The Annual Variation of Vertical Profiles of Weibull Parameters and their Applicability for Wind Energy Potential Estimation

Transcription

1 The Annual Variation of Vertical Profiles of Weibull Parameters and their Applicability for Wind Energy Potential Estimation M. Bilstein; Institute for Geophysics and Meteorology, University of Cologne S. Emeis (Corresponding author); Institute for Meteorology and Climate Research, Karlsruhe Institute of Technology, Garmisch M. Bilstein EXTERNAL ARTICLE English Introduction The vertical profiles derived from Weibull-distribution parameters and wind energy availability over sea is in most instances uncharted due to the lack of suitable measurements. But this knowledge is essential for the estimation of the wind power potential of offshore-parks. For this reason four years of FINO1 data (Sept. 03 Aug. 07) was analysed by focusing on the annual distribution of vertical gradients. Furthermore, a comparison between the annual wind energy derived from the Weibull distributions and that derived directly from 10 min-averaged wind speed time series is performed. Measuring Site and Methods This investigation uses four years of data (Sept. 03 Aug. 07) from the FINO1 research-platform located 45 km north of the island Borkum in the German Bight (Neumann, Nolopp, & Herklotz, 2004). 10 min-averaged wind speed measurements at eight heights ( m) are the foundation of this study. The direct mast shadow of the measurement platform was not excluded, since it caused only a 5 % error in Weibullparameter estimation. This is evident when comparing the parameters at 90 and 100 m heights. The two parameter Weibull distribution (2.1), where u is wind speed, a is the scale factor and b is the shape parameter, is the most widely used distribution for wind speed analysis. (2.1) (2.2) In this investigation the parameters a and b are identified by a graphical method (Wilker, 2004) based on a line assimilation for seasons and years. To get a line function the logarithm of (2.1) must be taken twice: (2.3) The horizontal flux of the kinetic energy of wind (in the following called wind energy, E Wind ) can be directly measured from a time series, where (2.4a) or (2.4b). The difference between (2.4a) and (2.4b) is whether the time average is calculated separately for density and wind speed or 42 DEWI MAGAZIN NO. 36, FEBRUARY 2010

2 Werbung GWU / Willmers 1/1 s/w

3 Fig. 1: Correlation between the two Weibull parameters at each height, where yellow are summer, green are spring, red are autumn and blue are wintertime. Within each seasonal result the different heights order from upper left (30 m) to lower right (100 m). Fig. 2: Schematic diagram of the correlation of the two Weibull parameters. The colouring is the same as in Fig. 1. not. The latter, Eq. (2.4b), should be more realistic. We will analyse the difference between both formulations. (2.5) Equation (2.5) is proportional to the third moment of the Weibull distribution (with Г = gamma-function, (Bronstein & Semendjajew, 1975) and ρ is the air density). A comparison of the wind energy potential estimations from (2.4a), (2.4b) and (2.5) will be the main target of this paper. Results Seasonal and Vertical Variation of the Weibull parameters From scatter plot of all heights of the seasonal Weibull parameters for the entire period (Fig. 1) it was found, that the scale factor a averaged between 7 and 15 m/s, while the shape parameter b, averaged between 1.9 and 2.9. Fig. 1 shows that the shape parameter decreases with the rising variability of wind speeds at higher levels, while the scaling factor increases with height. Over the ocean, atmospheric friction is not as great as over land, so the surface layer (also called Prandtl-layer) is not as thick (Türk, 2008). For this reason, the vertical gradient of the scaling parameter (, s. Tab. 1) is not as big as in the similar height over land (, see, e.g. (Emeis, 2001)). Furthermore, the two Weibull parameters show a clear seasonal dependence. Smaller parameters are detected in summer, higher parameters in winter, while spring and autumn are between both extremes. Due to the enhanced heat capacity of water, the stability of the marine atmosphere is out of phase by about 3 months compared to the stability of the atmosphere over land (Coelingh, van Wijk, & Holtslag, 1996). Consequently the atmosphere is stable in spring, neutral/stable in summer, unstable in autumn and neutral/unstable in winter. On the whole those seasons, which are stable or neutral/ stable have parameters smaller in magnitude compared with unstable seasons. It is noted, that shape parameters with larger scaling factors (autumn and winter) have a higher variability compared with ones with smaller scaling factors (spring and summer). Fig. 2 shows a schematic diagram of this correlation, where intervals for each season and parameter are presented. A seasonal variation of the vertical gradients of the Weibull parameters is detected as well. Higher gradients are detected in spring time, where the marine atmosphere is stable (s. Fig. 1 green points), and lower gradients in summer, autumn and winter (s. Fig. 1 yellow, red and blue points). However, sea surface roughness and subsequently the thickness of the Prandtl-layer are also important factors. The data presented here seem to indicate that the roughness length is more significant than atmospheric stability. But, due to the limited data set it cannot finally be decided, whether thermal stability or layer thickness has a stronger influence on the vertical profiles. Beeken (Beeken & Neumann, 2008), Riedel (Riedel, Durante, Neumann, & Strack, 2005) and Lange (Lange, Larsen, Højstrup, & Barthelmie, 2004) find that vertical profiles over sea are more influenced by the thermal stability. 44 DEWI MAGAZIN NO. 36, FEBRUARY 2010

