823
1 INTRODUCTION
Bytheendof2017,Europeleadedtheglobaloffshore
energymarket,with83.9%shareofthetotalinstalled
capacity of 18.814 MW from 4.149 grid‐connected
wind turbines of 92 offshore wind farms in 11
countries. The UK has the largest amount
representing 43.3%, followed by Germany.
The total
Europeanoffshorewindcapacityisforecastat25GW
by 2020 and 70 GW by 2030 (by then 7–11% of the
EU’s electricity demand is produced by offshore
wind). Besides, the Chinese offshore wind energy
marketbeganin2016(14.9%marketshare), followed
byVietnam,Japan,SouthKorea
andtheUS.Withthe
growing engagement in the offshore wind industry
worldwide,itisnaturalto investigatetheoperations
and maintenance problems of the offshore wind
farms. Given the difficulty in the techniques,
availability, and accessibility due to the uncertain
ocean wind environment, the maintenance costs for
theoffshorewind
farmscanformupto25–30%ofthe
energy cost and is typically estimated at five to ten
timesoftheonshoremaintenancecost.Onceafailure
occurs,alonger systemdowntime, andmore lossin
revenue follow. Therefore, it is useful to study the
maintenance problem of the offshore
wind farms
Zhongetal.(2019).
In recent literature we find several papers that
studythemaintenanceproblemoftheoffshorewind
farms. Below we discuss some of the most accurate
referencesinthesolutionoftheproblemposed:
Alcobaetal.(2017)proposeadiscreteoptimization
model that chooses an
optimal fleet of vessel to
support maintenance operations at Offshore Wind
Farm.Themodel is presented as a bi‐levelproblem.
Onthefist(tactical)level,decisionsaremadeonthe
fleet composition for a certain time horizon. On the
second (operational) level, the fleet is used to
optimize the
schedule of operations needed at the
Offshore Wind Farm, given events of failures and
weatherconditions.
Zhong et al. (2018) proposed a non‐linear multi‐
objective programming model including two newly
definedobjectiveswiththirteenfamiliesofconstraints
suitable for the preventive maintenance of offshore
wind farms. In order to solve
our model effectively,
Integrated Maintenance Decision Making Platform for
Offshore Wind Farm with Optimal Vessel Fleet Size
Support System
J
.Szpytko&Y.Salgado
A
GHUniversityofScienceandTechnology,Krakow,Poland
ABSTRACT: The paper presents a model to coordinate the predictive‐preventive maintenance process of
OffshoreWindFarm(OWF)withoptimalVesselFleet(VF)sizesupportsystem.Themodelispresentedasabi‐
levelproblem.Onthefirstlevel,themodelcoordinatesthe
predictive‐preventivemaintenanceoftheOWFand
thedistributedPowerSystemminimizingtheriskofExpectedEnergynotSupply(EENS).Theriskisestimated
with a sequential Markov Chain Monte Carlo (MCMC) simulation model. On the second level the model
determiningtheoptimalfleetsizeofvesselstosupportmaintenance
activitiesatOWF.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 13
Number 4
December 2019
DOI:10.12716/1001.13.04.15
824
the non‐dominated sorting genetic algorithm II,
especially for the multi‐objective optimization is
utilizedandPareto‐optimalsolutions ofschedulescan
be obtained to offer adequate support to decision‐
makers.Finally,anexampleisgiventoillustratethe
performances of the devised model and algorithm
andexploretherelationships
ofthetwotargetswith
thehelpofacontrastmodel.
Zhong et al. (2019) formulate a fuzzy multi‐
objectivenon‐linearchance‐constrainedprogramming
modelwithnewlydefinedreliabilityandcostcriteria
and constraints to obtain satisfying schedules for
windturbinemaintenance.Tosolvetheoptimization
model,a2‐
phasesolution frameworkintegratingthe
operational law for fuzzy arithmetic and the non‐
dominated sorting genetic algorithm II for multi‐
objective programming is developed. Pareto‐optimal
solutions of the schedules are obtained to form the
trade‐offs between the reliability maximization and
costminimizationobjectives.Anumericalexampleis
illustratedto
validatethemodel.
