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

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

3. Contents Introduction Objective Methodology Results and Conclusions

4. Importance of Extreme Wind The 50-year maximum 10-minute average wind speed V ref 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: V ave V ref Site 27.9 m/s34 m/s Site 34.6 m/s36 m/s

6. IEC 61400-1? V ref = 5 · V ave Where do we get the information from? 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 V ave =8m/s decreasing k

8. V ref = factor · V ave Source: EWTS EWTS V ref /V ave Weibull shape parameter k

9. 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 Where do we get the information from?

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 V ref ? Compare different methods using short-term data IEC EWTS Gumbel

11. Method Long-time series are split in shorter sub-sets, each method is applied to each sub-set. LT Sub-set 1 → V ref Sub-set 2 → V ref Sub-set 3 → V ref Sub-set 4 → V ref Sub-set 5 → V ref We need a ”true” reference value for comparison!

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

13. Method Results from all methods have been normalised with this ”true” value. N subsets → N results per method → Standard deviation → Bias POT: LT → ”True” V ref Sub-set 1 → V ref Sub-set 2 → V ref Sub-set 3 → V ref Sub-set 4 → V ref Sub-set 5 → V ref

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. 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 V ave with –Normalise result with “true” value Gumbel

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

20. 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%

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

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 V ref 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.www.winddata.com