4 Fig. 3: Vertical profile of the wind energy in the year 2005 with the difference between the three modes of evalutation (blue (2.5), red (2.4a), green (2.4b)). The error bars follow from the normal error propagation. Seasons Scaling factor in 90m Scaling factor in 40m Difference SON (autumn) DJF (winter) MAM (spring) JJA (summer) Tab. 1: Mean of the scaling factor a in m/s for all seasons at 90 and 40 m and their vertical difference in m/s. Comparison of Wind Potential Estimations Vertical profiles of calculated wind energy from (2.4a), (2.4b) and (2.5) for the year 2005 are depicted in Fig. 3 as an example. They show a nearly linear vertical slope. The blue line is calculated according to (2.5), the red line with (2.4a) and the green line with (2.4b). Taken all four years together, the Weibull distribution underestimates directly measured wind energy (2.4b) by about 100 W/m², an error of above 5 %. If the air density is averaged separately (2.4a), wind energy is underestimated by up to 50 W/m², with a nearly constant error at each height. The difference of the wind energy between 40 and 90 m averages 175 W/m². Between seasons the wind energy potential changes with the scaling factor. Consequently, summer will yield the lowest wind energy followed by spring then autumn with winter yielding the largest wind energy. This trend aligns with the structure of the correlation in Fig. 2. The difference between m is due to the mast shadow, which is not excluded in this work. This difference is about %. The relative underestimation of wind energy by the Weibull parameters is illustrated for the 100 m height in Fig. 4. There is an overestimation with respect to the directly measured wind energy in only four periods (one by only a small amount). Two of these periods are overestimated by about 5 10 % and can be attributed to errors in the approximation of to this seasonal wind speed distribution by the Weibull distribution. The other two cases are summer periods. Thus, it can be assumed that there may be only an overestimation in summer. On average, an underestimation of 5 10 % is evident for all seasons. The blue circles denote the meteorological years (Sept.03 Aug.04 a.s.o.). Three of these underestimate the measurements by %. The Weibull parameter estimation method (2.5) is thus a conservative estimate. The wind energy as calculated by the Weibull distribution averages over one year at about 1000 W/m², which underestimates by 105 W/m² (10.5 %) the directly measured wind energy of the time series (Fig. 4), which is a significant difference. Tab. 2 shows the distribution of the available wind energy for each of the four seasons. Here the trend follows similarly to that evident in vertical gradients (Tab. 1). However, the year 2005/2006 was exceptional. The reason for this exception is in the very warm winter in that year where persistent high pressure situations prevailed. In addition there were many low-pressures situation in spring, which let the wind energy grow in this season. Discussion and Outlook Weibull parameters have been analysed from four years of FINO1 data. The correlation between the two Weibull parameters shows an annual trend which is mostly determined by sea surface roughness, the thickness of the Prandtl-layer and the stability of the marine atmosphere. For seasonal evaluations, the average shape parameter is between 1.9 and 2.9 and the scaling factor is between 7 and 15 m/s with smallest values in summer and highest values in winter. Vertical gradi- DEWI MAGAZIN NO. 36, FEBRUARY