Stalhane et al. (2016) determine the optimal fleet
size and mix of vessels to support maintenance
activities at offshore wind farms. A two‐stage
stochastic programming model is proposed where
uncertainty in demand and weather conditions are
considered.Themodelaimstoconsiderthewholelife
span
ofanoffshorewindfarmandshouldatthesame
time remain solvable for realistically sized problem
instances. The results from a computational study
basedonrealisticdataisprovided.
Florian and Sorensen (2017) present how
applicationsofriskandreliability‐basedmethodsfor
planningof Operation andMaintenance(O&M), can
positivelyimpactthecostofmaintenance.Thestudy
focuses on maintenance of wind turbine blades, for
whichafracturemechanics‐baseddegradationmodel
issetup.Basedonthismodel,andtheuncertaininput
interms ofcrackingontheblades atthestart ofthe
lifetime,aninitialreliability
estimateismade.During
the operation period, inspections are performed at
regulartimeintervals,andtheresultsarethenusedto
update the reliability estimates using Bayesian
networks. Based on the updated estimate, decisions
onrepairsaretaken,thuspotentiallyminimizingthe
maintenance effort while maintaining a target
reliability level. To
showcase the potential cost
reduction, a study is made using a discrete event
simulator. Two different preventive approaches are
used. The first is a traditional time/condition‐based
strategy, where inspections are made with a fixed
annual frequency and defects are repaired on
detection.Thesecondapproachconsistsofrisk‐based
inspection planning, using the methodology
described in the first part of the paper, and the cost
and availability savings relative to the previous
strategyareunderlined.Adetaileddescriptiononthe
advantages of disadvantages of the risk strategy is
givenintheendofthepaper.
Halvorsen‐Weare et al. (2017)
introduces a meta‐
heuristic solution method to determine cost‐efficient
vesselfleetstosupportmaintenancetasksatoffshore
wind farms under uncertainty. It considers weather
conditions and failures leading to corrective
maintenance tasks as stochastic parameters and
evaluates candidate solutions by a simulation
program.Thesolutionmethodhasbeenincorporated
in a decision support tool. Computational
experiments,includingcomparisonofresultswithan
exact solution method, illustrate that the decision
support tool can be used to provide near‐optimal
solutionswithinacceptablecomputationaltime.
1.1 Contributionofthis work
Based on the previous references, in this paper we
contributewithanother
approachtothemaintenance
problem solution of the offshore wind farms. In the
firstpartofthepaper(LevelI)weanalyzetherelation
between the Power System and the offshore wind
farmand in thesecondpart(LevelII) we propose a
newobjective functionbasedon workers demand
to
determinate the composition of the vessel fleet size
supportsystem to carryoutthe maintenance taskin
theoffshorewindfarms.Onbothlevelsweoptimize
non‐linearstochasticfunctions.
2 MATERIALSANDMETHODS
The bi‐level optimization model formalized in this
section to coordinate the Predictive‐Preventive
Maintenance Scheduling
(PPMS) of the OWF with
optimalvesselfleetsizesupportsystemisstructured
in two steps. The first one consists in modeling the
Power System and OWF with MCMC simulation
modelestimating therisk indicatorEENSandbased
inthisindicatorandcoordinatethePPMS,thesecond
oneindetermining
theoptimalfleetsizeofvesselsto
supportmaintenance activities atOWF based on the
workersdemandandthefleetsizecapacity.
2.1 LevelI:PowerSystem
2.1.1 Thermalunitmodeling
The operation of a thermal generating unit is
continuous, eventually fails and is repairable. This
random behavior can be described
from Markov
processes Yan et al. (2016). The Markov process
allows modeling two stages: available and
unavailable.Forthiscase,transitionratesaredefined
betweenthetwostatesinwhichthegeneratorcanbe.
Iftheprobabilityfunctionofthetransitionratesfrom
onestatetoanotherisexponential,they
aredenoted
asλ(failurerate)andμ(repairrate)ofthegenerator.
Figure 1 shows a Markov process with two states:
available and unavailable, and its transition rates λ
andμ. Forthetwo‐statesystemrepresentedinFigure
1, the system of differential equations with initial
conditionsP
0(t)+P1(t)=1,P0(0)=1andP1(0)= 0,that
modelstheMarkovprocessisshownin(1).
