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2 Contents Aim: why this work? Probabilistic design Some results Conclusions

3 Why this work? (1) Cost [ct/kWh]WindConventional Generation4-74 External (environment)02-7 TOTAL

4 Why this work? (2) Cost [ct/kWh]WindConventional Generation4-74 External (environment)02-7 Financing (economic life) 3-6 (10 years) 0 (40 years) TOTAL

5 Why this work (3) For wind to make a breakthrough (?): Generation cost must be brought down Financing cost must be brought down, one way is to reduce uncertainty So: Wind turbines should be exactly as heavy as necessary, but no heavier The failure probability must be known

6 Objectives 1.Given target failure rate, find a set of optimal partial safety factors, giving minimum weight safe design. Factors may be for: 1.loads 2.modelling 3.material properties 2.Better insight in uncertainties in calculation methods 1.improved risk assessment 2.most important uncertainty 3.Because of time constraints, work is limited to fatigue of the structure, ultimate loads are not considered.

7 Minimum weight design How large γ f and γ m must be is determined by probabilistic considerations: which failure probability is allowed?

8 Which failure probability is allowed? Failure is not an option. Gene Kranz, during the rescue of the Apollo 13, Failure is an option, we just don’t want it to happen very often. Dick Veldkamp, How often may be set by public safety considerations or by economic optimisation.

9 Economically optimal safety factor

10 Probabilistic design: example Tower For simplicity, think of two stochastic parameters: Wind load Tower strength Monte Carlo-method

11 Tower failure

12 Experiment: times 1. Build a turbine 2. Measure wind load and tower strength 3. Result (failure yes/no) Failure probability 2. Simulate wind load and tower strength by Monte Carlo analysis ‘throwing dice’ 1. Design a turbine

13 Monte Carlo analysis: draw from distributions X X Y Y

14 Tower failure probability

15 Back to the real life problem We have designed a turbine, but it is not known exactly in which conditions it can hold, because of: Aerodynamic model uncertainty Errors in FEM Variation in fatigue strength … When the turbine is put up there are more uncertainties: The actual conditions (wind speed, turbulence, inflow angle, wind shear, wake effects, …) The actual turbine (eigenfrequencies, geometry, …) Fatigue life under variable loading (Palmgren-Miner sum) … Establish distributions, and find the failure probability

16 Back to the real life problem We have designed a turbine, but it is not known exactly in which conditions it can hold, because of: Aerodynamic model uncertainty Errors in FEM Variation in fatigue strength … When the turbine is put up there are more uncertainties: The actual conditions (wind speed, turbulence, inflow angle, wind shear, wake effects, …) The actual turbine (eigenfrequencies, geometry, …) Fatigue life under variable loading (Palmgren-Miner sum) … Establish distributions, and find the failure probability

17 Fatigue strength & life prediction VA

18 Base case IEC class 2 design, IEC class 2 site U_design = U_site = 8.5 m/s at hub height TI_design=18%, TI_site=16% + 2% for windfarm wakes Wind spectrum: G_design=3.9 (Kaimal), G_site=3

19 Annual failure probability

20 Probabilistic design: variation in Z(x) = R(x) – S(x) R S Z=R-S

21 Distribution of variation in limit state function Z(x)

22 Economically optimal safety factors ComponentBladeHubNacelleTower Standard Safety factor Standard cost (turbine) Cost optimal safety factor New cost (turbine)

23 Conclusions & to do 1.Based on best available knowledge, safety factors smaller for blades, larger for hub, nacelle, tower (but there is hidden safety!) 2.Greatest uncertainty in fatigue strength and fatigue life prediction, so more research necessary on turbine specific materials 3.Extend the method to ultimate loads 4.Fix target failure probability and use this for design

24 Questions?