1. Reliability Analysis of Wind Turbines
Authors:
Henrik Stensgaard Toft, Aalborg University
John Dalsgaard Sørensen, Aalborg University / Risø-DTU

2. Content Limit states for wind turbines.
Example: Reliability of wind turbine tower.
Conclusion.

3. 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
Only wind turbine blades and tower are considered – The approach
taken is general and could be extended to other components

4. 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.

5. 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

6. 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.

7. Ultimate Loading – Operational Condition
IEC : 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.

8. 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.

9. 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:

10. 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.

11. 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
Standard deviation for turbulence in the wakes depends on:
Mean wind speed
Ambient turbulence standard deviation
Distance between wind turbines

12. 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.
The distribution function for the stress ranges can be calculated for different directions dependent on wakes from surrounding wind turbines.

13. 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

14. 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.

15. 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
Five surrounding wind turbines (distance four rotor diameters)
Bilinear SN-curve with lower cut of limit (Eurocode 3)

16. 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
0.23
98 % I
Turbulence intensity
0.11 - XR
Load bearing capacity model
Xdyn
Dynamic response
Xexp
Exposure
0.20/0.10
Xst
Statistical uncertainty
0.10
Xaero
Lift and drag coefficients
Xstr
Stress from wind loading
0.03
Xsim
Limited simulations N 
Miners rule
0.30
XRFC
Rainflow-counting
0.02
Xwake
Wake generated turbulence
0.15

17. Reliability of Wind Turbine Tower
Limit state
Annual reliability index 
Accumulated reliability index 
Ultimate loading
(standstill position)
3.08
2.19
(operational condition)
2.92
2.41
Fatigue loading
3.14
2.49
The reliability index is consistent between the individual limit states.

18. 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.

19. Reliability Analysis of Wind Turbines
Authors:
Henrik Stensgaard Toft, Aalborg University
John Dalsgaard Sørensen, Aalborg University / Risø-DTU