In recent years lidar technology found its way into wind energy for resource assessment and control. For both fields of application it is crucial to reconstruct the wind field from the limited information provided by a lidar system. For lidar assisted wind turbine control model based wind field reconstruction is used to obtain signals from wind characteristics such as wind speed, direction and shears in a high temporal resolution. This work shows how these methods can be used for lidar based wind resource assessment in complex situations, where high accuracy is important, but cannot be archived by conventional technique. The reconstruction is validated for ground based lidar systems with measurement data and for floating lidar systems with detailed simulations

Cheng, Po Wen

Courtney, Mike

Haizmann, Florian

Hofsäß, Martin

Rettenmeier, Andreas

Schlipf, David

Online Publikationen der Universität Stuttgart

MODEL BASED WIND VECTOR FIELD RECONSTRUCTION FROM LIDAR DATA
David Schlipf1, Andreas Rettenmeier1, Florian Haizmann1, Martin Hofsa¨ß1, Mike Courtney2, Po Wen Cheng1
1 Stuttgart Wind Energy (SWE), Universita¨t Stuttgart, Germany
2 DTU Wind Energy, Risø Campus, Denmark
Summary
In recent years lidar technology found its way into wind energy for resource assessment and control. For both fields of application
it is crucial to reconstruct the wind field from the limited information provided by a lidar system. For lidar assisted wind turbine
control model based wind field reconstruction is used to obtain signals from wind characteristics such as wind speed, direction and
shears in a high temporal resolution. This work shows how these methods can be used for lidar based wind resource assessment
in complex situations, where high accuracy is important, but cannot be archived by conventional technique. The reconstruction is
validated for ground based lidar systems with measurement data and for floating lidar systems with detailed simulations.
1. Introduction
Lidar (light detection and ranging) systems for site as-
sessment in flat terrain have been established over the
last years and show good correlation with met masts
based on 10 min averages [1]. However, lidar systems
in complex terrain and offshore on floating platforms
show problems and solving them is still a subject of
current research ([2], [3]). Another field of investiga-
tion is lidar assisted wind turbine control. For this pur-
pose model based approaches are used ([4], [5]) to
calculate signals such as wind speed, direction and
shears. Lidar measurements and the wind field are
modeled and then identified similar to the observer de-
sign method used in control theory. First field tests [6]
show that with these methods nacelle based lidar sys-
tems are able to provide signals with good correlations
in the range of 10 s, which can be used in real time to
improve collective pitch control.
This paper examines the extension of the model based
wind field reconstruction for ground based and floating
lidar systems. The conventional reconstruction meth-
ods used by commercial lidar systems also use an in-
ternal wind model (homogeneous flow). Therefore, the
intention of this work is not to propose a totally new ap-
proach, but provide a system theoretical view on wind
reconstruction which can be useful to improve the lidar
measurements in situations, where the conventional
technique fails.
2. Basic Idea
The basic idea of model based wind field reconstruc-
tion is to retrieve useful information on the wind from
the lidar measurements depending on the application.
But this system theoretical view also gives a frame-
work to evaluate and optimize the level and the relia-
bility of the reconstructed wind information, which will
be explained in this section.
A lidar system can be regarded in a system theoreti-
cal way (see Figure 1): All known settings such as the
scan trajectory can be considered as inputs to the sys-
tem. All unknown influences to the measurements are
the disturbances and the measurements themselves
are the outputs of the system. In system theory [7] a
disturbance observer can be used to reconstruct the
disturbances from the system in- and outputs, if ob-
servability is given. Robustness evaluates, how well
this is done in the presence of model and measure-
ment uncertainties. Whereas observability and robust-
known
trajectory
measured
wind
measured
line-of-sight
wind speeds
observed
wind
lidar
observer
Figure 1: System theoretical view on lidar measure-
ments and wind field reconstruction.
ness for dynamic systems are complex, for static sys-
tems they can be simplified to the questions, whether
a unique disturbance can be found which caused the
measured output with given input and how sensible it
is for uncertainties. For this purpose, a model of the
system (analytically or CFD) is needed, similar to a
simulation model and the observation can be consid-
ered to be inverse to a simulation.
A lidar located in [x0 y0 z0] measuring in point i can be
simulated by
vlos,i = lxiui + lyivi + lziwi, (1)
which is a projection of the local wind vector [ui vi wi]
and the normalized vector of the laser beam focusing
in the point [xi yi zi] with a focus length fi:

