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PROYECTO FIN DE CARRERA
EVALUATION OF SCANNING STRATEGIES OF A NACELLE MOUNTED
LIDAR FOR INFLOW AND WAKE MEASUREMENTS ON A WIND TURBINE
Valeria Basterra Taramona
MADRID, Septiembre de 2008
UNIVERSIDAD PONTIFICIA COMILLAS ESCUELA TÉCNICA SUPERIOR DE INGENIERÍA (ICAI)
INGENIERO INDUSTRIAL
EVALUACIÓN DE ESTRATEGIAS DE ESCANEO DE UN SISTEMA
LIDAR MONTADO SOBRE LA GÓNDOLA DE UNA TURBINA EÓLICA Autora: Basterra Taramona, Valeria. Directores: Linares Hurtado, José Ignacio; Kühn, Martin.
En colaboración con: Universidad de Stuttgart, Alemania.
RESUMEN DEL PROYECTO La industria eólica vive un momento de auge desde hace varios años y la
investigación a nivel mundial está siendo dirigida a aumentar la eficencia de los
aerogeneradores. Esta mejora del aerogenerador requiere un desarrollo paralelo de
los sistemas de medida del viento. Hoy en día una de las tecnologías de medida más
prometedoras es el LIDAR, un sistema láser capaz de caracterizar el viento
basándose en el efecto Doppler. Los sistemas LIDAR ofrecidos comercialmente han
sido concebidos para la obtención de los perfiles verticales de viento desde el suelo.
Su objetivo es el reemplazo de los mástiles utilizados en las mediciones tradicionales
basadas en anemómetros de copas.
En la Cátedra de Energía Eólica de la Universidad de Stuttgart (SWE) se está
desarrollando una nueva aplicación del sistema en la
cual el dispositivo LIDAR se situa encima de la
góndola para poder así escanear el viento aguas
arriba y abajo (Figura 1). La medida del campo de
viento aguas arriba abre las puertas a estrategias de
control avanzadas, mientras que la medida aguas
abajo permite la verificación de los modelos para
cálculo del efecto de estela, que cobran gran
importancia al tratar de reducir las cargas de los
aerogeneradores que componen un parque. Figura 1: Sistema LIDAR sobre la góndola escaneando el campo de velocidades aguas arriba y abajo.
Un sistema LIDAR Windcube™, desarrollado por la compañía Leosphere® para
mediciones desde el suelo, ha sido adquirido recientemente por SWE. Este obtiene
un vector de viento a diferentes alturas cada cinco segundos, una tasa muy baja
cuando se trata de obtener un campo de velocidades completo para estrategias de
control. Por ello esta nueva aplicación de LIDAR desde la góndola requiere cambios
en su principio de funcionamiento, tanto en el software como en el hardware.
SWE tiene planificadas unas campañas de medida a principios de 2009 en una
turbina de 5MW instalada en el norte de Alemania. Este proyecto tiene como objetivo
proponer adaptaciones del Windcube™ para su nuevo uso y desarrollar una
herramienta de simulación para analizar y optimizar las diferentes variables de
operación derivadas de las adaptaciones. La configuración que lleve a calcular el
campo de velocidades más exacto será entonces recomendado para dichas
campañas.
En la primera parte del proyecto se caracteriza el sistema LIDAR y se proponen
adaptaciones del sistema. Actualmente los puntos de medición (enfoque) del
Windcube™ describen círculos a diferentes alturas sobre el suelo. Esta trayectoria
es generada por medio de un solo prisma que desvía el láser de tal forma que se
describe un cono con eje vertical, pero parece insuficiente para describir un campo
desde la góndola. Para definir curvas más complejas se debe cambiar el sistema
óptico. En este proyecto se recomiendan dos sistemas: los prismas Risley y los
espejos galvanométricos. Las adaptaciones de software suponen un cambio en la
velocidad del aparato y en la frequencia de escaneo. WindcubeTM tiene un láser con
una frequencia fija de 20 KHz y necesita ponderar 10000 espectros para obtener una
mediad del viento, lo que se traduce en una medida de alta precisión pero lenta
obtención. Con el fin de acelerar el proceso se intenta reducir esta cifra
incrementando la frequencia de puntos escaneados por segundo y la precisión del
campo escaneado. La precisión de la medida no se puede simular, por lo que el
óptimo es encontrar la frecuencia de puntos escaneados más baja con la que se
obtengan campos precisos.
En la segunda parte del proyecto se desarrolla WITLIS, herramienta de simulación
del LIDAR escrita en MATLAB. El programa se divide en tres partes: el pre-
procesador, el procesador y el post-procesador. En el pre-procesador se caracteriza
el LIDAR con las diferentes configuraciones. En el procesador se escanea el viento
en los puntos determinados por la trayectoria en un campo de velocidades sintético
generado con Vindsim. En el post-procesador se interpolan los puntos de medida a
la rejilla utilizada por el campo sintético mediante la triangulación de Delaunay para
comparar los dos campos, el calculado con el sintético. Para una comparación más
exacta se calculan dos estadísticos chi-cuadrado para cada configuración, uno
espacial y uno temporal. El estadístico espacial se calcula a partir de los campos
promediados en el tiempo, mientras que para hallar el temporal se necesitan los dos
vectores de velocidades promediados en el espacio. Cuanto menores sean los
estadísticos, más parecidas son las medidas de los dos campos y, en consecuencia,
mejor la configuración utilizada.La comparación entre todas las configuraciones se
realiza en la tercera parte del proyecto, en la que se escoge la más ventajosa y se
recomiendo para un posterior uso en las campanas de medida.
La mejor trayectoria según criterios de exactitud y amplitud del campo escaneado ha
sido la curva de Lissajous definida para parámetros a=3, b=2 y un ángulo de pi/2. Se
han descrito figuras en uno y dos segundos. Los campos definidos con trayectorias
descritas en un segundo son ligeramente más precisos que los que han necesitado
dos segundos por figura. Sin embargo se recomienda la descripción de trayectorias
en dos segundos, ya que conllava a la obtención de medidas más precisas. La
frecuencia de puntos escaneados por segundo que harmoniza mejor precisión del
campo y área interpolada es 13 Hz.
La simulación del efecto de la colisión de los rayos láser contra las palas del
aerogenerador muestra que aproximadamente se pierden el 40% de las medidas.
Este efecto se soluciona doblando la frecuancia de puntos escaneados por segundo.
La corrección de la dirección también ha sido simulada y analizada. Es sistema
LIDAR mide la velocidad sobre el rayo de
visión, por lo que, a menos que el rayo láser
esté alineado con el vector de velocidad, la
medida registrada por LIDAR estará
subestimada. Con el fin de solventar este
progrma se ha supuesto que la velocidad
del viento es perpendicular al rotor las
simulaciones han demostrado que esta
corrección ha reducido los estadísticos
drásticamente. Figura 2: Instantánea definida con la configuración recomendada: curva Lissajous 8 descrita en dos segundos con 26 puntos y corrección de la dirección. El origen de coordenadas coincide con la posición de la rueda del rotor.
Las simulaciones han demostrado que la descripción de curvas es más ventajosa
que la de líneas rectas, lo que llevaría a elegir los prismas Risley como nuevo
aparato óptico, ya que estos tienden a describir curvas. Sin embargo, la restricción
de la velocidad por parte de la frequencia y velocidad aquí propuestas llevan a
sugerir el uso de espejos galvanométricos.
Los resultados obtenidos mediante simulación son muy prometedores, ya que
muestran que hay determinadas configuraciones de las que se derivan campos de
velocidad calculados con errores comparables a los de los anemómetros. Sin
embargo, a este error de interpolación hay que añadir el de la incertidumbre de
medida en sí.
En resumen, tras el estudio realizado en este proyecto se recomienda la descripción
de una figura Lissajous en dos segundos mediante 26 puntos (Figura 2) con espejos
galvanométricos y la corrección de la dirección en la medida. La herramienta de
simulación será utilizada en el proyecto de investigación “Desarrollo de tecnologías
LIDAR para los campos offshore alemanes”.
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EVALUATION OF SCANNING STRATEGIES OF A NACELLE
MOUNTED LIDAR FOR INFLOW AND WAKE MEASUREMENTS ON A
WIND TURBINE
Author: Basterra Taramona, Valeria. Directors: Linares Hurtado, José Ignacio; Kühn, Martin:
In collaboration with: University of Stuttgart, Germany:
SUMMARY There has been a dramatic increase within the developments of the wind industry in
recent years. The continuous improvement of the different elements of the turbine
requires a parallel upgrading of the means to measure the wind.
Nowadays the most promising measurement technology is the LIDAR, a laser that
characterizes the wind based on the Doppler Effect. It was developed primarily to
obtain vertical profiles of the wind vector, but in the Endowed Chair of Wind Energy of
the University of Stuttgart (SWE) a new application of the LIDAR is being developed.
A LIDAR system is mounted on top of the nacelle to measure the in-flow and the
wake (Figure 1). The first one opens the door to a sophisticated control of the turbine,
while the second one verifies the wake models, which are of main importance for
turbine loadings.
Windcube™, a LIDAR system developed by
Leosphere® acquired recently by SWE, obtains a
wind vector every 5 seconds, a very low output
rate if a whole wind field has to be scanned. Thus
this new deployment of the LIDAR entails changes
on its working principle. In this Project all the
different configurations derived from these
changes are simulated in order to find the most
advantageous one. Then it is going to be applied
in the LIDAR system for the measurement
campaigns that are taking place the incoming year
in the north of Germany by the SWE., saving this
way both money and time. Figure 1: LIDAR system on top of the nacelle scanning the wake and the in-flow.
In the first part of the Master Thesis the LIDAR is characterized and hardware and
software adaptations for the new application are suggested. Currently the
Windcube™ describes a cone with a single edge. This system seems insufficient to
describe more complex trajectories. Therefore new optical devices are compared and
analyzed. Finally either the Risley prisms or the galvanometer scanners are
proposed. The software adaptations are mainly two: the time on which a full trajectory
is scanned and the scanned points per second frequency. Windcube™ has a LASER
with a fixed frequency of 20 KHz and needs to average 10000 spectrums to obtain a
wind measurement. This value has to be reduced to increase the scanned points per
second frequency and speed up the process. But the decrease of the averaged
spectrums leads to a parallel decrease of the accuracy of the measurement.
Therefore a minimum scanned points per second frequency that still describes the
wind field accurately is required.
In the second part of the Thesis the simulation tool WITLIS is developed, a program
wrote in MATLAB that simulates the measurements of the LIDAR for the new
proposed configurations. The program is divided in three parts: the pre-processor,
the processor and the post-processor. In the pre-processor the configurations derived
from the software and hardware adaptations are defined. These configurations are
mainly characterized by different scanning trajectories, speed mode and scanned
points per second frequency. In the processor the LIDAR is simulated and the points
defined by the trajectories are scanned from a synthetic wind field, input of the
program generated with Vindsim. In the post-processor the scanned points are
interpolated with the Delaunay triangulation to the grid of the synthetic field. Next the
calculated wind fields are compared with the synthetic wind field from which they
were obtained and a statistical analysis is carried out. For this statistical analysis two
different concepts are handled: the spatial and the temporal error and a chi-square
statistic is calculated for each. The spatial statistic shows in average the relative error
of each point of the grid in the transversal dimension, while the temporal one shows
the average of the relative errors of each snap shot. The lower the statistic is, the
more alike are the measurements. In the third part of the Thesis the different
configurations are compared in order to find the most advantageous one and
recommend it for further use.
The trajectory that shows the best performance is a Lissajous curve defined by a=3,
b=2 and an angle of pi/2 (Figure 2). Despite the lower statistics obtained with the fast
mode, under which a whole trajectory was defined in one second, a slow mode has
been further used and two seconds have been needed to describe a trajectory.
That’s because the advantages for the accuracy of the wind measurement derived
from the slow mode were higher than the lost of accuracy of the whole wind field. The
lower scanned points per second frequency that harmonizes the best way accuracy
of the interpolated wind field and large calculated area is 13 Hz.
The simulation of the effect of the collision against the rotor blades and the nacelle
when pointing in the in-flow direction has shown that it leads to the lost of the 40% of
the shots. But this effect is overcome by doubling the scanned points per second
frequency.
Another situation has been also analyzed, the direction correction. Since the LIDAR
measures in the line of sight, the obtained measurement is always underestimated,
unless the ray is aligned with the wind direction. Therefore a correction of the
direction has been applied and it has been supposed that the direction of the wind is
perpendicular to the rotor of the turbine. The results show that this correction
diminishes considerably the errors.
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Figure 2: Calculated snap shot defined with the recommended configuration, Lissajous curve 8 defined in two seconds with 26 points with correction of the direction. The origin of the axis is the hub.
The simulations have shown that the description of curves is recommendable, what
would lead to choose the Risley as optical device, since it leads to describe curves.
Nevertheless, the suggested frequency and speed mode restrict the speed of the
optical device and, given that the galvanometers present a better speed performance
than the Risley, the galvanometers scanners are suggested
The results obtained through simulation are very promising, since they show that
there are configurations that present a very good performance when scanning a
whole wind field. The errors achieved with the configuration here recommended are
comparable to the uncertainty that anemometers present. Nevertheless the
uncertainty of the measurement itself has to be added to this error due to the
interpolation. In short, the description of a Lissajous figure with a=3 b=2 through 26
scanned points in 2 seconds with galvanometer scanners and the correction of the
direction are here recommended for further measurement campaigns.
Contents
8
Contents
CONTENTS........................................................................................................................................................... 8
1. INTRODUCTION........................................................................................................................................... 10
2. WIND MEASUREMENT TECHNIQUES................................................................................................... 14
2.1. CUP ANEMOMETER ..................................................................................................................................... 14 2.2. ULTRASONIC ANEMOMETER ...................................................................................................................... 15 2.3. SODAR ANEMOMETER.............................................................................................................................. 16 2.4. LASER ANEMOMETER................................................................................................................................. 17
2.4.1. LIDAR Basics .................................................................................................................................... 18 2.5. COMPARISON OF THE DIFFERENT MEASUREMENT DEVICES......................................................................... 22
3. CHARACTERIZATION OF LEOSPHERE................................................................................................ 25
3.1. FUNCTIONAL SPECIFICATIONS AND PERFORMANCE .................................................................................... 26 3.1.1. Output data........................................................................................................................................ 26 3.1.2. Performances..................................................................................................................................... 26
3.2. TECHNICAL SPECIFICATIONS AND TECHNOLOGY ........................................................................................ 28 3.2.1. Emission ............................................................................................................................................ 28 3.2.2. Detection and acquisition.................................................................................................................. 28 3.2.3. Windcube’s hardware........................................................................................................................ 29 3.2.4. Windcube’s software: ........................................................................................................................ 29 3.2.5. Calculation of the resulting wind vector............................................................................................ 30
4. ADAPTATION FOR NACELLE MEASUREMENTS ............................................................................... 31
4.1. PROPOSAL OF HARDWARE ADAPTATIONS OF THE SCANNING MODE ............................................................ 31 4.1.1. Introduction ....................................................................................................................................... 31 4.1.2. Option A: Risley Prims ...................................................................................................................... 32 4.1.3. Option B: Two rotating mirrors ........................................................................................................ 34 4.1.4. Option C: One mirror with 2 DOF.................................................................................................... 35 4.1.5. Option D: Galvanometer Scanner ..................................................................................................... 36 4.1.6. Decision Matrix ................................................................................................................................. 39
4.2. PROPOSAL OF THE SOFTWARE ADAPTATIONS ............................................................................................. 42
5. WITLIS............................................................................................................................................................ 45
5.1. OVERVIEW ................................................................................................................................................. 46 5.2. DEFINITION OF PARAMETERS OF EVALUATION ........................................................................................... 51
5.2.1. Trajectory .......................................................................................................................................... 51 5.2.2. Speed mode........................................................................................................................................ 56 5.2.3. Scanned-points-per-second................................................................................................................ 57
Contents
9
5.2.4. Rotor collision ................................................................................................................................... 57 5.2.5. Correction of line-of-sight wind speed .............................................................................................. 58 5.2.6. Position of LIDAR ............................................................................................................................. 60
5.3. DEVELOPMENT OF THE TRAJECTORIES ....................................................................................................... 63 5.4. WIND SIMULATION ..................................................................................................................................... 68
5.4.1. Characteristics of the Wind ............................................................................................................... 68 5.4.2. Computational simulation of the wind............................................................................................... 71
5.5. WIND FIELD INTERPOLATION...................................................................................................................... 74 5.5.1. General interpolation procedure....................................................................................................... 74 5.5.2. Delaunay triangulation...................................................................................................................... 76
6. EVALUATION OF SCANNING MODES. .................................................................................................. 80
6.1. STATISTICAL ANALYSIS ............................................................................................................................. 81 6.2. MEASUREMENTS ........................................................................................................................................ 83
6.2.1. Measurements of the synthetic wind field .......................................................................................... 84 6.2.2. Measurements of the calculated wind fields. Comparison with the synthetic one. ............................ 85
CONCLUSIONS ............................................................................................................................................... 101
REFERENCES.................................................................................................................................................. 103
APPENDIX A: ECONOMICAL ANALYSIS ................................................................................................ 105
APPENDIX B: PLOTS OF SYNTHETIC FIELD......................................................................................... 108
APPENDIX C: PLOTS OF CALCULATED WIND FIELD FOR DIFFERENT TRAJECTORIES. ...... 109
APPENDIX D: PLOTS OF CALCULATED WIND FIELD WITH CORRECTION OF DIRECTION . 128
APPENDIX E: PLOTS OF CALCULATED WIND FIELD WITH COLLISION..................................... 132
APPENDIX F: PLOTS OF CALCULATED WIND FIELD WITH VARIABLE SPEED MODE ........... 136
APPENDIX G: PLOTS OF CALCULATED WIND FIELD WITH VARIABLE FREQUENCY............ 138
APPENDIX H: PLOTS OF CALCULATED WIND FIELD WITH VARIABLE FREQUENCY UNDER
COLLISION CONDITIONS ........................................................................................................................... 149
Introduction
10
1. Introduction
There has been a surge within the wind industry in the last few years. Every day new
wind parks are projected and governments from all around the word are betting on
this means of creating energy. Nevertheless, at the present time this kind of energy is
in general not profitable without the financial support of the different official
organizations. That’s why engineers are working hard everyday to improve the
efficiency of wind turbines and to reduce costs. It is these aforementioned goals
which are the objective of this project.
At present, there is an increasing need for more reliable and economical wind
measurement technologies.
The most promising technology in this field is the remote sensing of wind speed with
LIDAR (Light Detection And Ranging), an optical remote sensing technology that
measures properties of scattered light to find range and/or other information of a
distant target. Besides its application in the Wind Energy field, LIDAR is also used in
archaeology, geography, geology, geomorphology, seismology, and atmospheric
physics.
Figure 1: Sketch of a ground based wind field measurement with LIDAR system
There are already available LIDAR systems in the market, but they are ground based
(Figure 1) and used for power curve measurements and wind resource assessment.
A LIDAR placed on top of the nacelle could measure the wind fields for wake and
inflow (Figure 2). Currently, there is no way to measure an entire wind field instantly,
Introduction
11
which would have important applications for both inflow and wake measurements.
The measurement of the inflow would open the door to sophisticated control
strategies and to a better definition of the power curve. It would make it possible to
predict the wind field that would then impact the rotor turbine a few seconds later.
The measurement of the wind behind the turbine would verify the wake model, and
with it, the layout of the wind park. It could even be the guide vane of the future.
This new application of LIDAR is being developed at the Endowed Chair of Wind
Energy (SWE) at the Stuttgart University, where a Windcube™ has been recently
acquired. Windcube™ is a LIDAR developed by the French company Leosphere®.
Figure 2: Sketch of wind field measurement with LIDAR on top of the nacelle
This new appliance requires modifications of the standard ground based LIDAR, both
in the hardware and software. The measurement system has to be characterised to
obtain the most accurate wind field. The outlines and objectives of this Master Thesis
are tailored to meet this purpose. Then the most advantageous configuration is
applied in the LIDAR for the measurement campaigns that are taking place the
incoming year (2009) in the north of Germany by the SWE.
After an introduction to the problem and to the existing technology in Chapters 1 and
2 the Leosphere® LIDAR system is characterized in Chapter 3 with respect to its
instrument working principles, signal processing, and data storage.
Optional hardware and software adaptations for wind field measurements from the
nacelle are proposed in Chapter 4. Among all the possible variables, this thesis
evaluates different trajectories, the time needed to describe a whole trajectory, and
Introduction
12
the scanning frequency (scanned points per second). Besides these configurations,
two situations are also considered. The first one refers to the collision and the second
situation has to do with the correction of the wind direction.
The new approach is tailored to provide accurate measurements of inflow and near
wake wind field.
The most important part of the thesis consists of the simulation of the LIDAR for
different setups developed in Chapter 5. To meet this aim algorithms for calculation
of focus point trajectories and estimation of the wind field through interpolation are
developed.
Finally, in Chapter 6 the new measurements approached through simulation are
evaluated and a comparison of the wind fields obtained from synthetic wind scanned
with a selected LIDAR setup with the original synthetic wind field is made.
Conclusions are drawn then about the performance of the particular selected LIDAR
setup.
The resources needed to meet these objectives are mainly computer programs.
WITLIS, the core of the program, is programmed in MATLAB. The inputs of WITLIS,
the three synthetic wind fields, are generated with VINDSIM.
The new application of the LIDAR studied in these pages is going to be tested in a
near shore park in Bremerhaven and in the projected offshore wind park Alpha-
ventus, the first offshore park in Germany.
Alphaventus is going to be situated at 45 Km north from the Borkum Island, in the
North Sea, at depths of 30 meters. Twelve wind turbines are planned to integrate this
park, among them 6 Multibrid M5000.
Introduction
13
Figure 3: Wind conditions in the North Sea. Alphaventus site and Bremerhaven [Source: Alphaventus]
These two sites can be seen in Figure 3. Bremerhaven is in the right corner, while the
Alphaventus site is marked with three wind turbines. The lines of wind show the
favourable wind conditions at ten meters height for the wind energy industry in this
area.
The previous simulation and analysis of the different configurations of the LIDAR
carried out in this Master Thesis are necessary in order to implement the most
favourable one in the measurement campaigns, saving this way both time and
money.
Wind Measurement Techniques
14
2. Wind Measurement Techniques
Wind is air in motion produced by the uneven heating of the earth’s surface by the
sun. Two factors are necessary to specify wind: speed and direction.
The wind has high temporal variations. Within few seconds, it can deviate
considerably from the mean value. Anemometers capture this variation. Their output
is an analogue or digital signal that is proportional to the wind speed.
The measurement of the wind is a key topic in the wind energy industry. Errors
associated with it are the major source of uncertainties in power performance testing
of wind turbines.
A bad calibrated anemometer may lead to the approval of a wind park while a good
anemometer would turn the project down. This bad measurement of the wind causes
the lost of a lot of money. Therefore quality anemometers are a key issue in the wind
energy industry.
