Statistics of 5-10 min averages of wind speed

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Statistics of 5-10 min averages of wind speed
H.M. Olsson, H.G. Beyer Institute of
Engineering University of Agder Grimstad, Norway

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Introduction

• Grid integrations of high shares of wind energy
  requires
• knowledge of the temporal pattern of the power
  flows
• on all time scales
• time scales 1h, 1s
  information (mostly)
• condition on-shore
  available
• time scales 5-10min
  information rarely
• condition off-shore
  available

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Data
Hywind off-shore 500s averages of wind
speed 1 year of data Lindesnes on-
shore 600s averages of wind speed 10 years of
data

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Data analysis

Wind speed (500s,600s ave.) increments incr
ements sorted by initial wind speed
v(t) example onshore
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Data analysis

• distribution of increments
• Standard deviation
• Kurtosis
• in dependence of initial wind speed

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Options for modelling of empirical distribution
Off- shore, initial wind speed 10m/s

• Gaussian distribution
• Castaing distribution

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Options for modelling of empirical distribution

• Castaing distribution
• used for analysing (short term) turbulence data
• parameters ?, ?s directy linked to standard
• deviation and kurtosis
• gives good representation
• for average
• initial wind speeds 6 m/s

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Castaing/Gaussian limitations

• Higher initial wind speeds
• Empirical asymmetric distribution of
  increments
• both, Gaussian and Castaing fail.

cumulative distribution of increments
offshore, initial wind speed20 m/s
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Heuristic model to cope with asymmetry and
increased kurtosis

• Model proposed
• parameters ? and ß
• control
• asymmetry and skewness

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Heuristic model to cope with asymmetry and
increased kurtosis

model performance on-shore initial wind
speed 20 m/s heuristic model well
applicable for all initial wind speeds
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Statistics of 5-10 min averages of wind speed
Conclusions

• For intermediate initial wind speeds the Castaing
  distribution gives a good representation of the
  distribution of wind speed increments from
  knowledge of standard dev. and skewness
• An heuristic model provides the most accurate
  results,
• notably for elevated initial wind speeds ?
• The heuristiclly added exponential term
• breaks the direct link of model parameters to
  mean and std.dev.
• The heuristic model needs a time consuming
  fitting process ?
• Acknowledgements
• data kindly made available by Agder energi AS
  and Statoil, Norway