Reliability Analysis of Wind Turbines

Authors:

Henrik Stensgaard Toft, Aalborg UniversityJohn Dalsgaard Sørensen, Aalborg University / Risø-

DTU

Content

• Limit states for wind turbines.

• Example: Reliability of wind turbine tower.

• Conclusion.

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Limit States for Wind Turbines

Ultimate Loading - Standstill Position• Extreme mean wind speed >25 m/s• The wind turbine is parked

Ultimate Loading - Operational Condition• Mean wind speed 4–25 m/s• Normal operation – pitch/stall control• Wake effects from surrounding wind turbines

Fatigue Loading• Normal operation – pitch/stall control• Wake effects from surrounding wind turbines

Only wind turbine blades and tower are considered – The approach

taken is general and could be extended to other components

Ultimate Loading – Standstill Position

Wind turbine parked and behave like a ‘normal’ civil engineering structure.

Limit state function:

Influence factor cinf determined from design equation.

Loads taken into account:• Wind loading• Gravity loading

Offshore wind turbines: Wave, Current and Ice Loading.

inf, exp inf,1 2R q p dyn st aero str sim gg X c P k I X X X X X X c G

Ultimate Loading – Standstill Position

• Physical uncertainties (Aleatory uncertainties)• Mean wind speed• Turbulence intensity• Material properties (Steel / Composites)

• Statistical uncertainties (Epistemic uncertainties)• Amount of wind data• Limited simulations for estimating the extreme load

effects

• Model uncertainties (Epistemic uncertainties)• Dynamic response• Exposure (Terrain roughness / Landscape topography)• Lift and drag coefficients• Load bearing capacity models / Stress calculation

Ultimate Loading – Operational Condition

Wind turbine in operational condition and the control system influence

the loads.

Limit state function:

Influence factors cinf determined from design equation.

Model uncertainties similar to ‘standstill position’.

Response L is obtained by numerical simulation of the wind turbine

during operation.

inf, expR l dyn st aero str simg X c L X X X X X X

Ultimate Loading – Operational Condition

IEC 61400-1: Load is determined from simulation of the response over the range of significant wind speeds.

Maximum tower mudline moment – 200 simulations of 10 min. at each

wind speed.

Ultimate Loading – Operational Condition

Peaks extracted by the Peak Over Threshold method – Normally used for response due to extreme climate conditions.

• Threshold – Mean plus 1.4 standard deviations.

• Independent peaks – Time separation.

• Individual 10 min time series are independent.

Ultimate Loading – Operational Condition

Response is assumed Weibull distributed for local extremes:

Statistical uncertainty in distribution parameters included.

Long-term distribution of the extremes for all wind speeds:

Characteristic value for response with a 50 year return period:

| , 1 explocal

lF l T U

| | ,out

in

Un U

long term local U

U

F l T F l T U f U dU

7| 1 3.8 10long term cF L T

Fatigue Loading

Behind a wind turbine is a wake formed where:• The mean wind speed decreases slightly• The turbulence intensity increases significantly

Frandsen, S. Turbulence and turbulence generated structural loading in wind turbine clusters,

Risø National Laboratory, 2007.

Fatigue Loading

Wakes from surrounding wind turbines will influence the fatigue loads

for wind turbine placed in clusters

Turbulence in wakes calculated based on IEC 61400-1.

Standard deviation for turbulence in the wakes depends on:• Mean wind speed• Ambient turbulence standard deviation• Distance between wind turbines

2 2

, 2

0.9

1.5 0.3 /T j u

j

UU

d U c

Fatigue Loading

Rainflow-counting of time series Distribution function for stress

ranges.

Relation between standard deviation for stress ranges and standard

deviation turbulence:

where (U) is an influence function dependent on the control system.

u UU Uz

Fatigue Loading

Fatigue damage is calculated based on the distribution function for the

stress ranges and Miners rule for linear damage accumulation.

The fatigue damage is integrated over:• Wind direction• Wind speed• Turbulence intensity

Additional model uncertainties – fatigue loading:• Miners rule• Rainflow-counting• Wake generated turbulence

0

|mD s f s U ds

Reliability of Wind Turbine Tower

The reliability index for wind turbine tower in the three limit states.

The reliability index is obtained by First Order Reliability Methods

(FORM) and defined as:

where Pf is probability of failure.

Design lifetime for wind turbines – 20 years.

1fP

Reliability of Wind Turbine Tower

Ultimate Loading• IEC class II turbulence class B – (Uref=42.5m/s and Iref=0.14)• Only exposed to wind loading

Fatigue Loading• IEC class II turbulence class B – (Uref=42.5m/s and Iref=0.14)• Five surrounding wind turbines (distance four rotor diameters)• Bilinear SN-curve with lower cut of limit (Eurocode 3)

Reliability of Wind Turbine Tower

Variable Dist. Type

Mean Value

COV Char. Value

Material strength LN 1 0.05 5 %

P Mean wind speed G 1 0.23 98 %

I Turbulence intensity LN 0.11 0.05 -

XR Load bearing capacity model

LN 1 0.05 -

Xdyn Dynamic response LN 1 0.05 -

Xexp Exposure LN 1 0.20/0.10

-

Xst Statistical uncertainty LN 1 0.10 -

Xaero Lift and drag coefficients G 1 0.10 -

Xstr Stress from wind loading LN 1 0.03 -

Xsim Limited simulations N 1 0.05 -

Miners rule LN 1 0.30 -

XRFC Rainflow-counting LN 1 0.02 -

Xwake Wake generated turbulence

LN 1 0.15 -

Reliability of Wind Turbine Tower

Limit state Annual reliability index

Accumulated reliability index

Ultimate loading(standstill position)

3.08 2.19

Ultimate loading(operational condition)

2.92 2.41

Fatigue loading 3.14 2.49

The reliability index is consistent between the individual limit states.

Conclusion

• The reliability level is lower than for civil engineering structures where the annual reliability level typically is = 3.8–4.7.

• The consequences of failures are less severe for wind turbines than for e.g. buildings, which could justify the lower reliability level.

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Reliability Analysis of Wind Turbines

Authors:

Henrik Stensgaard Toft, Aalborg UniversityJohn Dalsgaard Sørensen, Aalborg University / Risø-

DTU