Estimation of Zero Plane Displacement Heights in the Vicinity of a Forest
J. Junge, A. Westerhellweg
DEWI GmbH, Wilhelmshaven, Germany;
+49-441-77937-119, [email protected]
1. Introduction
Forested regions are challenging for wind resource
predictions with models based on the assumption of
a logarithmic wind profile. The increase of wind
speed with height above ground depends
significantly on the roughness length (z0) of the
forests and the height displacement of the
logarithmic curve (zd) caused by the flow pattern of
air masses inside and above forests (see Fig. 1).
Fig. 2: Research area
Flat terrain is characteristic for the examined wind
farm site, which is enclosed by dense monoculture
pine forest with a height of approximately 22 m from
the northeast to the west. Especially in the southeastern part of the wind farm, the turbines are
located close to forested areas (see Fig. 2).
2. Height displacement as a function of distance
to the forest and wind speed
Fig. 1: Wind profiles for low vegetation (upper graph) and
for forest areas (lower graph). Adapted with changes from
Gardiner 2004 [1].
Subject of the presented study was the estimation of
the aerodynamic displacement z = zd + z0 in the
transition area from woodland to open terrain and
the application of its values to WAsP [2] modelling.
Calculation results were compared to operational
data of the wind turbines erected at a site in eastern
Germany, where wind measurements had been
carried out beforehand.
In order to estimate the aerodynamic displacement
z = zd + z0 of the logarithmic wind profile, the
method of experimental determination was applied.
Between April 2005 and August 2006 wind speed
profiles were measured in the heights of 35 m, 64
m, 80 m, 98 m, and 100 m and the wind direction
was taken at 64 m and 98 m. The collected data
was stored in 10 minute averages. For each
measured wind profile z was determined by
logarithmic regression. The following quality criteria
were developed and applied to select convenient
wind profiles for further analysis.
•
•
•
•
R2 >= 0.9 (Wind profiles which fit logarithmic
regression pattern)
u100m > 2.5 m*s-1 (Cut-in wind speed of planned
turbines)
Deviation of vanes in 64 m and 98 m smaller
than 5°
Only wind profiles with directions between 210°
and 329° were evaluated (site-specific criterion)
Values compliant to the quality criteria were
associated with the distance to forest in the
corresponding wind direction from the mast position
and assigned to seven classes of wind velocity. For
each of these classes, linear function parameters
were determined to describe the course of z with
increasing distance d to the forest with the equation
z = a * d + z(d=0) (see Fig. 3).
with a weighted mean regarding the Weibull
distribution of each wind sector allowed for an
estimation of z assigned to each wind sector at the
turbine locations. Negative values were set to zero.
Slope
Offset
a
z(d=0)
WT_07
WT_10
WT_11
WT_12
WT_14
WT_15
WT_16
1
-0.075
8.92
2.6
4.5
2
-0.076
9.13
3.8
5.7
5.3
3
-0.077
9.92
4.9
5.7
2.9
6.7
6.7
4
-0.078
9.81
3.4
6.7
6.4
6.4
7.0
5
-0.078
9.82
6.3
6.4
3.2
7.1
6
-0.078
9.84
6.2
5.8
3.5
6.6
7
-0.079
10.06
5.3
4.9
0.2
4.5
9.7
4.1
2.7
Sector
z
4.5
8
-0.079
9.96
3.5
9
-0.079
10.24
3.5
4.5
9.4
8.7
6.0
10
-0.078
9.99
8.6
11
-0.078
9.69
7.7
12
-0.075
9.08
Table 2: Height displacement z of the affected turbines
assigned to the wind direction sectors. Sector numbers
start in the north (345°- 14°) and continue in clockwise
direction.
Fig. 3: Median displacement z [m] dependent on distance
to the forest edge d [m] for velocity class 4.
Table 1 gives a complete overview of the linear
function parameters. The Offset values confirm the
observation made by Dellwick et al. (2006) [3] and
Klemm et al. (2006) [4], that height displacement is
dependent on the wind velocity u [m*s-1] in a way,
that for increasing u also z increases up to a certain
-1
point (in this case ~ 6 m*s ), while from thereon z
tends to slowly decrease with higher wind speeds.
Slopes range from - 0.056 at 3 m*s-1 to - 0.096 at
-1
6 m*s with the corresponding offset values of
5.75 m and 11.86 m at the forest edge.
Velocity
class
Slope a
Offset
z(d=0)
The gathered values were integrated into WAsP
calculations realized with and without the application
of height displacement. Displacement values were
applied assuming a reduction of the turbine hub
height by the amount of z. The maximum loss of
energy due to height displacement was determined
to be 5.7 % for the most affected wind turbine
considering the losses of all 12 sectors.
Sector
WT_7
WT_10
WT_11
WT_12
WT_14
WT_15
1
7.3
.
