Reliability Analysis of Wind Turbines
Authors:
Henrik Stensgaard Toft, Aalborg University
John 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:
g   X R  cinf,q P 1  2k p I X dyn  X exp X st X aero X str X sim  cinf, g G
Influence factor cinf determined from design equation.
Loads taken into account:
• Wind loading
• Gravity loading
Offshore wind turbines: Wave, Current and Ice Loading.
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:
g   X R  cinf,l L X dyn X exp X st X aero X str X sim
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.
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:
  l    
Flocal  l | T ,U   1  exp   

    


Statistical uncertainty in distribution parameters included.
Long-term distribution of the extremes for all wind speeds:
Flong term  l | T  
U out

Flocal  l | T ,U 
nU 
fU U  dU
U in
Characteristic value for response with a 50 year return period:
Flong term  Lc | T   1  3.8 107
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
 T , j U  
0.9U 2
1.5  0.3 d
j
2
U /c

2
 u
Fatigue Loading
Rainflow-counting of time series  Distribution function for stress
ranges.
Relation between standard deviation for stress ranges and standard
deviation turbulence:
  U     U 
 u U 
z
where (U) is an influence function dependent on the control system.
Fatigue Loading
Fatigue damage is calculated based on the distribution function for the
stress ranges and Miners rule for linear damage accumulation.

D      s m f   s |   U   ds
0
The fatigue damage is integrated over:
• Wind direction
• Wind speed
• Turbulence intensity
Additional model uncertainties – fatigue loading:
• Miners rule
• Rainflow-counting
• Wake generated turbulence
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:
   1  Pf 
where Pf is probability of failure.
Design lifetime for wind turbines – 20 years.
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.
www.vestas.com
Reliability Analysis of Wind Turbines
Authors:
Henrik Stensgaard Toft, Aalborg University
John Dalsgaard Sørensen, Aalborg University / Risø-DTU