4.5 Prediction of the wind regime
4.5.3 Measure-Correlate-Predict-Methode
For most planning sites wind measurements seldom exist for a sufficiently long period (minimum 20 years), on one hand. On the other, the wind regime at the site should be predicted as exact as possible for the expected operating period of 20 years because of the strong variations of the mean annual wind speed from year to year (cf. Fig. 4-17).
If a long-term time series of wind speed and direction is available for at least one reference site in the region of the planning site (minimum measuring period 20 years) then there is the possibility to generate a long-term wind prediction by correlation between the reference site and the planning site.
The purely statistical method Measure-Correlate-Predict (MCP) is based on the assumption that there is a linear correlation between simultaneous measure- ments at the planning site and the reference site. Using, e.g., the hourly mean values of the wind speed vRi at the reference site as x-coordinate and the simulta- neous ones vPi from the planning site as y-coordinate, these pairs of values may be
drawn in a Cartesian coordinate system. Under the assumption of a linear relation it is then allowed to draw a regression line through the points. The gradient of the line is a measure for the relation of wind speed vP at the planning site to the wind speed of the reference site vR. Calculating the correlation between the measuring data from reference site and planning site allows estimating statistically the rela- tion between the wind regimes at the considered sites using the correlation coeffi- cient R². It gives the linear correlation between the simultaneously recorded data as well as the scattering (variance). From the obtained averages and standard deviations of the sample it is possible to determine e.g. the Weibull distribution function, cf. section 4.2.2. If the correlation is sufficiently high, i.e. R2 ! 0.70, it is allowed to transfer the factors of the wind speed distribution at the reference site to the planning site.
Wind farm planning is in general based on the sectorised wind data, with usu- ally 12 sectors, cf. Fig. 4-22. It follows that also the correlation between reference site and planning site has to be performed sector by sector: The distributions factors obtained for one individual wind direction sector of the wind rose at the reference site are transferred by the correlation to the corresponding sector of the planning site to achieve its individual distribution factors. In course of this proce- dure, many problems arise: If in the considered region a certain wind direction dominates the wind regime of the year or season there will be some sectors of the wind rose where there are less individual events than required for a correlation, meaning that the transformation from the reference site to the planning site is not possible. Moreover there may be a time delay between the reference and the plan- ning site for the occurrences of distinct meteorological events, e.g. weather fronts.
This leads to simultaneously recorded pairs of data which are not correlated. Due to the time delay it is moreover possible that in course of the passage of weather fronts there is a shift of the prevailing wind direction between the sites, and con- sequently the wind speeds of the meteorological event are located at the reference and planning site in different wind rose sectors.
All these problematic issues which reduce the quality of the correlation are reduced by choosing the sample length as long as possible, i.e. minimum one-year data sets. There are different ways for trying by methodological extensions to circumvent or reduce the effects of the mentioned deficits which is discussed extensively in the corresponding literature, e.g. [28].
Since the presented MCP method is a purely formal-statistical procedure, the physical conditions like orography, plant cover or building are not considered.
For the reliability of the correlation investigation it is important to choose either a suitable sample length to represent the annual wind cycle, or at best the correlation of an entire annual wind record of the reference and planning site.
The disadvantage of the method is that the calculated wind speed is valid only for the individual measuring height exactly at position of the measuring mast. A transformation of the long-term corrected wind regime to other points than the one measured (in measuring height at the mast position) is only possible by physical models which consider the effects of the local site conditions on the flow.
4.5 Prediction of the wind regime 166
References
[1] Petersen E.L., Mortensen N.G., Landberg L., Hứjstrup J., Frank H.P.: Wind Power Meteorology, Risứ-I-1206, 1997
[2] Meteorological Aspects of The Utilisation of Wind as an Energy Resource, WMO Rep.
No. 575, Geneva, 1981
[3] IEA: Recommended Practices for Wind Turbine Testing, Part 11. Wind Speed Measure- ment and Use of Cup Anemometry, 1999
[4] IEC 61400-12-1: Wind Turbine Generator Systems – Part 12: Wind Turbine Perform- ance Testing, 2005
[5] Troen I., Petersen E.L.: European Wind Atlas, Risứ National Laboratory, 1989 [6] Mortensen N.G., Petersen E.L.: Influence of Topographical Input Data on the Accu-
racy of Wind Flow Modeling in Complex Terrain, Proceedings of the European Wind Energy Conference, Dublin, Ireland, 1997
[7] Hübner H., Otte J.: Windenergienutzung im Mittelgebirgsraum (Wind energy applica- tion in the low mountain range)), University of Kassel, Germany, 1990
[8] Antoniou I. et al: On the Theory of SODAR Measurement Techniques, Risứ-R- 1410(EN), 2003, Risứ National Laboratory, Roskilde Denmark
[9] Energia Eolica: Le Gouriérès, Masson, 1982
[10] Meyers kleines Lexikon der Meteorologie (Meyer’s small encyclopaedia on meteorol- ogy), Meyers Lexikon-Verlag, Mannheim, 1987
[11] Courtney M.S.: An atmospheric turbulence data set for wind turbine research, Pro- ceedings of the 10th British Wind Energy Association Conference, London 22-24 March 1988
[12] Burton T., Sharpe D., Jenkins N., Bossanyi E.: Wind Energy Handbook, John Wiley &
Sons, 2001
[13] Kristensen L., Hansen O.F.: Distance Constant of Risứ Cup Anemometer, Risứ-R- 1320(EN), 2002, Risứ National Laboratory, Roskilde Denmark
[14] Mann J., Ott S., Jứrgensen B.H., Frank H.P.: WAsP Engineering 2000, Risứ-R- 1356(EN), 2002, Risứ National Laboratory, Roskilde Denmark
[15] Lange B.: Modelling the Marine Boundary Layer for Offshore Wind Power Utilisa- tion, PhD thesis, University of Oldenburg, Germany 2002
[16] Stull R.B.: An Introduction to Boundary Layer Meteorology, 1988, Kluwer Acad.
