Page 168 - Fluid Power Engineering

W ind Resource Assessment 141

Wind Speed Bins (reference)
Sectors 0–1 m/s 1–2 m/s . . . 7–8 m/s . . . 24–25 m/s
N v = (0.5,0.4) (0.55,0.45) (0.92,0.5) No data
θ = (14,4) (16,5) (22,5)
NNE v = (0.3,0.1) (0.45,0.35) (0.92,0.5) No data
θ = (15,3) (16,5) (22,5)
...
WNW v = (0.3,0.1) (0.35,0.25) No data No data
θ = (13,3) (19,5)

∗ Wind speed bins and wind direction sector bins form the matrix. Each cell of the
matrix contains mean and standard deviation of wind speed-up and wind veer.
TABLE 7-10 Illustration of the Matrix Method for Prediction ∗

In order to have a full set of transfer functions such that any wind
speed and direction combination in the long-term reference dataset
can be converted into onsite predicted dataset, regression functions
are defined. This will provide values for cells in the matrix with “No
data” or cells with a small dataset from which meaningful statistics
cannot be computed. It also smoothes the changes between bins. A
pictorial representation of this is in Fig. 7-14a and b.
Two regressions are performed for each direction sector. The first
regression function computes the wind speed-up as a function of wind
speed.

long v
long v
v = f v + ε (7-7)
j j ref,j j
v
where j = 1 to 12 or 16 is the direction sector index, and ε is the
j
residual term.
The second regression function computed the wind veer as a func-
tion of wind speed.
long θ
long θ
θ j = f j v ref,j + ε j (7-8)

These regression functions become transfer functions that use long-
term reference data to compute onsite long-term prediction of wind
speed and wind direction. It is assumed that the relationships hold for
all periods. The next step is to add the residual term to the predicted
wind speed time series. A simple method would be to assume inde-
pendence between the distribution of wind speed-up and wind veer.
Under this assumption, the standard deviation for wind speed-up and
wind veer in each cell is used to create the corrected time series for
wind speed and wind direction. A more sophisticated method is to