Other anemometer types including ultrasonic or laser anemometers detect the phase
shifting of sound or coherent light reflected from the air molecules. Hot wire
anemometers detect the wind speed through minute temperature differences
between wires placed in the wind and in the wind shade.
In the following pages both is-situ and remote sensing wind measurement
Techniques are analyzed. The two first technologies belong to the in-situ group while
the last two are remote sensors.
2.1. Cup anemometer
Nowadays the most common way to measure the wind speed in weather stations is
using a cup anemometer. It is also the standard instrument used for mean wind
speed measurement in the wind energy industry. Cup anemometers are being used
all around the world in numerous masts for wind energy assessments. They are
applied for certification and verification purposes, and for purposes of optimization in
research and development.
Wind Measurement Techniques
15
The cup anemometer has a vertical axis and three cups which capture the wind
(Figure 4). The force exerted by the wind is greater on the inside surface of the cup
than on the outside so the cups rotate. The rate of rotation is directly proportional to
the wind speed and thus the wind speed can be measured.
Figure 4: Sketch of Risoe P2546 with main dimensions and its photo [Source: Risoe]
In the Figure 4 a Risoe cup anemometer is represented. It has been normalized
according to the IEC 61400-12 standard on power performance [1]. In general the
anemometer is fitted with a wind vane to detect the wind direction.
2.2. Ultrasonic Anemometer
Ultrasonic anemometers (Figure 5), first developed in the 1970s, use ultrasonic
sound waves to measure wind speed and direction. They measure wind velocity
based on the time of flight of sonic pulses between pairs of transducers.
Measurements from pairs of transducers can be combined to yield a measurement of
1-, 2-, or 3-dimensional flow. The spatial resolution is given by the path length
between transducers, which is typically 10 to 20 cm.
Wind Measurement Techniques
16
Figure 5: Ultrasonic Anemometer [Source: Fondriest]
Ultrasonic anemometers can take measurements with very fine temporal resolution,
20 Hz or better, which make them well suited for turbulence measurements. The lack
of moving parts makes them appropriate for use in automated weather stations. Their
main disadvantage is the distortion of the flow itself by the structure supporting the
transducers, which requires a correction based upon wind tunnel measurements to
minimize the effect.
Ultrasonic anemometers provide very accurate measurements but till now they have
been used almost exclusively for research purposes due to its high cost.
2.3. SODAR Anemometer
SODAR (SOnic Detection And Ranging) is a meteorological instrument that
measures the scattering of sound waves by atmospheric turbulence. SODAR
systems are used to measure wind speed at various heights above the ground and
the thermodynamic structure of the lower layer of the atmosphere.
Most SODAR systems operate by issuing an acoustic pulse (Figure 6) and then
listening for the return signal for a short period of time. Generally, both the intensity
and the Doppler (frequency) shift of the return signal are analyzed to determine the
wind speed, wind direction and turbulent character of the atmosphere.
Wind Measurement Techniques
17
Figure 6: Sodar principle [Source: Scintec]
A profile of the atmosphere as a function of height is obtained by analyzing the return
signal at a series of times following the transmission of each pulse. The return signal
recorded at any particular delay time provides atmospheric data for a height that can
be calculated based on the speed of sound. SODAR systems typically have
maximum ranges varying from a few hundred meters up to several hundred meters
or higher. Maximum range is typically achieved at locations that have low ambient
noise and moderate to high relative humidity. But at desert locations, SODAR
systems tend to have reduced altitude performance because sound attenuates more
rapidly in dry air. Another drawback from SODAR is its big size.
2.4. Laser Anemometer
The acronym LIDAR stands for LIght Detection And Ranging, an optical analogue of
RADAR (Radio Detection and Ranging). The conventional version of LIDAR requires
a laser transmitter to launch short pulses of coherent light, which are scattered from
atmospheric targets of interest back to an optical receiver, with a time delay that is
determined by the range of the target. Optical phenomena in the Earth's atmosphere
contribute to the amplitude of the optical signals returning to the receiver; their
characteristic wavelength dependence allows the measurement of the concentration
and velocity distributions of different atmospheric molecules and aerosol particles
[WEIT05]. LIDAR backscattering in the infrared (IR) region is well suited to detect
aerosols.
Wind Measurement Techniques
18
Laser anemometry (LIDAR) offers a method of remote wind speed measurement.
The technique was first demonstrated in the 1970s and has been used in a number
of research applications. Widespread deployment of the technique has so far been
disadvantaged by the expense and complexity of LIDAR systems. However, the
recent development of LIDAR systems based on optical fiber and components from
the telecommunications industry promises large improvements in cost, compactness,
and reliability so that it becomes viable to consider the deployment of such systems
on large wind turbines for the advance detection of fluctuations in the incoming wind
field. Potential advantages of this approach include increased turbine energy output
and reduced turbine fatigue damage (increased lifetime).
2.4.1. LIDAR Basics
A LIDAR instrument is divided into three subsystems [BROW04][3]: the transmitter,
the receiver and the detector (Figure 7).
Figure 7: LIDAR’s sketch
Transmitter: The transmitter of a LIDAR is the subsystem that generates light pulses
and directs them into the atmosphere. For most LIDAR systems it is better to have a
transmitted beam with low divergence. The field of view of the detection system
affects the background scattered light. A small field of view leads to a small
measured background. Most LIDARs require the transmitted laser beam to be within
Wind Measurement Techniques
19
the field of view of the detection system, thus a low field of view requires a low
divergence laser beam. Many LIDAR systems incorporate a beam expander to
reduce the divergence of the laser beam before transmission.
The inherent narrow spectral width of the laser has been used as an advantage.
Transmitting a beam with a narrow spectral width allows the detection optics of a
LIDAR to spectrally filter incoming light and selectively transmit photons at the laser
wavelength.
Receiver: The receiver of a LIDAR collects and processes the scattered laser light
and then directs it to a photodetector. The size of the optical element that collects the
light scattered back from the atmosphere is an important factor to determine the
effectiveness of a LIDAR system. The size of it depends on the use of the LIDAR.
The smaller aperture optics are used in LIDAR systems designed to work at close
range, for instance, a few 100 m.
After the collection of the light by this optical system, the light has to be processed
before being directed to the detector system. The simplest way to do so is the use of
narrowband interference filter tuned to the laser wavelength.
Detector: The current detectors convert the light into an electrical signal and the
recorder, an electronic device or devices, processes and stores it. In this manner the
backscattered intensity, and possibly wavelength and/or polarization, are recorded as
a function of altitude.
Incoherent LIDAR systems operating with visible or Ultra Violet (UV) light use
photomultiplier tubes (PTMs) as detectors. PMTs convert an incident photon into an
electrical current pulse large enough to be detected by sensitive electronics. There
are two different ways to record the output of the PMTs, photon counting and analog
detection. The suitable one depends on the average rate at which output pulses are
produced.
On the other hand, coherent detection is used in a class of LIDAR designed for
remote velocity measurement. The principle of this kind of LIDARs relies on a simple
principle: a beam of coherent radiation illuminates the target and a small fraction of
the light is backscattered in the receiver. The motion of the target along the beam
direction changes vδ in the light’s frequency via the Doppler shift, given by Eq. (1)
Wind Measurement Techniques
20
λδ LOSLOS
vV
vc
V 22== (1)
where
c is the speed of light (3x108 m/s)
VLOS is the component of target speed along the line of sight
v laser frequency
λ wavelength
This frequency shift is precisely measured by mixing the return signal with a portion
of the original beam and picking up the beats on a photodetector at the difference
frequency.
The reference beam or local oscillator (LO) is very important in the operation of a
Coherent Laser Radar (CLR). Firstly, it defines the region of space in which light
must be scattered for detection of the beat signal; radiation from other sources is
rejected, so CLR systems are usually completely immune to the effect of background
light. The LO also provides a stable reference frequency to allow precise velocity
determination; as a consequence, CLR systems are inherently calibrated, provided
there are no gross drifts in laser frequency. Finally, the LO amplifies the signal via the
beating process to allow operation at a sensitivity that approaches the shot-noise
limit, a fundamental limit to the optical intensity noise. This high sensitivity permits the
operation of CLR systems in an unseeded atmosphere, relying only on detection of
weak backscattering from natural aerosols.
Coherent LIDAR has more critical signal level requirement s than the incoherent
LIDAR. For the first one a certain minimum signal level has to be maintained to
ensure valid measurements. That’s why Coherent Doppler LIDAR is used extensively
in wind field mapping from the ground and from the air, since in this lower
atmosphere the density of aerosols is much higher.
LIDAR Configurations and their application for wind speed measurement:
Bistatic vs. Monostatic
There are two different kinds of LIDAR configurations, bistatic and monostatic.
Wind Measurement Techniques
21
Figure 8: Monostatic and Bistatic configurations
The bistatic configuration involves a considerable separation of the transmitter and
receiver to achieve spatial resolution in optical probing study while the monostatic
one has the transmitter and receiver locating at the same setting, so that in effect one
has a single-ended system (Figure 8). The precise determination of range is enabled
by the nanosecond pulsed lasers. A monostatic LIDAR can have either a coaxial or
biaxial arrangement.
In a coaxial system, the axis of the laser beam is coincident with the axis of the
receiver optics, while in the biaxial arrangement, the laser beam only enters the field
of view of the receiver optics beyond some predetermined range (transmitter and
receiver are slightly separated).
Biaxial arrangement avoids the near-field backscattered radiation saturating photo-
detector. The near-field backscattering problem in a coaxial system can be solved by
the use of a fast chopper.
Although bistatic Continuous Wave (CW) are normally used for hard target
applications they have also been successfully probed for the wind measurement
applications. It has a big advantage: the improved probe volume definition. However,
various disadvantages of this kind of LIDARs make them inappropriate for this use.
They are much more complex, requiring more optical components and calibration
process and also susceptible to vibrations.
CLR vs. Incoherent Doppler LIDAR
Incoherent Doppler LIDARs are also an alternative for atmospheric measurement of
wind speed. These pulsed systems usually operate in the UV and rely on molecular
scattering to provide the return signal. While the capabilities of incoherent LIDAR are
impressive (they are being considered for space-based global wind measurements),
Wind Measurement Techniques
22
their current size, cost, and complexity suggest the technique is inappropriate for the
turbine-mounted application considered here.
Continuous Wave vs. Pulsed LIDAR
Pulsed and CW (continuous wave) LIDARs have different strengths and weaknesses.
The CW LIDAR has greater redundancy associated with its conical scan and has no
spectral broadening due to the degradation of frequency resolution by a finite pulse
length, therefore exhibits better intrinsic velocity resolution.
On the other hand, the pulsed LIDAR’s simple sensitivity function, constant height
resolution, greater number of height gates, and measurement at effectively
concurrent heights should allow more accurate deconvolution of volume averages of
arbitrary wind shear profiles.
2.5. Comparison of the different measurement devices
Here the different wind measurement techniques are compared. First the remote
sensing technologies are contrasted with the in-situ anemometers to be followed by
the comparison of the technologies that compound each group. Finally the cup
anemometer is contrasted with the LIDAR. Despite the different object of study
(LIDAR measures in a volume instead of in a point), the comparison between the
wind measured with a cup anemometer and a LIDAR shows that their measurements
correlate very well.
The remote sensing technologies LIDAR and SONAR have some advantages in
comparison with the in situ anemometers. The most remarkable one is the high
altitudes at which these devices can measure. Nevertheless they also have some
drawbacks compared to tall towers fitted with in-situ wind sensors. The most
significant one may be the fact that LIDAR and SODAR systems generally do not
report valid data during periods of heavy precipitation.
Cup anemometers are the in-situ wind measurement technology more broadly
spread. It overcomes the disadvantage that mechanical anemometers present in
comparison with the non-mechanical ones, a higher sensitivity to icing, by the
implementation of special models with electrically heated shafts. This way cups may
be used in arctic areas.
Wind Measurement Techniques
23
For the application studied in this report the LIDAR is fairly superior to the SODAR.
SODAR involves the emission of sound pulses and relies on the detection of weak
echo scattered from temperatures and velocity fluctuations in the atmosphere. It
measures the wind velocity via the Doppler shift of the acoustic pulses in a manner
analogous to LIDAR. The background acoustic noise in a turbine- mounted location
would disturb the measurement, leading to false return. Another consideration is that
SODAR systems primarily provide measurements of mean wind. Other wind
parameters, such as wind speed standard deviation, wind direction standard
deviation and wind gust, are usually either not available or not reliable. This is
because to obtain a wind measurement SODAR systems sample over a volume and
at multiple points in space and time, whereas an in-situ wind sensor on a tall tower
samples instantaneously at a point in space and time.
Deutsche Wind Guard, a consulting German company in the field of the wind energy,
has run some experiments in order to evaluate the WindcubeTM for commercial use.
In this context a WindcubeTM has been tested against conventional wind
measurements with a 98.7 m high mast mounted cup anemometer[HARR05].
The measurements took place 10km away from the North Sea, in Simonswolde. The
town was characterized by flat farmland with open appearance.
The WindcubeTM was positioned adjacent to the mast, 3 meters away from it and the
mast was positioned 191 m away from the first of a four Enercon E-66 turbine wind
park. These turbines have 86 m hub height.
Two cup anemometers of type Thies First Class were mounted at 98.7 m height at
the top of the met mast.
Both the measurement site and the wind measurements with the mast followed the
requirements of IEC 61400-12-1 [IEC605].
The WindcubeTM was set-up with a scan angle of 28.33° and a pulse length of
187.5ns for eight different heights (40m, 66m, 80m, 98.4m, 130m, 160m, 190m,
220m). The measurement campaign took a month and a total of 2956 10-minute
periods were covered in this time.
After the filtering of the data the ten minute averages of the horizontal wind speed
component as measured by the WindcubeTM versus the values measured by the cup
anemometer have been calculated. As the correlation coefficient (R2=0.996) shows
Wind Measurement Techniques
24
the measurements of the WindcubeTM and the cup anemometer correlate very well.
The regression parameters are almost perfect, given that the slope is close to the
unity (1.004) and the offset is almost zero (-0.079).
The mean deviation between the measurements of the WindcubeTM and the cup
anemometer is -0.3%, what lies below the standard uncertainty of the cup
anemometer.
The WindGuard report concludes that the WindcubeTM has so far shown an excellent
agreement to cup anemometer and vane measurements at 98.7 m height above
ground, even in periods of high precipitation.
Characterization of Leosphere
25
3. Characterization of Leosphere
The WindcubeTM is an active remote sensor based on Light Detection And Ranging
technique (Figure 9). The heterodyne LIDAR principle relies on the measurement of
the Doppler shift of laser radiations backscattered by the particles in the air. A laser
pulse is sent into the atmosphere and the backscattered light is collected, converted
into an electronic signal and sent to a computer [AUSS07]. A specific signal
processing algorithm is used to determine the scattered signal Doppler shift and the
wind speed along the line of sight (LOS). The range to the target is determined by the
time of traveling back and forward.
Figure 9 : WindcubeTM - Principle of Measurement [LEOS08]
The WindcubeTM meets most of its applications on the Wind power energy field. It is
useful not only in the first phase of a project (pre evaluation, initial site assessment),
but also during the operation time of the wind park. It may also be practical for the
manufacturers and turbine designers, since they get to know impact of the vertical
profile and turbulences on turbine efficiency.
WindcubeTM has also many other applications besides the Wind Energy industry. It is
used in the meteorology and air quality control field in order to calibrate the short
term forecasting models with wind vertical profiles. It may also be used in airports to
monitor the real time turbulences and wind shears, which can cause accidents during
take off and landing.
In this project a new application of the WindcubeTM in the Wind power energy field is
studied and developed.
Characterization of Leosphere
26
3.1. Functional specifications and performance
3.1.1. Output data
The WindcubeTM technology provides the user with many different components of the
wind[5]:
• Real-time Wind coordinates u,v,w
• Radial wind speed variance
• Signal-to-Noise Ratio (the ratio of a signal power to the noise power corrupting
the signal)
• 1min/10min horizontal wind speed and directional average
• Turbulence and wind shear data (cross-products)
• More than 10 user- defined heights
3.1.2. Performances
Accumulation Time: The Laser Pulse repetition rate is 20 KHz. The User’s Manual [6]
recommends keeping the ´Shots/Loop´ value at 100 and ‘Averaging loops´ at 100,
resulting the total number of shots in 10.000. If the transfer time was not taken into
consideration, the accumulation time would be 500 ms. Since 100x100 pulses
acquisition and transfer to the main computer memory are needed, the overall
acquisition of the 10.000 pulses takes about 700 ms.
Data Output Frequency: The 90° rotation to move to the next scanning point takes
about 500 ms. Time to rotate could be decomposed into two different parts: one
which is independent of the angle and which stands for the acceleration and
deceleration time, while the other is proportional to the angle of rotation. In view of
the fact that the accumulation time is about 0.7 seconds and the rotation takes about
0.5 seconds, we can count with a data output frequency of 1.2 sec/direction (0.833
Hz).
Range: Maximum and Minimum Ranges depend on the pulse of length, their values
being 200 m and 40 m respectively for a 20 m pulse. A distance lower than 40 m is
not recommended in order to avoid the underestimation of the horizontal wind speed
due to the possible light strayed inside the instrument.
Characterization of Leosphere
27
Summary of the performances
The Table 1 summarizes the main characteristics of the WindcubeTM. Performance
Range 40 to 200 m
Accumulation Time 0,5 s
Data output frequency 1,2/ 2,4 Hz
Probed length 20m
Scanning cone angle 28,XX°
Speed Accuracy 0,2 m/s
Speed range Up to 60 m/s
Direction Accuracy 2°
Data Availability > 95% up to 150 m*
Laser
Wavelength 1,54 µm
Pulse energy 10 µJ
Eye safety IEC 60825-1
Environmental
Temperature Range
-10 to +40°C with Temperature Control
Unit*
Operating humidity IP65
Rain protection Wiper (with water pump), rain detector
Compacity Portable (2persons)
Dimensions
Weight 50 Kg
Dimensions 900X550X550mm
Power Supply Specifications
Electric Power Supply 24 DC
Power consumption
120 W / 300 W with Temperature Control
Unit
Data
Format ASCII/ Binary
Transfer GSM/Ethernet
* for indication
Table 1: Performance of WindcubeTM
Characterization of Leosphere
28
3.2. Technical specifications and technology
3.2.1. Emission
The laser source of the WindcubeTM is a fiber laser that emits pulses of 1543 nm with
an energy of 10 µJ. This wavelength has various benefits. Among others this width
provides the WindcubeTM with discretion, since it belongs to the infrared range, what
means that the beam is invisible. This wavelength also makes the WindcubeTM eye-
safe. It is harmless for the retina if the exposure to the beam doesn’t exceed 10
minutes. The 1.54 µm wavelength presents a good atmospheric transmission. And
since the 1.54 µm wavelength is a standard telecom wavelength the developed
components are reliable and more economical
3.2.2. Detection and acquisition
Above has already been explained that the LIDAR operation relies on the
Heterodyne principle. The Heterodyne principle is a method of detecting radiation by
non-linear mixing with radiation of reference frequency. The reference radiation is
known as the local oscillator. The signal and the local oscillator are superimposed at
the mixer.
Figure 10: WindcubeTM - Principle of Measurement
The trajectory described by the laser is a cone. In it four lines of sight are sequentially
scanned to perform a three dimensional analysis of the speed in the centre of the
cone. The measured wind field corresponds to an average of around 25m thick
atmosphere layer centered on up to ten defined altitudes. The habitual scanning
cone is about 30°. WindcubeTM also offers an additional scanning cone of 15° for
accurate wind profiling in complex terrain.
Characterization of Leosphere
29
3.2.3. Windcube’s hardware
The WindcubeTM is composed of 4 main elements (Figure 11):
• Optical Head: containing the emission and reception optics
• Electronics Unit: containing optoelectronic elements from laser source to
detector
• Computer: for data acquisition, signal processing and data saving
• A DC uninterrupted power supply wit battery
Figure 11: WINDCUBETM Front panel
Additionally WindcubeTM can comprise optional units as for example temperature
control unit.
The two lateral doors provide a flexibility to easily accommodate the possible addition
of future optic elements.
3.2.4. Windcube’s software:
The following values are required to start the measurement (introduced in the
Settings Window of the Windsoft program):
• The ten different altitudes of performance (from 40 to 200 m).
• A scanning cone angle of 28,30°. Changing the prism it can be switched to
15°.
• A wavelength of 1543 µm.
• The value ‘shots/loop’, as said above, defines the number of shots per loop.
Compromising measurement speed and accuracy a value of 100 is
recommended.
Characterization of Leosphere
30
• ‘Nb of Averaged/Shot defines the total number of shots. A number of 10.000 is
suggested.
• The Carrier to Noise Ratio (CNR or C/N)) threshold. It defines the threshold
under which the measured value is rejected. This value depends on the
number of averaged shots. It is strongly recommended keeping this parameter
to -22dB for 10.000 shots.
• The ‘Wiper Parameter’, which sets the CNR threshold below which the wiper is
switched on.
• The user has to choose between a fast drive position (1 measurement/1.2 sec)
and a slow one (1 measurement/2,4 sec).
3.2.5. Calculation of the resulting wind vector
Windcube® uses the Doppler Beam Swinging techniques (DBS) to calculate the
components of the wind [5]. The DBS technique is based on the following equation:
)sin()cos()sin()cos()cos( ϕϕθϕθ ⋅+⋅⋅+⋅⋅= wvuvr (2)
where u, v and w are the wind vector components and θ and ϕ the azimuthal and
zenithal angles of the wind vector.
Windcube® measures one radial velocity for each cardinal point, i.e. for θ=0°, θ=90°,
θ=180° and θ=270°. Thus, the following equations are obtained:
)sin()cos()sin()cos(
)sin()cos()sin()cos(
270
180
90
0
ϕϕϕϕ
ϕϕϕϕ
⋅+⋅−=⋅+⋅−=
⋅+⋅=⋅+⋅=
wvvwuv
wvvwuv
r
r
r
r
With the first 3 equations the azimuthal angle of the wind vector θ, the zenithal angle
φ and the wind speed V are determined. When inserting these values in (3)Fehler! Verweisquelle konnte nicht gefunden werden. the error expressed in is obtained.
270_ 270 _r meas r cale V V= − (3)
If the error is smaller than a maxe fixed by the constructor the values are validated,
otherwise they are not considered.
The knowledge of θ, φ and V allows the calculation of the wind components u, v, w
and then the horizontal wind speed V
Adaptation for nacelle measurements
31
4. Adaptation for nacelle measurements
The new deployment of the LIDAR on top of the nacelle requires changes in both the
hardware and software. The objective of this Master Thesis is to propose and
analyze the different configurations derived from these changes.
In this chapter the different adaptations for hardware and software of LIDAR are
proposed.