5 Meteorological Years (Sept.-Aug.) Autumn (SON) Winter (DJF) Spring (MAM) Summer (JJA) 2003/ / / / Mean Year Tab. 2: Wind energy in W/m² for all seasons for four years at 100 m height (computed from (2.5)). Fig. 4: Difference between wind energy calculated according to a Weibull distribution and directly measured energy (2.4b) in per cent. Blue dots mark meteorological years (Sept. - Aug., ) and red triangles the meteorological seasons (Sept./ Oct./Nov., Dec./Jan./Feb., Mar./Apr./May, Jun./Jul./Aug.). ents are smaller here than over land, an indicator that the mast resides within the Ekman-layer for most of the time. Analysis of directly measured wind energy givesa information about the quality of the approximation of the Weibull distribution. It is shown here that a Weibull approximation of the available wind energy is a conservative estimate by %. Furthermore, it would be useful to perform such an analysis with data from different locations since other factors not accounted for in the current correlation may have an influence. Meteorological conditions should be considered as well and incorporated into the Weibull-parameter estimation to improve the evaluation. Acknowledgements This study was financially supported by Forsknings- og Innovationsstyrelsen at the Danish Ministeriet for Videnskab, Teknologi og Udvikling with the Sagsnr within the projekt: Large wind turbines the wind profile up to 400 m. It is part of the Bachelor thesis of the first author, which was accepted by the Institute for Geophysics and Meteorology, University of Cologne, in autumn References: Beeken, A., & Neumann, T. (2008). Five Years of Offshore Measurements at the Fino1 Platform in the German Bight. DEWI-Magazin (33), pp Betz, A. (1926). Windenergie und ihre Ausnutzung durch Windmühlen. Göttingen: Vandenhock&Ruprecht, 64 p. Bronstein, L., & Semendjajew, K. (1975). Taschenbuch der Mathematik (15. Ausg.). Zürich + Frankfurt/Main: Harri Deutsch, 585 p. Coelingh, J., van Wijk, A., & Holtslag, A. (1996). Analysis of wind speed observations over the North Sea. Journal of Wind Engineering and Industrial Aerodynamics (61), pp Emeis, S. (2001). Vertical variation of frequency distributions of wind speed in and above the surface layer observed by sodar. Meteoro lo gische Zeitschrift (10), pp Lange, B., Larsen, S., Højstrup, J., & Barthelmie, R. (2004). Importance of thermal effects and sea surface roughness for offshore wind resource assessment. Journal of Wind Engineering and Industrial Aerodynamics (92), pp Neumann, T., Nolopp, K., & Herklotz, K. (2004). First Operating Experience with the FINO1 Research Platform. DEWI-Magazin (24), pp Riedel, V., Durante, F., Neumann, T., & Strack, M. (2005). Das erste Mess jahr auf der FINO1-Plattform in der Nordsee - Auswertung und Analy se des Windprofils und Abschätzung des statistischen Langzeitmittels. DEWI- Magazin (26), pp Türk, M. (2008). Ermittlung designrelevanter Belastungsparameter für Offshore Windkraftanlagen. Univerität zu Köln: Doktorarbeit, 126 p. Wilker, H. (2004). Weibull Statistik in der Praxis - Leitfaden zur Zuver lässigkeits ermittlung technischer Produkte. Norderstedt: Books on Demand GmbH, 330 p. 46 DEWI MAGAZIN NO. 36, FEBRUARY 2010

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