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. www.vestas.com

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

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.

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.

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:

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

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.

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

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.

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)

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

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.

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