lxilyi
lzi

 = 1
fi

xi − x0yi − y0
zi − z0

 . (2)
Since there is only one equation for three unknowns, it
is impossible to reconstruct the local wind vector from
vlos,i. Observability can be restored by changing the
wind model, e.g. it can be assumed, that the wind vec-
tor in 3 measurement points is the same, which yields
3 equations for 3 unknowns. The wind model has to be
chosen according to the application and the quality of
the results depends on the validity of the model. In the
following sections this will be illustrated by the appli-
cation of this basic idea to ground based and floating
lidar systems.
1
xy
z
xL
yL
zL
Figure 2: Measurement campaign at Risø Campus.
The wind vector in the center (cross) is reconstructed
using the measurement in the points marked with gray
dots for 3.1 or inside the circles for 3.2.
3. Application to Ground Based Lidars
In this first example a scanning lidar system [8] was
installed at the Risø Campus tilted by ΘL = 25 deg,
scanning the wind circulating around a met mast, see
Figure 2, with a 3x3 grid trajectory on 5 horizon-
tal planes within 2 s. The center points of the third
focus distance were located close to the ultrasonic
anemometers installed on the met mast. For the fol-
lowing investigations all data sets are used, including
low wind speeds and wind directions orthogonal to the
main measurement direction.
3.1. Reconstruction in Flat Terrain
If the tilt angle is known, the wind can be reconstructed
in the [x y z] coordinate system, assuming that the
wind is homogeneous in planes parallel to the ground.
Furthermore, it is assumed that the vertical wind w
can be neglected. This simple wind model can be
combined with the simple lidar measurement model
(1) and the line-of-sight wind speeds of the two points
next to the center anemometer could be simulated by

vlos,1:
vlos,n


︸ ︷︷ ︸
m
=


x1
f1
y1
f1
z1
f1
: : :
xn
fn
yn
fn
zn
fn


︸ ︷︷ ︸
A

uv
w


︸ ︷︷ ︸
s
. (3)
In the 2D case of real measurements the wind can be
reconstructed simply by a matrix inversion
[
u
v
]
= A−1
[
vlos,1
vlos,2
]
. (4)
This simple example shows why observations can be
considered to be inverse to simulations and that cir-
cular or arc scans normally used for lidar measure-
ments are not necessary. Figure 3 depicts better cor-
relation with the sonic anemometer on the met mast
for u compared to v. This is due to the higher val-
ues in the second line of A−1 and thus measurement
errors in the line-of-sight wind speeds have more ef-
fect on v. An appropriate measure for robustness can
be defined in the following way: The condition num-
ber of A describes the worst case factor which trans-
fers relative errors from measurement vector m to the
searched vector s. This approach can be used to opti-
mize the setup of lidar measurements: in this case the
condition number could have been reduced from 5.23
to 1, by approaching the lidar to the met mast, setting
x1 = x2 = y1 = −y2.
3.2. Reconstruction in Complex Terrain
The investigation above used the knowledge of the tilt
angle ΘL and assumed that the flow is parallel to the
ground. In complex terrain this assumption is not al-
ways useful: e.g. the wind will be parallel to a linear
slope at lower heights, but parallel to the surface of
the earth at higher heights. Due to the vertical shear
the results of conventional reconstruction methods will
change for the worse.
In a further investigation the knowledge of the tilt an-
gle is not used and the wind is reconstructed in the
[xL yL zL] coordinate system, by including the verti-