4.1. Proposal of hardware adaptations of the scanning mode
4.1.1. Introduction
The current optical method used by Leosphere™ is a single wedge that rotates and
describes a cone. In order to create new trajectories, new optical devices are
needed. Different methods to develop the desired trajectories with different hardware
elements will be analyzed:
Option A: Risley Prisms
Option B: Two rotating mirrors
Option C: One mirror with 2 Degrees Of Freedom (DOF)
Option D: Galvanometer scanner
In order to compare and rank the methods above a decision matrix is realized. The
variables to consider are:
• Accuracy
• Resolution
• Size
• Robustness
• Wavefront quality
• Speed
• Multiple directions
• Tendency to linear/sinusoidal trajectories
• Market availability
Besides the characteristics above listed other parameters have to be taken into
consideration: the beam diameter at source output (50 mm, bigger than for other
Adaptation for nacelle measurements
32
scanner utilities), temperature range (from -10°C to +35°C if no temperature
regulation) and laser wavelength (1543 nm).
Each of the four options above is more likely to create one kind of scanning pattern
(linear or circular/sinusoidal). It is not possible to opt for a system till the different
scanning patterns are analyzed in the Chapter 6 of this paper, in view of the fact that
without knowing which pattern is most convenient, a sound decision cannot be made.
4.1.2. Option A: Risley Prims
In the Option A a refractive method is considered, a system of three Risley prisms.
Normally this device consists of a pair of rotary wedged elements that redirect the
laser beam by refraction [SCHW06]. A typical Risley prism pair is shown in Figure 1.
Figure 1: Risley prism pair
With a pair of Risley prisms it is possible to orient the beam by employing the
appropriate angles of prism rotation in order to make any spatial trajectory. Linear
displacements of the beam along any direction are achieved by changing the relative
angle between prisms, while circular displacements around any direction result when
prisms are rotated without changing the relative angle between them.
Adaptation for nacelle measurements
33
Figure 2: Ray incident along the optical axis passing through a pair of wedge prism from the object to the detection plane
The most remarkable advantages of using a Risley pair are, among others, the high
resolution, wavefront quality and the compactness and robustness they achieve.
However, this system presents also drawbacks: singularity – excessive prism rotation
speed for angles approaching on-axis (boresight); tolerances – wedge angle,
alignment, temperature and pressure all affect alignment; blind spot – boresight dead
zone on axis.
To avoid problems with singularity and the blind spot, some researches in California
[SULL06] recommend the addition of a third Risley prism. This third prism introduces
an additional degree-of-freedom that pushes the boresight off-axis. Continuous
orientation of the third prism allows tracking through the boresight.
Conversely, introducing the additional prism makes the system under constrained.
Therefore the control system must deal with an infinite number of solutions for the
same elevation and azimuth target angles.
Figure 3: Cross Section of RP
Adaptation for nacelle measurements
34
The most important parameters for this Risley prism mechanism are summarized in
Table 1.
Clear Aperture (CA) 100 mm Optics must be oversized to allow for steering
Wavelength 1550 nm Silicon optics
Wedge angle 7° Affects range and resolution
Field of Regard (FOR) ±72° Achieved with material choice, wedge angle, and thickness
Operational T -50 – 70 °C Allowance made for CTEs of different materials
Pointing Accuracy 1 mrad Depends on thermal environment
Slew Rate 10°/sec Provided by the torque motors
Control Bandwidth 23 Hz Includes mechanical slew and settle time
Optical Throughput 85 – 96% Even with AR coatings, back-reflections were an issue
Wavefront Quality Diffraction-limited Surface figure error on wedge faces <ë/50 rms
Pointing Resolution 100 µrad Limited by optical encoder resolution
Table 1: Summary of performance parameters for Risley Beam Pointer (RBP)
The three following systems are reflective given that they use mirrors as the optical
device.
4.1.3. Option B: Two rotating mirrors
Two mirrors can be mounted on the rotor shafts of two variable speed motors.
Depending on the slight angle of each mirror and the speed of the rotors different
trajectories can be reflected in the mirrors. If the speed of each rotor can be adjusted
independently, a great variety of Lissajous Patterns can be created .
The layout of the device is shown in Figure 4. The two mirror-motor assemblies are
so positioned, that the laser beam follows a Z-shaped path, from the laser to the area
to scan.
Adaptation for nacelle measurements
35
Figure 4: Lissajous Laser device using two rotating mirrors
Despite the easy concept of this optical system it presents a few drawbacks. The
most remarkable one is its big size. The layout of the two mirrors with motors
requires from space in between.
4.1.4. Option C: One mirror with 2 DOF
In Option C a galvanometric silicon scanning mirror of 2 DOF is considered
[SCHO07][10]. Parallel current paths are on the edge of a rotating plate, as shown in
Figure 5. Due to a radial magnetic field Lorentz forces act on the plate. Since they
flow in the same direction, Lorentz forces on both edges act always to the opposite
direction, producing the same torque. To build up the radial magnetic field, a
permanent magnet is aligned beneath the mirror.
Figure 5: Torque induced by magnetic field
Two different driving currents are required, one for the mirror and one for the frame.
The rotation of each axis is controlled independently by adjusting amplitude and
frequency of each current. Various Lissajous trajectories (see Chapter 5.3) are
obtained through different frequency ratios of the mirror current and the movable
frame current.
Adaptation for nacelle measurements
36
Figure 6: Reproduction of Lissajous Figures
This optic device is very rapid and very small, two great advantages for the
deployment studied in these pages. Nevertheless, it is not available in the market for
big laser diameters.
4.1.5. Option D: Galvanometer Scanner
The last option comprises a pair of mirrors each with one DOF and each moving in
different directions. These devices are known as galvanometer scanners, but they
differ from the electrical measuring devices called galvanometers, since the scanners
require a higher speed. As shown in Figure 7 laser scanners are built "inside out"
from the typical electrical measurer; the coils are wound on the armature, and a
magnetic or soft iron rotor, suspended in the gaps of the pole pieces, moves the shaft
with the mirror.
Figure 7: Cross section of a galvanometer
The rotor is mounted in small precision bearings, diminishing this way the friction.
The shaft has a spring to return the rotor to the central at-rest position when no
current is applied. The two permanent magnets create a magnetic flux that goes
Adaptation for nacelle measurements
37
through the rotor. It will be moved in response to variations in the magnetic flux
created by the application of current in the drive coils.
Figure 8: Closed loop scanner block diagram
There are two kinds of galvanometer scanners: open loop and close loop. Only this
last one will be considered in this paper, since it provides fast, accurate scanning due
to its high-precision optical position detector (see Figure 8).
To produce the desired scanning pattern two galvanometer scanners are required,
one oriented on an X-axis, the other on the Y-axis. One galvanometer scanner
moves the beam horizontally; the other moves it vertically, resulting a rectangular
raster pattern.
The motion of each mirror is coordinated to form the raster pattern, and the scanning
speed is regulated by the speed and angular extend of mirror deflection. The function
principle of the galvanometers is shown in Figure 9.
Figure 9: Function principle of the galvanometer scanner
Adaptation for nacelle measurements
38
SPECIFICATION UNITS PERFORMANCE
Excursion Degrees Optical +/- 48
Rotor Inertia Gram·Centimeters² 5.1
Recommended Beam Apertures Millimeters 20 - 50
Small Step Response (5.8 gm*cm² load) Microseconds (Matched Inertia Load) 650
Torque Constant Dyne*cm/Amp 2.8*10 5
Coil Inductance Micro Henrys (at 1000Hz) 450
Coil Resistance Ohms 5.8
Angular Sensitivity Micro Amps/Degree 100
Repeatability Micro Radians 2
Linearity (+/- 20 degrees) Percent, Minimum 99.9
Zero Drift µrad./degree C, Max 9
Gain Drift ppm/degree C, Max 30
Table 2: Specifications Table of the moving magnet galvanometer QuantumScan-30
After a comparative study between the Nutfield Technology's QuantumScan-30 (QS-
30) galvanometer scanners (Figure 10) and the Cambridge Technology Optical
Scanner Model 6900, the QS-30 is going to be consider in this paper because of its
better properties. The limited rotation of its moving magnet motor is coupled to a
highly sensitive position detector. The device is controlled through a PID based servo
driver to provide amazingly fast and accurate closed loop control. The different
specifications of the QS-30 are shown in Table 2: Specifications Table of the moving
magnet galvanometer QuantumScan-30
Figure 10: A pair of X-Y QS-30 galvanometer scanners
Adaptation for nacelle measurements
39
4.1.6. Decision Matrix
In order to compare and rank the different methods above exposed a decision matrix
is realized. Decision
Matrix
Weighting
Factor OpA OpB OpC OpD Annotation
System Risley 2RotMir 1Mir Galv.
grade 5 3 5 5
Accuracy 10% 10% 6% 10% 10%
As a refractive optic, Risley prisms are
less sensitive to mechanical tilts than
reflective systems, resulting a good
accuracy.
grade 3 2 4 5 Resolution
15% 9% 6% 12% 15%
The resolution of QS-30 is much smaller
than the Risley's one (2 vs.100 µrad)
grade 3 1 5 1
Size 5% 3% 1% 5% 1%
The use of 2 mirrors requires more
space. Op A is compacter than B or D
despite the use of multiple prisms due to
the common axis they share.
grade 4 3 2 3 Robustness
10% 8% 6% 4% 6%
grade 5 3 4 3
Wavefront
Quality 15% 15% 9% 12% 9%
Thanks to the no recess or protrusion to
the air stream in Op A, the Risley beam
director generates less turbulence than a
traditional, reflective system, being able
to maintain a higher wavefront quality.
Op. B and D have a lower WQ since they
use 2 mirrors.
grade 1 2 4 4 Speed
15% 3% 6% 12% 12%
Risley´s slew rate of 10°/sec is extremely
slow. The use of bearings and magnetic
fields diminish the friction in Op C&D.
grade 2 2 3 5 Multiple
Directions 5% 2% 2% 3% 5%
The simple rotation of a mirror allows an
easy change of direction
grade 2 2 3 5 Tendency to
linear
trajectories 5% 2% 2% 3% 5%
The natural linear movement of the
galvanometer mirrors leads to the
reproduction of linear trajectories.
grade 4 5 3 1 Tendency to sinusoidal trajectories 5% 4% 5% 3% 1%
Rotating devices lead to sinusoidal
trajectories
Market grade 3 1 0 5 The galvanometric silicon scanning mirror
Adaptation for nacelle measurements
40
availability
15% 9% 3% 0% 15%
is not yet available for such a big laser
beam diameter (50mm). Galvanometer
scanners are in contrast already
implemented in the market.
Result 100% 65% 46% 64% 79%
Table 3: Decision Matrix
In Table 3 the different requirements the systems should fulfill are listed. Each
system has a score for each requirement depending on the grade of fulfillment,
ranging from 0 (not fulfilled) to 5 (satisfactory fulfillment). The punctuation is
qualitative, what means that a 4 in speed is not two times faster than a 2. Some
requirements are more important than others, therefore a weighting factor for the
different necessities is applied. For instance, the wave front quality is really important;
for that reason it has a weighting factor of 15%. The market availability is also very
significant; since this is not only a theoretical project and the results studied here may
be implemented.
The decision matrix’s results are only estimative, what means that the engineer’s
sense may prevail over these.
As seen in the Table 3 the resolution has a bigger weighting factor than the accuracy
(15% vs. 10%). In scanning the wind aiming a specific point (accuracy) is less
important than in other scanner applications. What is most important is to know
exactly where the laser is pointing (resolution). The precision is also relevant, since a
mean value wind speed in one point will be calculated from a bus of data in this point
(shot frequency=20 KHz). The resolution is related to the precision with which the
measurement is made (see Figure 11).
Figure 11: Accuracy and precision
Adaptation for nacelle measurements
41
According to the decision-matrix and assuming a weighting factor for linear and
sinusoidal trajectories of 5%, the most suitable method are the galvanometer scanner
mirrors, followed by the Risley System. If a bigger mirror like the described in Op. C
would be available, it should be taken into consideration. As written at the beginning
of this document, the results that are going to be achieved in this project will influence
and improve these results.
Adaptation for nacelle measurements
42
4.2. Proposal of the software adaptations
Besides from the hardware adaptations additional adjustments of the software
system are needed in order to define the different scanning configurations.
While the hardware adaptations influence directly the kind of trajectory, the software
adaptations have to do with the speed of the optical device and its frequency.
As it has already been explained in the Characterization of Leosphere in Chapter 3
three different concepts of frequency are handled when talking about the LIDAR’s
frequency: the frequency of the machine itself, which implies how many times per
second does LIDAR shot a laser ray, the ‘shots/loop’, which defines the number of
shots per loop and the Nb of Averaged/Shot, that implies the recommended number
of shots to obtain a speed value for a point. From these last two values a third
frequency is calculated ((4Fehler! Verweisquelle konnte nicht gefunden werden.), the loops per point frequency.
LoopShots
ScannedPoShots
poloops intint/ = (4)
A value of 10.000 shots per scanned point and 100 loops with 100 shots each are
recommended to compromise both, measurement speed and accuracy.
Nevertheless it is necessary to introduce a new frequency concept for the application
developed in this Thesis: the scanned-points-per-second.
The actual application of Windcube™ has a scanned-points-per-second of one, but
this value has to be increased. Since the frequency of the LASER cannot be
changed, the increase of this scanned-points-per-second is traduced in a decrease of
the shots per loop and loops per scanned point.
Now on these two concepts, the shots per loop and loops per scanned point
frequencies, are joined and a new notion of frequency, the multiplication of both, is
used. This new frequency is called shots-per-point.
Fehler! Es ist nicht möglich, durch die Bearbeitung von Feldfunktionen Objekte zu
erstellen. (5)
Adaptation for nacelle measurements
43
ondpersposcannedfrequency
secint −−−=point-per-shoots (6)
In the application studied in these pages two different concepts of accuracy must be
handled. The first concept refers to the accuracy of the measurement of the speed for
a certain point in space. The higher the shots-per-point frequency gets, the better is
this accuracy. The speed is obtained through an average spectrum of the data
acquired from the LIDAR, therefore the more data the average has, the more exact is
the calculation.
The second concept considers the accuracy of the entire scanned wind field. The
higher the scanned-points-per-second frequency is, the better is this second
accuracy.
Since the LASER frequency is fixed to 20 KHz the other two have to be settled in
order to maximize both accuracies.
WITLIS assumes a “perfect” estimation of the line of sight wind speed, this means
that no averaging of spectra, or line-of-sight wind speed, is performed and in
consequence just one shot is needed at a spatial point to obtain the exact wind
speed in the line-of-sight. Because of this reason WITLIS always considers better the
configurations with high scanned-points-per-second frequency without taking into
account the possible degradation of the accuracy for each point due to less shots-
per-point.
Therefore with WITLIS it is only possible to analyze the second concept of accuracy.
The optimal combination of frequencies is the one with the minimum scanned-points-
per-second frequency that still leads to an accurate wind field.
Windcube™ has two speed modes: slow and fast, but this can be extensible in
WITLIS.
The user has to choose between a fast drive position and a slow one. The fast mode
implies that a full snap shot is obtained every 1.2 seconds, while for the slow mode
2.4 seconds are needed. This entails that a snap shot calculated with slow mode has
two times as many points as the fast mode, so the distance between points is
reduced to the half.
Adaptation for nacelle measurements
44
In WITLIS these fast and slow speed variable has been considered, but instead of
1.2 and 2.4 seconds per snap shot, 1 and 2 seconds have been measured.
Since Windcube™ works with a pulsed laser it is capable to make simultaneous
measurements at different ranges. In the case that WITLIS has an input of more than
one distance the coordinates calculated for this reference distance have to be
transformed. This is implemented in the function transformrange.
In reality, the more ranges at which measurements are required simultaneously, the
lower allowed scanned-points-per-second frequency due to a lack of computing
capacity. However, this problem can be solved by adding an additional computer in
parallel. This fact is not considered in WITLIS because this problem cannot be
simulated.
WITLIS
45
5. WITLIS
The acronym WITLIS stands for WInd Turbine LIDAR Simulator. The objective of this
program, core of the Master Thesis, is to simulate the different setups of the LIDAR
and compare and evaluate their capability of reproducing accurately wind fields in the
instantaneous and statistical sense. The LIDAR system “measures” wind speed at
discrete points of the synthetic wind field where it is embedded. A new wind field is
reconstructed, through interpolation of the “measured” wind speed, and finally
compared to the original wind field.
This pre-analysis is needed for the future adaptation of the standard Windcube™ for
measurements from the nacelle of the multi-MW wind turbine which have to be
performed at the SWE.
The program can be mainly divided in three parts: the preprocessing, a first part in
which the setup is defined; the processing, where the LIDAR is simulated and the
measurements for a certain period of time take place, and the post-processing, a
third part in which the output of this simulation is studied.
The processor involves the development of algorithms for the calculation of the focus
points and the obtainment of the speed in the line of sight for the different
trajectories. Then the calculated wind field is calculated through linear interpolation
Delaunay triangulation to a grid defined in WITLIS. The synthetic wind field is also
interpolated to the same grid. The algorithms are implemented in subroutines which
are coupled with in house available software for synthetic wind field generation.
The post-processor of WITLIS consists in the evaluation of the new measurement
approaches through statistical analysis. The wind fields obtained from synthetic wind
scanned with a selected LIDAR setup are compared with the original synthetic wind
field. To do so both wind fields, the synthetic and the calculated one, have to be
interpolated to the same grid. Finally, conclusions are drawn about the performance
of the particular selected LIDAR setup.
WITLIS
46
This chapter starts with an overview and a flow-chart of the program and follows with
the description of the different variables of study. Then key parts of WITLIS are
explained: the development of the trajectories, the simulation of the wind and the
interpolation method.
5.1. Overview
The core of WITLIS reads a synthetic wind field which is generated with a stochastic
wind field generator. Then this is scanned according to the configuration entered and
finally a new scanned field is created through interpolation.
The different configurations of the LIDAR characterized mainly by the trajectory,
speed mode and the scanned-points-per-second frequency in the pre-processor lead
to different scanned wind fields.
The core of WITLIS is contained in the following functions:
Runningmode calculates the different routines or trajectories depending on the
input scanning mode. The outputs of the function are the position uvector, the
range at which the trajectory has been calculated and the time.
Rotorcollision detects if something is blocking the laser beam. If the LIDAR is
pointing into the inflow wind from the nacelle, it will mainly collide with the rotor
blades and to a less extent with the nacelle itself. The output of the function is
a logical variable and in case of collision it generates another variable that
Scanned wind
field after
interpolation
Original
Synthetic
inflow
Simulation LiDAR
scanning
Rotor collision
detection
LiDAR with variable
scanning modes
WITLIS
47
reflects the object with which the laser is colliding. This function has been
created by David Schlipf.
Getvlos gets the speed of the line of sight (vlos) for certain coordinates at a
certain time (input). This function has been created by Juan José Trujillo.
Interpol Interpol is the function that interpolates the speed obtained from getvlos
to the grid specified in WITLIS.
Statistics calculates the statistics of the wind fields necessary to compare and
evaluate the different LIDAR setups. This is more extensively explained in
Chapter 6.1.
All these main functions are contained in a basic flow-chart of WITLIS. In it the
program is divided in the pre-processor, where the LIDAR is configured, the
processor, where the measurements take place, and the post-processor, where the
results obtained in the processor are analyzed.
WITLIS
48
.
Fehler! Verweisquelle konnte nicht gefunden werden. : Flow-chart of WITLIS
WITLIS
49
In the flow-chart only the most important variables are shown. The output of
runningmode is matposition, a matrix that contains the different positions to be
scanned in a snap shot depending on the selected trajectory. The processor is
defined mainly by two loops: one for the scanning of a snap shot, another one for the
number of snap shots, limited by the total time, and a third one for the different
ranges. Even though WITLIS is able to measure at different ranges, it is not done in
this Thesis, since the over-load this produces cannot be simulated.
If according to the selected speed mode it takes one second to describe a snap shot
and a scanned-points-per-second frequency of 100 is selected for a total simulation
time of 180 seconds,180 snap shots are obtained, each of them defined with 100
points. It means that the functions contained in the inner loop are called 180*100
times.
For each point the position is read in matposition and the time is controlled with a
counter. With this two values and the value at which the measurement is required
rotorcollision calculates if there is collision. In case there is collision, an error value of
9999 is inserted in matrix. If there is no collision the vlos is calculated in getvlos from
the synthetic wind fields and inserted in matrix.
After the description of all the snap shots the calculated wind field is estimated in
interpol through linear interpolation. Finally this calculated field is compared with the
synthetic one in statistics.
WITLIS has been developed and implemented mainly with MATLAB, a numerical
computing environment and programming language. The task of wind field
generation is done by Vindsim which is called externally when necessary.
MATLAB allows the use of structures for storage of variables with different types.
This is of advantage for organizing all the calculation parameters in WITLIS, in effect
two structures are used in the program, namely parameters for those variables that
remain constant during a simulation, i.e. mainly initialization values, and states for
those variables that are changed and/or calculated.
Coordinate systems:
Three different coordinate systems have been used in WITLIS, namely the global or
earth, the nacelle and the LIDAR coordinates. The global reference frame has its
WITLIS
50
origin at the base of the tower and is fixed with the x-axis looking in the in-flow
direction. The nacelle system is translated up to the hub height, thus it has [0; 0; hub
height] global coordinates. The origin of the LIDAR system is situated at the laser’s
mirror output and two different positions of it are studied here.
In order to change the coordinates from one to another transformation functions have
been used. These consist on a translation and a rotation.
The coordinates of the nacelle are expressed in the global system, while for
convenience the LIDAR position is referred to the nacelle. The synthetic wind field is
situated at the hub height; therefore it is easier to express it in the nacelle
coordinates. Thus, the coordinates of the trajectory are defined to the nacelle system,
since it is calculated at a certain distance in front of the rotor and also centered to the
hub.
WITLIS
51
5.2. Definition of parameters of evaluation
The different operational parameters to be studied during the project are presented in
this section. They are parameters of the LIDAR system dealing with the data
acquisition and processing which are software specific along with the scanning mode
which is hardware specific.
5.2.1. Trajectory
The optical device used by the LIDAR system to direct the laser beam influences
directly the scanning path and therefore the measured wind field. As seen in Section
4.1 some devices are more appropriate to describe curves, while others straight
lines. In this respect a comparison between straight and curved trajectories has to be
made to be able to come to a sound decision about which optical device is the best
for nacelle measurements.
In general there is a trade off between flexibility and complexity and therefore cost of
the optical system. In regards to this it is necessary to quantify the accuracy of the
different scanning trajectories in order to take a decision on the optical device which
should be constructed. In other words, the selection of high flexibility of the optical
device has to be supported by a higher accuracy with respect to a non-flexible
system.
