Wind speed and power curve measurements by a LIDAR by pharmphresh33

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									     Influence of wind characteristics on turbine performance

  Ioannis Antoniou (1), Rozenn Wagner (1), Søren M. Pedersen (1), Uwe Paulsen (1), Helge A.
                             Madsen (1), Hans E. Jørgensen (1),
               Kenneth Thomsen (2), Peder Enevoldsen (2), Leo Thesbjerg (3)

 (1): Wind Energy Department, Risø,DTU, Frederiksborgvej 399, Postboks 49, 4000 Roskilde, Denmark, e-mail:
                   (1): Risø,DTU (2): Siemens Wind Power (3): Vestas Wind Systems A/S

The uncertainty of power performance measurements is closely related to the uncertainty of the wind speed
measurement. An inherent uncertainty in the method of measuring the power curve is by using the wind speed at
hub height. The assumption behind this is that the wind speed is representative of the wind over the whole turbine
rotor. While this assumption was adequate for smaller wind turbines, this is barely true for the modern multi-MW
ones. As a consequence considerable deviations often occur between the expected and the produced power. Wind
shear, directional changes and varying turbulence with height as a result of either meteorological and / or terrain
conditions call for the adoption of a new measurement method. The size of the rotor combined with the machine
hub height means that turbines are often exposed to highly varying wind conditions comprising large wind shear,
turbulence variations and direction shear within the rotor. These parameters will affect both the production as well
as the structural safety of the turbine. Better predictions of power and loads require a more representative wind
measurements over the turbine’s rotor.
The wind profiles at the Danish test station for wind turbines in Hovsore, have been analyzed up to a height of
165m for a one year period and for a narrow sector in order to reduce met tower influences. The profiles shapes
were found to extend from flat to high shear and on many occasions sharp local maxima were also observed at
about 80 to 100m. The measurement heights of the profiles cover the rotor of a Siemens 3.6MW turbine erected at
the test site. In order to compare the power in the profiles, all profiles having hub height wind speeds between
6m/s and 8m/s have been normalised at 7m/s and have been grouped to a number of mean shear profiles with
varying occurrence frequency.
To identify the influence of the wind shear and turbulence on the performance of the wind turbine, the above
results are used as input to a simplified version of the aeroelastic model HAWC2, the AE_N_WIND code which
contains the same aerodynamic and wind modules as the full HAWC2 code and can be considered as a Blade
Element Momentum model operating in the time domain, thus with the possibility to include wind turbulence. The
AE_N_WIND code has the option of user defined mean wind speed and turbulence shear.
The sensitivity analysis has been carried out as time series simulations with input based on the above wind shear
and turbulence profiles and using power as the primary characterization parameter. As a result, the measurements
over the whole rotor have allowed the measurement of the electrical power as a function of an “equivalent wind
speed” where wind shear and turbulence intensity are taken into account. This reduced the statistical unc
uncertainty as compared to the results based on the hub height wind speed. The results are significant and support
the introduction of the multi-point measurement concept that should contribute to a more accurate measurement of
the power curve and a better basis for validation of the prediction models.

Keywords: wind shear, profiles, turbulence, aeroelastic simulations, equivalent wind speed
1. Introduction
Power performance measurement have always been an important issue in relation to wind energy. Poul Lacour
was one of the pioneers making performance tests back in the 1888. Since then the topic has been investigate
through several research projects and papers, see Ref. [2-9]. It is still the same parameters which are relevant for
wind power production. The influences from these parameters are even more important today, where the area of
the rotor disk is significantly increased since modern wind turbine became commercially available. In order to use
information of the wind shear and turbulence over the whole rotor, a new definition of power curve is needed. This
paper presents some power performance simulations showing that the measurement uncertainty of the power
performance can significantly be reduced if additional information of the wind conditions over the whole turbine
rotor is used.

