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### How to generate a wind timehistory with a given PDF and PSD

Posted: Wed Oct 25, 2017 3:31 am
Hi all,

I would like to know if someone knows how to generate a wind timehistory in MATLAB with a given Weibull PDF and a given PSD .

### Re: How to generate a wind timehistory with a given PDF and PSD

Posted: Wed Oct 25, 2017 6:58 am
Dear Alessandro,

I'm not sure I'm answering your question, but NREL's TurbSim software (https://nwtc.nrel.gov/alphas) has an option whereby a time history of wind can be generated based on a given PSD.

The Weibull PDF applies to a a long-term wind statistics (for the life of a wind wind turbine), whereas TurbSim applies to stationary wind i.e. for a given mean wind speed (a given bin of the Weibull PDF) within a short period of time (10 - 60 minutes) where wind turbine aero-elastic simulations are run. The wind TurbSim produces will have a Gaussian PDF.

Best regards,

### Re: How to generate a wind timehistory with a given PDF and PSD

Posted: Thu Oct 26, 2017 2:28 am
Dear Jason,

Thank you for your answer. I was thinking about generating a short wind time history (many seconds) from a given PSD and with a WEibull PDF. so in your opinion is it meaningless to generate a short time history with a Weibull PDF ? Should I use a Gaussian PDF for this case?
thank you!

### Re: How to generate a wind timehistory with a given PDF and PSD

Posted: Thu Oct 26, 2017 6:47 am
Dear Alessandro,

I would not expect short-term wind statistics to have a Weibull PDF. While short-term wind statistics are not necessarily Gaussian, this is typically a reasonable assumption to make. Search for "Gaussian" and "non-Gaussian" wind in the literature for detailed research on this subject.

Best regards,

### Re: How to generate a wind timehistory with a given PDF and PSD

Posted: Mon Oct 01, 2018 8:21 am
Dear Jason

I think my question is relevant to the current post topic.

I have been using TurbSim for stationary wind i.e., for a specified mean wind speed, but have some questions about it's potential use in other cases. I am considering combining shorter TurbSim run outputs e.g., less than 1 minute (over a range of windspeeds, but not demanding that it will constitute a Weibull distribution) for the purposes of combining them to create a non-stationary wind. I realise there will be possible limitations with that approach, e.g. continuity between datasets.

My questions are:

1. It is recommended that the AnalysisTime parameter is at least 600 seconds. Will the quality of the data produced be affected if values less than this are chosen? I think the underlying question is 'how does TurbSim generate the data?', and are the time parameter recommendations based upon the data generation method, or upon what the user does with the resulting data?

2. Similarly, it is recommended that the TimeStep parameter is set at 0.05 seconds.
Will the quality of the data produced be affected if values greater than this are used?

Thanks

Aidan

### Re: How to generate a wind timehistory with a given PDF and PSD

Posted: Mon Oct 01, 2018 8:57 am
Dear Aidan,

My answer is, "yes" to both questions. The AnalysisTime determines the frequency step used by the inverse Fourier transform in TurbSim to derive the time series from the spectra; using a small AnalysisTime will result in a large frequency step and thus poor resolution of the spectra. The TimeStep determines the frequency range used by the inverse Fourier transform in TurbSim to derive the time series from the spectra; using a large TimeStep will result in a small frequency range and thus cut-off the spectra prematurely.

Best regards,

### Re: How to generate a wind timehistory with a given PDF and PSD

Posted: Tue Oct 02, 2018 6:19 am
Hi Jason

Thanks for the information.

Then I think the best solution will be to generate the data for AnalysisTime=600s at TimeStep=0.05s intervals and then just trim the output datasets as required.

Cheers

Aidan