Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder...
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Transcript of Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder...
![Page 1: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/1.jpg)
Going to Extremes: A parametric study on Peak-Over-Threshold
and other methods
Wiebke Langreder
Jørgen Højstrup
Suzlon Energy A/S
![Page 2: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/2.jpg)
Source: Wind Power Monthly
Nightmare... Extreme Winds...
![Page 3: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/3.jpg)
Contents
Introduction
Objective
Methodology
Results and Conclusions
![Page 4: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/4.jpg)
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
![Page 5: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/5.jpg)
General Problem
Extreme winds are not related with mean wind speed.
Example: Vave Vref
Site 2 7.9 m/s 34 m/s
Site 3 4.6 m/s 36 m/s
![Page 6: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/6.jpg)
IEC 61400-1?
Vref = 5 · Vave
Where do we get the information from?
Source: IEC 61400-1 ed 2
![Page 7: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/7.jpg)
0
0.02
0.04
0.06
0.08
0.1
0.12
0 10 20 30
Wind Speed [m/s]
Fre
qu
ency
[%
]
1.25
1.5
1.75
2
2.25
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
![Page 8: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/8.jpg)
Vref= factor · Vave
Source: EWTS
EWTSV
ref/V
ave
Weibull shape parameter k
![Page 9: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/9.jpg)
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?
![Page 10: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/10.jpg)
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
![Page 11: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/11.jpg)
Method
Long-time series are split in shorter sub-sets, each method is applied to each sub-set.
LT
Sub-set 1 → Vref
Sub-set 2 → Vref
Sub-set 3 → Vref
Sub-set 4 → Vref
Sub-set 5 → Vref
We need a ”true” reference value for comparison!
![Page 12: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/12.jpg)
”True” Reference Value
Assumption
The “true” Vref is determined applying :
• Gumbel distribution
• FULL data set
• POT (Peak-over-Threshold)
![Page 13: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/13.jpg)
Method
Results from all methods have been normalised with this ”true” value.
N subsets → N results per method
→ Standard deviation
→ Bias
POT: LT → ”True” Vref
Sub-set 1 → Vref
Sub-set 2 → Vref
Sub-set 3 → Vref
Sub-set 4 → Vref
Sub-set 5 → Vref
![Page 14: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/14.jpg)
Test Data
Where Period Mean wind speed [m/s]
Weibull shape factor
Site 1 South of Spain 5 years 7.7 2.04Site 2 North of France 5 years 7.9 2.08Site 3 Colorado 10 years 4.6 1.34Site 4 Denmark 10 years 7.3 2.05Site 5 Netherlands 10 years 4.7 1.68Site 6 Minnesota 10 years 7.8 2.25Site 7 Korea 10 years 3.3 1.96
![Page 15: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/15.jpg)
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
![Page 16: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/16.jpg)
Findings - IEC
R2 = 0.6221
50%
60%
70%
80%
90%
100%
110%
120%
130%
140%
150%
160%
1.00 1.50 2.00 2.50 3.00
Weibull k factor
Nor
mal
ised
50-
year
max
win
d sp
eed
![Page 17: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/17.jpg)
Findings - IEC
• IEC is dependent on Weibull k factor
• Standard Deviation is 26%!!!
• Average of all results fits the “true” value bias = 0%
![Page 18: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/18.jpg)
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
![Page 19: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/19.jpg)
EWTS does not specify:
• Shall we use the 360 degree k factor?• Shall we use a sector-specific k factor?
EWTS
![Page 20: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/20.jpg)
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%
![Page 21: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/21.jpg)
The objective
Compare different methods
• IEC
• EWTS
• Gumbel
How to identify maxima?
![Page 22: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/22.jpg)
Methods to identify maximum wind speeds
Two commonly used methods:
• POT Peak-over-Threshold (using WindPRO)
• PM Periodical Maximum
![Page 23: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/23.jpg)
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.
![Page 24: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/24.jpg)
Ideal Gumbel Plot
![Page 25: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/25.jpg)
POT-Problems start...several slopes
![Page 26: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/26.jpg)
POT: Influence of threshold
Two sub-sets from one site
![Page 27: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/27.jpg)
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%
![Page 28: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/28.jpg)
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
![Page 29: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/29.jpg)
Findings Gumbel - PM
![Page 30: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/30.jpg)
Findings Gumbel - PM
POT vref= 35m/s
PM vref= 40m/s
![Page 31: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/31.jpg)
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
![Page 32: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/32.jpg)
Summary Findings
+/- 1 std dev
70%
80%
90%
100%
110%
120%
130%
IEC EWTS360 degr
EWTSsector
POTwind
POTpressure
No
rmal
ised
50-
year
max
win
d s
pee
d
![Page 33: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/33.jpg)
Summary Findings
Methoddependend on Weibull k factor
bias Std Dev
IEC yes none 26%EWTS 360 degr no - 9 % 16%EWTS sector no + 7 % 16%POT wind no +4 % 12%POT pressure no - 4 % 11%
Methoddependend on Weibull k factor
bias Std Dev
IEC yes none 26%EWTS 360 degr no - 9 % 16%EWTS sector no + 7 % 16%POT wind no +4 % 12%POT pressure no - 4 % 11%
![Page 34: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/34.jpg)
Brute Force?
When added
Combined EWTS no - 1% 13%
Methoddependend on Weibull k factor
bias Std Dev
EWTS 360 degr no - 9 % 16%EWTS sector no + 7 % 16%
![Page 35: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/35.jpg)
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
![Page 36: Going to Extremes: A parametric study on Peak-Over-Threshold and other methods Wiebke Langreder Jørgen Højstrup Suzlon Energy A/S.](https://reader033.fdocuments.in/reader033/viewer/2022051215/56649ec05503460f94bcbec8/html5/thumbnails/36.jpg)
Acknowledgement
We would like to thank www.winddata.com for providing data.