists of 80 turbines of the type Adwen AD 5-116 with a total nominal power output of 400 MW. It is located in the German North Sea approximately 100 km from the coast.
For the measurement campaign we had knowledge about the coordinates of all turbines, as well as a subset of 1 Hz supervisory control and data acquisition (SCADA) data, including active and reactive power output, nacelle orientation, wind speed, wind direction and turbine status.
The scanning long-range Doppler lidar we used for this investigation is a Leosphere WindCube 200S (serial number WLS200S-024) (see Fig.
Image of the WindCube200S installed on the transition piece of the wind turbine in the offshore wind farm Global Tech I. Picture taken by Stephan Voß.
In the following the results of the HT, the SSL and the PTM are presented for the reference case.
Since the lidar was installed on the platform southwest of the tower of wind turbine GT58, we could not see a large part of the wind farm Global Tech I (GT I) from the lidar. But the turbines north and southeast were visible. When we installed the lidar it was oriented south-southeast. We made a rough estimate for the lidar's uncorrected north orientation of
Figure
Result of the HT. The blue symbols represent the turbine layout. The orange dots are the hard target measurements
For comparison, we applied HT not only to the entire set of detected wind turbines (WTs) but also to the individual WTs (Scenario 1: “individual turbines”), a subset of the various WTs located up to a certain range away from the lidar (Scenario 2: “increasing range”) and a subdivision of the WTs into northern and southern WTs from the lidar (Scenario 3: “north/south”). These three additional scenarios allowed us to observe the sensitivity of the method with respect to the set of available hard targets and their distances.
In the first scenario we applied the HT to the 17 individual turbines which could be detected from the lidar's point of view (see Fig.
In the second scenario, we artificially limited the range of the lidar. We considered six cases in which we increased the range in 1000 m increments from 1000 to 6000 m, with the goal of investigating how the results change with the addition of more hard targets.
Figure
Result of the HT for increasing range (Scenario 2). The blue graph shows the evolution of the
In the third scenario, we divided the hard targets into two groups: those from the lidar to the north and the southern hard targets. The mean value for the alignment from these two groups is
In Table
Results of the HT for three scenarios.
In the first step, we determined the intersections of the laser beam of the lidar with the sea surface for the sea surface levelling scans according to Sect.
Figure
Example fitting of the modelled sea surface distances to the measured distances for a complete SSL scan.
We repeated this procedure for every available SSL scan from our measurement campaign (see Sect.
Figures
Height above sea level determined during 3 d of continuous measurements. The blue dots represent the height of the lidar's scanning head above the sea surface as measured by SSL for a contiguous subset of the SSL scan data. Offset-corrected sea surface height from the NEMO model provided by the EU Copernicus Marine Service is shown in red.
Roll
To easily process the results of the SSL along with the SCADA data needed to determine the platform tilt, we resampled the data to 5 min time steps using 5 min averages. With this we have a joined set of 1142 measurements.
After fitting the PTM to the measurements we achieved the following results for the three parameters:
The parameter
In Fig.
Comparison of the measured tilt angle
The maximum modelled tilt angle is around
In Fig.
Comparison of the modelled tilt angle
In Fig.
Table
The hard targeting scans and sea surface levelling scans are very valuable measurements for an offshore lidar campaign. They do not require additional equipment and only take a rather small amount of time but can help improve the accuracy of the measurement campaign significantly. The knowledge of the correct orientation and position of the lidar is essential for measurement campaigns in which local effects, e.g. turbine wake and induction zone, are analysed. Information about the levelling of the device is useful for all measurements but especially for long-range measurements since the error in measurement height due to a misalignment scales linearly with the range.
HT to determine the north alignment and position of a long-range lidar is a commonly used technique that probably evolved from cross bearing in navigation and is based on standard geometry. Nevertheless, we have not found a consistent description of the method in the literature that relates to the calibration of long-range Doppler wind lidars and can be easily applied in a wind farm. Therefore, we wanted to dedicate a small part of this paper to the presentation of a simple method that can accurately determine the position of the lidar in addition to the north orientation. In our study we applied the method to a subset of the available hard targets in three different scenarios to investigate the sensitivity of the method towards the amount of suitable data.
In Scenario 1 we applied the HT to the 17 individual wind turbines we could detect in the hard target scans and computed mean and standard deviation of the orientation and positioning. The results show that the method is not very accurate when applied to individual turbines. Especially in the case of positioning, there are larger deviations in the results. This is due to the fact that the detection of individual hard targets is not very accurate because of probe length averaging. In addition, only the coordinates corresponding to the centre of the tower were available for the individual turbines. Unfortunately, no statement could be made about the accuracy of these coordinates.
Comparison of the roll
Error statistics of the modelled roll and pitch angles to the measured roll and pitch angles.