cal wind shear in the wind model. Using more than
one focus distance to distinguish between shears and
inflow angles was proposed in [4] and tested in simu-
lations in [5], ignoring the drift of the shear due to the
flow angle. Therefore, the five parameter model from
[4] is modified. First, the wind measured in point i is
defined as
uWi = v0 + δHyWi + δV zWi, (5)
where v0 is the wind speed in the origin and δV the
vertical and δH the horizontal shear. The wind coor-
dinates [xWi yWi zWi] can be transformed to the lidar
coordinate system by a rotation of the horizontal and
vertical inflow angle, αH and αV . With a given set
of v0, αH , αV , δH , δV the coordinates of the measure-
ments can be transformed to the wind coordinates and
the line-of-sight wind speed can be simulated by
vlos,i =
xWi
fi
uWi. (6)
This simulation model again can be used to estimate
the five parameters using the measured vlos,i. A nu-
merical inversion for the nonlinear equations can be
achieved by solving the least-squares minimization
problem
min
v0,αH ,αV ,δH ,δV
n∑
i=1
(
vlos,i −
xWi
fi
uWi
)
2
, (7)
and the wind vector in lidar coordinates can be cal-
culated with (5) and the inverse transformation. The
linear model (3) which only accounts for the sloped
inflow and the nonlinear model neglecting δH are ap-
plied to the data using n = 12 points (see Figure 2),
both using the least squares method. The coefficient
of determination can be improved from R2 = 0.666 to
0.943 for the w component. The results from Figure 3
show, that it is possible to enhance the measurement
of the 3D wind vector in the presence of vertical shear,
but it is necessary to investigate under which condi-
tions observability is given and how higher robustness
can be obtained.
2
wL [m/s]
0.962 wL - 0.236 m/s
R2 = 0.943
vL [m/s]
0.929 vL + 0.019 m/s
R2 = 0.971
uL [m/s]
0.986 uL + 0.030 m/s
R2 = 0.998
vL [m/s]
0.933 vL + 0.043 m/s
R2 = 0.975
u
S
/
v
S
/
w
S
[m
/s
]
uL [m/s]
1.000 uL + 0.006 m/s
R2 = 0.998
−10 0 10−10 0 10−10 0 10−10 0 10−10 0 10
−10
0
10
Figure 3: Regression between lidar and sonic anemometer for the linear (left) and the nonlinear model (right).
4. Application to Floating Lidars
Floating lidars are a promising option to replace ex-
pensive floating met masts for the evaluation of off-
shore wind resources. The wave motion disturbs the
measurement, which is why several attempts have
been made to compensate the effect either by stabi-
lization of the floating platform with active or passive
hardware solutions or by software solutions [3].
Here, a software solution is proposed, which uses the
model based wind field reconstruction approach. For
this purpose, the floating lidar is first simulated.
The wave height η is according to the Airy wave the-
ory:
η(x, t) =
H
2
cos(kx− ωt), (8)
where H is the wave peak-to-peak amplitude, k the
angular wavenumber and ω = 2pi
Tp
the angular fre-
quency, depending on the wave period Tp. For deep
water, wavenumber and frequency are connected by
the acceleration due to gravity g = ω2
k
. For this inves-
tigation Tp = 5 s and H = 4 m are chosen.
In a simplified simulation it is assumed that the floating
platform follows the wave surface (z0 = η) and is only
able to change its vertical position (x0 = y0 = 0 m),
resulting in two degrees of freedom (DOF) out of six.
Hence, for the pitch angle ΘL (rotation around y axis)
of the floating lidar following the wave surface it holds:
tan(ΘL(x, t)) = −
Hk
2
sin(kx− ωt). (9)
To simulate the measurement of the floating lidar sys-
tem, the lidar coordinates have to be transformed to
the inertial system:

