Wind farm output
| industrial collaborators: | E.ON Engineering |
| academic collaborators: | ESGI64 |
| initiated : | 2008/05/21 |
| last updated: | 2010/05/25 |
Study Group report 2008: wind farm outputs (E.ON)
This is the final report on the problem of simulating the distribution and cross-correlation of wind farm output, brought to ESGI64 by E.ON Engineering. Click on the link at the bottom to download the full report as a pdf document.
Report coordinator
David Allwright (Industrial Mathematics KTN)
Executive summary
The problem was to devise a simulation method for the wind speeds at
a set of sites, that has the correct autocorrelation, cross-correlation and
distributions. The report includes one way of doing this, using a mul-
tivariate auto-regressive system, and other comments and observations
that may lead to better ways of achieving the aim.
Introduction
Figure 1: A UK wind farm.
When wind is used to generate electricity, intermittency can be a problem. Since it is unlikely to be calm simultaneously over a large area, one way to make intermittency less of a problem is to have a portfolio of wind farms spread over a wide geographical area. To run simulations to estimate this effect quantitatively, and for other purposes, E.ON wish to have a method of generating wind speed time series at a set of sites, with the correct statistical properties.
One property is that the correlation coefficient R between the wind speeds
at 2 sites separated by a distance d should be a decreasing function of d,
for instance of the form
Another property is that the correlation in time of the wind speed at a single site should be correct. E.ON consider that enough accuracy is provided by an auto-regressive first-order (AR(1)) model of the form
where yt is the wind speed and nt is random noise. If t is measured in half-hours, A is usually at least 0.95.
The third property that E.ON wish to have correct is the distribution of
wind speed at a single site, which should follow a Weibull distribution with
scale λ and shape k, so the density function is
We call this the Weibull(k) distribution. Typical values of k obtained by fitting to observed data are in the range 1.6 to 2.3.
If the simulation method can fit the joint spatio-temporal correlation struc- ture as well as the space and time correlations individually, that would be an added advantage.
Data available
The data provided by E.ON for this study was wind speed data averaged
over 10-minute intervals from 7 wind farm sites taken at various times during
the 4 years 2002–2005. The data (after some cleaning described in Section 7)
is displayed in Figure 2. Data for an individual site is present for between
8 and 20 months out of the 4 years, so coverage is somewhat sparse, but
there is, for instance, a 3-month period in which there is synchronized data
for 5 sites.
Figure 2: Measured wind speeds in m/s averaged over 10-minute in- tervals from 7 sites. The horizontal axis is the row index. In the data this runs from 1 to 210384 but here we only display from the start of the main record in column 2. This covers the 38 month period from November 2002 to December 2005.
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