Component 142: wind data

Specifications

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General 

This component allows to specify and calculate relevant wind data for one or several wind turbines (Component 143).

The relation between the power output P of a wind turbine, the undisturbed wind speed v₁ at hub height, and the power coefficient c_P is as follows:

For modern wind turbines, the hub height typically is at 100m or higher. As the undisturbed wind speed v₁ as measured value at hub height is not available for a plant in the planning stage, it is calculated from existing data (mostly measurements at a height of 10m averaged over several years). Fig. 1 shows the schematic representation of the logarithmic vertical speed profile and the correlation between the wind speed values at different heights.

Fig. 1: Schematic representation of the logarithmic vertical speed profile assuming the Prandtl boundary layer

The calculation of the wind speed at hub height can be done according to various calculation algorithms. The most simple method is based on the assumption of a logarithmic vertical wind speed profile (Prandtl boundary layer, see Fig. 1). A complex algorithm additionally considers the influence of the atmospheric stability. This influence is related to the vertical temperature profile of the air near the ground. A distinction is made between three categories (see Fig. 2). In the case of the unstable stratification, the air close to the ground is warmer than the one above (typical of summer months with a strong heating of the ground). In the case of the stable stratification, the air temperature at the ground is lower than in the layers above (typical of winter months, when the ground cools off significantly). In the case of the neutral stratification, there is neither a warming nor a cooling in the air layer close to the ground. To consider the influence of the atmospheric stability, the data of the season, the position of the sun, and the cloud coverage data are required, among others. As these data are characteristic for a location, it is enough the carry out the calculations in one Component 142 and then adopt them for each wind turbine of a wind farm.

Fig. 2: The vertical temperature profile (left) and the corresponding wind speed profile (right) depending on the atmospheric stability

The calculation of the wind speed at hub height

Algorithm 1: Calculation without considering the atmospheric stability (or for neutral stratification) assuming that the two heights z₁ (the reference height at which the corresponding wind speed v₁ is known) and z₂ (the hub height) are located in the boundary layer (Fig. 1).

Here the roughness length z₀, the heights z₁ and z_2, and the wind speed v₁ are used as inputs. The result is the wind speed v₂.

Algorithm 2: Improvement of Algorithm 1, consideration of the atmospheric stability.

Additional inputs are the total cloud overage in eights, months, and time of day, from which the position of the sun and the corresponding times for sunrise and sunset are determined. The previous formula is expanded by an empirical stability function Ψ as follows:

The stability function Ψ depends on the so-called Monin-Obukhov length L_M and corrects the wind speed distribution by the corresponding temperature stratification. The precise form of the stability function Ψ can be found in [2]. The Monin-Obukhov length L_M can be determined from the ground roughness length z₀ and the dispersion category according to Klug/Manier, according to Table 17 from [3]. The dispersion category according to Klug/Manier in turn depends on the wind speed at a height of 10m, the total cloud coverage in eights, and the position of the sun (season, hours of night, hours of day, hours before and after sunrise/sunset).  The algorithm described in [3] (Appendix A) is used for determining the dispersion category according to Klug/Manier.

[1] recommends the following values for the roughness length z₀ 

In Component 142, the Monin-Obukhov length L_M can either be specified by the user directly or calculated on the basis of [3]-[4]. Subsequently, the Monin-Obukhov length from component 142 can be used in Components 143 for calculating the wind speed at hub height according to [2].

Table 17 from [3] for the determination of the Monin-Obukhov length L_M depending on the dispersion category according to Klug/Manier and the  roughness length z₀ is shown below

The geographic positions of the location are taken over from Component 117 (The sun). The same applies to the specification of the time when calculating with time series dialogs. From this the position of the sun and the dispersion category according to Klug/Manier are determined according to [4].

As in Component 143 (Wind turbine) the power characteristic of the manufacturer refers to the wind speed normalized according to IEC 61400-12-1, it is necessary to know the air temperature and air pressure required for the normalization according to IEC 61400-12-1. These values are also the same for all wind turbines of the wind farm and are therefore specified in one Component 142.

References

[1] Windkraftanlagen. Grundlagen, Entwurf, Planung und Betrieb. R. Gasch, J. Twele 8 Auflage (in German)

[2] VDI 3783 Blatt 8: Environmental meteorology – Turbulence parameters for dispersion models supported by measurement data (In German: Umweltmeteorologie Messwertgestützte Turbulenzparametrisierung für Ausbreitungsmodelle)

[3] Technische Anleitung zur Reinhaltung der Luft – TA Luft 2002 (In German)

[4] VDI 3782 Blatt 1: Environmental meteorology - Atmospheric dispersion models Gaussian plume model for air quality management (In German: Umweltmeteorologie Atmosphärische Ausbreitungsmodelle. Gauß’sches Fahnenmodell für Pläne zur Luftreinhaltung)

User Input Values

Result values

Component displays

Display option 1

Example

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