Figure1.Two‐statemodelforageneratingunit.
825
0
01
1
10
dP
P
tPt
dt
dP
P
tPt
dt
(1)
The stationary solution of the differential
equations system is denoted as availability A and
unavailability U of a thermal generating unit. The
parameter used to evaluate the static capacity of a
thermalgeneratingunitistheunavailability(2),also
knownastheForcedOutageRate(FOR).
r
FOR U
mr
(2)
where the Mean Time to Failure (MTTF) is equal to
1
,andtheMeanTimetoRepair(MTTR) isequalto
1
.
TheMTTFandMTTRparametersarevalidonlyif
the random variables follow an exponential
distribution. If the random behavior of Time to
Failure (TTF) and Repair Times (TTR) is known, its
averagevalue can beobtainedandconsequentlythe
FORforeachunit.
The generating units in the Power
System are
represented by a two‐state model or a multi‐state
model.Inthetwo‐statemodel,thegeneratingunitis
considered fully available or totally unavailable to
generate electricity (see Figure 1) and the two‐state
modelisusedtorepresentthegeneratorsthatoperate
as base load.
However, in the Power Systems there
are peak load units or intermittent operating units.
Thefunctionalcharacteristicthatdistinguish them is
that they are turned on and off frequently. It is
necessarytoconsiderthisbehaviorinthegenerating
units’ model. The Sub‐Committee on Application of
Probabilistic Methods of the
IEEE proposed a four‐
state model Billinton and Huang (2006) for these
generating units. This model is shown in Figure 2,
where T is the average reserve shutdown time
betweenperiodsofneed, Disthe averagein‐service
timeperoccasionofdemandandPsistheprobability
of
startingfailure.
Figure2.Four‐statemodelforplanningstudies.
Thefour‐statemodel,likethetwo‐statemodel,is
representedasaMarkovprocess.Thetime‐dependent
solutionofthedifferentialequationssystemshownin
(3)allowsknowingtheprobabilitiesofeachstate.For
the system of differential equations (3), the initial
conditionsareP
0(t)+P1(t)+P2(t)+P3(t)=1,P0(0)=0,
P
1(0)=1,P2(0)=0andP3(0)=0.
0
013
1
102
2
2013
3
32
() 1 1 1
() () ()
() 1 1 1 1
() () ()
() 1 1 1 1
() () () ()
() 1 1 1
() ()
dP t Ps Ps
Pt Pt Pt
dt T T D r
dP t Ps
Pt Pt Pt
dt D r T m
dP t Ps
P
tPtPtPt
dt m D T r T
dP t
Pt Pt
dt r T D
(3)
whentheprobabilitiesassociatedwitheachstateare
known, the Utilization Forced Outage Probability
(UFOP)istheprobabilityofathermalgeneratingunit
not being available when needed (4); therefore, the
four‐statemodelisreducedtoatwo‐statemodel.
2
12
P
UFOR
PP
(4)
Thestochasticcapacity
()
i
Ut
atthetimeinstantt
of a thermal generating unit i is determined by the
MTTF
i,MTTRiand
i
C
.TheparametersMTTFi,MTTRi
and
i
C
allow to simulate with (5) the behavior of
()
i
Ut
generating k independent random numbers,
assumingthattheyfollowanexponentialprobability
distribution with parameter
1
ii
M
TTF
and
1
ii
M
TTR
, which we will denote in this
investigationasTTF
i,kE(
i)andTTRi,kE(
i).
On the other hand, one of the factors that affects
thePowerSystemcapacity,isnotstochasticandisnot
consideredarandomphenomenon,itismaintenance
processofthegeneratingunits.Maintenanceprocess
is contemplated within the Power System strategies
because it guarantees planned work time for the
generating
units.Maintenanceistheactivitydesigned
to prevent failures in the production process and in
thiswayreducetherisksofunexpectedstopsdueto
system failures. In the case of preventive
maintenance, it is the planned activity in the
vulnerable points at the most opportune moment,
destinedto avoid
failuresinthesystem. Itiscarried
out under normal conditions, that is, when the
productive process works correctly. In a Power
System, to perform some preventive maintenance
tasksitisnecessarythatthegeneratingunitsdoesnot
work, and this causes loss of capacity in the Power
System to supply
the load. Due to this reason, it is
advisablethatthismaintenanceprocessbecarriedout
atthetimeoftheyearwheretheleastloadexists,so
thatequilibriumandadequateflowareguaranteedin
thePowerSystem.Toconsiderthiseffect,inthiswork
the parameters TTM
i,k and TDMi,k of the generating
unitiareintroducedandtheequation(5).