xy
z

 = Tpitch(ΘL)

xLyL
zL

+

x0y0
z0

 . (10)
With a hydrodynamic simulation the missing transla-
tional and rotational degrees of freedom can be con-
sidered in a similar way.
For this investigation a continuous-wave lidar is sim-
ulated, focusing in zL = 100 m and measuring in 50
points per second on a circular scan with a half open-
ing angle of 30 deg. Figure 4 shows the measurement
z
[m
]
x [m]
−100 −50 0 50 100
80
100
120
Figure 4: Path of the focus point due to waves.
path of the focus point during one wave period, us-
ing (10). By scanning a three dimensional wind field
(u, v, w over t, y, z) and using Taylor’s frozen turbu-
lence hypothesis (connecting x and t), the line-of-sight
wind speeds can be calculated with (1).
4.1. Constant Wind
In the first simulation a constant wind of u = 10 m/s
at 100 m and a vertical shear of δV = 0.05 1/s is
used. Conventional VAD technique assumes the 3D
wind vector to be constant over the last full circle and
uses the least squares method to fit the line-of-sight
wind speeds to a sinus curve, which for a circular scan
is mathematically equivalent to using (3). Figure 5
shows, that the conventional wind reconstruction has
a periodic error, leading to an underestimation of 6%.
This description of the VAD technique in coordinates
rather than in trigonometry shows the problem and
guides to a solution: conventional wind reconstruction
uses the non-transformed lidar coordinates and thus is
not inverse to the simulation and not able to find a cor-
rect solution (see Figure 5). Furthermore, due to the
non-linearity of the movement, more measurements
are done below 100 m (see Figure 4). Therefore, the
nonlinear model (5) with the wind speed v0, the ver-
tical shear δV and the wind direction αH is used for
the reconstruction. Furthermore, it is assumed, that
in a perfect case the inclination ΘL and the heave z0
can be measured, to correct the lidar coordinates and
in the more realistic case, that only ΘL can be mea-
sured. Figure 5 depicts that in the perfect case there
is no error, due to the perfect inversion. If only ΘL can
be measured, there is a periodic, zero-mean error.
3
u
[m
/s
]
time [s]
5 10 15
8
9
10
11
12
Figure 5: Reconstruction of constant wind speed:
common technique (dark gray); nonlinear model with
inclination information (light gray) and additional heave
information (black).
u
[m
/s
]
time [s]
40 45 50
8
9
10
11
12
Figure 6: Reconstruction of turbulent wind speed:
common technique (dark gray); nonlinear model with
inclination information (light gray) and fixed lidar
(black).
4.2. Turbulent Wind
In a second simulation a turbulent wind field with a
mean wind of 10 m/s, a turbulence intensity of 21%
and a IEC-conform shear for offshore conditions is
used. Furthermore, a continous wave weighting func-
tion [9] is applied. As a reference the wind field is also
scanned with no waves. In Figure 6 it can be seen that
the conventional reconstruction still has a non-zero-
mean error (−2.98% over the 10 min simulation), while
the model based reconstruction methods are closer to
the fixed lidar independend from whether the heave in-
formation is considered or not. In total they only have
an error of 0.05% and 0.04%.
5. Conclusion
In this work a system-theoretical view on wind field re-
construction for site assessment based on lidar mea-
surements is given. Conventional technique uses the
same wind model in all situations, which causes prob-
lems in complex terrain or on floating platforms, al-
though detailed simulation models exist. These mod-
els can be used for wind reconstruction, if they can be
inverted with a unique solution.
The methods are first evaluated with real measure-
ments for a ground based lidar: By including a more
detailed model, the reconstruction of the wind vector
can be significantly improved. Secondly, the model
based approach is applied to floating lidar simulations:
By including the inclination information and the vertical
shear into the model, the measurement error caused
by the motion can be compensated.
Acknowledgment
Thanks to all persons from DTU Risø Campus and
SWE involved in the campaign. Part of this research
is funded by the German Federal Ministry for the En-
vironment, Nature Conservation and Nuclear Safety
(BMU) in the framework of the German joint research
project “LIDAR II” and “LIDAR complex”.
References
[1] Clifton, A., Elliott, D., and Courtney, M., “Recom-
mended practices for remote sensing for wind en-
ergy applications,” Tech. rep., 2012.
[2] Bradley, S., Perrott, Y., Behrens, P., and Oldroyd,
A., “Corrections for Wind-Speed Errors from So-
dar and Lidar in Complex Terrain,” Boundary-Layer
Meteorology , Vol. 143, 2012, pp. 37–48.
[3] Gottschall, J., Lilov, H., Wolken-Mo¨hlmann, G.,
and Lange, B., “Lidars on floating offshore plat-
forms,” EWEA, Copenhagen, Denmark, 2012.
[4] Schlipf, D., Kapp, S., Anger, J., Bischoff, O.,
Hofsa¨ß, M., Rettenmeier, A., Smolka, U., and
Ku¨hn, M., “Prospects of Optimization of Energy
Production by LiDAR Assisted Control of Wind Tur-
bines,” EWEA, Brussels, Belgium, 2011.
[5] Kapp, S. and Ku¨hn, M., “A Five-Parameter Wind
Field Estimation Method Based on Spherical Up-
wind Lidar Measurements,” TORQUE , Oldenburg,
Germany, 2012.
[6] Schlipf, D., Fleming, P., Haizmann, F., Scholbrock,
A., Hofsa¨ß, M., Wright, A., and Cheng, P. W.,
“Field Testing of Feedforward Collective Pitch Con-
trol on the CART2 Using a Nacelle-Based Lidar
Scanner,” TORQUE , Oldenburg, Germany, 2012.
[7] Lunze, J., Regelungstechnik 2, Springer, Berlin,
Germany, 2010.
[8] Rettenmeier, A., Bischoff, O., Hofsa¨ß, M., Schlipf,
D., Trujillo, J. J., and Ku¨hn, M., “Wind field analy-
ses using a nacelle-based LIDAR system,” EWEC,
Warsaw, Poland, 2010.
[9] Simley, E., Pao, L. Y., Frehlich, R., Jonkman, B.,
and Kelley, N., “Analysis of Wind Speed Measure-
ments using Continuous Wave LIDAR for Wind
Turbine Control,” AIAA, Orlando, USA, 2011.
4


Model based wind vector field reconstruction from lidar data

http://elib.uni-stuttgart.de/bitstream/11682/8153/1/SchlipfEtAl_DEWEK2012_MODEL_BASED_WIND_VECTOR_FIELD_RECONSTRUCTION_FROM_LIDAR_DATA.pdf

Model based wind vector field reconstruction from lidar data

Abstract

Similar works

Full text

Available Versions

Online Publikationen der Universität Stuttgart