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Contents

• Aim: why this work?

• Probabilistic design

• Some results

• Conclusions

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Why this work? (1)

Cost [ct/kWh] Wind Conventional

Generation 4-7 4

External (environment)

0 2-7

TOTAL 4-7 6-11

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Why this work? (2)

Cost [ct/kWh] Wind Conventional

Generation 4-7 4

External (environment)

0 2-7

Financing (economic life)

3-6(10 years)

0(40 years)

TOTAL 7-13 6-11

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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

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Objectives

1. Given target failure rate, find a set of optimal partial safety factors, giving minimum weight safe design. Factors may be for:1. loads2. modelling3. material properties

2. Better insight in uncertainties in calculation methods1. improved risk assessment2. most important uncertainty

3. Because of time constraints, work is limited to fatigue of the structure, ultimate loads are not considered.

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Minimum weight design

• How large γf and γm must be is determined by probabilistic considerations: which failure probability is allowed?

SR

fm

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Which failure probability is allowed?

• Failure is not an option.• Gene Kranz, during the rescue of the Apollo 13, 1969.

• Failure is an option, we just don’t want it to happen very often.• Dick Veldkamp, 2006.

• How often may be set by public safety considerations or by economic optimisation.

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Economically optimal safety factor

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Probabilistic design: example

• Tower

• For simplicity, think of two stochastic parameters:• Wind load• Tower strength

• Monte Carlo-method

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Tower failure

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Experiment: 100.000 times

1. Build a turbine

2. Measure wind loadand 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

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Monte Carlo analysis: draw from distributions

0

10

20

30

40

50

60

30 35 40 45 50 55 60 65 70 75

Fai

lure

pro

bab

ilit

y [%

]

Strength R

Load S

X

XY

Y

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Tower failure probability

0.E+00

2.E-05

4.E-05

6.E-05

8.E-05

1.E-04

0 2 4 6 8 10 12 14 16 18 20

Life [year]

Cu

mu

lati

ve

fa

liu

re p

orb

ab

ilit

y [

-]

U=8.0 m/s U=8.5 m/s U=9.0 m/s U=8.5 m/s, COV_U doubled

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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

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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

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Fatigue strength & life prediction

VA

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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

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Annual failure probability

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

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.5 1.0 1.5 2.0

Resistance Load Z = R - S

R

S

Z=R-S

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Distribution of variation in limit state function Z(x)

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Economically optimal safety factors

Component Blade Hub Nacelle Tower

StandardSafety factor

1.50 1.38 1.38 1.27

Standard cost(turbine)

1.00 1.01 1.06 1.32

Cost optimal safety factor

1.29 1.72 1.99 1.86

New cost(turbine)

1.00 1.00 1.01 1.02

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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

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Questions?