An overview of the different trajectories to study is summarized in Table 4. The kind
of trajectory is codified in WITLIS as scanningmode Scanning mode Description
1 a vertical line in one direction
2 a vertical line in both directions, it goes up and down
3 a horizontal zigzag
4 a vertical zigzag
5 an hourglass
6 Lissajous figure with a=1 and b=1
7 Lissajous figure with a=1 and b=2
8 Lissajous figure with a=3 and b=2
9 Lissajous figure with a=5 and b=4
10 Lissajous figure with a=5 and b=8
11 Lissajous figure with a=5 and b=6
12 Lissajous figure with a=9 and b=8
13 a spiral
Table 4: Brief description of the trajectories
WITLIS
52
The first five trajectories belong to the straight lines class and the rest are all curves.
The trajectories from 6 till 12 are Lissajous figures with different parameters. The last
trajectory to study corresponds to a spiral.
Straight trajectories
Scanning modes 1 and 2
The first two trajectories are vertical straight lines. In scanning mode 1 the trajectory
is followed only in one direction, e.g. from bottom to top, and in scanning mode 2 it is
followed in two ways. It can be said in advance that these simple trajectories will not
lead to the best results, but since it is a very easy to implement trajectory it is always
interesting to compare it with the others.
-40 -30 -20 -10 0 10 20 30 40-40
-30
-20
-10
0
10
20
30
40Scanning mode 1&2
Figure 12: Blue line represents a straight trajectory used in scanning modes 1 and 2. The origin represents the position of the wind turbine hub
Scanning modes 3 and 4
The scanning modes 3 and 4 are a horizontal and a vertical zigzag, respectively. At
first sight it may seem not necessary to probe the two zigzags. Nevertheless there is
a big difference in the way they both sweep the area: the horizontal zigzag (Figure
13) gets a better approach to the vertical limits, while the vertical trajectory only gets
a few points in these areas. On the other hand, these few points are more uniformly
distributed in time.
To describe these trajectories the number of triangles is initialized in the
parameter.zz.triangles.
WITLIS
53
-60 -40 -20 0 20 40 60-60
-40
-20
0
20
40
60Scanning mode 3
-60 -40 -20 0 20 40 60-60
-40
-20
0
20
40
60Scanning mode 4
Figure 13: Scanning modes 3 (left) and 4 (right) with parameter.zz.triangles=6
Scanning mode 5
The scanning mode 5 (Figure 14) corresponds to the horizontal version of an hour
glass.
-60 -40 -20 0 20 40 60-60
-40
-20
0
20
40
60Scanning mode 5
Figure 14: Blue line represents a straight line codified as scanning mode 5
Curved trajectories
Scanning modes from 6 to 12
The scanning modes 6 and up belong to the group of curved lines. The six first are
described as Lissajous figures and the scanning mode thirteen is a spiral. The
definition of the Lissajous curves is extensively explained in Section 5.3.
The first curve is the simplest closed Lissajous curve. It has a ratio a/b=1 with a=1
and b=1, and when the height and width of the area in which it is calculated are equal
a circle is obtained (Figure 15). Otherwise it is an ellipse.
The simulation of this trajectory is of main importance, since this is the path
described by the standard Windcube™. Given that the rotor blades also describe a
circle it seems a very reasonable and intuitive trajectory. On top of that it is a very
easy to describe trajectory.
WITLIS
54
However, the lack of scanned points for all the area within the circle may be
disadvantageous. But given that WITLIS only interpolates due to the impossibility of
the Delaunay triangulation to extrapolate (see section 5.5), it may work better than
trajectories with a lot of scanning points in the middle of the area and few in the
periphery, losing this way a lot of interpolated area at the outside part.
If simulations and statistical analysis show that the error committed by the use of this
trajectory is not much higher than for a much more complicated path it may not be
necessary to change the optical device that Leosphere currently uses (a simple edge
that rotates).
-40 -30 -20 -10 0 10 20 30 40-40
-30
-20
-10
0
10
20
30
40Scanning mode 6 a=1 b=1
Figure 15: Scanning mode 6, Lissajous Figure with a and b=1
The following scanning mode, the 7th, describes a Lissajous figure with parameter
a=1 and b=2. It reminds to an infinite symbol or to an eight (Figure 16) and is also
relevant because it is the curved version of the scanning mode 5. The comparison of
these two trajectories is an indicative of the suitableness of the straight and curved
lines and it shows if it really makes a difference to use one or another.
-40 -30 -20 -10 0 10 20 30 40-40
-30
-20
-10
0
10
20
30
40Scanning mode 7 a=1 b=2
-60 -40 -20 0 20 40 60-60
-40
-20
0
20
40
60Scanning mode 5
Figure 16: Scanning mode 7, Lissajous Figure with a=1 and b=2 (left), Comparison with Scanning mode 5 (right)
WITLIS
55
The following scanning modes (8,9 and 10) (Figure 17,Figure 18 Figure 19) are more
complex. The more complex the figure is (Figure 19), the bigger is the length of the
curve that has to be described by the optical device and therefore, as explained in
the next chapter, the faster its speed (under the same speed mode and frequency
conditions).
-40 -30 -20 -10 0 10 20 30 40-40
-30
-20
-10
0
10
20
30
40Scanning mode 8 a=3 b=2
Figure 17: Scanning mode 8, Lissajous Figure with a=3 and b=2
-40 -30 -20 -10 0 10 20 30 40-40
-30
-20
-10
0
10
20
30
40Scanning mode 9 a=3 b=4
-40 -30 -20 -10 0 10 20 30 40-40
-30
-20
-10
0
10
20
30
40Scanning mode 10 a=5 b=4
Figure 18: Scanning modes 9 and 10, Lissajous Figure with a=3 and b=4 (left) and a=5 and b= 8 (right).
-40 -30 -20 -10 0 10 20 30 40-40
-30
-20
-10
0
10
20
30
40Scanning mode 11 a=5 b=6
-40 -30 -20 -10 0 10 20 30 40-40
-30
-20
-10
0
10
20
30
40Scanning mode 12 a=9 b=8
Figure 19: Scanning modes 11 and 12, Lissajous Figure with a=5 and b=6 (left) and a=9 and b=8 (right.
WITLIS
56
Scanning mode 13
The last trajectory is a spiral. It is analyzed in these pages since its implementation
does not require a complete new optical device. The actual single wedge could be
controlled and tilted while rotating. This way a spiral is described.
The Figure 20 shows this path. The blue lines join the scanned points; they are not
the actual trajectory. Therefore it does not seem a spiral at first sight. In the figure it is
appreciated that in the outside there are less scanned points than in the center of the
area. The consequences of this fact are analyzed in the chapter 6.
-40 -30 -20 -10 0 10 20 30 40-30
-20
-10
0
10
20
30Scanning mode 13
Figure 20: A spiral trajectory
5.2.2. Speed mode
Another relevant variable to study is the speed mode or, in other words, the
measurement rate. WITLIS has two speed modes: slow and fast, but this can be
extended to any desired rate. The fast mode implies that a full snap shot is obtained
every second, while for the slow mode two seconds are needed. This entails that a
snap shot calculated with slow mode has two times as many points as the fast mode.
This variable is of great importance when trying to answer the question about what
provides a better result, if fast snap shots that reduce the time between measurement
in a certain point, or a slower mode that covers the area much better.
The application of these speed modes to the calculation of the trajectories is
reasonably simple. The speed needed to describe the desired trajectory at a certain
distance is calculated from the speed mode (see Equation (7) codified in WITLIS as
snapshottime. For this calculation the length of the curve is needed.
WITLIS
57
mesnapshottilength scurve'speed = (7)
Once the speed is known and the scanned-points-per-second frequency is fixed (for
instance 100 points) a variable called step is calculated.
second-per-points-scannedspeedstep = (8)
The step is the distance between two consecutive points of the trajectory and is only
needed for the development of straight trajectories, since the curves step is defined
through the time. This is also explained in detail in section 5.3.
5.2.3. Scanned-points-per-second
As explained in Chapter 4.2 the optimal combination of frequencies is the one that
reduces as much as possible the scanned-points-per-second frequency. This way
more samples or shots per point can be taken, what leads to a more reliable
measurement of the wind.
Having this fact in mind, the effect of the rate of the scanned-points-per-second
frequency is analyzed in section 6.2 by simulating the LIDAR for different rates and
quantifying the accuracy. There is a lower rate value at which the accuracy drops
down suddenly. Then, the lowest frequency that still leads to an acceptable accuracy
is considered.
5.2.4. Rotor collision
Not as a variable but the two situations, with and without collision, are also
compared. The simulation of the collision reflects the percentage of shots that are
lost under this circumstances and the comparison of this situation with the one
without collision shows the influence of it.
The comparison of the influence over different trajectories is also carried out.
It may be that a zigzag follows the rotor blades and avoids the collision. Or a
Lissajous figure may be better, since the points are not positioned from left to right.
WITLIS
58
The collision is simulated in the bladecollision function which needs the geometry of
the nacelle and of the rotor blades, both defined in the initialization. The simulation of
the movement of the rotor blades is carried out in the main loop of witlis with a
counter called states.blade.deltaangle. states.blade.deltaangle (see Equation (9)
depends on the rotational speed of the blades (states.blade.rotorspeed), the
shots/loop frequency and the speed mode and it represents the incremental degree
of each blade for each loop.
60/int360..
⋅⋅=
figuresporotorspeeddeltaanglebladestates (9)
The output of the collision function is a logical variable that is positive when the ray
collides and a code that shows the cause of the collision. Table 5 shows the way the
different cases are coded. Code Meaning
0 No collision
1 Collision with rotor blade 1
2 Collision with rotor blade 2
3 Collision with rotor blade 3
4 Collision with nacelle
Table 5: Collision code
5.2.5. Correction of line-of-sight wind speed
Since the LIDAR measures the wind speed in the line of sight, it is only possible to
know the instantaneous wind vector when the mean is aligned with the axis.
Otherwise the wind is underestimated.
In view of the fact that the y and z components of the wind speed are very small it
could be assumed that the wind speed direction is completely horizontal
In order to analyze the committed error when projecting the wind speed to the
horizontal direction two different situations are simulated. A first one in which no
corrections are made and in which the losV is the projection of the real wind speed
over the laser vector. In this case the output of the function getvlos in WITLIS is the
speed over the line of sight. It is calculated from the dot product between the
direction of the laser and direction of the wind vector ((10).
wVlosVVlosrr
•= (10)
WITLIS
59
This vector Vw could be any of the three vectors represented in the Figure 21 since
they are all over the perpendicular line to lidV . In all cases the wind speed is
underestimated, since loslid VV ⋅ is always smaller than any of the a, b and c vectors.
Figure 21: Diagram of vlos and possible vw vectors
The second situation will try to solve this underestimation by assuming that the wind
speed is horizontal and assuming that the measured losV comes from bV (Figure 21).
To calculate this corrected speed ( corrV ) (Equation (11) the scalar losV has to be
divided by the dot product between the direction of the laser and the unity vector of
the horizontal direction [1;0;0].
corrVlidVVlos
Vcorr ˆ•= r (11)
This way the underestimation is substituted by a lower underestimation or a small
overestimation. The Figure 21 shows these two possible situations. If the real winds
speed direction was the one represented by Va this assumption would lead to an
underestimation of the speed, while if the real one was Vc the value of the wind
speed would be overestimated.
For instance, if the LIDAR is scanning a point at [40;40;0], it is describing a 45°
angle with the actual speed direction. According to the Equation (12 the measured
vlos by LIDAR is underestimated around a 30%.
VrealVrealVrealVlos ⋅=⋅=⋅= 71.02245cos (12)
vlos
va
vb
vc
WITLIS
60
5.2.6. Position of LIDAR
The position of the LIDAR, despite its importance, is not analyzed in detail in these
pages. In this project only two positions are studied.
In the first position the LIDAR is placed inside the hub of the wind turbine. This is
intuitively the optimum location, yet in practice complicated to implement. This
location has big advantages: there is collision neither with the nacelle nor with the
rotor blades, the LIDAR is already centered with the wind field and the rotation of the
hub provides the LIDAR with an initial rotation. This additional rotation is not
simulated. On the other hand it also presents some drawbacks: this location makes it
impossible to measure the wake and it encounters big problems in its deployment.
The second position analyzed in these pages is on the helicopter platform of a wind
turbine. This location does not require a change in the displacement of the elements
inside the hub like for the first position. It is simply attached on top of the platform. In
terms of the nacelle coordinate system the LIDAR is placed at [-6.5; -5.5; 3.7] m,
what means that is 5.5m to the right when looking to the inflow. This deviation of the
coordinate’s origin with respect to the hub presents some problems when the
measurements take place at a distance than differ to the reference one.
The reference distance is the distance at which WITLIS calculates the step defined
by the speed mode; the trajectory is calculated at this range.
Since Windcube™ works with a pulsed laser it is capable to make simultaneous
measurements at different ranges. If WITLIS has an input of more than one distance
the coordinates calculated for this reference distance have to be transformed. This
change is carried out by the function transformrange.
If the LIDAR is placed on the y=0 line, this transformation is simple and the trajectory
remains centered. But if the LIDAR is not over this line, only the trajectory at the
reference distance remains centered.
Therefore it is recommendable to set the reference distance at the range at which the
measurements are required. The reference distance is normally one time the rotor
diameter, what means that the maximum aperture angle of the optical device used is
+/- 30°.
The area at which the trajectory is defined is also variable, but a square area with the
side length of the rotor diameter is here considered.
WITLIS
61
The figure above represents the effect of not measuring at the reference distance
(D). The scale has been modified, so that the effects of the position and range are
better observed.
If the measurements are requested at a smaller range, at half diameter for instance,
only a small part of the area is scanned. On the other hand, if the range is bigger
than the reference distance we may be scanning points of low interest. In WITLIS we
may be pointing outside the synthetic wind fields, thus erroneous values will be
obtained.
If the LIDAR is situated in the y=0 line all the ranges are centered with the rotor, but
in case the LIDAR is displaced (position LIDAR 2), the area is not centered any more.
Therefore the original trajectory only is scanned at the reference distance. At the
other ranges the figure is disturbed. Nevertheless, in the figure is observed how this
second position lead to scan a bigger area for shorter ranges and more points are
Position LIDAR 2
Position LIDAR 1
D/2 D 3D/2
y=0
WITLIS
62
within the synthetic wind field when the range exceeds the reference one. This is
because it is situated further.
WITLIS
63
5.3. Development of the trajectories
Trajectory, a function with the parameters and states as input and the matposition as
output, is the function in charge of describing the different trajectories. Matposition is
a matrix with the trajectory coordinates.
Trajectory consists on a loop that has to be repeated as many times as the desired
amount of scanned points per snap shot. It is assumed that exactly the same
trajectory is repeated for all snap shots; therefore it is not necessary to call this
function more than once.
In each loop the sub function runningmode is called, which selects the function that
describes the trajectory defined by the scanning mode parameter. The outputs of this
function are the coordinates of a certain point and they are stored in the matposition
matrix.
The coordinates are always calculated assuming that the origin is the bottom corner
to the left, hence before saving the coordinates in matposition they have to be
transformed in traytocenter to a coordinate system in which the origin is in the middle
of the area. This point is aligned with the hub.
The trajectories are calculated at a certain distance called reference distance. The
reference distance is variable, but a value of one time the diameter is recommended
since this is the distance at which normally the wind is going to be measured.
According to the IEC 61400-12 a met mast for the anemometers should be at a
distance of between 2 and 4 times the rotor diameter. But since the rotor diameters of
the modern turbines exceed the hundred meters this distance is inappropriate. If
measurements of 10 m/s are taken 300 m away from a 100 m rotor-diameter-turbine,
it takes 30 seconds for the wind to impact the rotor, what is too much for the
controlling. This distance even exceeds the maximum range at which the LIDAR can
measure. Therefore a distance of one diameter is more convenient.
Straight Lines
The first group of trajectories differentiates from the second group the way they are
calculated. The straight curves need a step to define the successive points. As
WITLIS
64
explained in the Chapter 5.2.2 the step is the distance between two consecutive
scanning points. This distance is defined over a straight line; it has to be transformed
to stepx and stepy. In some cases these values remain the same, like for the zigzag,
but in the case of the hourglass they change.
The speed parameter has a clear influence over this distance between points: the
faster a snap shot with the same frequency, the bigger the distance between points.
This fact can be appreciated in the Figure 22. They both correspond to a trajectory
with mode 5 and scanning frequency of 100, but the Figure 22 (left) responds to a
fast mode and the Figure 22 (right) to a slow one. That means that, according to
Equation (13)Fehler! Verweisquelle konnte nicht gefunden werden., the first one
scans 100 points per snap shot, while the second one scans 200.
-60 -40 -20 0 20 40 60-80
-60
-40
-20
0
20
40
60Scanning mode 5 Mode fast
-60 -40 -20 0 20 40 60-80
-60
-40
-20
0
20
40
60Scanning mode 5 Mode slow
Figure 22: Scanning mode 5 with mode fast (left) and slow (right)
An interesting characteristic of the zigzag trajectories is that their points are so
distributed, that it seems that they describe horizontal or vertical lines (Figure 23).
The advantage over these simple lines is the sequence, as the zigzags do not cover
these lines at once but every few milliseconds.
shotsnapfrequencyscanningshotsnapspo .sec/../.int ⋅= (13)
WITLIS
65
-60 -40 -20 0 20 40 60-60
-40
-20
0
20
40
60Scanning mode 3
-60 -40 -20 0 20 40 60-60
-40
-20
0
20
40
60Scanning mode 4
Figure 23: Distribution points for Scanning modes 3 (left) and 4 (right)
Lissajous figures
The Lissajous curves, sometimes known as Bowditch curves after Nathaniel
Bowditch [CUND89], are the family of curves described by the following parametric
equations:
)sin( δ+= atAx
)sin(btBx =
The variable is the time t and δ is the phase. The constants A and B determine the
size of the curve while its shape depends on the ratio of frequencies a and b.
These two equations, which describe complex harmonic motion, make it easy to
describe the Lissajous figures in MATLAB. The WITLIS function that describes these
trajectories is called lissajous. In it A is defined as the half of
parameter.windfield.width, the width of the area at which the trajectory is described;
and B as the half of parameter.windfield.height. The angle remains constant to a
value of pi/2.
In this case a step between points is not required. The control over the points is
carried out with the time. As the first line of code of the function shows the time
needed pro snap shot is considered. This way if an entire path has to be described
every two seconds, the distance in grades per second is not 2pi, but one pi.
The desired Lissajous figures is selected changing the frequencies a and b since the
appearance of the figure is highly sensitive to the ratio a/b. The Table 6 shows these
parameters for each scanning mode here considered and the resulting figure. To
obtain closed figures the ratio a/b must be rational.
WITLIS
66
-40 -30 -20 -10 0 10 20 30 40-40
-30
-20
-10
0
10
20
30
40Scanning mode 6 a=1 b=1
-40 -30 -20 -10 0 10 20 30 40-40
-30
-20
-10
0
10
20
30
40Scanning mode 7 a=1 b=2
-40 -30 -20 -10 0 10 20 30 40-40
-30
-20
-10
0
10
20
30
40Scanning mode 8 a=3 b=2
-40 -30 -20 -10 0 10 20 30 40-40
-30
-20
-10
0
10
20
30
40Scanning mode 9 a=3 b=4
-40 -30 -20 -10 0 10 20 30 40-40
-30
-20
-10
0
10
20
30
40Scanning mode 10 a=5 b=4
-40 -30 -20 -10 0 10 20 30 40-40
-30
-20
-10
0
10
20
30
40Scanning mode 11 a=5 b=6
-40 -30 -20 -10 0 10 20 30 40-40
-30
-20
-10
0
10
20
30
40Scanning mode 12 a=9 b=8
a 1 1 3 3 3 5 9
b 1 2 2 4 4 6 8
Table 6: Lissajous parameters a and b
For a ratio of 1, the figure obtained is an ellipse, with special cases including circles
when A and B are equal and the angle is pi/2.
It may not seem necessary to study all these different combinations, since it seems
clear that the figure defined with a=9 and b=8, the last one, covers the area much
better than any of the other paths. But due to the fact that the laser simulated in
WITLIS is pulsed and not continuous, not all the “blue lines” are scanned, but only a
few points. Thus it can be that even though the optical device describes such a
complicated figure, the distribution of the points is quite similar to the distribution
obtained with another figure. In that case it is more advantageous to describe a
simpler figure given that the mirrors do not have to move so fast.
-60 -40 -20 0 20 40 60-60
-40
-20
0
20
40
60
-60 -40 -20 0 20 40 60-60
-40
-20
0
20
40
60
Figure 24: Distribution of points for modes 9 (left) and 12 (right).
The distribution of points of mode 9 and mode 12 (Figure 24) differ from each other;
the first one seems more linear while the second one is more chaotic, but both cover
the area. The simulations carried out in the next chapter help analyzing if it is worthy
to describe such a complicated figure as the scanning mode 12 or if the distribution
obtained with a simpler scanning mode is good enough.
WITLIS
67
Spiral
The spiral defined by the 13th scanning mode is described in the function spiral:
)()(
)(
ycimaginaryayycrealax
eyc ts
⋅=⋅=
= ⋅−
The spiral rate, s, is obtained adding 0.01 to a counter in each loop.
The spiral defined with these parameters covers the central area well, while it only
scans few points in the periphery. The Figure 25 represents this trajectory. It does not
look like a spiral since MATLAB joins the points with straight lines instead of curves.
-40 -30 -20 -10 0 10 20 30 40-30
-20
-10
0
10
20
30Scanning mode 13
Figure 25: Distribution of points for the Spiral
WITLIS
68
5.4. Wind simulation
With the increase in computer power it has become more and more common to
estimate dynamic wind loads on wind turbines, large bridges and other large
structures by time domain simulation of the forces and movements of the structure.
Time domain simulation is particularly widespread among wind turbine designers
because of non-linearities in the equations of motion and complex control strategies.
An important input to this kind of simulation is a time series of the fluctuating wind
(turbulence). For spatially extended structures, such as wind turbines, it is often
necessary to simulate entire fields of the atmospheric turbulence.
Since WITLIS finds mostly its application in the mid to large size wind turbines,
spatial variations in the turbulence have to be considered and a three dimensional
wind simulation is required. In order to explain how this simulation works a brief
introduction to the wind is required.
5.4.1. Characteristics of the Wind
Wind is the flow of air or other gases that compose an atmosphere. Although wind
may have a relatively constant mean speed over time periods over an hour, over
shorter times it is characterized by stochastic property changes. Wind has different
features like turbulence intensity or a power spectral function. These have been tried
to be modeled over the years with stochastic reproductions, based on characteristics
in the frequency domain carried out by measurements performed with anemometers.
Spectral Model of the Turbulence
The wind has two main stochastic components, the turbulence (short term
component) and the medium-term and long-term wind speed evolution (slower
component).
A power-spectrum analysis of horizontal wind speed is made over a wide range of
frequencies by piecing together various portions of the spectrum. There appear to be
two major eddy-energy peaks in the spectrum; one peak occurs at a period of about
4 days, and a second peak occurs at a period of about 1 minute (see Figure 26).