.
.
0.3
.
7
2
6.8
.
.
.
0.2
.
6.6
3
0.1
4.5
0.1
.
4.5
.
4.5
4
5.4
10.4
5.4
.
5.4
.
5.4
5
.
4.9
5.1
.
0.2
.
9
6
.
4.4
4.4
.
4.3
.
8.6
7
.
7.7
3.9
.
3.8
.
7.7
8
.
4.7
.
5
4.8
4.4
9.6
9
.
3.9
.
.
.
8.3
7.9
.
7.7
.
.
4.7
.
.
.
3.6
5.7
U1
U2
U3
U4
U5
U6
U7
2.5 < U1 < 3.5
3.5 < U2 < 4.5
4.5 < U3 < 5.5
5.5 < U4 < 6.5
6.5 < U5 < 7.5
7.5 < U6< 8.5
8.5 < U7
10
.
.
.
.
-0.056
-0.077
-0.067
-0.096
-0.089
-0.066
-0.08
11
.
.
.
.
10.33
12
.
.
.
.
All
0.6
3.8
1.3
0.5
5.75
7.96
8.93
11.86
11.76
10.28
Table 1: Function parameters of the linear regressions for
each velocity class.
3. Application of height displacement in WAsP
In order to designate the influence of the Slope and
Offset parameters derived from the measurement
data on the energy yield calculations the parameters
were transferred to the wind turbine locations. For
each turbine the distance to the forest (d) was
determined in all twelve wind sectors according to
the European Wind Atlas [5]. Averaging a and z(d=0)
WT_16
.
2.0
Table 3: Calculated reduction of energy yield [%] by height
displacement for each wind sector.
Operational data of the wind farm gathered from
June 2008 to July 2009 was compared to the model
results. An increase of z0 for the forest areas during
the modelling did not compensate for the effect that
turbines erected fairly close to the trees in reality did
not produce the calculated amount of energy.
Uncertainties in the farm efficiency and an
underestimation of z are believed to be possible
reasons for the deviations of model calculations
from real energy production data.
4. Conclusion
This study was realized to achieve a better
understanding of zero plane displacement close to
forests.
Up
to
now,
there
were
only
recommendations on how it could be applied to
energy
yield
assessments,
but
these
recommendations had not been proven by direct
measurements. Therefore, the results of this study
might be considered for future energy yield
calculations.
One of the main results were the slope values which
specify the decrease of height displacement with
increasing distance to the forest edge. The
determined mean slopes considering the Weibull
distribution show only slight variations with values
between a = - 0.075 and a = - 0.079. As the greatest
changes of slope take place in the lower velocity
classes, which seldom occur at wind farm sites,
such low variations could be expected. These
values differ significantly from the WAsP
recommendations [6] to apply a slope of around
a = - 0.2.
The determined linear equations do not support
asymptotes . Logistic and exponential function types
were tested against the linear one, but did not show
a better goodness of fit (see Fig. 4). Due to the
measurement setup, which was not customized for
this study, the areas close to the forest edge
(d  0) had to be extrapolated. A final decision on
the appropriate regression model could possibly be
made with an optimized measurement setup.
Fig. 4: Different types of regression for velocity class U2.
Another observed aspect is the importance of the
frequency distribution of the wind sectors. When
height displacement is applied to wind turbine
locations, the effect on the estimated energy yield
strongly depends on the frequency of occurrence
and the wind potential of the affected sectors (see
Table 3).
5. References
[1] Gardiner B. (2004), ‘ Airflow Over Forests and
Forest Gaps‘ BWEA Tree Workshop Forestry
Commission March 2004.
[2] Mortensen, G., Landberg, L., Troen, I. &
Petersen, E. L. (1993), Wind Atlas Analysis and
Application Program (WAsP), Risø National
Laboratory, Roskilde.
[3] Dellwik, E., Landberg, L. & Jensen, N.O. (2006),
‘WAsP in the Forest’, Wind Energy 9, 211-218.
[4] Klemm, O., Held, A., Forkel, R. Gasche, R.,
Kanter, H.-J., Rappenglück, B., Steinbrecher, R.,
Müller, K., Plewka, A., Cojocariu, C., Kreuzwieser,
J., Valverde-Canossa, J., Schuster, G., Moortgat,
G.K., Graus, M. & Hansel, A. (2006) Experiments on
forest/atmosphere exchange: Climatology and
fluxes during two summer campaigns in NE Bavaria,
Atmospheric Environment 40, 3-20.
[5] Troen, I. & Petersen, E. L. (1989), European
Wind Atlas, Riso National Laboratory, Roskilde.
[6] Dellwik, E., Landberg, L. & Jensen, N.O. (2004),
‘Winds and forests: general recommendations for
using WAsP‘, BWEA – Workshop on Trees,
Scotland.