The model proposed to simulate conventional
generatingunitsisdefinedbelow:
,,1
,,1 ,,
,,1 ,,
12
12 12
12 12
if
0if
0if
im im
im im im im
in in in in
i
i
CtSS
Ut S S t S S
A
AtAA
(5)
where:i=1,2,…,N
G;
,
1,
1
im
m
ik
k
S TTF
form=2,3,…,
MN
i;
,
2,
1
im
m
ik
k
S TTR
for m = 2, 3, …, MNi;
,
1,
1
in
n
ik
k
A
TTM
for n = 2, 3, …, NKi.;
,
2,
1
in
n
ik
k
A
TDM
forn=2,3,…,NKi.
826
2.1.2 OWFmodeling
The two‐state model is used to simulate the
stochastic of faults and repairs in offshore wind
turbines.ThestochasticgenerationcapacityPWT(t)of
an OWF at the moment of time t is determined by
MTTF
i,MTTRiandPi(t)ofeachoffshorewindturbine
i.Thedifferencebetweenthermalandoffshorewind
turbinegeneratingunits,inthiscase,isthatthepower
P
i (t) depends on the wind SWt. In the proposed
modelweuseWeibullsimulationapproachesforthe
wind speed [Atwa et al. (2011)], so Weibull model
generates random values from the density function
adjusted with historical values. In the case of the
power delivered by each offshore wind turbine we
use the non‐linear relationship between
wind speed
andwindturbinepowergivenbyKarkietal.(2012).
The wind speed is simulated with the Weibull
model [Atwa et al. (2011)] estimating approximately
the shape and scale parameters of the probability
distribution density function with μ
sw and σsw. The
Weibull probability distribution function for wind
speedvisdenotedasf(v),βandδaretheshapeand
scale parameters of the distribution function
respectively.
1
()
v
v
fv e
(6)
The parameters β and δ are obtained with the
followingexpressions:
1.086
sw
sw
(7)
(1 1 )
sw
(8)
Theinverseofcumulativeprobabilitydistribution
function (9) allows us to simulate the wind speed
generatingu uniformlydistributedrandom numbers
[0,1]asshownin(10).
() 1
v
Fv e
(9)
1/ 1/
ln 1 ln
t
SW v u u
(10)
The power delivered by each wind turbine is
estimated with the function (11). The non‐linear
relationship between wind speed and wind turbine
powerisgivenby,
2
(if
if
0if
0if0
(() ))
()
tci
ttrcitr
rrtco
tco
SW V
A
B SW C SW P V SW V
Pt
P
VSWV
SW V
(11)
where P
r, Vci, Vr and Vco are nominal output power,
wind speed necessary for start‐up, wind speed
corresponding to the nominal power of the wind
turbine and cutting wind speed per wind turbine
safetyreasonsrespectivelyKarkietal.(2012).
TheconstantsA,B,andCdependonV
ci,VrandVco
asshownin(12)Karkietal.(2012).
2
3
3
2
3
2
1
()4
() 2
1
4( ) (3 )
() 2
1
24
(2
)
ci r
ci ci r ci r
ci r r
ci r
ci r ci r
ci r r
ci r
ci r r
VV
AVVVVV
VV V
VV
BVV VV
VV V
VV
C
VV V
(12)
Thestochasticbehavioroffailuresandrepairs,and
the PPMS is incorporated in PE
i(t), modifying a
parameterof(5),asshownin(13).
,,1
,,1 ,,
,,1 ,,
12
12 12
12 12
() if
0if
0if
im im
im im im im
in in in in
i
i
Pt t S S
PE t S S t S S
A
AtAA
(13)
ThepoweroftheOWFisdefinedbelowas:
1
() ()
NA
i
i
P
WT t PE t
(14)
wherei=1,2,…,NA.