Between the two peaks, a broad spectral gap is centered at a frequency ranging from
1 to 10 cycles per hour. The spectral gap seems to exist under varying terrain and
synoptic conditions.
WITLIS
69
Figure 26: Van der Hoven’s spectral model
The most basic form to measure the turbulence is with the turbulence intensity TI. It
is defined by the ratio of the standard deviation of the wind speed to the mean (see
Equation (14).
In order to calculate the short-term mean wind speed it has to be referred to mean
wind speed averaged over some short time period. This time period has to be longer
than the characteristic time of the fluctuations in the turbulence [MANW02][12], which
according to Figure 26 is around one minute. Therefore the time period can be as
short as few minutes and as long as an hour. In the industry this value is normally
taken as ten minutes. The sample rate is normally at least once per second.
In the case studied in this Master Thesis the short term speed and high sampling rate
are of great importance, since a quick controlling of the turbine within seconds is
desired.
The turbulence intensity, TI, is defined as:
UTI σ
= (14)
where σ is the standard deviation, given in sampled form by:
2
1)(
11 ∑
=
−−
=N
ii UU
Nσ
Turbulence Power Spectral Densities
Many models of power spectral densities (SPDs) have been proposed. The most
important ones have been the von Karman [KARM48], the Frost [FROS78] and the
WITLIS
70
Kaimal [KAIM72] models. The norm IEC 61400-1 Ed.3 [IEC604] includes two
stochastic turbulence models, the Mann uniform shear model and the Kaimal spectral
and exponential coherence model. For both the turbulent velocity fluctuations are
assumed to be a stationary, random vector field whose components have zero mean
Gaussian statistics.
But it has been the Kaimal model with some modifications that has been used as
standard in the wind turbine industry.
The component power spectral densities are given in non-dimensional form by:
352
)/61(
/4)(
hubk
hubk
k
k
UfL
UfLffS
+=
σ
where
f is the frequency in Hz
k is the index referring to the velocity component direction
Sk is the single-sided velocity component spectrum
σk is the velocity component standard deviation
Lk is the velocity component integral scale parameter
And with
∫∞
=0
2 )( dffSkkσ
The turbulence spectral parameters σk and Lk depend on σk and 1Λ respectively,
standard deviation and scale parameters of the turbulence.
Coherence
The coherence function is a frequency dependent measure of the amount of
correlation between the wind speeds at two points in space. The usual form of the
coherence function is exponential; the one given by Frost is expressed in:
( ) ( )( ) ⎥⎦⎤
⎢⎣⎡ +−=
5,022 /12,0/12exp),( chub LrUfrfrCoh
where
Coh(r,f) is the coherence function defined by the complex magnitude of the
cross-spectral density of the longitudinal wind velocity components at two spatially
separated points divided by the auto spectrum function
WITLIS
71
r is the magnitude of the projection of the separation vector between the
two points on to a plane normal to the average wind direction
f is the frequency in Hz
Lc =8,1 1Λ is the coherence scale parameter
From time to space domain The turbulence models help defining the speed for a fixed point in the time domain.
And the Taylor’s hypothesis describes from it a wind field in the space domain The
Taylor’s hypothesis [HOLM05] assumes that the advection contributed to the bulk
wind field by turbulent circulations themselves is small; therefore the advection of a
turbulent field past a fixed point can be taken to be entirely due to the mean flow. The
other name this hypothesis receives, “frozen turbulence”, illustrates well this idea.
It only holds if the relative turbulence intensity is small; that is:
1<<Uu
where U is the mean velocity and u the eddy velocity. Then the wind speed series
can be transformed from time domain into space domain by using the relation t = x/U
is a good approximation. This basic principle leads to a full-field method, since it
completely fills the three dimensional block of space with a grid of instantaneous wind
speeds.
5.4.2. Computational simulation of the wind
The synthetic wind field evaluated in this project is generated with Vindsim, a
turbulence simulator based on stochastic wind field simulation. The basic working
mode of the Vindsim method is the simulation of stochastic wind speed time series at
several points in a proper grid for wind turbine simulation. Most of the wind simulator
programs store the data in a Cartesian grid, but Vindsim uses a Polar one with centre
at hub height and parallel to the wind turbine rotor. The time series are forced to
retain the statistics and spectral characteristics found in the atmosphere explained in
section 5.4.1.
Vindsim makes use of the Kaimal turbulence model. That means that the inputs of
the program are single point power spectral densities and the coherence function,
WITLIS
72
which describes how turbulence is correlated as a function of spatial separation,
mean wind speed and frequency.
Basic Fourier Simulation
It is assumed that in turbulent flow the actual flow velocity is equal to the average
velocity U plus the fluctuating turbulent velocities u,v,w in the x,y,z directions,
respectively. The x-axis is taken in the direction of U , so the instantaneous flow
velocity vector is (U + u, v, w), assuming average transversal (V ) and vertical (W )
wind speed equal to zero. The y-direction is across the wind, and the z-direction is
upwards. It is not possible to specify the values of u,v,w as functions of time, but from
their randomness a statistical description is possible. By definition, the average
velocities are zero, but their variances, the average values of their squares, are not.
The distribution of the velocities does not appear to be Gaussian on small scales, but
large-scale turbulence is approximately Gaussian [NIEL04].
In this sense, developing methods for turbulence simulation it is convenient to
operate with Gaussian variables, since these may be added and the sum is still
Gaussian. Any linear combination of a set of Gaussian variables produces a new
Gaussian variable. This implies that Fourier transformation maps Gaussian time
series onto Gaussian spectral representations and vice versa, allowing the simulation
of a stationary process in frequency domain X(f) and subsequently its transformation
into time domain x(t) by inverse FFT [PRES92]. This is done by:
∑=
Δ=M
k
ftikK eXtx
0)(
where M is the length of the time series, which must be a power of 2 to take
advantage of the efficient FFT algorithm. The Fourier modes are random, and their
ensemble averaged variance should match the empirical power spectrum S (f).
μ=oX
kk fyfkSX ΔΔ= )( for k=1…M/2
Here, the basic frequency step is defined by the duration of the time series Δf =2_/T,
and yk is a set of independent pseudo-random Gaussian variables with zero mean
and unit variance.
WITLIS
73
The Fourier simulation method is widely used. The aeroelastic simulation program
FLEX (Øye 1992) and its turbulence simulator Vindsim normalize the simulated time
series such that each simulation matches the prescribed variance exactly.
WITLIS
74
5.5. Wind field interpolation
Simulated wind fields have a discrete character; this means that winds speed is
defined at particular nodes in a particular grid representing three dimensional space.
Due to limitations in memory and computational time this grid can have a rather
coarse distribution. Therefore an interpolation to the whole area is needed.
.The line of sight speed (vlos) is calculated through an interpolation of the synthetic
field calculated with Vindsim and the relative spatial error field is calculated from two
interpolated fields. This relative error field is then used in the function statistics to
weight how good certain variables (like trajectory or scanned-points-per-second
frequency) are to scan the wind.
It is known for all that an error is derived from an interpolation, but this is not a major
problem when this fact is taken into account when the conclusions are made.
5.5.1. General interpolation procedure
The interpolation method used by WITLIS is a linear interpolation using a
discretization of the interpolating area with a Delaunay triangulation, which is already
implemented in MATLAB.
The synthetic field is calculated with Vindsim. This program generates a cylindrical
wind field with polar coordinates. The definition of the fields used for this project is
9x39.
The sequence of the interpolation and measurement of the wind is significant. There
are two main possibilities: to calculate the vlos from the polar grid with a definition of
9x39, like shown below in Method 1, or to interpolate the synthetic field first to the
WITLIS grid to measure vlos afterwards (shown in Method 2).
WITLIS
75
Method 1
The main advantage of the first method is the save of space, a big issue in this
project. The WITLIS grid is normally bigger than 9x39, what means that if the
interpolation to the WITLIS grid is only needed to calculate a mean field, this can be
firstly calculated and then interpolated, saving this way both program running time
and memory space. But numerous errors are derived from this interpolation. If the
speed on the line of sight is measured from the polar grid, the further comparison
between synthetic and calculated fields, both interpolated to the grid according to
WITLIS, will also include the errors from the interpolation of the synthetic field.
On the other hand, if the synthetic field is firstly interpolated to the WITLIS grid and
then the speed on the line of sight is measured from there, the comparison between
Calculated wind field Synthetic field
interpolated to the
WITLIS grid
vlos
coordinate
Comparison
Points of trajectory Polar
synthetic field
WITLIS
76
fields is much fairer, since the errors are mainly due to the input characteristics of the
scanning mode, the object of study of this project, not to the interpolation.
Method 2
Despite the additional running time and the lost of space WITLIS operates according
to the second method, because a good statistical evaluation of each scanning mode
is of main importance to meet the objective of this project.
5.5.2. Delaunay triangulation
The so called Delaunay triangulation was proposed by Boris Delaunay in 1934 [17]. It
is a triangulation such that no point of a set of points is inside the circumcircle of any
other triangle. Therefore the triangulation from Figure 27 (left) is erroneous: the
circumferences contain more than 3 points.
Polar
synthetic field
vlos
Comparison
Points of trajectory
Synthetic field
interpolated to the
WITLIS grid
Calculated wind field
WITLIS
77
Figure 27: Erroneous Delaunay triangulations
Delaunay triangulations also try to maximize the minimum angle of the triangles. So if
looking at two triangles ABD and BCD with the common edge BD (Figure 27 right),
the sum of the angles α and γ has to be less than or equal to 180° to meet the
Delaunay condition. In this case the sum of α and γ is bigger than 180°, so the
Delaunay conditions are not met.
In these two cases the problem can be solved by switching the common edge BD for
the common edge AC, the so called flipping technique (Figure 28).Now the conditions
of the empty circles and of the angle are met.
Figure 28: Correct Delaunay triangulation
MATLAB uses this kind of interpolation by default when using the function griddata.
Two examples of the triangulation done by WITLIS are shown below. It can be seen
that for the scanning mode 3 (horizontal zigzag) the size of the triangles is very
regular (Figure 29). On the contrary, for the 8th trajectory (Figure 30) much more
irregular triangles are obtained. This is partly due to the high concentration of points
on the edges on the Lissajous figures, whereas the distribution of the points of the
zigzag, and its triangular shape itself, help for a more uniformed distribution. But this
last trajectory has a big drawback. It leaves a lot of space that cannot be extrapolated
on both sides. This means that no data will be obtained for this area.
WITLIS
78
-60 -40 -20 0 20 40 60-60
-40
-20
0
20
40
60
Figure 29: Delaunay triangulation for trajectory 3 and 100 shooting points
-60 -40 -20 0 20 40 60-60
-40
-20
0
20
40
60
Figure 30: Delaunay triangulation for trajectory 8 and 100 shooting points
But not every Lissajous trajectory covers the field as well as in Figure 30. If a circle is
described, for instance, a lot of space is lost. Besides, the triangles described within
WITLIS
79
this figure are even more irregular than for the 8th trajectory. As shown in Figure 31
the inner triangle has an excessive size, resulting from it a very poor interpolation.
-60 -40 -20 0 20 40 60-60
-40
-20
0
20
40
60
Figure 31: Delaunay triangulation for trajectory 6 and 100 shooting points
Evaluation of scanning modes.
80
6. Evaluation of scanning modes.
The simulations performed for evaluation of the scanning modes are shown in this
chapter along with the analysis procedures used for comparison of the accuracy of
each scanning configuration.
It is intended to simulate a time series of 10 minutes which is the standard time used
in the wind industry. Therefore, the amount of memory required by WITLIS is
relatively high due to the large size of the wind fields. Particular characteristics of
MATLAB’s memory management have turned to be a weak point of WITLIS; although
measures to optimize memory usage have been taken, there is no possibility yet to
simulate full 10-minutes time series.with a normal desktop computer. It may be the
usage of structures for the different variables what leads to a inefficient use of the
memory in MATLAB.
The time step used by Vindsim has been 0.08 seconds, which is 1second/0.08= 12.5
generated cross sections per second. Vindsim has generated ten minutes (12.5x600
sec) with a 9x32 nodes grid, resulting this way a 289x8192 matrix. But, as explained
in chapter 5.5, these three matrixes (one for each wind component) have to be
interpolated to the grid expressed in WITLIS, 27x27. The interpolated matrixes
themselves do not represent a problem, but the further handle of these, the
calculation and plotting of figures, videos and new matrixes runs out the memory in a
manner that is not fully understood yet.
Another problem has been the running time of the program. To try to make it as fast
as possible only a few loops have been used, trying always to handle the matrixes in
a vectorized way.
Instead of calculating and interpolating always the three synthetic wind fields over
and over again, these are saved under a key name that encapsulates the diameter of
the wind, the mean speed, the turbulence and the seed used by VINDSIM. So when
WITLIS is run, it tests first if the interpolated wind fields for these characteristics have
already been saved. In case they have, the program just loads them under a certain
name. If not, they have to be calculated, so the program needs more time to get the
final results.
Evaluation of scanning modes.
81
Even though the matrixes have been minimized and the program has been handled
very efficiently, it has been not possible to simulate ten minutes. Instead a value of
180 seconds has been proposed, since it meets both accuracy and time
management. The simulation for three minutes reflects the tendency of the
measurement statistics and lets perform the calculations in a sensible time span (in
average one hour for a scanned-points-per-second frequency of 100).
6.1. Statistical Analysis
All the statistical analysis takes place in the statistics function in WITLIS. The main
inputs of this function are the calculated and the synthetic interpolated wind fields.
The statistical analysis has been divided into two parts: one part analyses how good
the estimated instantaneous wind field is with respect to the spatial distribution on an
area transversal to the main wind; and one second part studies the accuracy with
respect to time. The first part illustrates better how good a trajectory is to define a
whole instantaneous wind field area. The second analysis shows what the turbine
“sees”.
Even though these two analyses present normally the same tendency or behavior, it
may be that some configurations are equally good to measure the spatial distribution,
in average, but they differ in the analysis of the time distribution. This is due to the
way the statistics are calculated, explained along this chapter.
To perform the spatial analysis an average of both, the synthetic and the calculated
fields in the temporal dimension is required. A mean value of the wind for each point
of the spatial grid along the 180 seconds is calculated and thus a two dimensional
matrix is obtained. According to Equation (15 these two averages are subtracted and
normalized to the synthetic one, obtaining this way a relative spatial error matrix,
which contains the error for each node in the transversal area.
spacesynth
spacecalcspacesynth
XXX
spaceError.
..100.−
⋅= (15)
Nevertheless it is difficult to compare the different relative error wind fields with their
plotting. The Figure 32 are the representation of the mean relative spatial error
without collision for modes 4 (left) and 8 (right). This representation is not enough to
Evaluation of scanning modes.
82
take a sound decision about which scanning mode leads to a lower spatial error and
therefore a quantitative analysis is required.
-60-40
-200 20
4060
-100
-50
0
50
100-4
-2
0
2
4
Height[m]
Mean relative spatial error windfield for 180 sec with mode 4
Transversal [m]
Ret
ativ
e er
ror (
%)
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-60-40
-200 20
4060
-100
-50
0
50
100-4
-2
0
2
4
Height[m]
Mean relative spatial error windfield for 180 sec with mode 8
Transversal [m]
Ret
ativ
e er
ror (
%)
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Figure 32: Mean relative spatial error representation for modes 4 (left) and 8 (right) for 180 sec. without collision.
A reasonable way to come to a parameter that measures the error is through the Chi
Square statistic. It is the addition of all the observed values compared to the
theoretical ones:
∑ −=
i ti
tioi
xxxX
22 )(
In this case the observed ( oix ) and the theoretical ( tix ) values correspond to the
estimated and the synthetic values, respectively. The better the estimation of the
wind field, the lower the statistic. In effect, if the statistic is zero, it means that the
observed and theoretical values are exactly the same.
The calculated wind field is not normally complete as a result of the missing speed
values, generally in the periphery. This is due to the impossibility of extrapolation in
the domain generated by the Delaunay triangulation. This fact shows difficulties when
calculating the relative spatial error, since MATLAB cannot operate with undefined
numerical results. This trouble is solved by avoiding or ignoring these undefined
results. This way, if a calculated wind field has a speed value for only the 80% of the
points, the relative error field also reduces its area on a 20%. On the other hand, this
method of eliminating the undefined results devirtualizes the value of the statistic. A
scanning arrangement that only scans the center of the area shows a much better
statistic than a configuration that scans the 95% of the area since the more analyzed
points, the higher the statistic. Therefore the statistic Chi Square has to be divided by
the number of summed points. The relative statistic is calculated according to
Equation (16Fehler! Verweisquelle konnte nicht gefunden werden. and it
Evaluation of scanning modes.
83
illustrates the mean error of each node of the grid. If it is a 1% it means that, in
average, the values calculated are 1% over the real value.
100
)(1
2
2 ⋅
−
=∑=
Nx
xx
X
N
i ti
tioi
r (16)
Despite its great significance, this value is not decisive. If only a 30% of the target
area is scanned with a certain configuration, it means that all the scanned points per
snap shot are within this small area. Then the values interpolated to the small area
are much more precise. That’s exactly why the scanning modes that tend to scan
small areas bring about lower chi-square spatial statistics than the trajectories that,
with the same configuration, scan larger areas, even though the correction of dividing
the statistic by the number of points is applied.
The scanned area has always to be considered when trying to choose the best
scanning configuration. It is inversely proportional to the density of scanned points.
The scanning mode that presents the best spatial statistic with a big scanned surface
is judged as the best option.
The second statistic test studies the time distribution. This analysis requires the
ensemble average of the wind speeds at all nodes in a snapshot. It means that an
average value of each snap shot is associated to the time. The representation of
these two vectors is interesting because it shows the wind that the turbine “sees”.
The relative spatial error vector is calculated according to Equation (17.
timesynth
timecalctimesynth
XXX
timeError.
..100.−
⋅= (17)
For the purposes expressed in Chapter 5.4.1 the mean value and the standard
deviation of the two wind fields are calculated. The standard deviation used to
calculate the turbulence intensity is the temporal one.
6.2. Measurements
In this section, it is shown the results of running WITLIS while varying only one
parameter at a time. For each step a table with the constant values and another one
with the results is displayed. The table with the constant values contain the total
simulated time under the name time, the direction of the measurements under wake,
the collision situation, the direction correction, the speed mode, the scanned-points-
Evaluation of scanning modes.
84
per-second frequency and the range at which the measurements are taken. When
the variable wake is set to no, it means that the LIDAR has measured the inflow.
The table with the results contains the spatial and the time relative chi-square
statistics and the scanned area in relation to synthetic one. This table also shows the
mean value of the calculated wind field and the spatial and time standard deviation.
6.2.1. Measurements of the synthetic wind field
The simulations have been performed using only one stochastic wind field with 8m/s
and 10% turbulence. These characteristics are assumed to be averages found at a
north location in Germany.
Synthetic
x [m/s]
Ssp [m/s] St
[m/s] 7,69 0,28 0,74
Table 7: Statistical values of the synthetic field
The mean value of the synthetic field for 180 seconds is 7,69 m/s with a spatial
standard deviation of 0,28 (Table 7). The temporal standard deviation is higher (0.74)
than the spatial one. This fact means that the wind suffers more variations in the time
than in the spatial dimension.
The length of the time period to measure the turbulence intensity is normally 10
minutes, but since these have been impossible to simulate the TI has been
calculated for a time period of 3 minutes. According to Chapter 5.4.1 this is possible
given that the period is bigger than the characteristic time of the fluctuations (one
minute). The degree of turbulence is calculated by:
=⋅== 10069,774,0
vTI σ 9,62 %
It is expected that, if the entire ten minutes had been analyzed, the mean value
would have been 8 m/s and the turbulence intensity 10%.
The mean synthetic wind field for 180 seconds for a mean value of 8m/s and a
turbulence of 10% is shown in Figure 33. In it the vertical wind shear, which is in fact
a logarithmic profile, is noticed.
In all the spatial figures represented in this chapter the coordinates shown in the X
and Y axes are expressed in the nacelle coordinates, what means that a zero in the
height axis corresponds with the hub height (102m).
Evaluation of scanning modes.
85
-60-40
-20 020
4060
-100
-50
0
50
1007
7.5
8
8.5
Height[m]
Mean sint. windfield in the space for 180 sec
Transversal [m]
Win
d sp
eed
[m/s
]
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
8.1
8.2
Figure 33: Mean spatial synthetic wind field for 180 sec.
The Figure 34 shows the temporal variation of the synthetic wind field with a time
averaging of two seconds. The mean values in the time change from 9,2m/s to
6,2m/s. This variation is much higher than the one that the spatial mean wind field
presents, as the standard deviations shown in Table 7 point out.
0 20 40 60 80 100 120 140 160 1806.5
7
7.5
8
8.5
9
9.5Mean synthetic wind speed in the time for 180 sec
Time [sec]
Win
d sp
eed
[m/s
]
Figure 34: Mean temporal wind speed distribution.
6.2.2. Measurements of the calculated wind fields. Comparison with the synthetic one.
During the analysis the different setups which did not show a good performance were
eliminated immediately. For instance, if in the first step it is probed that the spiral
shows a bad performance, it is no longer analyzed.
Evaluation of scanning modes.
86
There are two different simulated positions. The first one assumed to be in the
spinner, inside the hub, looking into the inflow and encounters no collision. The
second position of the LIDAR has been determined by a geometry which should be
similar to that of the multi-MW wind turbines to be installed in offshore wind farms.
The LIDAR is assumed to be positioned at a side of the helicopter platform at a
position which is not interfering with the normal work of the maintenance crew. Its
coordinates referred to the nacelle system are negative in the x and y directions and
positive in the z direction.
Trajectories
The first variable studied has been the trajectory. All the trajectories have been
simulated for the configuration shown in Table 8: Configuration for the analysis of the
trajectories.
Time [s] 180 Wake No Collision No Direction Correction No Mode fast Freq [Hz] 100 Range [m] 116
Table 8: Configuration for the analysis of the trajectories
The first two scanning modes have been impossible to implement as the interpolation
method used by WITLIS (see Chapter 5.5) does not work for aligned points.
Nevertheless it is known in advance that they are not good trajectories to describe an
entire area. The errors at the borders would have been enormous.
.
Calculated
Scanning Mode X2
r Spatial X2r Time Area
x [m/s]
Ssp [m/s]
St [m/s]
3 zz6 2,71% 0,37% 79% 7,15 0,32 0,71 4 zz6 2,44% 0,32% 78% 7,19 0,29 0,72
5 4,27% 0,51% 84% 7,07 0,35 0,67 6 4,18% 0,81% 69% 6,91 0,18 0,66 7 3,25% 0,43% 82% 7,11 0,28 0,71 8 3,15% 0,36% 85% 7,16 0,31 0,70 9 3,21% 0,37% 86% 7,15 0,31 0,70
10 3,14% 0,35% 86% 7,16 0,32 0,69 11 3,13% 0,35% 86% 7,16 0,32 0,70 12 3,21% 0,36% 86% 7,16 0,32 0,70 13 0,22% 0,15% 28% 7,41 0,15 0,75
Table 9a: Statistical values for the different trajectories
Evaluation of scanning modes.