This paper describes some results derived from the IMPER research programme [1] with focal point on the
problematic use of a single hub-height mounted anemometer for power performance measurements on large wind
turbines. The IMPER objectives are:
     •    To provide an evaluation of the influence of wind field characteristics (turbulence, wind shear etc.)
          which influence the performance of large wind turbines
     •    To develop a new method to characterize the performance of large wind turbines in flat terrain, taking
          into account the wind field measurement covering the complete rotor area
     •    To create the background to improve the accuracy in wind potential measurement methods
     •    To contribute to further development and use of remote sensing methods in wind energy in order to
          improve the energy yield and reduce the financial risk
     •    To extend the above method for performance measurements from flat to complex terrain.

This paper documents the variation in power in the wind profiles with constant wind speed at a predefined height,
which correspond to the hub height of a MW turbine. Subsequently the measured wind profiles are used as input to
an aeroelastic model in order to investigate how the power in the wind profiles is captured by the turbine. Different
parameters (equivalent wind speed) derived from the input wind field are compared to the power produced by the
wind turbine in order to investigate how a better correlation between the wind field and the power production can
be archived. The wind profiles were measured at Høvsøre, the National Danish Test Station for Large Wind

2. The site
The wind profiles were measured at the National Danish Test Station for Large Wind Turbines, which is situated
in the northwest of Denmark, close to the North Sea. The test site is flat, surrounded by grassland with no major
obstacles and is situated a distance of 1.7 km from the west coast of Denmark. The prevailing wind direction is
from the west. Figure 1, shows the site layout and the instruments used. The wind profiles have been produced
combining the measurements from two met masts at the Høvsøre test site. The two met masts are the aviation light
met mast, and the met mast to the right of the picture.

                                                          Cup anemometer, boom mounted on aviation met        160m
                                                                  Cup anemometer top mounted                 116.5m
                                                          Cup anemometer, wind vane, sonic anemometer,        100m
                                                           temperature, differential temperature, relative
                                                                      humidity, air pressure
                                                          Cup anemometer, sonic anemometer, differential      80m
                                                          Cup anemometer, sonic anemometer, differential      60m
                                                                     temperature, wind vane
                                                          Cup anemometer, sonic anemometer, differential      40m
                                                                        Sonic anemometer                      20m
                                                          Cup anemometer, sonic anemometer, differential      10m
                                                                     temperature, wind vane

    Figure 1 The test site and the heavily instrumented met tower along with a list of the available instruments
3. The method
The electrical power produced by a wind turbine is the result of the wind flow through the turbine rotor. Energy is
captured by the rotor and for grid-connected wind turbines; this energy is converted to electrical power.
The measured power curve is usually expressed as power vs. wind using the relation below:
P = 1 ρ AU 3C P
P         the electrical power,
ρ         the air density
A                the rotor area
U                the wind speed and

Cp               the power coefficient.
In order to measure the turbine’s power curve in flat terrain, the wind speed measurements take place using a cup
anemometer mounted at hub height and at a distance of 2.5 rotor diameters away from the turbine. The relation
between the electrical power and the wind speed is found by averaging the measured parameters over a 10 minutes
period. The wind speed varies with time and its average value is given by the relation:
U=           Udt                                                  (2)

where T is the averaging period and               U the instantaneous value of the wind speed expressed as a mean and a
fluctuating part:
U = U + u , for which u =                       udt = 0 .
Following de Vries [11],the average energy flux within the time period                T   , over a unit area and assuming unit air
density, is given by the following relation:

                     (        )
            1         3

              ∫ U + u dt = U + 3U ⋅ u + 3u ⋅U + u
                            3    2
    3                                     2       3
U           T 0
           3⎛     u 2 u3 ⎞    3⎛      u2 ⎞
        = U ⎜1 + 3 2 + 3 ⎟ = U ⎜ 1 + 3 2 ⎟                                          (3)
U           ⎜         U ⎟      ⎜      U ⎟
            ⎝     U      ⎠     ⎝         ⎠

