# Autocorrelation of 10 minute mean wind speed

I am aware that this topic may well be out of place here, but I try nevertheless to post it, hoping in some expert opinion. It has nothing to do with TurbSim.

My problem is the following: I have real anemometer data, for a dozen different sites, spanning about 1-2 years, sampled with the usual 10 minute interval. I am trying to define something like the “duty cycle” of a turbine if installed in one of those sites. It is not enough to use a Weibull distribution to say that, for example, 27% of the time the wind speed is above V_rated; I also would like to extract the information: how long will a given velocity remain in the same bin.

For example, say that I have now registered one interval of 10 minutes where V=Vrated. How much is the probability that in the next interval V remains, say in the bin [Vrated-1 m/s, Vrated + 1 m/s]? And in the next one, and so on? Which is the “mean duration” of a given bin?

I found in literature that the autocorrelation function should provide some kind of answer to this question, but, although I have already computed it on my 10 minute data, I am not very sure how to use it… also because the source I am using shows it applied to seconds time scales, NOT to 10 minutes… (“Wind Energy Explained” - J.F. Manwell et al, pag. 40).

Thanks a lot
Claudio

As I understand it you have calculated the autocorrelation over a 10-minute period I presume using the data at the original sampling rate; i.e., 1/sec or something like that. To get an estimate of the correlation time for a given wind speed bin you will need to use the time sequence of the 10-minute wind speeds or 144 per day. The correlation time is the integral of the autocorelation function over the period of record. Thus to obtain a good estimate for a given site you will need a long record. I would think that a full month may be adequate as long as the seasonal variation does not seriously influence the observed variation; i.e. the process is reasonably stationary over a four week period. If not, you may have use a shorter record such as two weeks or even one.

No. I have only the 10 minutes means, and a lot of them. I have computed the autocorrelation function over 1 YEAR of 10 minutes data.
I am not very strong in statistic, and my problems are:

1. does this make sense (to use 10 minutes data over long time instead of 1 second data over 10 minutes)?
2. how do I use the resulting curve (for example: how do I predict the “duration” of a given velocity bin: is that some kind of integral of the curve)?

Basically I would like to answer the question: if at the time t0 I have a 10’ velocity mean of V0, which is the probability that at the time t0+k*10’ the velocity is in the V0 bin [V0-0.5 m/s, V0+0.5 m/s] or something like this?

best regards from foggy Italy
Claudio

Claudio,

I gave your situation some more thought. You might consider doing the following which I have illustrated with an example of a years worth of 10-minute mean wind speeds from the 50-m level on our site meteorological mast from the year 1999.

First I wrote a short FORTRAN program called “bin_ws.for”. I then ran it on the column vector of mean wind speeds from our tower. The output gives you the number of contiguous records or groups over the year during which the mean 50-m wind speed remained greater than rated (in this case I chose 10 m/s) and which I have converted into the equivalent number of hours. I have provided graphic plots of the probability of the number of contiguous hours exceeded this rated wind speed and a cumulative probability plot as well. They along with the program “bin_ws.for” can by found at
http://wind.nrel.gov/public/Kelley/Pedrazzi

I hope this is of some use.

Regards,

Neil
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Neil,
this is really very kind of you, to develop a program for us! I am grateful and I am immediately going to test it on my own data.

Actually I was also beginning to think that the autocorrelation is certainly an interesting tool of analysis for time series, but does not necessarily answer directly to my question.

As an “exchange” to your program, I wish to show you two examples of autocorrelation, computed exactly following the definition found in “Manwell et al - Wind Energy explained” page 40. The data are the 10 minute mean wind speeds over around 1 year, in two of our sites.

I think that these plots have certainly something to say about the “persistency” of the wind speed, but I do not know exactly how to interpret them, and quantitatively use them.

I will now go on and test your program on my data.

I wish to thank you again and say you all at NREL/NWTC that it is a pleasure to be able to cooperate like this in this forum, having the possibility to ask for an expert opinion and sharing methods and ideas!

Best regards
Claudio