Publ. Dordrecht, 666pp
[17] Petersen T.F., Gjerding S., Ingham P., Enevoldsen P., Hansen J.K., Jứrgensen H.K.:
Wind Turbine Power Performance Verification in Complex Terrain and Wind Farms, Risứ-R-1330(EN), 2002, Risứ National Laboratory, Roskilde Denmark
[18] FGW (Federation of German Windpower): Technische Richtlinien für Windener- gieanlagen, Teil 2: Bestimmung von Leistungskurve und standardisierten Energieer- trọgen (Technical Guidelines for Wind Energy Converters, Part2: Determining the Power Performance and Standardised Energy Yields), Rev. 13, 2000
[19] IEC 61400-1, Ed.3: Wind Turbine Generator Systems – Part 1: Safety Requirements, 2005
[20] Germanischer Lloyd: Richtlinie für die Zertifizierung von Windenergieanlagen (Guideline for the Certification of Wind Turbines), Hamburg 2003
[21] DIBt (Center of competence in civil engineering): Richtlinie für Wind turbinen (Guideline for Wind Energy Plants), 1993, 1996, 2004
[22] Kaiser K., Langreder W.: Site Specific Wind Parameter and their Effect on Mechani- cal Loads, Proceedings EWEC, Copenhagen, 2001
[23] Frandsen S., Thứgersen L.: Integrated Fatigue Loading for Wind Turbines in Wind Farms by Combining Ambient Turbulence and Wakes; Wind Engineering, Vol. 23 No.
6, 1999
[24] Katic I., Hứjstrup J., Jensen N.O.: A Simple Model for Cluster Effeciency, European Wind Energy Association Conference and Exhibition, 7-9 October 1986, Rome, Italy [25] Hửgstrửm U.: Non-dimensional wind and temperature profiles, Bound. Layer Meteor.
42 (1988), 55-78
[26] Barthelmie R., Hansen O.F., Enevoldsen K., Motta M., Pryor S., Hứjstrup J., Frandsen S., Larsen S., Sanderhoff P.: Ten years of Measurements of offshore Wind farms – what have we learnt and where are Uncertainties?, Proceedings The Art of making Torque of Wind EAWE, Delft, 2004
[27] Kaiser K., Langreder W., Hohlen H.: Turbulence Correction for Power Curves, Pro- ceedings EWEC 2003, Madrid 2003
[28] Riedel V., Strack M.: Entwicklung verbesserter MCP-Algorithmen mit Parameterop- timierung durch Verteilungsanpassung (Development of improved MCP algorithms with parameter optimization by distribution fitting), Deutsche Windenergie- Konferenz, Wilhelmshaven, 2002
[29] Thomsen K., Madsen H.A.: A new simulation method for turbines in wake – applied to extreme response during operation, Proceedings: The Art of making Torque of Wind, EAWE, Delft, 2004
[30] IEC 61400-121,88/163/CDV: Wind Turbine Generator Systems – Part 121: Power Performance Measurements of Grid Connected Wind Turbines
[31] Obukhow A.M.: Turbulence in an Atmosphere with non-uniform temperature. Transl.
in Boundary Layer Meteor., 1946
[32] TA-Luft: Technische Anleitung zur Reinhaltung der Luft (German Technical Instruc- tions on Air Quality), Bundesministerium für Umweltschutz, Raumordnung und Reak- torsicherheit (German Federal Ministry of the environment, Nature Conservation and Nuclear Safety, Bonn, Juli 2002
[33] Molly, J.P.: Windenergie (Windenergy), C.F. Müller-Verlag, Karlsruhe, 1990
[34] Manwell, J.F., u.a.: Windenergy explained – Theory, Design and Application, John Wiley & Sons Ltd., USA/UK, 2002
[35] Thomsen, W.T.: Theory of vibration, 4th edition, Chapter 13: Random vibration, Pren- tice Hall, New Jersey, USA, 1993
[36] Christoffer, J., Ulbricht-Eissing , M.: Die bodennahen Windverhọltnisse in der BR Deutschland (The surface wind regimes in Germany), Offenbach, Deutscher Wetterdi- enst (German Weather Service), Bericht Nr. 147, 1989
[37] Hoffmann, R.: Signalanalyse und –erkennung (signal analysis and recognition), Springer-Verlag, Berlin, 1998
[38] Ammonit: Messtechnik für Klimaforschung und Windenergie (Measuring equipment for climatic research and wind energy) 2006/07), Ammonit Gesellschaft für Messtechnik mbH, 2006
R. Gasch and J. Twele (eds.), Wind Power Plants: Fundamentals, Design, Construction 168 and Operation, DOI 10.1007/978-3-642-22938-1_5, © Springer-Verlag Berlin Heidelberg 2012
5 Blade geometry according to Betz and Schmitz
With the help of the Betz or the Schmitz (Glauert) theory [1, 2, 7], designing a wind turbine is relatively straightforward. These theories provide the blade chord and the blade twist relative to the radius, after the design tip speed ratio, the aero- dynamic profile and the angle of attack or the lift coefficient have been specified.
The Betz theory only takes into account the axial downstream losses. Schmitz, additionally, takes into account the downstream swirl losses, due to the rotational wake. For rotors with a low tip speed ratio (design tip speed ratio of ȜD < 2.5), this results in a blade geometry significantly different from that determined by the Betz theory. Profile losses and losses resulting from the air flow around the blade tips are ignored in both theories. They have to be accounted for by an additional reduction in the turbine’s power. The number of blades is not an issue as this only affects the tip losses.