Basics of Renewable Energy Supply - Renewable Energy: Technology, Economics and Environment - page 66

values. They are, however, only limited to a small range of velocities. With an
increasing average wind velocity, the absolute height of the maximum occurrence
probability decreases; at the same time the frequency distribution is significantly
more balanced.
Mathematical approximations to such probability distributions can be made
with different functions that can be described by means of only a few parameters.
For the distribution of wind velocities either the Weibull or the Rayleigh Distribu-
tion can be used (Fig. 2.35, on the right). Today, mainly the Weibull Distribution
is used being the more generally defined distribution function. The corresponding
density function is defined according to Equation (2.20). k is the so-called shape
parameter and A the scaling factor (Table 2.4). v Wi describes the wind velocity.

This results, for example, in the calculated shape and scaling factors compiled for various
sites in Germany and shown in Table 2.4. According to this table, the shape factor is gener-
ally characterised by smaller values and a decreasing mean annual velocity.

Table 2.4 Shape and scaling factors of the annual mean wind velocity for the example of
various sites in Germany /2-22/
Site Annual mean wind speed

in m/s

Scaling factor
in m/s

Shape factor

Helgoland
List
Bremen
Brunswick
Saarbrücken
Stuttgart

7.2
7.1
4.3
3.8
3.4
2.5

8.0
8.0
4.9
4.3
3.9
2.8

2.09
2.15
1.85
1.83
1.82
1.24

k

v

( k − 1 ⎛ ⎞

k v

Wi
A

⎛ ⎞

−

⎜
⎝

⎟
⎠

(2.20) f ( v ) = e

⎝

Wi

⎠

Wi

A A

2.4 Run-of-river and reservoir water supply

Of the total solar energy incident on earth approximately 21 % or 1.2 10 6 EJ/a are
used for maintaining the global water cycle of evaporation and precipitation. But
only scarcely 0.02 % or 200 EJ/a out of this amount of energy are finally available
as kinetic and potential energy stored in the rivers and lakes of the earth /2-23/.