Equation (3), takes its final form assuming that the probability distribution for u is symmetrical, in which case the
last term in the middle expression becomes zero. Furthermore equation (3) shows that, for a given integration
interval, the difference between the true average energy flux             U       and the energy flux estimated from the average
wind velocity U over a rotor area, is a function of the turbulence in the flow.
The effect of turbulence intensity on the turbine power performance is complicated and only partly understood. It
depends on both the aerodynamics of the rotor and the control of the turbine. It can be positive, negative or neutral.
Thus the turbine will not always exploit the additional energy, due to the presences of turbulence. For modern
variable pitch / variable speed turbines, this relation depends also on the control algorithm. As a rule the turbine
will not respond to turbulent fluctuations which have frequencies above the turbine’s frequency response of the
rotor torque.
However the turbine always responds to changes in the mean wind speed. That the turbine’s power curve has
traditionally been measured as a function of the wind speed measured only at hub height is a simplification based
on the assumption that the wind speed at hub height is representative of the wind over the whole rotor. In practice,
changes of the wind speed within the rotor will influence the power production. Therefore it is expected that the
measurement of the wind at more heights within the turbine rotor, is a better approximation than the measurement
of the wind speed at hub height only.

In the present case, where the wind speed is measured over a number of heights within the rotor area, a new
parameter, the weighted or “equivalent” wind speed, is defined as:

                          Ui ⋅A
U eqM 1 =                                                         (4)
                 i                 i

In the case where the turbulence of the flow is accounted for, as in Eq. (3), the above equation take the form:
                A ∑ Ai ⋅          U i3
U eqT 1 =                     3                                 (5) and

As an alternative, the equivalent wind speed can be expressed as the wind speed which results in the same energy
flux over the rotor. In this case equation (5) takes the form:
                     1⎛                 ⎞
U eqT 3 =       3             U i3 ⋅ Ai ⎟                         (6)
                      ⎝ i               ⎠

where     denotes the specific height, A the rotor area and U i , Ai the wind speed and area corresponding to the
specific height and assuming zero tilt and yaw error. This is schematically shown in figure 2, in the case where the
wind speed is measured over a rotor at five heights.





Figure 2 The wind profile measured over a number of heights within the rotor area of a wind turbine
In the following paragraphs, the power output of a turbine will be simulated for a number of measured profiles
which have been measured at the Danish National Test station for large wind turbines of Hovsore. The turbine
power will be presented as a function of the wind speed at hub height and as a function of the wind speed as
defined through the above equations (4) to (6). The goal is to, through simulations; investigate how a more detailed
measurement of the wind speed in front of the rotor may reduce the uncertainty in the power curve measurement.
Other issues to be investigated are the influence of turbulence and whether a “true-flux” wind speed is
advantageous for the more accurate presentation of the wind speed.

3. Wind profiles in flat terrain
The analysis is carried using data from the met-mast at Høvsøre, see Figure 1. For the present analysis only cup
wind speeds at 40m, 60m, 80m, 100m, 116m and 165m are used together with the wind direction. To illustrate the
importance of the profile as a whole for the power production, Figure 3 and Figure 4 show two examples of wind
shear situations at the site. The wind shear is mainly determined by the atmospheric stability. Thus in Figure 3, a
situation where the atmosphere is stable during the night (large wind shear) and unstable during the day (well-
mixed flat profiles) is shown. In Figure 4, the atmosphere is stable during the whole day and the wind profile has a
local maximum at 80m height. Such situations will have an impact on the turbine power curve and it is reasonable
to expect that a wind turbine with a hub height of 80m would be seen to under produce if the wind speed is
measured at the hub height only.

                         Figure 3. The wind profile during the 29th of March, 2007

                          Figure 4 The wind profile from the 18th of January 2006
For the needs of the simulation, the wind profiles from 6m/s to 8m/s for the height of 80m, and for one year period
were chosen. Within this period, 2340 profiles were found from the easterly directions between 60° and 120°,
which were binned and categorized according to their shape into 173 profiles, non-equally weighted, Figure5a.
Subsequently all mean profiles were normalized so that the wind speed at 80m became equal to 7m/s,
U 80 = 7 m / s , using the ratio Ri = 7 / U i80 , where i is the profile number, see Figure 5(b). The same ratio is used to
normalize the standard deviations at all heights; in this way the turbulence intensity at all heights remains the same
as in the original profiles.