87
The scanning modes 3 and 4, the zigzags, have been firstly calculated for a defined
number of 6 triangles. That means that 12 triangles (six forth and six backwards)
have been described pro snap shot.
The Table 9Fehler! Verweisquelle konnte nicht gefunden werden. illustrates the
values obtained for each trajectory. The trajectories that present a good performance
are highlighted.
The performance in terms of covered area of the scanning mode 5 is better than the
zigzag trajectories, 84% vs. 78%, but its relative statistics are lower. These values
are not enough to make a decision about which mode is better. The mean values and
the standard deviations of the zigzags show that the mode 5 approximates to the
synthetic values less than the zigzags.
The sixth trajectory corresponds to the description of a circle, the actual trajectory
described by the Windcube™ at a defined range. This path leads to a very small
interpolated area (68 %), smaller than the area achieved with any of the straight
lines, while its relative error statistics are higher. As seen in Figure 35 the details
within the area are not detected; Its mean wind speed (6,91 m/s) is also the worst
from all scanning modes since it is the most distant mean value to the real one (7,69
m/s). The low standard deviations show that this trajectory reflects neither the spatial
nor the time variations.
-60 -40 -20 0 20 40 60-60
-40
-20
0
20
40
60
Height[m]
Snapshot of calculated windfield. Scanning mode:6. Frequency: 100Hz. At 116m with mode fast
Tran
sver
sal [
m]
6.5
7
7.5
8
8.5
Figure 35: Snap shot of the calculated wind field for the sixth scanning mode.
The comparison of the scanning modes 5 and 7 is interesting in order to analyze the
suitableness of the straight lines and the curves. Figure 36 and Figure 37 are the X-Y
view of a snap shot of the modes 5 and 7 respectively. Both trajectories are very
similar, but the first one leads to a major number of interpolated points. The wind
speeds represented with different colors are also different. But according to the
values shown in the table above the second ones are more accurate.
Evaluation of scanning modes.
88
-60 -40 -20 0 20 40 60-60
-40
-20
0
20
40
60
Height[m]
Snapshot of calculated windfield. Scanning mode:5. Frequency: 100Hz. At 116m with mode fast
Tran
sver
sal [
m]
6
6.5
7
7.5
8
8.5
Figure 36: Snap shot of the calculated wind field for the scanning mode 5.
-60 -40 -20 0 20 40 60-60
-40
-20
0
20
40
60Snapshot of calculated windfield. Scanning mode:7. Frequency: 100Hz. At 116m with mode fast
Height[m]
Tran
sver
sal [
m]
6
6.5
7
7.5
8
8.5
Figure 37: Snap shot of the calculated wind field for the scanning mode 7.
The rest of the scanning modes but the 13th are more complicated Lissajous figures
and they all obtain similar results. These paths lead to an interpolated area close to
86% and have pretty low statistics values. The comparison of these values with the
ones obtained for the 5th path show that the Lissajous figures are better than this last
one, since the interpolated area is the same but present lower statistics.
Given that the simplest good trajectory is required, the scanning mode 8 is
considered to be better than the other Lissajous figures. The length of this curve is
shorter than the one described by the others, what means that the optical devices
can move slower.
The 13th trajectory describes a spiral. It may have good chi square results, but its
scanned area is a 28.2% of the interpolated area.
The chi-square statistics obtained in this first step are relatively high. That’s because
no correction of the direction, as explained in Section 5.2.5, has been yet applied.
Evaluation of scanning modes.
89
This fact can be observed in Figure 38, where the mean relative spatial error for
mode 8 is shown. In the center the error is close or equal to zero, because the laser
beam is parallel with the mean wind vector. But in the periphery, where the speed
vector on the line of sight separates more and more from the mean speed vector, the
error increases till a 15%.
-60-40
-20 020
4060
-100
-50
0
50
100-5
0
5
10
15
20
Height[m]
Mean relative spatial error windfield for 180 sec with mode 8
Transversal [m]
Ret
ativ
e er
ror (
%)
0
2
4
6
8
10
12
14
16
-60 -40 -20 0 20 40 60-2
0
2
4
6
8
10
12
14
16
18
Height[m]
Mean relative spatial error windfield for 180 sec with mode 8
Ret
ativ
e er
ror (
%)
0
2
4
6
8
10
12
14
16
Figure 38: Mean relative spatial error for mode 8 from two views (angular and X-Z view)
Another remarkable fact, the vertical shear of the wind field, is noticed when plotting
the calculated wind field for 180 seconds (Figure 39). In it the effect of the direction of
the vector is also noticed.
-60-40 -20
020
4060
-100
-50
0
50
1006
6.5
7
7.5
8
Height[m]
Mean calculated windfield for 180 sec with mode 8
Transversal [m]
Win
d sp
eed
[m/s
]
Figure 39: Mean calculated wind field for 180 seconds for mode 8
This first step has shown that the most suitable trajectory is either the 4th one or the
8th one. Given that the 4th has proved high potential the variable of the number of
triangles described has also been studied. It has been diminished and augmented in
one unit (Table 10b).
Evaluation of scanning modes.
90
Calculated
Scanning Mode X2r Spatial X2r Time Area
x [m/s]
Ssp [m/s]
St [m/s]
4-->zz5 2,74% 0,33% 81% 7,182 0,297 0,71 4-->zz6 2,44% 0,32% 78% 7,19 0,29 0,72 4-->zz7 2,62% 0,32% 76% 7,19 0,31 0,70
Table 10b: Statistical values for different number of triangles described for the scanning mode 4
Even though all three variables lead to similar results there is a tendency: the more
number of triangles described the more interpolated area. Nevertheless, the more
number of triangles, the more distance to be covered by the optical devices and
higher the speed. A value of 6 triangles is further considered because harmonizes
both, good statistical results with a lower distance to describe than for higher values.
Direction Correction
After the analysis of the trajectories, that shows that either the 4th or the 8th
trajectories are the best, a correction to the direction is applied.
Time [s] 180 Wake No Collision No Direction Correction YES Mode Fast Freq [Hz] 100 Range [m] 116
Table 11: Configuration for the analysis of the direction correction
These two simulations have been run with the values shown in Table 11Fehler! Verweisquelle konnte nicht gefunden werden.. As seen in Table 12 the correction
of the direction has reduced the statistics drastically.
Calculated Scanning
Mode X2r Spatial X2
r Time Area x
[m/s] Ssp [m/s]
St [m/s]
4-->zz6 0,029% 0,004% 79% 7,69 0,29 0,77
8 0,029% 0,003% 85% 7,69 0,27 0,75
Table 12: Statistical values for the trajectories 4 and 8 when a direction correction is applied
The spatial chi-square statistic for the 8th mode has been reduced from a 3,15%
down to a 0,029% (Table 12). This improvement is shown in Figure 40. Now the
maximum error is a -3%, while without correction it even reaches a 16%. It is also
appreciated that now the error is more homogeneous, not like in Figure 38, where all
the errors were concentrated in the periphery.
Evaluation of scanning modes.
91
Due to the reduction of the statistics obtained the correction of the direction is
applied. Nevertheless, its deployment in the measurement campaigns will lead to a
higher error, since the direction of the wind may not be completely perpendicular to
the rotor. It also increases the processing time.
-60 -40 -20 0 20 40 60-4
-3
-2
-1
0
1
2
3
Height[m]
Mean relative spatial error windfield for 180 sec with mode 8
Ret
ativ
e er
ror (
%)
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Figure 40: X-Z view of mean relative spatial error for mode 8
In the first step of this analysis the advantage of the scanning mode 4 over the 8 one
was its lower relative statistics, but after the direction correction this difference has
been diminished. It has not happened the same with the bigger interpolated area
achieved with the 8th path, so it can be conclude that the eight trajectory leads to
better results for the conditions expressed in Table 11.
Collision
The influence of the collision has been simulated for the scanning modes 4 and 8
under the characteristics summarized in Table 13Fehler! Verweisquelle konnte nicht gefunden werden..
Time [s] 180 Wake No Collision YES Direction Correction yes Mode fast Freq [Hz] 100 Range [m] 116
Table 13: Configuration for the analysis of the collision
As recorded in Table 14 the number of collisions suffered for each trajectory was
slightly different With the zigzag trajectory the ~40% of the shots did not give a valid
measurement since they collided either with the rotor blades or with the nacelle. The
scanning mode 8 leaded to the lost of the ~44% of the shots, what is a total of 7884
non scanned points.
Evaluation of scanning modes.
92
Calculated Ner of collisions Scanning
Mode X2
r Space X2
r Time Area x
[m/s] Ssp [m/s]
St [m/s] Absolute Relative
4-->zz6 0,02% 0,05% 58% 7,65 0,17 0,76 7236 40,20%
8 0,04% 0,04% 68% 7,69 0,20 0,69 7884 43,80%
Table 14: Statistical values for the trajectories 4 and 8 when the collision is analyzed
These missing values reduce both, the interpolated area and the density, because
also points without the scanned area get lost. Without collision the scanning mode 8
leads to an interpolated area of 85%, while the collisions reduce this value down to a
68%. The Table 15 shows the relative change produced in the statistics and area due
to the collision. According to this table the area is reduced for the scanning mode 4 to
a ~74% of the area obtained without collision.
Influence of collision over the
variables Scanning
Mode X2r Sp X2
r Time Area 4-->zz6 72,09% 1129,88% 74%
8 126,17% 1349,10% 80%
Table 15: Statistics and interpolated area in case of collision related to the ones obtained without collision
The statistics increase all due to the collision with a rare exception, the space relative
spatial error for the scanning mode 4. In has been reduced on a 28%. This is due to
the smaller scanned area.
The collision has a stronger effect on the statistics based on the time domain than on
the space domain, which increase about 1200%. This value changes depending on
the path.
0 20 40 60 80 100 120 140 160 180-4
-3
-2
-1
0
1
2
3
4
5
6Mean relative time error for 180 sec with mode 8 and collision
Time [sec]
Erro
r (%
)
0 20 40 60 80 100 120 140 160 180-4
-3
-2
-1
0
1
2
3
4
5
6Mean relative time error for 180 sec with mode 8
Time [sec]
Erro
r (%
)
Figure 41: Relative time error for mode 8 with (left) and without (right) collision
Evaluation of scanning modes.
93
Figure 41 reflects the increment of the time error due to the collisions. The errors
under collision conditions reach a 5% while the non-collision case had a maximum of
2%.
Relatively the error has been highly incremented, but in absolute values the time
errors obtained with collision are still acceptable. The relative statistics for the
scanning mode 8 of 0,04% mean a 0,3 m/s error, a comparable value to the
uncertainty of the anemometer calibration (0,2 m/s) [21].
Speed Mode
The next variable to study is the speed mode. All the simulations run till now have
been configured for a fast speed mode, what means that it takes one second to
describe a whole trajectory. Now the speed mode is variable (Table 16) and the other
values remain constant.
Time [s] 180 Wake No
Collision No Direction Correction Yes
Mode variable Freq [Hz] 100 Range [m] 116
Table 16: Configuration for the analysis of the speed mode
According to Table 17 the statistics obtained for the slow mode are slightly superior to
the ones derived from the fast one, while the scanned area remains the same. It was
expectable for the temporal statistic to be bigger for the slow mode, since a snap shot
is obtained in two seconds instead of one, losing this way temporal resolution. On the
contrary the spatial resolution was expected to be bigger for the slow mode, since
just half of the points are scanned per snap shot.
Calculated Speed Mode X2
r Space X2r Time Area
x [m/s]
Ssp [m/s]
St [m/s]
Slow 0,06% 0,01% 85% 7,69 0,28 0,74 Fast 0,05% 0,004% 85% 7,69 0,27 0,75
Table 17: Statistical values for the 8th trajectory with speed modes slow and fast.
Nevertheless the increment of the statistics for the slow mode is small (+0,01 %) and
it supposes double shots per point frequency, increasing this way the accuracy of the
punctual speed. Because of this reason now on the slow mode is considered, even
though the fast mode leads to better results.
Evaluation of scanning modes.
94
Scanned-points-per second Frequency
Till now all the simulations have been run for a scanned-points-per-second frequency
of 100. That means that a total number of 100 wind measurements per second have
been achieved. Assuming a fixed laser frequency of 20 KHz this scanned-points-per
second frequency traduces in a total shots per point frequency lower than 200. The
faster the optical device moves, the higher is this shots per point frequency.
Even though it cannot be proved or analyzed with WITLIS, for a fixed laser frequency
the higher the scanned-points-per second frequency is, the less accurate is the
measurement per point.
This relation depends on the weather conditions, since the accuracy is reduced in
case there are few aerosols in the atmosphere.
There is a frequency though at which the accuracy is inadmissible. It would be
interesting to simulate this fact. Thus the simulation would drop a maximum scanned-
points-per-second frequency that should not be exceeded. Otherwise the accuracy of
the scanned points would not be reliable.
If WITLIS proves that the minimum scanned-points-per-second frequency needed to
obtain reliable wind fields is higher than the maximal frequency that leads to accurate
wind speeds, either the LIDAR technology has to be improved or further trajectory
researches have to be done.
In order to calculate the minimum scanned-points-per-second frequency that still
leads to accurate results various simulations for different frequencies are done (Table
18).
Time [s] 180 Wake No
Collision No Direction Correction Yes
Mode slow Freq [Hz] variable Range [m] 116
Table 18: Configuration for the analysis of the speed mode
The scanned-points-per second frequencies 100, 50, 25, 20, 13, 10 and 5 Hz have
been simulated. The statistical values obtained with each of these frequencies are
summarized in Table 19. In it the influence of the frequency over the area is shown:
the lower the scanned-points-per second frequency, the less interpolated area. Both
spatial and time statistics increase for decreasing frequencies, nevertheless not in
the same proportion. The time statistic boosts from a 0,01% to a 0,18%, what
Evaluation of scanning modes.
95
responds to an increment close to a 1800%.The spatial statistic increment, however,
reaches the 433%.
Calculated
Freq X2r Space X2
r Time Area x
[m/s] Ssp [m/s]
St [m/s]
5 0,26% 0,18% 62% 7,77 0,23 0,82 10 0,08% 0,08% 79% 7,67 0,28 0,69 13 0,07% 0,02% 85% 7,70 0,26 0,77 20 0,07% 0,02% 85% 7,70 0,27 0,72 25 0,06% 0,01% 85% 7,69 0,28 0,71 50 0,05% 0,01% 85% 7,69 0,27 0,74 100 0,06% 0,01% 85% 7,69 0,28 0,74
Table 19: Statistical values for the 8th trajectory with different shooting frequencies.
The optical device describes the path independently of the scanned-points-per
second frequency. But the lower the frequency gets, the less alike is the distribution
of points to the Lissajous figure. The Figure 42 illustrates this tendency. When the
scanned-points-per second frequency is reduced down to 5 Hz the scanned points
describe a circle instead of the 8th Lissajous figure and, as seen in the comparison of
the trajectories, this is a non reliable path. The use of this scanned-points-per second
frequency for this trajectory is senseless, since the optical devices have to describe a
relatively complicated path in vane.
-60-40
-20 020
4060
-100
-50
0
50
1000
5
10
15
Height[m]
Snapshot of calculated windfield. Scanning mode:8. Frequency: 5Hz. At 116m with mode slow
Transversal [m]
Win
d sp
eed
[m/s
]
7
7.5
8
8.5
9
9.5
10
Figure 42: Snap shot of the calculated wind field for a slow mode of the 8th trajectory with a scanned-points-per-second frequency of 5 Hz.
The distribution of points obtained with a scanned-points-per second frequency of 13
Hz, despite its limited number of scanned points, in more alike to the Lissajous figure
(Figure 43). There are enough points in the periphery, what leads to a big
Evaluation of scanning modes.
96
interpolated area. In the centre there are a few points that help obtaining a detailed
distribution of the wind.
-60-40
-200 20
4060
-100
-50
0
50
1000
2
4
6
8
10
Height[m]
Snapshot of calculated windfield. Scanning mode:8. Frequency: 13Hz. At 116m with mode slow
Transversal [m]
Win
d sp
eed
[m/s
]
6.5
7
7.5
8
8.5
9
9.5
Figure 43: Snap shot of the calculated wind field for a slow mode of the 8th trajectory with a shooting freq. of 13 Hz.
The optimal frequency is the one that brings into being a good interpolated area and
low statistics at the same time. In order to find this frequency the Figure 44 has been
plotted. It represents the scanned-points-per-second frequency in relation to the
relative chi square statistics. In it is appreciated how the temporal statistic increases
slightly when reducing the scanned-points-per-second frequency till a value of 13 Hz.
From this value on the slope of the curve increases considerably. The spatial statistic
increases at a higher rate, but still acceptable, till a frequency of 10 Hz. For values
lower than this the slope gets very steep.
Evaluation of scanning modes.
97
Frequency vs. Relative Statisticals
0,00%
0,05%
0,10%
0,15%
0,20%
0,25%
0,30%
0 10 20 30 40 50 60 70 80 90 100
Frequency [Hz]
Stat
istic
als
Relative time Chi Square Statistical
Relative spatial Chi Square Statistical
Figure 44: Frequency vs. relative Statistic for a slow speed mode without collision.
Frequency vs. Interpolated area
60%
65%
70%
75%
80%
85%
90%
0 10 20 30 40 50 60 70 80 90 100
Frequency [Hz]
Inte
rpol
ated
are
a
Figure 45: Frequency vs. Interpolated Area for a slow speed mode without collision.
Figure 45 represents the interpolated area versus the scanned-points-per-second
frequency with which it was achieved. All the frequencies in the range between 13
Evaluation of scanning modes.
98
and 100 scanned points per second lead to scan about the 85%, but this value
decreases very rapidly when the frequency gets any lower.
From the analysis of these two figures it is concluded that a scanned-points-per-
second frequency of 13Hz is the value that harmonizes the objectives of this point in
a best way, since it reduces the scanned-points-per-second frequency keeping the
statistics at low values and the interpolated area big enough.
Influence of the collision to the minimum frequency
It has been analyzed in the step before that approximately a 40% of the shots are
lost due to the collision. Then the question about the equivalency of a configuration
with a scanned-points-per-second frequency fixed to 13 scanned points per second
under collision circumstances to a configuration of 0,6x13 Hz without collision arises.
In case they are equivalent situations the optimum value of 13 Hz has to be
incremented in a 68% when the laser collides the rotor blades. In this way, when the
collisions occur, an optimal total of 13 points are scanned.
According to Equation (18 the optimum scanned-points-per-second frequency in case
of collision would be about 22 Hz for the scanning mode 8.
sOfLostShotPercentageeqOptShootingFrioneqIfCollisShootingFr
−=
1 (18)
In order to analyze the effect of the collision over a configuration of 13 scanned
points per second the values obtained for each situation, with and without collision,
are shown in Table 20. The lost of 40% of the scanned points leads to a reduction of
the scanned area of 18%. This reduction favors the keep of the spatial distribution.
Nevertheless the temporal statistic is incremented from a 0,02% to a 0,11%.
In order to analyze the consequence of the scanned-points-per-second frequency on
a 70% approximately the configuration for 25 Hz has also been calculated. As seen
in Table 20 this increment doesn’t lead to the statistics obtained for 13Hz without
collision since the statistics are still higher. Calculated
Freq [Hz]
Collision
X2r Space
X2
r Time
Area
x [m/s]
Ssp [m/s]
St [m/s]
13 No 0,07% 0,02% 85% 7,70 0,26 0,77 13 Yes 0,07% 0,11% 60% 7,71 0,18 0,72 25 Yes 0,05% 0,07% 66% 7,68 0,21 0,70
Table 20: Statistical values for a scanned-points-per-second frequency of 13 Hz with and without collision and for 25 Hz with collision.
Evaluation of scanning modes.
99
Given that the problem of the lost of 40% of the shots cannot be solved by simply
increasing the frequency up to a 100% considering the first one a 60%, a parallel
study to the one carried out above to find the optimal frequency under collision
conditions is made. Then the optimal 13 Hz frequency for a situation without collision
has been incremented up to 100 Hz. A higher frequency is not recommendable, since
it leads to a very low accuracy of the measurements.
Frequency vs. relative Statisticals
0,00%
0,02%
0,04%
0,06%
0,08%
0,10%
0,12%
0 20 40 60 80 100
Frequency [Hz]
Stat
istic
als
Relative temporal Chi SquareStatistical
Relative spatial Chi SquareStatistical
Figure 46: Frequency vs. relative Statistic for a slow speed mode with collision.
Figure 46and Figure 47 illustrate the statistics and interpolated area obtained for this
range of frequencies respectively. The temporal relative error decreases as the
frequency increases, above all when the frequency is higher than 25 Hz. However;
the spatial error tendency does not decrease constantly when increasing the
frequency. It reaches its minimum at 50Hz.
Evaluation of scanning modes.
100
Frequency vs. interpolated Area
58%
60%
62%
64%
66%
68%
70%
72%
74%
0 20 40 60 80 100
Frequency [Hz]
Inte
rpol
ated
Are
a
Figure 47 Frequency vs. interpolated Area for a slow speed mode with collision.
The interpolated area increases abruptly from 13 Hz to 20 Hz. Therefore, the
minimum recommendable scanned-points-per-second frequency that brings together
low statistics for big interpolated area in case of collision is increased to 25 Hz.
Evaluation of scanning modes.
101
Conclusions
In the first part of this work a number of hardware and software adaptations to a
LIDAR system have been proposed for its usage as anemometer from a wind turbine
nacelle. The study of hardware adaptations has shown that the best optical device to
implement is either a Risley prism or a galvanometer scanner. The first one tends to
describe curves, while the second one finds less difficulty when describing straight
lines. In order to make a sound decision about which optical device is more
advantageous different scanning trajectories have been simulated and the effect on
estimated wind fields has been evaluated. In the field of software adaptations the
speed mode and the scanned-points-per-second frequency have been analyzed.
In order to find the most advantageous arrangement of the LIDAR scanning system
the different configurations derived from the different adaptations have been
analyzed with WITLIS, a Wind Turbine Lidar Simulator developed in this thesis that
evaluates the performance of the different scanning configurations. At the moment
there is a limitation in memory usage by WITLIS with a maximum of three minutes
wind field length. This has to be solved in a future optimization of the program in
order to simulate up to ten minutes. However for the analysis of this project it does
not present a major problem. Moreover, it is assumed that the LIDAR senses
perfectly the value of the line-of-sight wind speed at the focus point. Therefore the
errors estimated by the simulator are due just to the interpolation from the scanned
points to the defined grid.
The accuracy of the calculated wind fields has been measured with two parameters:
a spatial and a temporal relative chi-square statistic. The spatial statistic shows in
average the relative error of each point of the grid in the transversal dimension, while
the temporal one shows the average of the relative errors of each snap shot. They
normally respond to the configuration changes the same way but with different
magnitudes.
