Extreme Response for Wind Turbines
Authors:
Henrik Stensgaard Toft, Aalborg University, Denmark
John Dalsgaard Sørensen, Aalborg University / Risø-DTU, Denmark
Contents
•
Introduction
•
Load Extrapolation based on Extreme Response in Storms
•
Numerical Example
•
Conclusion
•
Future Work
Introduction
The extreme load can occur in two situations:
•
Standstill position – The wind turbine is parked and behave like a “normal”
civil engineering structure (wind speed > 25m/s).
•
Operational condition – The wind turbine is producing power and behave
like a machine (wind speed 3-25m/s).
www.vestas.com
Introduction
The extreme load during operation is dependent on:
•
The mean wind speed.
•
The turbulence intensity.
•
The type and settings of the control system.
Tower Mudline Moment
Pitch controlled wind turbine
Flap Bending Moment
Pitch controlled wind turbine
Introduction
IEC 61400-1: Extreme load determined from 10min. simulations of the
response during operation over the range of significant wind speeds.
The method is based on the following assumptions:
•
Local extremes in the response are independent.
•
Individual 10min. time series are independent.
In the present paper are these assumptions investigated.
www.vestas.com
Introduction
•
In the present paper is a new method for estimation of the extreme load
presented.
•
By comparing the extreme load determine by this method and the method
in IEC 61400-1 can the assumptions about independence be studied.
•
The new method uses a long measured time series which rarely is available
– Therefore is the new method only used for validation of the existing
method.
Load Extrapolation based on Extreme Response in Storms
The new method for estimating the extreme load is based on:
•
Existing methods for estimating e.g. the extreme wave height.
•
Assumption about independent storms.
www.vestas.com
Load Extrapolation based on Extreme Response in Storms
•
A storm wind speed Ustorm should be defined so extreme loads occur for
mean wind speeds above Ustorm.
10min M ean Wind Speed
10min M ax Flap Bending
Nominal Wind Speed
0
6
12
18
24
Time [h]
30
36
42
48
Load Extrapolation based on Extreme Response in Storms
•
Ustorm is defined from the nominal wind speed Unom (typically 10-15 m/s)
and the standard deviation for the turbulence 1.
U storm  U nom  k p 1
1  I ref  0.75U storm  c 
•
Independence of storms:
• Storms are combined if the mean wind speed between them not are
below a percentile of Ustorm.
• Storms are separated a minimum number of hours.
Load Extrapolation based on Extreme Response in Storms
1. The measured time series is divided into independent storms.
2. For each storm is the extreme response extracted.
3. To the 25-30 largest extreme responses is a distribution function fitted.
  l    
Fresponse  l | S   1  exp   

    



Fresponse  l | S   exp  exp    l    
l 

4. The characteristic load is calculated for the probability:
Fresponse  l | S   1 
1
Tr
Numerical Example
•
Stall controlled onshore wind turbine.
•
Dataset for response measured over 62 days in winter and spring.
(52 days of complete measurements)
•
Dataset for mean wind speed measured over 4 years.
•
Site: Less severe than class III in IEC 61400-1. Turbulence intensity Iref =
0.12.
0.14
Site
IEC Class III
Density Value [-]
0.12
0.1
0.08
0.06
0.04
0.02
0
0
5
10
15
Wind Speed [m/s]
20
25
Numerical Example
Investigation of storm definition.
•
Storms are combined if the mean wind speed between them not are
below 80% of Ustorm.
•
Storms are separated at least 2 hours.
•
Higher nominal wind speed leads to less and shorter storms.
Nominal
wind speed
Unom
Storm
wind speed
Ustorm
Storms
per year

Length
of storm
Ts
14m/s
9.5m/s
202
8.0h
15m/s
10.2m/s
165
7.4h
16m/s
11.0m/s
135
6.7h
Numerical Example
Load extrapolation according to IEC 61400-1.
•
Extremes extracted by the Peak Over Threshold method.
•
Characteristic loads calculated with/without statistical uncertainty
(Hessian matrix).
•
Normalized characteristic loads.
1-Flong-term(l|T)
10
10
10
10
10
0
without stat. unc.
with stat. unc.
-2
Threshold
-4
without stat. unc.
with stat. unc.
1.4
1.000
1.037
2.0
1.041
1.091
1 year
-6
50 year
-8
0
0.2
0.4
0.6
0.8
Normalized Response l
1
1.2
Characteristic load
Numerical Example
Load extrapolation based on extreme response in storms.
•
25 largest extremes from independent storms are used.
•
Measured time series are short – 52 days of complete measurements
•
Choice of distribution function has a significant influence on the results.
1
Fresponse (l|S)
0.8
Distribution
0.6
without stat. unc.
with stat. unc.
Weibull
1.106
1.348
Gumbel
1.303
1.401
0.4
Measurements
Weibull
Gumbel
0.2
0
0.55
0.6
0.65
0.7
0.75
Response [-]
0.8
0.85
0.9
Characteristic load
Conclusion
•
New method for calculation of the extreme response is proposed.
•
Definition of a storm is proposed.
•
Higher characteristic load using the new method which could indicate that
the 10min. time series or local extremes are dependent.
•
Based on a stall controlled wind turbine and a short measured time series.
www.vestas.com
Future Work
•
Refinement of the storm definition based on:
• Longer measured time series.
• More severe sites.
•
Estimation of the “correct” long-term distribution for the extreme
response:
• Weibull
• Gumbel
• Etc.
•
Comparison of the new method and IEC 61400-1 for a long measured
time series.
Extreme Response for Wind Turbines
Authors:
Henrik Stensgaard Toft, Aalborg University, Denmark
John Dalsgaard Sørensen, Aalborg University / Risø-DTU, Denmark