The offshore access problem and turbine availability

probabilistic modelling of expected delays to repairs

Dr. Julian FeuchtwangProf. David Infield

Background:

Aim: Estimate expected delay times to turbine repairs due to sea-state (and/or wind) and how they are influenced by key factors, especially vessel access limits and time required

Contributes as part of a ‘Cost of Energy’ model including risks

Why use a probabilistic method?

Monte Carlo approach needs:– Long, continuous, time series data (real or synthesised?)– Many runs (for statistical validity)

Probabilistic approach needs:– Time series data (best but scant)– or duration statistics– or simple wave height statistics (less accurate)– Allows trends and sensitivities to be explored quickly and easily

Estimating subsystem down-times

Site wind & wave

data / stats

Failure types

Access limit

conditions

Failure rates

Repair times

Statistical model of

access and repair

Expected down-time

O & M cost

Lost revenue

Event tree

fault

is access

possible?

is there

enough access time left?

waitfor next ‘weather window’

carry out repair

no

yes

yes

no

Assumption:No travel without forecast

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

13/10 18/10 23/10 28/10 02/11 07/11

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

13/10 18/10 23/10 28/10 02/11 07/11

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

13/10 18/10 23/10 28/10 02/11 07/11date

sig

nif

ican

t w

ave

hei

gh

t H

s (m

)

Sea-state conditions & Event tree

After 1, 2a or 2b, low sea-state periods may again be too short leading to more delays

0: repair can go ahead

1: waves too high

2a: period

too short

2b: fault too late

required duration

For a given threshold wave height Hth

the wave height probability density function is p( Hth )

Wave height distribution

exceedence probability is

thH

thth dHHHHHP )p()Prob()(

0 1 2 30

0.2

0.4

0.6

0.8

0

0.2

0.4

0.6

0.8

numerical prob densnumerical exc prob

Wave height distribution from Dowsing - original data

significant wave height Hs (m)

prob

abili

ty d

ensi

ty

exce

eden

ce p

roba

bilit

y

Wave height –Maximum likelihood Weibull fitFor a given threshold wave height Hth the wave height exceedence probability

k

c

ththth H

HHHHH 0expProbP

H0 location parameter

HC

scale parameter

kshape parameter

0 1 2 30

0.2

0.4

0.6

0.8

0

0.2

0.4

0.6

0.8

numerical prob densWeibull fit pdfnumerical exc probWeibull fit xp

Wave height distribution from Dowsing - Weibull fit (ML)

significant wave height Hs (m)

prob

abili

ty d

ensi

ty

exce

eden

ce p

roba

bilit

y

Wave height duration joint distributionsFor a given threshold wave height Hth

and a ‘storm or calm’ duration treq

reqt

xreqthreqth dttttHHtH )(q)&Prob(),(Qx

the storm duration exceedence probability is found by integration:

the storm duration probability density function is q( H > Hth , t ) = qx( t )

0.1 1 10 100 1 103

0.01

0.1

1

10

0

0.2

0.4

0.6

0.8

1

calm prob densstorm prob denscalm exc probstorm exc prob

Wave height storm/calm duration from Dowsing, Hth = 2m

duration t (hr)

prob

abili

ty d

ensi

ty

exce

eden

ce p

roba

bilit

y

the mean storm duration

)(qM)(q x10

tdttt xx

Duration exceedence - M.L. Weibull fit

n

n

reqnreqthn

tgtH

exp),(Qthe calm duration exceedence probability is

τn is the mean calm

duration

αn is the shape

factor

is a normalisation factor

11ng

0.1 1 10 100 1 103

0

0.2

0.4

0.6

0.8

1

calm numerical exc probcalm Weibull exc pf

Wave height calm duration from Dowsing, Hth = 2m

calm duration (hr)

exce

eden

ce p

roba

bilit

y

Wave-height Non-exceedence-Duration curvescalm duration exceedence

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 24 48 72 96 120 144 168 192 216 240

operation time treq (hrs)

pro

bab

ilit

y o

f ex

ceed

ing

du

rati

on

3.0

2.8

2.6

2.4

2.2

2.0

1.8

1.6

1.4

1.2

1.0

wave height threshold Hth (m)

Estimating delay times

Partial

Moments etc.

∫dtAccess limits Hthr & treq

Wave-height data

Storm & calm

duration distnsqx(H,t)qn(H,t)

Storm / calm time

series

Expected delay time

E(tdel(Hthr))

Lost revenue

O&M cost

Estimating delay timesif no time-series data

& no duration statistics:Kuwashima & Hogben method

Access limits Hthr & treq

Wave-height Weibull

parameters

Storm & calm

duration distnsqx(H,t)qn(H,t)

K&H

Kuwashima & Hogben method

based on data correlations mostly from North Sea

from H0 HC & k → gives estimates of τn & αn

Partial

Moments etc.

