Extrapolation of Extreme Response for Wind Turbines based on Field

Measurements

Authors:

Henrik Stensgaard Toft, Aalborg University, DenmarkJohn 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).

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Introduction

The extreme load during operation is dependent on:

• The mean wind speed.

• The turbulence intensity.

• The type and settings of the control system.

Flap Bending MomentPitch controlled wind

turbine

Tower Mudline MomentPitch 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.

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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.

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Load Extrapolation based on Extreme Response in Storms

0 6 12 18 24 30 36 42 48Time [h]

10min Mean Wind Speed10min Max Flap BendingNominal Wind Speed

• A storm wind speed Ustorm should be defined so extreme loads occur for mean wind speeds above Ustorm.

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.

• 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.

1 0.75ref stormI U c

1storm nom pU U k

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.

4. The characteristic load is calculated for the probability:

| 1 expresponse

lF l S l

| exp expresponseF l S l

1| 1response

r

F l ST

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 5 10 15 20 250

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Wind Speed [m/s]

Den

sity

Val

ue [

-]

SiteIEC Class III

Numerical Example

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

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.

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.

Threshold

Characteristic load

without stat. unc.

with stat. unc.

1.4 1.000 1.037

2.0 1.041 1.0910 0.2 0.4 0.6 0.8 1 1.2

10-8

10-6

10-4

10-2

100

1 year

50 year

Normalized Response l

1-Flong-term

(l|T)

without stat. unc.

with stat. unc.

Numerical Example

0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.90

0.2

0.4

0.6

0.8

1

Response [-]

Fresponse(l|S)

MeasurementsWeibullGumbel

Distribution

Characteristic load

without stat. unc.

with stat. unc.

Weibull 1.106 1.348

Gumbel 1.303 1.401

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.

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.

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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.

Extrapolation of Extreme Response for Wind Turbines based on Field

Measurements

Authors:

Henrik Stensgaard Toft, Aalborg University, DenmarkJohn Dalsgaard Sørensen, Aalborg University / Risø-DTU, Denmark