Page 162 - Fluid Power Engineering

136 Chapter Seven

In the Valentine example, X is the 25 years of NCAR wind data at 42 m
elevation and Y is the 25 years of wind speed prediction (hindcasting)
at Valentine at 40 m elevation. Note, in this example, the resolution of
prediction is 6 h.
If hourly airport is used as the long-term reference data instead
of NCAR data, and 10-min measurement data is available, then a
process similar to the example may be deployed, except the resolution
of prediction will be 1 h.
The statistical distribution of the residual term is computed using
measurement data by:

ε i = YM i − f (X i ) (7-3)

where YM i is the onsite measurement data and f (X i ) is the predicted
data for the measurement time period i. ε i should be a random time
series, that is, the distribution should be Gaussian with zero mean. The
quality of the prediction method is reflected in the distribution of ε.
When prediction methods are applied to each of the 12 or 16 direction
sectors (of the reference time series), then each sector’s ε should be
independent of wind speed. For example, it should not be the case
that at lower wind speeds ε has a positive mean and at higher wind
speeds ε has a negative mean.
The final prediction time series is created using Eq. (7-2). Note
not only is the transfer function f applied to X, but the residual is
added. Residual is computed using a randomization method, like
Monte Carlo simulation. This is called the long-term corrected wind
distribution; it is an artificial time series that has been randomized by
9
adding the residual. This addition is not in vain, because energy is
a cubic function of wind speed; a positive residual contributes much
more to increasing energy compared to the contribution of negative
residual in lowering energy.
In the following sections, four prediction methods are described.

Regression
The most common regression models used for wind speed estimation
are linear and quadratic. Within the two models there are two vari-
ations: Regression through (0, 0) and regression with no constraints
(see Table 7-8).
The regression parameters a 1 , a 2 , a 3 are computed using least-
squares algorithm. Although regression through (0, 0) is intuitive, it
is not a good representation at higher wind speed, which is where
energy production happens. An unconstrained regression method is,
therefore, used. As stated above, in addition to the regression param-
eters, the distribution of the residual is computed and added to the
prediction.