∫dt

Expected delay time

E(tdel(Hthr))

Expected 1st delays of different types:

1st order:Wave height

above threshold P(H) is the storm probability

τx is the mean storm duration

Mqqx(H) is the 2nd moment (non-dim)

of the storm distribution

Etdel1 H( ) P H( ) Mqqx H( ) x H( )

Expected 1st delays of different types:

2nd order (a):Wave height below

threshold, insufficient duration

2nd order (b):Wave height below

threshold, insufficient time left

Mqn(H,t) is the 1st moment (non-dim)

of the calm distribution

Mqqn(H,t) is the 2nd moment (non-dim)

of the calm distribution

Etdel2a H t( ) 1 P H( ) Mqqn H t( )

P H( ) Mqn H t( )

n H( )

Etdel2b H t( ) P H( ) Qn H t( ) t 1t

2 x H( )

Qn(H,t) is the calm duration probability

Further delays of different types:

After 2nd order (a or b):Wave height is above

threshold

After 1st and 3rd order:Wave height is below threshold but duration

may be short

E tdel3| del2 τx=

E tdel4|del1,3 Mqn H t( ) n H( )

all these components can be calculated:

•directly from time-series data by numerical integration

•from Weibull parameters from duration data(uses exponential and Gamma functions)

•or from estimated Weibull parameters (K&H)

Estimated delay timesexpected delay time

0

100

200

300

400

500

600

700

800

900

1000

0 20 40 60 80 100 120 140 160 180 200

operation time treq (hrs)

exp

ecte

d d

elay

tim

e (h

rs)

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.5

3.0

wave height threshold Hth (m)

In order to use this model, we need:

• Failure rate data per fault type– Tavner et al (D & DK)– Hahn Durstewitz & Rohrig (D & DK)– DOWECS (D & DK)– Ribrant & Bertling (SE – includes gearbox

components)– All the above are land-based data. No offshore data available

• Repair times– ditto

• Vessel Operational limits– 2 types of vessel modelled

• Site climate data– in UK: CEFAS, BOCD, NEXT (parameters only)

– in NL: Rijkswaterstaat

– elsewhere: ?

Baseline Case DataBaseline case: failure rates & down-time per failure

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Rotor b

lades

Air bra

ke

Mec

h. bra

ke

Mai

n shaf

t/bea

ring

Gearb

ox

Gener

ator

Yaw s

yste

m

Elect

ronic

Contro

l

Hydra

ulics

Grid/e

lect

rical

Sys

Mec

h/pitc

h contro

l sys

.

fail

ure

s/yr

0

20

40

60

80

100

120

140

160

180

200

hrs

/yr

failure rate

on-land downtime perfailure

Baseline Case Results:annual down-time by subsystem

0

100

200

300

400

500

600

700

800

900

1000

Rotor b

lades

Air bra

ke

Mec

h. bra

ke

Mai

n shaf

t/bea

ring

Gearb

ox

Gener

ator

Yaw s

yste

m

Elect

ronic

Contro

l

Hydra

ulics

Grid/e

lect

rical

Sys

Mec

h/pitc

h contro

l sys

.

hrs

/yr

repair time

travel time

delay time

lead time

Influence of repair time on availability

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0% 20% 40% 60% 80% 100% 120%

repair time factor

% a

vail

abil

ity

Influence of site on availability

Barrow

Lytham

North Somercotes

Lowestoft

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

20% 25% 30% 35% 40% 45%

crane vessel accessibility

% a

vail

abil

ity

Influence of large vessel threshold on availability

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6

threshold wave height Hth (m)

% a

vail

abil

ity

Influence of small vessel threshold on availability

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5

threshold wave height Hth (m)

% a

vail

abil

ity

Ribrant

TavnerLWK

HahnTavner

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.0 0.5 1.0 1.5 2.0 2.5 3.0

whole turbine failure rate /year

% a

vail

abil

ity

dataset

datasetfailure rateDrive-train reliability scaledIndividual Turbine Models

Enercon E66

Nacelle Crane

Nordex N52/54

Vestas V39-500

Enercon E40

Tacke TW600

Influence of failure rate on availability

Conclusions:

Probabilistic method allows rapid exploration of sensitivity to different factors – vessel operability– site climate – reliability– repair times

Offshore exacerbates differences in– reliability– time to repair– accessibility

Highly dependent on access to data but so are other methods