                    12                                                                                                       180
                                                                                                                             160                 12.13%
                    10                                                                                                                           8.20%
                                                                                                                             140                 8.12%
 wind speed (m/s)

                     8                                                                                                                           6.92%

                                                                                                                Height (m)
                     6                                                                                                       100                 3.16%
                                                                                                                              80                 2.69%
                                                                                                                              60                 2.39%
                     2             wsp116        wsp100       wsp80
                                   wsp60         wsp40        wsp165
                     0                                                                                                        20
                         1    15   29 43    57   71   85   99 113 127 141 155 169                                                  4         5            6          7           8   9   10
                                                  no of profile                                                                                               wind speed (m/s)
                                                                                                    (a)                                                                                       (b)
        Figure 5 (a): The classified 173 easterly wind profiles, (b): the 10 most common normalised profiles
                                          and their percentage of occurence.
Assuming a virtual rotor disk as the one shown in Figure 2, the energy flux distribution per unit of the rotor area
following Eq. (3) and (6) is shown in the Figure 6. The variation in energy is significant and in fact following the
distribution in Figure 6, the highest energy flux is twice the magnitude of the lowest one. These large flux
variations will also result in significant variations in the electrical power produced from the turbine, following the
equation below.

P =                            C p ρA U EqT 3
However the above results were made possible only because the wind speed is registered at more heights within
the rotor disk. In the opposite case, where the wind speed was only measured at hub height, which in the present
case is constant, the variations in electrical power would be understood as uncertainty in the measurement.

                                                                  No of profiles

                                                                                        0.0   0.2            0.4                       0.6                0.8
                                                                                              Energy flux per unit area (kW/m2)

                                                 Figure 6 The energy flux for the 173 normalized wind profiles.

4. Aeroelastic simulations
The normalised wind profiles are used as input to the aeroelastic simulations for a wind turbine. The primary
objective of this part of the work is to identify the sensitivity of the wind field parameters on the performance of
the wind turbine. Relevant wind field parameters are mean shear profiles, turbulence shear profiles and wind
vector slope and yaw angles. Wind slope and yaw angles will not be considered in the work presented.
A simplified version of the aeroelastic model HAWC2 is used in the analysis, the AE_N_WIND code. It contains
the same aerodynamic and wind modules as the full HAWC2 code and can be considered as a Blade Element
Momentum model operating in the time domain, thus with the possibility to include wind turbulence. The
AE_N_WIND code has the option of user defined mean wind fields and user defined turbulence shear. So the wind
speed variations with height are taken into account while for a given height, the mean wind speed is considered
constant. The simulation results depend on the aerodynamic model used in the code. The way the induction
correction is implemented can have different effects under different situations. Despite this difficulty, the results
are considered to be generally applicable.
The sensitivity analysis will be carried out as a number of time series simulations with different wind field input.
The primary performance characterization parameter will be the power and the ranges of the wind field parameters
which are chosen from measurements of the wind profiles as described above. The Mann model of turbulence [11]
is used to generate different turbulence fields which are added to the mean wind speed in order to model the
random feature of the wind. A number of simulations have been carried out in order to map the statistical variation
in normal turbulence fields, see Figure 7. These simulations have illustrated a significant variation across the rotor
disk of the wind statistics. On this background 10 realizations were decided adequate in order to reduce the
statistical variation to a reasonable level.

  Figure 7 Variation of mean wind speed and wind speed standard deviation for a 600 s simulation. A
                                   power law shear was specified.
5. The wind turbine and the input modifications
The sensitivity analysis will be carried out on a model of the Siemens 3.6MW turbine with a hub of 90m height, a
rotor diameter of 107.16 meters and a constant rotation speed of 0.99 rad/s. Siemens Wind Power has provided the
data for the modeling. The implementation has been compared to other aerodynamic models and simulations
carried out by Siemens, Figure 8. In the AE_N_WIND simulations (and WT4 simulations) no loss in drive train or
generator has been assumed.
                                     3500                                    WT4