It has been noticed that some trajectories tend to scan more area than others. The
frequency also plays an important role when it comes to define the scanned area.
Therefore, the interpolated area has also been a criterion to have into account in
order to choose the best variables.
Evaluation of scanning modes.
102
The simulations have shown that both straight and curved trajectories show good
performance. But among all the simulated trajectories the simplest figure that leads to
accurate results is the Lissajous curve with parameters a=3 and b=2 for an angle of
pi/2. The best straight trajectory has been the zigzag.
The configuration of the software variables that combines in a best way accuracy and
speed is a frequency of 13 scanned points per second which corresponds to 26
points pro snap shot in a slow speed mode. The fast mode has shown a slightly
better performance than the slow mode, however the slow mode has been further
considered. That’s because the increase of the accuracy of the measurement with a
slow mode is higher than the increase of the accuracy of the wind field obtained with
a fast mode.
The effect of the collision of the laser rays with the rotor blades, nacelle and ground
has been also simulated. An average of 40% of the shots has been lost,
independently of the kind of trajectory or frequency. This effect is overcome by
doubling the scanned-points-per-second frequency.
LIDAR measures in the line of sight, therefore its measurement is underestimated
unless the laser ray is aligned with the speed vector. As an attempt to solve this
problem a correction of the direction has been applied. In it, it has been supposed
that the wind had a perfect perpendicular direction to the rotor. This correction has
considerably decreased the errors, above all in the periphery. The use of this
correction is recommended for the further use of the configuration here proposed.
The errors of the calculated wind fields obtained with the configuration here
recommended are very small compared to the standard uncertainty of wind speed
measurements. This means that the errors due to the interpolation are relatively
small in comparison to the errors due to the measurement itself.
The simulations have shown that the description of curves is recommendable, what
would lead to choose the Risley as optical device. Nevertheless, the suggested
frequency and speed mode restrict the speed of the optical device and, since the
galvanometers present a better speed performance than the Risley, the
galvanometers scanners are suggested
Evaluation of scanning modes.
103
References
[1] [IEC605] IEC 61400-12-1, Wind turbines, Part 12-1: “Power
performance of electricity producing wind turbines”, 2005.
[2] [WEIT05] Weitkamp, Claus, “LIDAR, Range- Resolved Optical
Remote Sensing of the Atmosphere”, Optical Sciences,
Springer, 2005.
[3] [BROW04] Brown, Th., Creath, H., Kogelnik, H., Kriss, M.A., Schmit,
J., Weber, M.J., “The Optics Encyclopedia, Basic
Foundations and Practical Applications”, Wiley,
Weinheim; VCH, DOI 10.1002/jrs.1560, Germany, 2004
[4] [HARR05] Harris, M.,Hand, M., “LIDAR for Turbine Control”, National
Renewable Energy Laboratory, November 30, 2005
[5] Windcube™ Product Information. July 2007
[6] [AUSS07] Aussibal Christine, Windcube™ User’s Manual, June
2007
[7] [LEOS08] www.leosphere.com on April 2008
[8] [SCHW06] Schwarze, C., “A new look at Risley Prisms”, OPTRA Inc,
June 2006.
[9] [SULL06] Sullivan, M., Synopsis of “Risley Prism Beam Pointer”.
Advanced Technology Center, Palo Alto, California,
November 2006.
[10] [SCHO07] Scholles, M., Bräuer. A, Frommhagen, K., Gerwig, Ch.,
Lakner, H., Schenk, H. and Schwarzenberg, M., “Ultra
compact laser projection systems based on two-
dimensional resonant micro scanning mirrors”, by
Fraunhofer Institure for Photonic Microsystems, Germany.
DOI: 10.1117/12.700093. Fraunhofer Institute for Applied
Optics and Precision Engineering, Germany, 2007.
[11] [CUND89] Cundy, H. and Rollett, A. "Lissajous's Figures." §5.5.3 in
Mathematical Models, 3rd ed. Stradbroke, England:
Tarquin Pub., pp. 242-244, 1989.
Evaluation of scanning modes.
104
[12] [MANW02] Manwell, J. F., McGowan, J. G., Rogers, A. L., “Wind
Energy Explained, Theory, Design and Application”,
WILEY, 2002.
[13] [KARM48] Karman, T., “Progress in the Statistical Theory of
Turbulence”; proceedings of the National Academy of
Science, 1948.
[14] [FROS78] Frost, W., B.H. Long, and R.E. Turner, “Engineering
Handbook on the Atmospheric Environmental Guidelines
for Use in Wind Turbine Development“ NASA Technical
Paper 1359, December, 1978.
[15] [KAIM72] Kaimal, J. C., J.C. Wyngaard, Y. Izumi, and O.R. Cote,
“Spectral Characteristics of Surface-Layer Turbulence,”
Quarterly Journal of the Royal Meteorological Society, 98,
1972
[16] [IEC604] IEC 61400-1 Ed. 3, Wind Turbines, edited by IEC TC88-
MT1, May 2004
[17] [HOLM05] Holm. D., “Taylor’s Hypothesis, Hamilton’s Principle, and
the LANS-α Model for Computing Turbulence”, Los
Alamos Science, 2005.
[18] [PRES92] Press, Flannery, Teukolsky & Vetterling “Numerical
Recipes in C - Example Book”, 2nd edn. Cambridge
University Press, Cambridge, 1992
[19] [NIEL04] Nielsen, M, Larsen, G. C., Mann, J, Ott, S, Hansen, K. S.,
Pedersen, B. J, “Wind Simulation for Extreme and Fatigue
Loads“, Risø–R–1437(EN), Risø National Laboratory,
Roskilde, Denmark, January 2004
[20] [DELA34] B. Delaunay: “Sur la sphère vide”, 7:793-800, 1934
[21] [IEC698] IEC 61400-12, 1998 (E)
[22] [GASC02] Gasch R., Twele J., “Wind Power Plants, Fundamentals,
Design, Construction and Operation”, Solarpraxis 2002.
Evaluation of scanning modes.
105
Appendix A: Economical analysis
This brief appendix analyzes the economical interest of the problem approached in
the first part. Is the use of a LIDAR on top of the nacelle profitable? Does it make
sense, economically speaking, to measure the inflow or wake wind field? Is its
application viable?
To answer all these questions a distinction between the two layouts of the LIDAR,
measuring in front of the nacelle or the wake, has to be made. They both have
different applications and hence different approaches to their economical viability.
If the LIDAR is used to measure the wind field in front of the rotor to have a precise
measurement of the power curve and to control the blade angles sophistically, it has
to be placed on top of the nacelle facing the wind direction. This procedure supposes
a continuous operation of the LIDAR, what means that a LIDAR system is needed for
the entire life time of the wind turbine.
Some studies [4] point out that this operation procedure can reduce the mechanical
loads on a 10%.
For the current date (July 2008) a LIDAR Windcube™ represents a high percentage
of the cost of the turbine. But the bigger the wind turbine, the lower the relative price
of the LIDAR. The average price for large, modern wind farms is around 1000€ per
kilowatt electrical power installed. A Windcube™ costs roughly 217.000€. That
means that a LIDAR represents almost 22% (19) of the cost of a 1MW wind turbine.
%7,21100€10001000
€000.217cos =⋅⋅
=
KWKW
tlativeWINDCUBEre (19)
Evaluation of scanning modes.
106
Figure 48: Development of the average Wind Turbine Size sold in different countries
But for all manufacturers there is a clear tendency of continuously increasing wind
turbine size. MW-size turbines have become the dominant machines in the
commercial market during recent years (Figure 48). Furthermore, projects like
UPWIND are looking towards the design of very large wind turbines (8-10MW), both
onshore and offshore. These big-sized wind turbines require a new conception of the
machine. They need the highest possible standards in design, advanced control and
measuring systems in order to obtain the highest possible degree of reliability. The
LIDAR becomes subsequently practical and profitable. The price of the laser machine
in comparison with the price of the entire wind turbine is substantially reduced and
the 10% of the reduced loads represent a higher benefit. This relative price is
especially reduced when talking about offshore, since its investment pro KW is,
depending on the depth of the sea, about a 50% more than onshore.
The LIDAR substitutes the anemometers that every single wind turbine requires.
These cannot be eliminated in the near future, because they are required by the
norms [21]. But once the precision and reliability of the LIDAR have been proved, this
norm will be sensible to change and then the price of the anemometers has to be
subtracted from the LIDAR’s price.
On the other hand, measuring the wind field downstream is useful in order to verify
the wake models used to plan wind parks. But this use of the LIDAR does not imply a
continuous performance like before; it doesn’t even imply a short use of it. It finds its
Evaluation of scanning modes.
107
application in the investigation field. Therefore, once the wake models have been
verified every single company with access to this information can be benefited from it
without having to acquire a LIDAR.
This fact makes it very difficult to measure the costs of the deployment of the LIDAR
measuring the wake in these investigations and the benefits derived from them. But it
seems obvious to think that the benefits obtained are fairly superior to the investment
costs because every single wind park of all around the world can be projected and
improved with the new wake models.
Further applications of the LIDAR on top of the nacelle could be analyzed. For
instance, the simultaneous measurement in flow at different ranges could also
measure the wake of the turbine in front of it and its tendency. This information could
be sent to the wind turbine that, according to the algorithms implemented in the
control system, is going to be affected by the wake. This sophisticated deployment
requires intercommunication between all the turbines of a wind park.
Evaluation of scanning modes.
108
Appendix B: Plots of Synthetic Field
-60-40
-20 020
4060
-100
-50
0
50
1007
7.5
8
8.5
Height[m]
Mean sint. windfield in the space for 180 sec
Transversal [m]
Win
d sp
eed
[m/s
]
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
8.1
8.2
0 20 40 60 80 100 120 140 160 1806.5
7
7.5
8
8.5
9
9.5Mean synthetic wind speed in the time for 180 sec
Time [sec]
Win
d sp
eed
[m/s
]
Evaluation of scanning modes.
109
Appendix C: Plots of Calculated Wind Field for different trajectories.
Now on the figures are in order of appearance:
1 Snap shot of calculated wind field
2 Mean spatial calculated wind field for 180 seconds
3 Mean temporal calculated wind field for 180 seconds
4 Mean spatial error for 180 seconds
5 Mean temporal error for 180 seconds
Collision: No Correction: No
Mode: Fast Freq: 100Hz
Mode: 3
-60-40
-20 020
4060
-100
-50
0
50
1000
2
4
6
8
10
Height[m]
Snapshot of calculated windfield. Scanning mode:3. Frequency: 100Hz. At 116m with mode fast
Transversal [m]
Win
d sp
eed
[m/s
]
6.5
7
7.5
8
8.5
Evaluation of scanning modes.
110
-60-40
-200 20
4060
-100
-50
0
50
1006
6.5
7
7.5
8
Height[m]
Mean calculated windfield for 180 sec with mode 3
Transversal [m]
Win
d sp
eed
[m/s
]
6.2
6.4
6.6
6.8
7
7.2
7.4
7.6
0 20 40 60 80 100 120 140 160 1806
6.5
7
7.5
8
8.5
9Mean calculated wind speed in the time for 180 sec with mode 3
Time [sec]
Win
d sp
eed
[m/s
]
-60-40
-20 020
4060
-100
-50
0
50
100-5
0
5
10
15
20
Height[m]
Mean relative spatial error windfield for 180 sec with mode 3
Transversal [m]
Ret
ativ
e er
ror (
%)
0
2
4
6
8
10
12
14
16
Evaluation of scanning modes.
111
0 20 40 60 80 100 120 140 160 1805
5.5
6
6.5
7
7.5
8
8.5Mean relative time error for 180 sec with mode 3
Time [sec]
Erro
r (%
)
Mode 4
-60-40
-20 020
4060
-100
-50
0
50
1000
2
4
6
8
10
Height[m]
Snapshot of calculated windfield. Scanning mode:4. Frequency: 100Hz. At 116m with mode fast
Transversal [m]
Win
d sp
eed
[m/s
]
6
6.5
7
7.5
8
8.5
9
-60-40
-200 20
4060
-100
-50
0
50
1006
6.5
7
7.5
8
Height[m]
Mean calculated windfield for 180 sec with mode 4
Transversal [m]
Win
d sp
eed
[m/s
]
6.4
6.6
6.8
7
7.2
7.4
7.6
Evaluation of scanning modes.
112
0 20 40 60 80 100 120 140 160 1806
6.5
7
7.5
8
8.5
9Mean calculated wind speed in the time for 180 sec with mode 4
Time [sec]
Win
d sp
eed
[m/s
]
-60-40
-20 020
4060
-100
-50
0
50
100-5
0
5
10
15
20
Height[m]
Mean relative spatial error windfield for 180 sec with mode 4
Transversal [m]
Ret
ativ
e er
ror (
%)
0
2
4
6
8
10
12
14
16
0 20 40 60 80 100 120 140 160 1804.5
5
5.5
6
6.5
7
7.5
8
8.5Mean relative time error for 180 sec with mode 4
Time [sec]
Erro
r (%
)
Evaluation of scanning modes.
113
Mode 5
-60-40
-20 020
4060
-100
-50
0
50
1000
2
4
6
8
10
Height[m]
Snapshot of calculated windfield. Scanning mode:5. Frequency: 100Hz. At 116m with mode fast
Transversal [m]
Win
d sp
eed
[m/s
]
6
6.5
7
7.5
8
8.5
-60-40
-200 20
4060
-100
-50
0
50
1006
6.5
7
7.5
8
Height[m]
Mean calculated windfield for 180 sec with mode 5
Transversal [m]
Win
d sp
eed
[m/s
]
6.2
6.4
6.6
6.8
7
7.2
7.4
7.6
0 20 40 60 80 100 120 140 160 1806
6.5
7
7.5
8
8.5
9Mean calculated wind speed in the time for 180 sec with mode 5
Time [sec]
Win
d sp
eed
[m/s
]
Evaluation of scanning modes.
114
-60-40
-20 020
4060
-100
-50
0
50
100-5
0
5
10
15
20
Height[m]
Mean relative spatial error windfield for 180 sec with mode 5
Transversal [m]
Ret
ativ
e er
ror (
%)
2
4
6
8
10
12
14
16
0 20 40 60 80 100 120 140 160 1804
5
6
7
8
9
10
11
12Mean relative time error for 180 sec with mode 5
Time [sec]
Erro
r (%
)
Mode: 6
-60-40
-20 020
4060
-100
-50
0
50
1000
2
4
6
8
10
Height[m]
Snapshot of calculated windfield. Scanning mode:6. Frequency: 100Hz. At 116m with mode fast
Transversal [m]
Win
d sp
eed
[m/s
]
6.5
7
7.5
8
8.5
Evaluation of scanning modes.
115
-60-40
-200 20
4060
-100
-50
0
50
1006.4
6.6
6.8
7
7.2
7.4
Height[m]
Mean calculated windfield for 180 sec with mode 6
Transversal [m]
Win
d sp
eed
[m/s
]
6.6
6.7
6.8
6.9
7
7.1
7.2
0 20 40 60 80 100 120 140 160 1805.5
6
6.5
7
7.5
8
8.5Mean calculated wind speed in the time for 180 sec with mode 6
Time [sec]
Win
d sp
eed
[m/s
]
-60-40
-20 020
4060
-100
-50
0
50
1000
5
10
15
Height[m]
Mean relative spatial error windfield for 180 sec with mode 6
Transversal [m]
Ret
ativ
e er
ror (
%)
6
7
8
9
10
11
12
Evaluation of scanning modes.
116
0 20 40 60 80 100 120 140 160 1804
6
8
10
12
14
16Mean relative time error for 180 sec with mode 6
Time [sec]
Erro
r (%
)
Mode: 7
-60-40
-200 20
4060
-100
-50
0
50
1000
2
4
6
8
10
Height[m]
Snapshot of calculated windfield. Scanning mode:7. Frequency: 100Hz. At 116m with mode fast
Transversal [m]
Win
d sp
eed
[m/s
]
6
6.5
7
7.5
8
8.5
-60-40
-200 20
4060
-100
-50
0
50
1006
6.5
7
7.5
8
Height[m]
Mean calculated windfield for 180 sec with mode 7
Transversal [m]
Win
d sp
eed
[m/s
]
6.4
6.6
6.8
7
7.2
7.4
Evaluation of scanning modes.
117
0 20 40 60 80 100 120 140 160 1806
6.5
7
7.5
8
8.5
9Mean calculated wind speed in the time for 180 sec with mode 7
Time [sec]
Win
d sp
eed
[m/s
]
-60-40
-20 020
4060
-100
-50
0
50
100-5
0
5
10
15
20
Height[m]
Mean relative spatial error windfield for 180 sec with mode 7
Transversal [m]
Ret
ativ
e er
ror (
%)
2
4
6
8
10
12
14
0 20 40 60 80 100 120 140 160 1805
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10Mean relative time error for 180 sec with mode 7
Time [sec]
Erro
r (%
)
Evaluation of scanning modes.
118
Mode: 8
-60-40
-20 020
4060
-100
-50
0
50
1000
2
4
6
8
10
Height[m]
Snapshot of calculated windfield. Scanning mode:8. Frequency: 100Hz. At 116m with mode fast
Transversal [m]
Win
d sp
eed
[m/s
]
6
6.5
7
7.5
8
8.5
9
-60-40
-200 20
4060
-100
-50
0
50
1006
6.5
7
7.5
8
Height[m]
Mean calculated windfield for 180 sec with mode 8
Transversal [m]
Win
d sp
eed
[m/s
]
6.4
6.6
6.8
7
7.2
7.4
7.6
0 20 40 60 80 100 120 140 160 1806
6.5
7
7.5
8
8.5
9Mean calculated wind speed in the time for 180 sec with mode 8
Time [sec]
Win
d sp
eed
[m/s
]
Evaluation of scanning modes.
119
-60-40 -20
020
4060
-100
-50
0
50
100-5
0
5
10
15
20
Height[m]
Mean relative spatial error windfield for 180 sec with mode 8
Transversal [m]
Ret
ativ
e er
ror (
%)
0 20 40 60 80 100 120 140 160 1805
5.5
6
6.5
7
7.5
8
8.5
9Mean relative time error for 180 sec with mode 8
Time [sec]
Erro
r (%
)
Mode: 9
-60-40
-20 020
4060
-100
-50
0
50
1000
2
4
6
8
10
Height[m]
Snapshot of calculated windfield. Scanning mode:9. Frequency: 100Hz. At 116m with mode fast
Transversal [m]
Win
d sp
eed
[m/s
]
6
6.5
7
7.5
8
8.5
9
Evaluation of scanning modes.
120
-60-40
-200 20
4060
-100
-50
0
50
1006
6.5
7
7.5
8
Height[m]
Mean calculated windfield for 180 sec with mode 9
Transversal [m]
Win
d sp
eed
[m/s
]
6.2
6.4
6.6
6.8
7
7.2
7.4
0 20 40 60 80 100 120 140 160 1806
6.5
7
7.5
8
8.5
9Mean calculated wind speed in the time for 180 sec with mode 9
Time [sec]
Win
d sp
eed
[m/s
]
-60-40
-20 020
4060
-100
-50
0
50
100-5
0
5
10
15
20
Height[m]
Mean relative spatial error windfield for 180 sec with mode 9
Transversal [m]
Ret
ativ
e er
ror (
%)
2
4
6
8
10
12
14
16
Evaluation of scanning modes.
121
0 20 40 60 80 100 120 140 160 1805.5
6
6.5
7
7.5
8
8.5Mean relative time error for 180 sec with mode 9
Time [sec]
Erro
r (%
)
Mode: 10
-60-40
-20 020
4060
-100
-50
0
50
1000
2
4
6
8
10
Height[m]
Snapshot of calculated windfield. Scanning mode:10. Frequency: 100Hz. At 116m with mode fast
Transversal [m]
Win
d sp
eed
[m/s
]
6
6.5
7
7.5
8
8.5
9
-60-40
-200 20
4060
-100
-50
0
50
1006
6.5
7
7.5
8
Height[m]
Mean calculated windfield for 180 sec with mode 10
Transversal [m]
Win
d sp
eed
[m/s
]
6.2
6.4
6.6
6.8
7
7.2
7.4
Evaluation of scanning modes.
122
0 20 40 60 80 100 120 140 160 1806
6.5
7
7.5
8
8.5
9Mean calculated wind speed in the time for 180 sec with mode 10
Time [sec]
Win
d sp
eed
[m/s
]
-60-40 -20
020
4060
-100
-50
0
50
100-5
0
5
10
15
20
Height[m]
Mean relative spatial error windfield for 180 sec with mode 10
Transversal [m]
Ret
ativ
e er
ror (
%)
0 20 40 60 80 100 120 140 160 1805
5.5
6
6.5
7
7.5
8Mean relative time error for 180 sec with mode 10
Time [sec]
Erro
r (%
)
Evaluation of scanning modes.
123
Mode: 11
-60-40
-20 020
4060
-100
-50
0
50
1000
2
4
6
8
10
Height[m]
Snapshot of calculated windfield. Scanning mode:11. Frequency: 100Hz. At 116m with mode fast
Transversal [m]
Win
d sp
eed
[m/s
]
6
6.5
7
7.5
8
8.5
9
-60-40
-200 20
4060
-100
-50
0
50
1006
6.5
7
7.5
8
Height[m]
Mean calculated windfield for 180 sec with mode 11
Transversal [m]
Win
d sp
eed
[m/s
]
6.2
6.4
6.6
6.8
7
7.2
7.4
7.6
0 20 40 60 80 100 120 140 160 1806
6.5
7
7.5
8
8.5
9Mean calculated wind speed in the time for 180 sec with mode 11
Time [sec]
Win
d sp
eed
[m/s
]
Evaluation of scanning modes.
124
-60-40
-20 020
4060
-100
-50
0
50
100-5
0
5
10
15
20
Height[m]
Mean relative spatial error windfield for 180 sec with mode 11
Transversal [m]
Ret
ativ
e er
ror (
%)
2
4
6
8
10
12
14
16
0 20 40 60 80 100 120 140 160 1805.5
6
6.5
7
7.5
8
8.5Mean relative time error for 180 sec with mode 11
Time [sec]
Erro
r (%
)
Mode: 12
-60-40
-20 020
4060
-100
-50
0
50
1000
2
4
6
8
10
Height[m]
Snapshot of calculated windfield. Scanning mode:12. Frequency: 100Hz. At 116m with mode fast
Transversal [m]
Win
d sp
eed
[m/s
]
6
6.5
7
7.5
8
8.5
9
Evaluation of scanning modes.
125
-60-40
-200 20
4060
-100
-50
0
50
1006
6.5
7
7.5
8
Height[m]
Mean calculated windfield for 180 sec with mode 12
Transversal [m]
Win
d sp
eed
[m/s
]
6.2
6.4
6.6
6.8
7
7.2
7.4
7.6
0 20 40 60 80 100 120 140 160 1806
6.5
7
7.5
8
8.5
9Mean calculated wind speed in the time for 180 sec with mode 12
Time [sec]
Win
d sp
eed
[m/s
]
-60-40 -20
020
4060
-100
-50
0
50
100-5
0
5
10
15
20
Height[m]
Mean relative spatial error windfield for 180 sec with mode 12
Transversal [m]
Ret
ativ
e er
ror (
%)
Evaluation of scanning modes.
