Statistical Tools - Wind Energy Meteorology: Atmospheric Physics for Wind Power Generation - page 155

Appenix A
Statistical Tools
This appendix introduces some statistical terms, distributions and techniques
which are used throughout the topic.
A.1 Time Series Analysis
The advected kinetic energy of an air stream is proportional to the third power of
the wind speed, see Eq. ( 1.1 ). The climatological mean wind speed is not sufficient
to assess the available wind energy at a certain site, because wind turbines can
adapt to the actual wind speed within seconds. Additionally, loads and vibrations
on structures such as wind turbines depend decisively on the high-frequency parts
of the wind spectrum. Therefore, it is important to characterize spatial structures
and temporal fluctuations of the wind speed as well. This can be done by com-
puting the wind speed distribution at a site from sufficiently long time series. Time
series have to be checked for homogeneity before computing statistical parameters
such as those given in Table A.1 . Sometimes instruments have been replaced by
newer ones at a given measurement site or even the measurement site has been
moved to a new position.
For the sake of simplicity and practicability, data distributions are often
approximated by mathematical functions that depend on a very low number of
parameters. Table A.1 gives an overview of frequently used statistical parameters
characterizing the wind.
Frequently, the wind is measured at one point and fluctuations are determined in
the time domain. For short time intervals, the ''frozen turbulence hypothesis'' (also
called Taylor's hypothesis) is often used. This hypothesis implies that turbulence
elements move with the mean wind and do not alter their shape during such short
periods. The frozen turbulence hypothesis allows for a conversion between time
and space domain for these short time periods.