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 . 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  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)  and Klemm et al. (2006) , 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 . 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  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  Gardiner B. (2004), ‘ Airflow Over Forests and Forest Gaps‘ BWEA Tree Workshop Forestry Commission March 2004.  Mortensen, G., Landberg, L., Troen, I. & Petersen, E. L. (1993), Wind Atlas Analysis and Application Program (WAsP), Risø National Laboratory, Roskilde.  Dellwik, E., Landberg, L. & Jensen, N.O. (2006), ‘WAsP in the Forest’, Wind Energy 9, 211-218.  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.  Troen, I. & Petersen, E. L. (1989), European Wind Atlas, Riso National Laboratory, Roskilde.  Dellwik, E., Landberg, L. & Jensen, N.O. (2004), ‘Winds and forests: general recommendations for using WAsP‘, BWEA – Workshop on Trees, Scotland.
© Copyright 2021 Paperzz