126
0 20 40 60 80 100 120 140 160 1805
5.5
6
6.5
7
7.5
8
8.5Mean relative time error for 180 sec with mode 12
Time [sec]
Erro
r (%
)
Mode: 13
-60-40
-20 020
4060
-100
-50
0
50
1000
2
4
6
8
10
Height[m]
Snapshot of calculated windfield. Scanning mode:13. Frequency: 100Hz. At 116m with mode fast
Transversal [m]
Win
d sp
eed
[m/s
]
6.6
6.8
7
7.2
7.4
7.6
7.8
8
8.2
8.4
8.6
-60-40
-200 20
4060
-100
-50
0
50
1006.8
7
7.2
7.4
7.6
7.8
Height[m]
Mean calculated windfield for 180 sec with mode 13
Transversal [m]
Win
d sp
eed
[m/s
]
6.9
7
7.1
7.2
7.3
7.4
7.5
7.6
Evaluation of scanning modes.
127
0 20 40 60 80 100 120 140 160 1806
6.5
7
7.5
8
8.5
9
9.5Mean calculated wind speed in the time for 180 sec with mode 13
Time [sec]
Win
d sp
eed
[m/s
]
-60-40
-200 20
4060
-100
-50
0
50
100-2
0
2
4
6
8
Height[m]
Mean relative spatial error windfield for 180 sec with mode 13
Transversal [m]
Ret
ativ
e er
ror (
%)
-1
0
1
2
3
4
5
6
7
0 20 40 60 80 100 120 140 160 180-4
-2
0
2
4
6
8
10
12Mean relative time error for 180 sec with mode 13
Time [sec]
Erro
r (%
)
Evaluation of scanning modes.
128
Appendix D: Plots of Calculated Wind Field with Correction of Direction
Collision: No Correction: Yes
Mode: Fast Freq: 100Hz
Mode 4
-60-40
-20 020
4060
-100
-50
0
50
1000
2
4
6
8
10
Height[m]
Snapshot of calculated windfield. Scanning mode:4. Frequency: 100Hz. At 116m with mode fast
Transversal [m]
Win
d sp
eed
[m/s
]
6.5
7
7.5
8
8.5
9
9.5
-60-40
-20 020
4060
-100
-50
0
50
1007
7.5
8
8.5
Height[m]
Mean calculated windfield for 180 sec with mode 4
Transversal [m]
Win
d sp
eed
[m/s
]
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
8.1
8.2
Evaluation of scanning modes.
129
0 20 40 60 80 100 120 140 160 1806.5
7
7.5
8
8.5
9
9.5Mean calculated wind speed in the time for 180 sec with mode 4
Time [sec]
Win
d sp
eed
[m/s
]
-60-40
-200 20
4060
-100
-50
0
50
100-4
-2
0
2
4
Height[m]
Mean relative spatial error windfield for 180 sec with mode 4
Transversal [m]
Ret
ativ
e er
ror (
%)
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 20 40 60 80 100 120 140 160 180-2
-1.5
-1
-0.5
0
0.5
1
1.5
2Mean relative time error for 180 sec with mode 4
Time [sec]
Erro
r (%
)
Evaluation of scanning modes.
130
Mode 8
-60-40
-20 020
4060
-100
-50
0
50
1000
2
4
6
8
10
Height[m]
Snapshot of calculated windfield. Scanning mode:8. Frequency: 100Hz. At 116m with mode fast
Transversal [m]
Win
d sp
eed
[m/s
]
6
6.5
7
7.5
8
8.5
9
-60-40
-20 020
4060
-100
-50
0
50
1007
7.5
8
8.5
Height[m]
Mean calculated windfield for 180 sec with mode 8
Transversal [m]
Win
d sp
eed
[m/s
]
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
8.1
0 20 40 60 80 100 120 140 160 1806.5
7
7.5
8
8.5
9
9.5Mean calculated wind speed in the time for 180 sec with mode 8
Time [sec]
Win
d sp
eed
[m/s
]
Evaluation of scanning modes.
131
-60-40
-200 20
4060
-100
-50
0
50
100-4
-2
0
2
4
Height[m]
Mean relative spatial error windfield for 180 sec with mode 8
Transversal [m]
Ret
ativ
e er
ror (
%)
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0 20 40 60 80 100 120 140 160 180-2
-1.5
-1
-0.5
0
0.5
1
1.5
2Mean relative time error for 180 sec with mode 8
Time [sec]
Erro
r (%
)
Evaluation of scanning modes.
132
Appendix E: Plots of Calculated Wind Field with Collision
Collision: Yes Correction: Yes
Mode: Fast Freq: 100Hz
Mode 4
-60-40
-20 020
4060
-100
-50
0
50
1000
2
4
6
8
10
Height[m]
Snapshot of calculated windfield. Scanning mode:4. Frequency: 100Hz. At 116m with mode fast
Transversal [m]
Win
d sp
eed
[m/s
]
6.5
7
7.5
8
8.5
9
-60-40
-20 020
4060
-100
-50
0
50
1007.2
7.4
7.6
7.8
8
8.2
Height[m]
Mean calculated windfield for 180 sec with mode 4
Transversal [m]
Win
d sp
eed
[m/s
]
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
Evaluation of scanning modes.
133
0 20 40 60 80 100 120 140 160 1806
6.5
7
7.5
8
8.5
9
9.5Mean calculated wind speed in the time for 180 sec with mode 4
Time [sec]
Win
d sp
eed
[m/s
]
-60-40
-200 20
4060
-100
-50
0
50
100-4
-2
0
2
4
Height[m]
Mean relative spatial error windfield for 180 sec with mode 4
Transversal [m]
Ret
ativ
e er
ror (
%)
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 20 40 60 80 100 120 140 160 180-4
-3
-2
-1
0
1
2
3
4
5
6Mean relative time error for 180 sec with mode 4
Time [sec]
Erro
r (%
)
Evaluation of scanning modes.
134
Mode 8
-60-40
-20 020
4060
-100
-50
0
50
1000
5
10
15
Height[m]
Snapshot of calculated windfield. Scanning mode:8. Frequency: 100Hz. At 116m with mode fast
Transversal [m]
Win
d sp
eed
[m/s
]
6.5
7
7.5
8
8.5
9
9.5
10
-60-40
-20 020
4060
-100
-50
0
50
1007
7.5
8
8.5
Height[m]
Mean calculated windfield for 180 sec with mode 8
Transversal [m]
Win
d sp
eed
[m/s
]
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
0 20 40 60 80 100 120 140 160 1806
6.5
7
7.5
8
8.5
9
9.5Mean calculated wind speed in the time for 180 sec with mode 8
Time [sec]
Win
d sp
eed
[m/s
]
Evaluation of scanning modes.
135
-60-40
-200 20
4060
-100
-50
0
50
100-4
-2
0
2
4
Height[m]
Mean relative spatial error windfield for 180 sec with mode 8
Transversal [m]
Ret
ativ
e er
ror (
%)
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 20 40 60 80 100 120 140 160 180-4
-3
-2
-1
0
1
2
3
4
5
6Mean relative time error for 180 sec with mode 8
Time [sec]
Erro
r (%
)
Evaluation of scanning modes.
136
Appendix F: Plots of Calculated Wind Field with variable speed mode
Collision: No Correction: Yes Mode: Variable
Freq: 100Hz Mode Slow
-60-40
-20 020
4060
-100
-50
0
50
1000
5
10
15
Height[m]
Snapshot of calculated windfield. Scanning mode:8. Frequency: 100Hz. At 116m with mode slow
Transversal [m]
Win
d sp
eed
[m/s
]
6.5
7
7.5
8
8.5
9
9.5
10
-60-40
-20 020
4060
-100
-50
0
50
1007
7.5
8
8.5
Height[m]
Mean calculated windfield for 180 sec with mode 8
Transversal [m]
Win
d sp
eed
[m/s
]
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
8.1
8.2
Evaluation of scanning modes.
137
0 10 20 30 40 50 60 70 80 906.5
7
7.5
8
8.5
9
9.5Mean calculated wind speed in the time for 180 sec with mode 8
Time [sec]
Win
d sp
eed
[m/s
]
-60-40
-200 20
4060
-100
-50
0
50
100-4
-2
0
2
4
Height[m]
Mean relative spatial error windfield for 180 sec with mode 8
Transversal [m]
Ret
ativ
e er
ror (
%)
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 20 40 60 80 100 120 140 160 180-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2Mean relative time error for 180 sec with mode 8
Time [sec]
Erro
r (%
)
Evaluation of scanning modes.
138
Appendix G: Plots of Calculated Wind Field with variable frequency
Collision: No Correction: Yes
Mode: Slow Freq: Variable
Mode : 8 Freq= 5 Hz
-60-40
-20 020
4060
-100
-50
0
50
1000
5
10
15
Height[m]
Snapshot of calculated windfield. Scanning mode:8. Frequency: 5Hz. At 116m with mode slow
Transversal [m]
Win
d sp
eed
[m/s
]
7
7.5
8
8.5
9
9.5
10
-60-40
-20 020
4060
-100
-50
0
50
1007
7.5
8
8.5
Height[m]
Mean calculated windfield for 180 sec with mode 8
Transversal [m]
Win
d sp
eed
[m/s
]
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
Evaluation of scanning modes.
139
0 10 20 30 40 50 60 70 80 906.5
7
7.5
8
8.5
9
9.5Mean calculated wind speed in the time for 180 sec with mode 8
Time [sec]
Win
d sp
eed
[m/s
]
-60-40
-20 020
4060
-100
-50
0
50
100-10
-5
0
5
Height[m]
Mean relative spatial error windfield for 180 sec with mode 8
Transversal [m]
Ret
ativ
e er
ror (
%)
-6
-5
-4
-3
-2
-1
0
1
2
0 20 40 60 80 100 120 140 160 180-10
-8
-6
-4
-2
0
2
4
6
8
10Mean relative time error for 180 sec with mode 8
Time [sec]
Erro
r (%
)
Evaluation of scanning modes.
140
Freq=10 Hz
-60-40
-20 020
4060
-100
-50
0
50
1000
5
10
15
Height[m]
Snapshot of calculated windfield. Scanning mode:8. Frequency: 10Hz. At 116m with mode slow
Transversal [m]
Win
d sp
eed
[m/s
]
7
7.5
8
8.5
9
9.5
10
-60-40
-20 020
4060
-100
-50
0
50
1007
7.5
8
8.5
Height[m]
Mean calculated windfield for 180 sec with mode 8
Transversal [m]
Win
d sp
eed
[m/s
]
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
8.1
0 10 20 30 40 50 60 70 80 906.5
7
7.5
8
8.5
9
9.5Mean calculated wind speed in the time for 180 sec with mode 8
Time [sec]
Win
d sp
eed
[m/s
]
Evaluation of scanning modes.
141
-60-40
-200 20
4060
-100
-50
0
50
100-4
-2
0
2
4
Height[m]
Mean relative spatial error windfield for 180 sec with mode 8
Transversal [m]
Ret
ativ
e er
ror (
%)
-3
-2
-1
0
1
2
3
0 20 40 60 80 100 120 140 160 180-8
-6
-4
-2
0
2
4
6Mean relative time error for 180 sec with mode 8
Time [sec]
Erro
r (%
)
Freq=13 Hz
-60-40
-20 020
4060
-100
-50
0
50
1000
2
4
6
8
10
Height[m]
Snapshot of calculated windfield. Scanning mode:8. Frequency: 13Hz. At 116m with mode slow
Transversal [m]
Win
d sp
eed
[m/s
]
6.5
7
7.5
8
8.5
9
9.5
Evaluation of scanning modes.
142
-60-40
-20 020
4060
-100
-50
0
50
1007.2
7.4
7.6
7.8
8
8.2
Height[m]
Mean calculated windfield for 180 sec with mode 8
Transversal [m]
Win
d sp
eed
[m/s
]
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
8.1
0 10 20 30 40 50 60 70 80 906.5
7
7.5
8
8.5
9
9.5Mean calculated wind speed in the time for 180 sec with mode 8
Time [sec]
Win
d sp
eed
[m/s
]
-60-40
-200 20
4060
-100
-50
0
50
100-4
-2
0
2
4
Height[m]
Mean relative spatial error windfield for 180 sec with mode 8
Transversal [m]
Ret
ativ
e er
ror (
%)
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Evaluation of scanning modes.
143
0 20 40 60 80 100 120 140 160 180-3
-2
-1
0
1
2
3Mean relative time error for 180 sec with mode 8
Time [sec]
Erro
r (%
)
Freq=20 Hz
-60-40 -20
020
4060
-100
-50
0
50
1000
5
10
15
Height[m]
Snapshot of calculated windfield. Scanning mode:8. Frequency: 20Hz. At 116m with mode slow
Transversal [m]
Win
d sp
eed
[m/s
]
6.5
7
7.5
8
8.5
9
9.5
10
-60-40
-20 020
4060
-100
-50
0
50
1007
7.5
8
8.5
Height[m]
Mean calculated windfield for 180 sec with mode 8
Transversal [m]
Win
d sp
eed
[m/s
]
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
8.1
8.2
Evaluation of scanning modes.
144
0 10 20 30 40 50 60 70 80 906.5
7
7.5
8
8.5
9
9.5Mean calculated wind speed in the time for 180 sec with mode 8
Time [sec]
Win
d sp
eed
[m/s
]
-60-40
-200 20
4060
-100
-50
0
50
100-4
-2
0
2
4
Height[m]
Mean relative spatial error windfield for 180 sec with mode 8
Transversal [m]
Ret
ativ
e er
ror (
%)
-3
-2
-1
0
1
2
0 20 40 60 80 100 120 140 160 180-4
-3
-2
-1
0
1
2
3Mean relative time error for 180 sec with mode 8
Time [sec]
Erro
r (%
)
Evaluation of scanning modes.
145
Freq= 25 Hz
-60-40
-20 020
4060
-100
-50
0
50
1000
5
10
15
Height[m]
Snapshot of calculated windfield. Scanning mode:8. Frequency: 25Hz. At 116m with mode slow
Transversal [m]
Win
d sp
eed
[m/s
]
7
7.5
8
8.5
9
9.5
10
-60-40
-20 020
4060
-100
-50
0
50
1007
7.5
8
8.5
Height[m]
Mean calculated windfield for 180 sec with mode 8
Transversal [m]
Win
d sp
eed
[m/s
]
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
8.1
8.2
0 10 20 30 40 50 60 70 80 906.5
7
7.5
8
8.5
9
9.5Mean calculated wind speed in the time for 180 sec with mode 8
Time [sec]
Win
d sp
eed
[m/s
]
Evaluation of scanning modes.
146
-60-40
-200 20
4060
-100
-50
0
50
100-4
-2
0
2
4
Height[m]
Mean relative spatial error windfield for 180 sec with mode 8
Transversal [m]
Ret
ativ
e er
ror (
%)
-3
-2
-1
0
1
2
0 20 40 60 80 100 120 140 160 180-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2Mean relative time error for 180 sec with mode 8
Time [sec]
Erro
r (%
)
Freq=50 Hz
-60-40 -20
020
4060
-100
-50
0
50
1000
5
10
15
Height[m]
Snapshot of calculated windfield. Scanning mode:8. Frequency: 50Hz. At 116m with mode slow
Transversal [m]
Win
d sp
eed
[m/s
]
6.5
7
7.5
8
8.5
9
9.5
10
Evaluation of scanning modes.
147
-60-40
-20 020
4060
-100
-50
0
50
1007
7.5
8
8.5
Height[m]
Mean calculated windfield for 180 sec with mode 8
Transversal [m]
Win
d sp
eed
[m/s
]
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
8.1
8.2
0 10 20 30 40 50 60 70 80 906.5
7
7.5
8
8.5
9
9.5Mean calculated wind speed in the time for 180 sec with mode 8
Time [sec]
Win
d sp
eed
[m/s
]
-60-40
-200 20
4060
-100
-50
0
50
100-4
-2
0
2
4
Height[m]
Mean relative spatial error windfield for 180 sec with mode 8
Transversal [m]
Ret
ativ
e er
ror (
%)
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Evaluation of scanning modes.
148
0 20 40 60 80 100 120 140 160 180-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2Mean relative time error for 180 sec with mode 8
Time [sec]
Erro
r (%
)
Evaluation of scanning modes.
149
Appendix H: Plots of Calculated Wind Field with variable frequency under collision conditions
Collision: Yes Correction: Yes
Mode: Slow Freq: Variable
Freq: 13 Hz
-60-40
-20 020
4060
-100
-50
0
50
1000
2
4
6
8
10
Height[m]
Snapshot of calculated windfield. Scanning mode:8. Frequency: 13Hz. At 116m with mode slow
Transversal [m]
Win
d sp
eed
[m/s
]
7
7.5
8
8.5
9
9.5
-60-40
-20 020
4060
-100
-50
0
50
1007.2
7.4
7.6
7.8
8
8.2
Height[m]
Mean calculated windfield for 180 sec with mode 8
Transversal [m]
Win
d sp
eed
[m/s
]
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
Evaluation of scanning modes.
150
0 10 20 30 40 50 60 70 80 906.5
7
7.5
8
8.5
9
9.5Mean calculated wind speed in the time for 180 sec with mode 8
Time [sec]
Win
d sp
eed
[m/s
]
-60-40
-200 20
4060
-100
-50
0
50
100-6
-4
-2
0
2
4
Height[m]
Mean relative spatial error windfield for 180 sec with mode 8
Transversal [m]
Ret
ativ
e er
ror (
%)
-4
-3
-2
-1
0
1
2
0 20 40 60 80 100 120 140 160 180-8
-6
-4
-2
0
2
4
6
8
10Mean relative time error for 180 sec with mode 8
Time [sec]
Erro
r (%
)
Evaluation of scanning modes.
151
Freq=20 Hz
-60-40
-20 020
4060
-100
-50
0
50
1000
5
10
15
Height[m]
Snapshot of calculated windfield. Scanning mode:8. Frequency: 20Hz. At 116m with mode slow
Transversal [m]
Win
d sp
eed
[m/s
]
6.5
7
7.5
8
8.5
9
9.5
10
-60-40
-20 020
4060
-100
-50
0
50
1007
7.5
8
8.5
Height[m]
Mean calculated windfield for 180 sec with mode 8
Transversal [m]
Win
d sp
eed
[m/s
]
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
0 10 20 30 40 50 60 70 80 906.5
7
7.5
8
8.5
9
9.5Mean calculated wind speed in the time for 180 sec with mode 8
Time [sec]
Win
d sp
eed
[m/s
]
Evaluation of scanning modes.
152
-60-40
-200 20
4060
-100
-50
0
50
100-4
-2
0
2
4
Height[m]
Mean relative spatial error windfield for 180 sec with mode 8
Transversal [m]
Ret
ativ
e er
ror (
%)
-3
-2
-1
0
1
2
0 20 40 60 80 100 120 140 160 180-8
-6
-4
-2
0
2
4
6
8Mean relative time error for 180 sec with mode 8
Time [sec]
Erro
r (%
)
Freq=25 Hz
-60-40
-20 020
4060
-100
-50
0
50
1000
5
10
15
Height[m]
Snapshot of calculated windfield. Scanning mode:8. Frequency: 25Hz. At 116m with mode slow
Transversal [m]
Win
d sp
eed
[m/s
]
7
7.5
8
8.5
9
9.5
10
Evaluation of scanning modes.
153
-60-40
-20 020
4060
-100
-50
0
50
1007.2
7.4
7.6
7.8
8
8.2
Height[m]
Mean calculated windfield for 180 sec with mode 8
Transversal [m]
Win
d sp
eed
[m/s
]
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
0 10 20 30 40 50 60 70 80 906.5
7
7.5
8
8.5
9
9.5Mean calculated wind speed in the time for 180 sec with mode 8
Time [sec]
Win
d sp
eed
[m/s
]
-60-40
-200 20
4060
-100
-50
0
50
100-6
-4
-2
0
2
4
Height[m]
Mean relative spatial error windfield for 180 sec with mode 8
Transversal [m]
Ret
ativ
e er
ror (
%)
-4
-3
-2
-1
0
1
2
Evaluation of scanning modes.
154
Freq=50 Hz
-60-40
-20 020
4060
-100
-50
0
50
1000
5
10
15
Height[m]
Snapshot of calculated windfield. Scanning mode:8. Frequency: 50Hz. At 116m with mode slow
Transversal [m]
Win
d sp
eed
[m/s
]
6.5
7
7.5
8
8.5
9
9.5
10
-60-40
-20 020
4060
-100
-50
0
50
1007
7.5
8
8.5
Height[m]
Mean calculated windfield for 180 sec with mode 8
Transversal [m]
Win
d sp
eed
[m/s
]
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
0 10 20 30 40 50 60 70 80 906.5
7
7.5
8
8.5
9
9.5Mean calculated wind speed in the time for 180 sec with mode 8
Time [sec]
Win
d sp
eed
[m/s
]
Evaluation of scanning modes.
155
-60-40
-200 20
4060
-100
-50
0
50
100-4
-2
0
2
4
Height[m]
Mean relative spatial error windfield for 180 sec with mode 8
Transversal [m]
Ret
ativ
e er
ror (
%)
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 20 40 60 80 100 120 140 160 180-6
-4
-2
0
2
4
6
8Mean relative time error for 180 sec with mode 8
Time [sec]
Erro
r (%
)
Freq= 100 Hz
-60-40
-20 020
4060
-100
-50
0
50
1000
5
10
15
Height[m]
Snapshot of calculated windfield. Scanning mode:8. Frequency: 100Hz. At 116m with mode slow
Transversal [m]
Win
d sp
eed
[m/s
]
6.5
7
7.5
8
8.5
9
9.5
10
Evaluation of scanning modes.
156
-60-40
-20 020
4060
-100
-50
0
50
1007
7.5
8
8.5
Height[m]
Mean calculated windfield for 180 sec with mode 8
Transversal [m]
Win
d sp
eed
[m/s
]
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
0 10 20 30 40 50 60 70 80 906.5
7
7.5
8
8.5
9
9.5Mean calculated wind speed in the time for 180 sec with mode 8
Time [sec]
Win
d sp
eed
[m/s
]
-60-40
-200 20
4060
-100
-50
0
50
100-4
-2
0
2
4
Height[m]
Mean relative spatial error windfield for 180 sec with mode 8
Transversal [m]
Ret
ativ
e er
ror (
%)
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Evaluation of scanning modes.
157
0 20 40 60 80 100 120 140 160 180-6
-4
-2
0
2
4
6
8Mean relative time error for 180 sec with mode 8
Time [sec]
Erro
r (%
)
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