Going to Extremes: A parametric study on Peak-Over-Threshold and other methods

1. Going to Extremes: A parametric study on Peak-Over-Thresholdand other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S

2. Nightmare... Extreme Winds... Source: Wind Power Monthly

3. Contents • Introduction • Objective • Methodology • Results and Conclusions

4. 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

5. General Problem • Extreme winds are not related with mean wind speed. • Example:

6. Where do we get the information from? • IEC 61400-1? • Vref = 5 · Vave Source: IEC 61400-1 ed 2

7. Where do we get the information from? • EWTS (European Wind Turbine Standard)? • connection between Weibull k factor and extreme winds Vave=8m/s decreasing k

8. EWTS Vref/Vave Vref= factor · Vave Weibull shape parameter k Source: EWTS

9. 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

10. 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

11. Sub-set 1 → Vref Sub-set 2 → Vref Sub-set 3 → Vref Sub-set 4 → Vref Sub-set 5 → Vref 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!

12. ”True” Reference Value • Assumption • The “true” Vref is determined applying : • Gumbel distribution • FULL data set • POT (Peak-over-Threshold)

13. Sub-set 1 → Vref Sub-set 2 → Vref Sub-set 3 → Vref Sub-set 4 → Vref Sub-set 5 → Vref 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

14. Test Data

15. 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

16. Findings - IEC

17. Findings - IEC • IEC is dependent on Weibull k factor • Standard Deviation is 26%!!! • Average of all results fits the “true” value bias = 0%

18. 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

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

20. 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% Findings EWTS

21. The objective • Compare different methods • IEC • EWTS • Gumbel • How to identify maxima?

22. Methods to identify maximum wind speeds • Two commonly used methods: • POT Peak-over-Threshold (using WindPRO) • PM Periodical Maximum

23. 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.

24. Ideal Gumbel Plot

25. POT-Problems start...several slopes

26. POT: Influence of threshold Two sub-sets from one site

27. 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%

28. 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

29. Findings Gumbel - PM

30. POT vref= 35m/s PM vref= 40m/s Findings Gumbel - PM

31. 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

32. Summary Findings +/- 1 std dev

33. Summary Findings

34. Brute Force? When added

35. Conclusion • IEC (factor 5) is not working • PM not suitable for short-term data sets (<5 years) • Always standard deviation >10% • 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

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