Wind Energy

16
Short Time Prediction of Wind Speeds
from Local Measurements
Holger Kantz, Detlef Holstein, Mario Ragwitz, Nikolay K. Vitanov
Summary. We compare different schemes for the short time (few seconds) prediction
of local wind speeds in terms of their performance. Special emphasis is laid on
the prediction of turbulent gusts, where data driven continuous state Markov chains
turn out to be quite successful. A test of their performance by ROC statistics is
discussed in detail. Taking into account correlations of several measurement positions
in space enhances the predictability. As a striking result, stronger wind gusts
possess a better predictability.
16.1 Wind Speed Predictions
Whereas the three dimensional velocity field of the air in the atmosphere
can be supposed to be described by the deterministic Navier–Stokes equations,
possibly augmented by equations for the temperature and humidity
(and hence density of the air) and with suitable boundary conditions, a local
measurement yields data which appear to be random. In fact, deterministic behaviour
of the local velocities is very unprobable, since (a) the Navier–Stokes
equations contain already non-local interactions through the self-generated
pressure field, and (b) the local wind speed changes due to the drift of the
global wind field across the measurement position.
Data analysis of wind speed recordings yields results which are fully consistent
with stochastic data. We use time series recorded in Lammefjord by
the Risø research centre [1]. These data are obtained from cup anemometers
mounted on measurement masts at heights of 10, 20, and 30 m above ground,
taken with 8 Hz sampling rate. The data sets report the absolute values of the
wind speeds in the x–y-plane, together with the angle of incidence. In total,
we use 10 days of data. Due to the non-stationarity of the data, the autocorrelation
function cannot be reliably determined. In any case, correlations of
the wind speed decay slowly, whereas the increments, i.e. the differences of succesive
measurements, seem to be uncorrelated. Histograms of the differences
vt − ¯vt of the data and the moving 1-minute mean velocities ¯vt, conditioned
to the value of ¯vt, show an almost Gaussian behaviour with variances which