Going to Extremes: A parametric study on PeakOverThreshold and other methods

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Going to Extremes A parametric study on
Peak-Over-Thresholdand other methods

• Wiebke Langreder
• Jørgen Højstrup
• Suzlon Energy A/S

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Nightmare... Extreme Winds...
Source Wind Power Monthly
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Contents

• Introduction
• Objective
• Methodology
• Results and Conclusions

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Importance of Extreme Wind

• The 50-year maximum 10-minute average wind speed
  Vref is one of the important factors to classify
  a site according to IEC 61400-1.

Source IEC 61400-1 ed 3
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General Problem

• Extreme winds are not related with mean wind
  speed.
• Example

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Where do we get the information from?

• IEC 61400-1?
• Vref 5 Vave

Source IEC 61400-1 ed 2
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Where do we get the information from?

• EWTS (European Wind Turbine Standard)?
• connection between Weibull k factor and extreme
  winds

Vave8m/s
decreasing k
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EWTS
Vref/Vave
Vref factor Vave
Weibull shape parameter k
Source EWTS
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Where do we get the information from?

• Gumbel Distribution?
• Extreme events in nature can frequently be
  described by a Gumbel distribution
• Measured maximum wind speeds are fitted to Gumbel
  distribution
• Gumbel distribution is extrapolated to 50-year
  recurrence time

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The objective

• Ideal
• Long-term data available with several occurances
  of
• 50-year event
• Real world
• Only short term data available (1 year or more)
• Task
• How well can we estimate Vref?
• Compare different methods using short-term data
• IEC
• EWTS
• Gumbel

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Method

• Long-time series are split in shorter sub-sets,
  each method is applied to each sub-set.

LT
We need a true reference value for comparison!
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True Reference Value

• Assumption
• The true Vref is determined applying
• Gumbel distribution
• FULL data set
• POT (Peak-over-Threshold)

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Method

• Results from all methods have been normalised
  with this true value.

POT LT ? True Vref
N subsets ? N results per method ? Standard
deviation ? Bias
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Test Data
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The objective

• Compare different methods
• IEC
• Determine mean wind speed of each sub-set
• Multiply with factor 5
• Normalise result with true value
• EWTS
• Gumbel

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Findings - IEC
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Findings - IEC

• IEC is dependent on Weibull k factor
• Standard Deviation is 26!!!
• Average of all results fits the true value
  bias 0

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The objective

• Compare different methods
• IEC
• EWTS
• Identify k factor of each sub-set
• Determine corresponding factor to multiply Vave
  with
• Normalise result with true value
• Gumbel

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EWTS

• EWTS does not specify
• Shall we use the 360 degree k factor?
• Shall we use a sector-specific k factor?

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Findings EWTS

• 360 degree
• Not dependent on k factor
• Negative bias of 9
• EWTS predicts less than our assumed true
  reference value
• Standard deviation is 16

• Sector
• Not dependent on k factor
• Positive bias of 7
• EWTS predicts more than our assumed true
  reference value
• Standard deviation is 16

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The objective

• Compare different methods
• IEC
• EWTS
• Gumbel
• How to identify maxima?

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Methods to identify maximum wind speeds

• Two commonly used methods
• POT Peak-over-Threshold (using WindPRO)
• PM Periodical Maximum

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POT Peak-over-Threshold

• Pick a threshold wind speed and identify all wind
  speeds above
• Introduce independency criteria
• Two options
• wind speed
• dynamic pressure (square of wind speed)
• Every result has been normalised with the
  reference value.
• The average of all results and their standard
  deviation has been calculated.

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Ideal Gumbel Plot
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POT-Problems start...several slopes
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POT Influence of threshold
Two sub-sets from one site
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Findings Gumbel - POT

• deviations from the Gumbel distribution lead to
  dependency of result from threshold
• strong variations between individual sub-sets
• inconclusive regarding how threshold influences
  result

• POT Wind
• Positive bias of 4
• Standard deviation is 12.

• POT Dynamic Pressure
• Negative bias of 4
• Standard deviation is 11

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Methods to identify maximum wind speeds

• Two commonly used methods
• POT Peak-over-Threshold
• PM Periodical Maximum
• Cut data set in sub-sections
• Identify maximum wind speed in each sub-section
• Ensure statistic independence between samples

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Findings Gumbel - PM
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Findings Gumbel - PM
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Findings Gumbel - PM

• Seasonal bias problematic but can be avoided
  choosing periods carefully
• Smallest recommended period is 6 months
• Method cannot be applied to the same sub-sets as
  the other methods because of seasonal bias
• Thus statistics cannot be compared with the other
  results

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Summary Findings
/- 1 std dev
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Summary Findings
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Brute Force?
When added
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Conclusion

• IEC (factor 5) is not working
• PM not suitable for short-term data sets (lt5
  years)
• Always standard deviation gt10
• Squared wind speed (dynamic pressure) results in
  lower Vref than wind data
• Combination of methods possible, leading to a
  small bias and standard deviation comparable to
  Gumbel

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Acknowledgement

• We would like to thank www.winddata.com for
  providing data.