The offshore access problem and turbine availability probabilistic modelling of expected delays to repairs Dr. Julian Feuchtwang Prof. David Infield
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