                                            0   5         10    15      20         25

                                      Figure 8 The calculated power curve
In order to validate the user defined mean and turbulence shear implementation, a number of simulations with
simplified input parameters have been carried out in order to check the implementation of the user defined mean
and turbulence shear fields (not presented here). Since the turbine is a variable speed pitch regulated turbine, which
operates at variable speed in the low wind speed region (optimal Cp tracking) and the AE_N_WIND code cannot
be used together with a controller (no generator or pitch degrees of freedom), it means that for a specific wind
speed, one fixed rotational speed must be used. For simulations with turbulence this results in a different behaviour
for the model turbine than for the real turbine. In order to investigate the constant/variable speed assumption two
power curves have been calculated, one with fixed speed and one with variable speed. For each of these options
two different shears have been considered: no shear and an extreme shear with a speed-down of 25% at rotor top
and bottom. The results are plotted in Figure 9 below.

                                                    (a)                                                         (b)
     Figure 9 (a): Calculated power curves with fixed and variable rotational speed. No shear, (b):
           Calculated power curves with fixed and variable speed. Extreme shear specified.
To assess the influence of the two different operational strategies – one fixed speed and one representing an ideal
controller – the power curves have been numerically integrated and weighted with a Gaussian wind speed
distribution N[6.5;0.65] to calculate the equivalent power. This equivalent power represents a power value, which
corresponds to the same accumulated production as if the correct power curve was followed. Due to the curvature
of the power curves, the equivalent values are larger than the quasi-steady power value at 6.5m/s. For larger
curvatures, larger power values are seen.

                                                   Var rpm             Cnt. rpm
                                     No shear                714.888         703.2166
                                     User shear             525.2578         519.7444
                                     ratio:                 1.361023         1.353005

                                       Table 1: Equivalent power values

The results, Table 1, reveal the same relative reduction in the equivalent power for the two different operational
strategies and it is concluded that the constant speed assumption can be applied

6. Results and Discussions
In order to use the above profiles for simulations, a parallel translation of 10m (from 80 to 90m) was assumed. The
simulations took place for a number of configurations and the results will be presented as a function of a number
of equivalent wind speeds as shown below in Table 2.

                                    U eqM 1       U eqT 1          U eqT 3          U eqL1   U eqL3
              3 profile points        √             √                   √               √      √
              5-profile points        √             √                   √               √      √
              One Pitot tube on a     √             √                   √               √      √
              blade (at 85%
              Two Pitot tubes on      √             √                   √               √      √
              a blade (at 45%
              and 85% radius)

                            Table 2 The simulation cases examined (L=laminar flow)

The mean wind speed and standard deviation shear were defined at five points, at the center and at symmetrical
positions above and below, along the vertical rotor diameter. The resulted wind speed time series at the
corresponding five points of the simulation output have subsequently been used for the calculation of the wind
speeds using the equations (4) to (6). In the case of the three-point simulation three points, one at the center and
two symmetrically placed between the five-point configurations have been used. In the case of the pitot tube
simulations, the five-point profile was used as input and the wind speed output was traced at 45% and 85% radius.

6.a 1, 3 and 5-point profiles
In the figure 10 below, the turbine’s power curve and the power coefficient are presented for the cases as described
above. As 1-point profiles we consider the wind speed at the center of the turbine which for the case of the
normalized profiles is equal to 7m/s. The resulting wind speeds are the weighted results using the equations (4) to
(6). The lines in the figures of the power curves and the power coefficients represent the fit of the corresponding
power curve or power coefficient points calculated using a flat profile as input in the AE_N_WIND code at the
corresponding wind speeds. In the case of turbulent flow, the user defined input standard deviation values, were
the weighted mean average of the standard deviation over the number of heights, measured for each wind speed
                                                     Power curve, laminar flow                                                                                  Cp, laminar flow
                                          Flat laminar                                                                       0.50
                                          1 point
 El. power (kW)

               1200                                                                                                          0.45
                                          3 points

