Wind speed distributions

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Wind speed distributions are commonly used to indicate the annual available wind energy. These distributions are estimated using measurements, wind maps or computer analysis. Tables or statistical functions can give the distribution.

Figure 5.1 shows the relative distribution h(v) of wind speed v in Karlsruhe, which is located in south Germany near the Black Forest. This distribution indicates how often a certain wind speed occurs. It is immediately obvious that the wind energy potential in Karlsruhe is very low. The sum of frequencies with wind speeds lower than 4 m/s is more than 70 per cent. In other words, for practical wind generator use, wind speeds above 4 m/s exist for only 30 per cent of the time.

The wind speed measurement interval can cause uncertainties in the estimation of wind speed frequency distributions. If the average of the wind

Figure 5.1 Wind Speed Distribution for Karlsruhe in Inland Germany in

1991/1992

Figure 5.1 Wind Speed Distribution for Karlsruhe in Inland Germany in

1991/1992

speed is recorded only every 10 min or even every hour, further calculations on wind generator yield can produce high errors because the energy of the wind does not depend linearly on the wind speed. A solution that avoids this error is to record the average of the wind speed cubed.

The mean wind speed can be easily calculated:

However, the mean wind speed can only partly describe the potential of a site, because the wind distribution may be continuous wind or long calm periods interspersed with periods of very high wind speeds. The wind energy in these two cases can be totally different. Nevertheless, the mean wind speed is often used to give the site quality.

Good wind maps that show the mean wind speed exist for most countries (e.g. Troen and Petersen, 1989). In coastal areas, mean wind speeds of 6 m/s or more can be reached; in inland areas it can be below 3 m/s. Mountainous regions also offer good wind conditions. Today digital wind maps also exist and computer programs can estimate wind speeds even for locations where no measurements have been taken (e.g. Ris0 National Laboratory, 1987).

A wind speed frequency distribution gives much better information about the wind conditions of a certain site than the mean wind speed. The frequency distribution can be given as tables with wind speed intervals or as statistical functions. The most common statistical functions that are used for wind power calculations are the Weibull and the Rayleigh distributions.

The Weibull distribution of wind speed v with shape parameter k and scale parameter a is given by:

Table 5.2 Weibull Parameters and Mean Wind Speed at a Height of 10 m for Various Locations in Germany

Location

k

a

v in m/s

Location

k

a

v in m/s

Berlin

1.85

4.4

3.9

Munich

1.32

3.2

2.9

Hamburg

1.87

4.6

4.1

Nuremberg

1.36

2.9

2.7

Hannover

1.78

4.1

3.7

Saarbr├╝cken

1.76

3.7

3.3

Helgoland

2.13

8.0

7.1

Stuttgart

1.23

2.6

2.4

Cologne

1.77

3.6

3.2

Wasserkuppe

1.98

6.8

6.0

Source: Christoffer and Ulbricht-Eissing, 1989

Source: Christoffer and Ulbricht-Eissing, 1989

The shape and scale parameters depend on the site. Table 5.2 gives some example parameters for various German locations.

The mean wind speed can be estimated approximately from the Weibull parameters (Molly, 1990):

The parameter a for k = 2 can be obtained from the mean wind speed: v a, , =

0.886 Vi

Wind Speed Distribution
Wind speed v in m/s

Figure 5.2 Rayleigh Distributions for Different Mean Wind Speeds v

Substituting a in the Weibull distribution and using k =2 results in the Rayleigh distribution:

The Rayleigh distribution needs only the average wind speed as a parameter. Figure 5.2 shows Rayleigh distributions for different mean wind speeds.

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