In Scenario 2, the method was applied to hard targets within a certain measurement range. The range was successively increased until all available data were included. This example demonstrates how adding additional hard targets ensures that the results for positioning and alignment each converge to a constant value.
In the third scenario, the set of available hard targets was divided into the northern and southern turbines when viewed from the lidar. The results show that the orientation is determined almost identically for both subsets, but there are differences of several metres in the positioning. This is due to the fact that for both subsets the vectors to the respective hard targets are almost linearly dependent on each other. For a more precise positioning, reference points are needed which are located in as different directions as possible (ideally orthogonal to each other).
Overall, the accuracy of the determination of position and orientation by the method presented here increases with the number of hard targets detected. The results from Scenario 2 show that especially the determination of the orientation has a very high accuracy.
In connection with hard target scans, it is recommended to investigate the pointing accuracy of the lidar's scanner unit as discussed in
The SSL is a rather new technique, which was first introduced in
Figure
A large source of uncertainty is the determination of the distance to the sea surface (Sect.
Nevertheless, the results of the SSL are considered very reliable. This is supported by the fact that successive measurements for levelling lead to very similar results, which can be seen in Fig.
SSL allows us to determine the levelling of a lidar. Thereby larger inclinations can be identified and corrected at the beginning of a measurement campaign. But even if a correction is not possible for logistic reasons and, as we discovered, dynamic variations of the levelling occur, it is helpful to know the exact orientation of a lidar so that the measurements can be interpreted accordingly, as was done in
The transition piece platform in our measurement campaign was mounted on a tripod with a water depth of about 40 m. Even though the water depth is comparatively large, we would expect that even larger tilt angles can occur at wind turbines that are mounted on a more flexible monopile and probably even larger at floating wind turbines. For nacelle-based lidar measurements the movement of the nacelle is in the order of 1 to 2
Furthermore, it should be explored how information from such sensors can be directly incorporated into the lidar control to dynamically correct the elevation of the scanner head, or whether it is possible to mount the lidar or the scanner of the lidar in a Cardan suspension.
The objectives of this paper were to present two methods for accurately estimating the position, orientation and levelling of a long-range lidar in an offshore environment and in addition to introduce a model that can estimate turbine-induced inclinations from turbine operating data. This information can be used to correct the position data of the measuring points of ongoing lidar measurements. On the one hand, a more precise orientation of the lidar helps to transfer the measurement points more accurately into the global coordinate system, and, on the other hand, it provides a better estimate of the actual height at which the wind speed was measured by a lidar. This helps to reduce uncertainties in long-range-scanning lidar data analysis.
HT, SSL and the PTM are described in detail and applied to data from an offshore measurement campaign.
For HT, we have shown that the presented method takes advantage of detecting multiple hard targets in different directions, thereby increasing the accuracy.
While we assume an error of about 1 m for the positioning of the instrument, the northing results in consistent values, which indicate a very high accuracy (see Table
The HT is not limited to being used offshore and should be applied to every long-range lidar campaign to estimate the orientation and positioning at the start of a measurement campaign. While the PTM presented here was developed specifically for use of a lidar on the platform of a transition piece, it can be extended to other offshore sites where tilt is related to the thrust of the wind turbine.
In general, knowledge about the positioning, orientation and levelling of remote sensing equipment is crucial for successful measurements at longer distances. We therefore consider it very important to perform calibration measurements as proposed in this paper during each measurement campaign.
The code and scripts developed in this research are published at the following:
The data used for the evaluation can be used as an illustration of the code and can be found here:
AR initiated and directed the research, developed the methods, prepared the computational scripts, analysed the measured data, was heavily involved in funding acquisition and research discussion, prepared the figures, and was lead author of the article. JS assisted with data provision and data processing, as well as derivation of the methods, and provided extensive feedback in several reviews. FT assisted in the development of the computational scripts, verified the calculations, provided support in countless discussions and gave extensive feedback in several interactions. JJTQ supported with his rich experience of lidar systems, was instrumental in drafting the research question and helped with extensive review. MK was instrumental in acquiring funding, supervised the research, and provided support with valuable comments and good advice.
The contact author has declared that neither they nor their co-authors have any competing interests.
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
We acknowledge the wind farm operator Global Tech I Offshore Wind GmbH for providing SCADA data, as well as their support of the work and the measurement campaign.
Thanks to EU Copernicus Marine Service Information for providing sea surface height data from the NEMO model used in Fig.
We performed the lidar measurements and parts of the work in the framework of the research projects “OWP Control” (grant no. FKZ 0324131A) and “X-Wakes” (grant no. FKZ 03EE3008D), both funded by the German Federal Ministry for Economic Affairs and Energy on the basis of a decision by the German Bundestag. The work of Frauke Theuer has been supported by the German Federal Environmental Foundation (DBU) (grant no. 20018/582).
This paper was edited by Jakob Mann and reviewed by two anonymous referees.