                                                                                                                     Cp ()
                                          5 points                                                                           0.40
                      800                                                                                                                       1 point
                                                                                                                             0.35               3 points
                                                                                                                                                5 points
                      400                                                                                                    0.30               flat laminar
                      200                                                                                                    0.25
                              5.5            6            6.5        7      7.5               8         8.5                         5.5           6             6.5         7       7.5         8        8.5
                                                                 UeqL1(m/s)                                                                                             UeqL1 (m/s)
                                                                                                               (a)                                                                                              (b)
                                                     Power curve, turbulent flow                                                                               Cp, turbulent flow
                    1600                                                                                                      0.55
                                           1 point
                    1400                   3 points                                                                           0.50
                                           5 points
 El. power (kW)

                    1200                                                                                                      0.45
                                           Poly. (power)

                                                                                                                      Cp ()
                                                                                                                                                1 point
                                                                                                                              0.35              3 points
                            600                                                                                                                 5 points
                                                                                                                              0.30              flat turbulent
                            400                                                                                                                 Poly. (flat turbulent)
                            200                                                                                               0.25
                                  5.5         6            6.5             7        7.5       8          8.5                         5.5              6          6.5          7           7.5       8     8.5
                                                                  UeqM1 (m/s)                                                                                           UeqM1 (m/s)
                                                                                                               (c)                                                                                              (d)
                                                     Power_5 points, turbulent flow                                                                         Cp_5 points, turbulent flow

                      1600                                                                                                    0.55
                                           UeqT1                  UeqM1
                      1400                                                                                                    0.50
                                           power                  Poly. (power)
                      1200                                                                                                    0.45
   El. power (kW)

                                                                                                                      Cp ()

                            600                                                                                                                    UeqT1                 UeqM1
                            400                                                                                                                    Cp                    Poly. (Cp)
                                                                                                                                     5.5            6            6.5          7           7.5   8         8.5
                                  5.5         6            6.5             7        7.5       8          8.5
                                                                                                                                                                       wind speed (m/s)
                                                                 wind speed (m/s)
                                                                                                               (e)                                                                                              (f)
                                            El. power_5 points_turbulent flow                                                                             Cp_5 points_turbulent flow

                            1600                                                                                                0.55
                            1400                 UeqT1                                                                          0.50
           El. power (kW)

                            1200                 Poly. (power)                                                                  0.45

                                                                                                                                0.40                      UeqT3
                                                                                                                                0.35                      UeqT1
                             600                                                                                                                          Cp
                             400                                                                                                                          Poly. (Cp)
                             200                                                                                                0.25
                                    5.5          6         6.5         7       7.5        8       8.5                                     5.5           6         6.5         7       7.5       8       8.5
                                                             wind speed (m/s)                                                                                      wind speed (m/s)
                                                                                                          (g)                                                                                                    (h)

Figure 10 (a),(b): laminar flow, (c),(d): turbulent flow, (e), (f): comparison between UeqT1 and UeqM1
               expressions, (g), (h): comparison between UeqT1 and UeqT3 expressions.
The results of the simulations show clearly that by increasing the number of measurement points over a given
profile, it results in a more unambiguous relation between power and wind speed. Among the weighted wind
speeds used, the weighted mean wind speed expression represents, for a given number of points, the best
approximation to the turbine’s power curve, relative to the rest of the simulations, see Figures 10e to 10h. When
accounting for the turbulence in the flow, equation (5), it is expected that the influence of the turbulence will
strongly depend on the shape of the power curve and whether it is convex or concave at the specific part. In the
case where the wind speed is defined in terms of a wind speed resulting in the same energy flux over the rotor,
equation (6), the correlation between wind and power is less good. The reason for this, as shown in Figure 5a, is
that the rotor is not able to extract the kinetic energy as efficient when the wind shear over the rotor is large, as the
power coefficient at higher wind speeds reduces in value, meaning that the turbine becomes less efficient to extract
energy from the wind. In Figure 11, the average standard deviation values between the simulation results for all
wind profiles and the polynomial fitted power curves are compared for different number of points.
                                                                                           Power Standard Deviation (kW)

