Wind Energy

ms prediction error [m/s]
16 Short Time Prediction of Wind Speeds from Local Measurements 95
2.5
2
1.5
1
0.5
Persistence
Extrapolation
AR(20)-model
Markov chain
0
0 1 2 3 4 5
time steps into the future [s]
rms prediction error [m/s]
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0 1 2 3 4 5
time into the future [s]
Fig. 16.2. Left panel: Prediction errors of different prediction schemes for data
from day 191. Right panel: Prediction errors of the Markov chain predictor for selected
subsamples where the standard deviation of the c-pdf p(vt+1|vt,...,vt−m+1)
is smaller than δ, δ =0.25, 0.3, 0.35,... from bottom to top
process with short range memory. In the left panel of Fig. 16.2 we show the
performance of these predictors on data from a rather turbulent day, as a function
of the prediction horizon (all parameters were empirically optimized). The
performance is measured in terms of the root mean squared (rms) prediction
error, ē = � 〈(ˆvt − vt) 2 〉. Since wind speed data are not smooth, predictions
by extrapolations are evidently bad. The fact that the three other predictors
perform almost equally demonstrates that the simple model vt+1 = αvt + ξt
with α ≈ 1 is rather good: Going beyond this hypothesis (which is fully incorporated
in the persistence predictor) yields only minor improvements. To
account for non-stationarity, the coefficients of the AR(20) model were fitted
on moving windows using the past 1,200 s of data. Markov chains of order
10–30 are again slightly superior.
The Markov chain model is flexible enough to model the observed nonconstant
noise amplitude. Using the variance of the c-pdf as additional information
during the forecast process, we can restrict forecasts to those times
t when the standard deviation of the actual c-pdf p(vt+k|vt,...,vt−m+1) is
smaller than some parameter δ. The rms forecast errors obtained from such
subsamples are systematically smaller (Fig. 16.2, right panel). Such an analysis
means that we consider our predictions only when we expect them to be
good, where, however, the model tells us whether they will be good before
the actual prediction error is computed. So the Markov chain yields also a
prediction of the state-dependent expected error, which would be a constant
for the AR-model.
16.2 Prediction of Wind Gusts
We define the gust of strength g as the rise of the velocity by more than g ms
within a time interval of 2 s (16 time steps), where the results are robust