Normality of data

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First found May 22, 2018

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Olive Schreiner
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Transcript

Use of nacelle lidar data
to explore impact of
non-linear averaging
Chris Slinger, John Medley, Rhys Evans
[email protected]
+44 1531 650 757
02 September 2014
Background. From the April 2014 PCWG meeting:
“Existing correction methods (, RE, TI renorm) do not fully explain observations...”
10 minute mean wind speeds used
Erik Tűxen reminded us a more fundamental measure of performance is the
relationship between the turbine’s electrical power and the wind’s kinetic power
The meeting also noted that averaging non-linear quantities can be misleading
Would 10 minute wind speeds based on mean energy be more useful than
existing approaches (e.g. mean wind speeds with TI renormalisation) ?
2
Aim of investigation
Use high frequency lidar measurement data to investigate these effects
– Compare efficiency plots derived from 10 minute
averaged wind speeds and those from 10 minute
cubed-root-mean-cubed wind speeds
– Compare power curves in a similar fashion
– Use validation / Round Robin tools to analyse data too
– e.g. Power deviations as a function of wind speed
and turbulence
Also use high frequency lidar data to explore validity of 10 minute normal wind
speed distribution assumption
– Normal distribution is assumed in the TI renormalisation procedure
3
First dataset to be used
Project Cyclops:
ZephIR DM on turbine
“Project Cyclops: the way forward in
power curve measurements ?”
Simon Feeney et al, EWEA 2014
New 2 MW Vestas turbine, flat on-shore
site in UK
Use 1s data from nacelle-mounted ZephIR
dual-mode lidar
Use 1s data from ground-based ZephIR
lidar too
Collaborate with RES UK, who will analyse
1s metmast data too
4
ZephIR DM on
ground
Initial results: normality of data
A graphical method of looking at the normality of a distribution is a QQ plot,
comparing quantiles from the data to expected Gaussian quantiles. Gaussian
data should give a straight line. Some examples are shown here:
5
Normality of data : skewness and kurtosis
Skewness and kurtosis are statistics that describe the shape of a probability
distribution
Skewness measures asymmetry of the distribution
Kurtosis measures the how peaked (or how heavy-tailed) the distribution is
Kurtosis = -1.56
6
Kurtosis = 0.00
Kurtosis = +13.1
Normality of data : skewness and kurtosis
Skewness and kurtosis are statistics that describe the shape of a probability
distribution
Skewness measures asymmetry of the distribution
Kurtosis measures the peakedness (or how heavy-tailed it is)
Other Normality tests are available, but a simple kurtosis filter looks easy to
implement and may be sufficient – let’s try it and see!
7

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