                                                              120                    1 point          3 points              5 points



















                                                                            UeqL1              UeqL3         UeqM1                  UeqT1             UeqT3

                   Figure 11 The average standard deviation of the power relative to the flat laminar/turbulent power
6.b One-and two-pitot tubes on the blade
A mentioned above, in the case of the pitot tube simulations, the five-point profile was used as input and we chose
to trace the wind speed output at 45% and 85% radius. The practical value of these simulations which do not
account for any rotor or blade induction, is to offer a first estimate of the configuration which could in principle
accurate measure the turbine’s power curve without using any ground based equipment.
In the case of the one pitot tube, the wind speed is traced at 85% blade radius. Again, this is the wind which the
pitot tube ideally “reads” in the absence of any induction or other influences from the presence of the rotor. The
results are shown in Figure 12a and b. The line in the figures corresponds to the polynomial fit of the power curve
points calculated as above using flat turbulent wind profiles as input to the AE_N_WIND code. The results show
that measuring the power curve using one pitot tube is not adequate to correctly reproduce the power curve. The
large differences between the UeqM and UeqT expressions of the weighted wind speed are due to wind shear in
the wind profiles which is understood as turbulence by the rotating pitot tube. However it is possible that the
results are influenced as the integration of the wind speed over the pitot path, does not weight the wind speeds
equally over the rotor profile. Some wind speeds are more represented relative to other ones and it is possible that
this has resulted to the below shown deviations between the pitot and flat profile power.

                                        Pitot tube at 85%                                                                                                    Pitot tube at 85%
                                UeqT              UeqM                                                                      0.50
                                power             flat turbulent
 El. power (kW)

                   1200                                                                                                     0.45
                                                                                                                    Cp ()

                                                                                                                                                 CpT                  CpM
                    400                                                                                                     0.30                 Cp                   Poly. (Cp)
                    200                                                                                                     0.25
                          5.5    6        6.5      7        7.5          8             8.5                                          5.5           6            6.5          7           7.5   8   8.5
                                           wind speed (m/s)                                                                                                          wind speed (m/s)
                                                                                                 (a)                                                                                                    (b)
                                 2 Pitot tubes (45% & 85%)                                                                                             2 Pitot tubes at 45% and 85%

                   1400                 UeqM1
   El power (kW)

                   1200                 Poly. (power)
                                                                                                                    Cp ()

                   1000                                                                                                     0.40

                    800                                                                                                     0.35
                    600                                                                                                                      CpM1               Cp
                    400                                                                                                                      Poly. (Cp)

                    200                                                                                                     0.25
                                                                                                                                   5.5           6             6.5          7           7.5   8   8.5
                          5.5    6        6.5      7        7.5         8            8.5
                                                                                                                                                                     wind speed (m/s)
                                           wind speed (m/s)                                                                                                                                             (d)
            Figure 12 The power curve and power coefficient as functions of the weighted wind speeds for two
                                              different configurations
In Figures 12c to d the power curve and the power coefficient are presented for the case of two pitot tube mounted
at 45 and 85% of the blade radius as a function of                                                    U eqM 1 .There is a major improvement on the results, yet the
wind speed seems still slightly underestimated relative to the flat profile simulations. A parametric study using
more pitot tubes, different measurement positions or a combination of both is still needed in order to find whether
further improvements in the accuracy of the measurements are possible when using pitot tubes. An alternative
approach to the subject of pitot measurements could though be that a new power curve using pitot tubes is defined
which includes the induction of the rotor and what remains is to verify this power curve for the specific pitot tube
configuration on the blade.

7. Conclusions
Large variations have been observed in the wind profiles over a flat terrain site. The results show that the profiles
do not follow always the logarithmic law; instead they heavily depend upon the atmospheric conditions. These
profiles were used as input to a sensitivity analysis concerning the response of the power production as a function
of wind and turbulence variations.
Using an increased number of points significantly improved the correlation between wind input and power output.
These results support the necessity for the introduction of a new definition for power performance measurements
using a distributed measurement of the wind over the rotor area instead of using only the hub-height wind speed.

The authors gratefully acknowledge the financial support of the Danish Energy Agency to the IMPER project
(journal no.: 3302-0106), which made possible this paper.

7. References
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