2.1.3 Loadcurvemodeling:
The load curve model is usually represented by
theDailyPeakLoadVariationCurve(DPLVC)orthe
Hourly Load Duration Curve (LDC) Billinton and
Allan (1996). We used LDC because integrates the
load curve chronological behavior. In the
medium‐
and long‐term planning studies, it is necessary to
knowtheexpectedgrowthoftheelectricaldemandof
thePower System. The morewidelyused modelsof
electrical demand forecast are the chronological
series. These models forecast electricity demand
based on historical behavior. ARIMA models (Auto
Regressive,Integrated,Moving
Average)aregeneral
modelsoftimeseries Aminiaetal.(2016).Thegeneral
model is complex, but the models usually used are
cases simpler. In this paper, an MA model is used,
assuming for the study a 5% electrical demand
growth and an uncertainty around the seasonal
averageof10%,being
expressedin(15)as:
( ) 1,05 0,10
tt
Dt
(15)
whereD(t)istheestimatedelectricaldemandattime
t, μ
t is the average electrical demand of the last ten
yearsattimet,α
tN(0,σt
2
)isawhitenoiseprocess
and σ
t is the standard deviation with respect to the
averageelectricaldemandofthelasttenyearsattime
t.
2.1.4 Riskindicatormodeling
TheriskfunctiondenotedasR(s)canbegenerated
withthesumX+Yoftherandom,independentand
non‐negativevariablesXand
Y.
827
TheproductofR(s)=P(s)Q(s)isdefinedwiththe
generating function
0
j
j
j
Ps ps
of X and the
generatingfunction
0
j
j
j
Qs qs
ofY.
Consequently, the generating function of R(s) is
definedbytheconvolutionformula(16).
1
k
kjkj
j
rpq
(16)
IfR(s)isarandom,independentandnotnegative
variable,thearithmeticmean(R
1+R2+…+Rn)/nofa
random sample R
1, R2, … Rn of the variable R(s) is
approximatelyequaltotheexpectedvalueE[R(s)],for
largevaluesofn.
Inthisinvestigation,Xdefinedinequation(17)is
probability distribution function of the thermal
generating units stochastic capacity of the Power
System,andYdefinedinequation(18)
isprobability
distributionfunction of the load curve incorporating
the power delivered by the offshore wind farm as a
negativedemand:
1
()
NG
i
i
X
Ut
(17)
1
() ()
NP
i
i
YDt PWTt
(18)
where NP is the number of offshore wind farms
consideredintheinstalledcapacityofthesystem.
Theriskfunctionisdenotedinthisinvestigationas
R. This function is the convolution product of
equations(17)and(18)definedinequation(19):
1
if
0if
T
tt tt
t
tt
YX XY
R
XY
(19)
The risk function expected value E[R] is usually
defined in the literature as Expected Energy Not
Supplied (EENS), when the generating units
capacities and the Power System electrical demand
are expressed in megawatts and t = 1, 2, …, T,
considersthe8760hoursofthe
year.Inthiswork, to
estimate E[R] the Monte Carlo simulation method is
used.
2.1.5 Optimizationmodel
The proposed model objective is to minimize the
expected value of the convolution function, between
the probability distribution function of the thermal
generating units stochastic capacity of the Power
System, and the
probability distribution function of
theloadcurve incorporatingthepowerdeliveredby
the offshore wind farm as a negative demand. The
modelisdefinedbelow:
,,
min [ ]
subject to:
0 8760
ik ik
ER
TTM TDM
(20)
The stochastic non‐linear optimization model
proposedforthePPMSproblemsolutionofthePower
Systempresentsonlycontinuousvariablesx=TTM
i,k
andisdefinedinthemodelconstraintintervals.The
independent variable of the objective function to be
optimizedx=x
1,x2,…,xNKidependsonthequantity
ofpreventivemaintenanceNK
ito becoordinatedfor
eachgeneratinguniti.Theoptimizationvariablesare
onlythestarttimesforthefirstmaintenanceofeach
unitTTM
i,1.OnceTTMi,1isestablished,theremaining
TTM
i,k are calculated adding the corresponding
maintenanceintervals,whichareinvariable.
2.2 LevelII:VesselFleetSizeSupport System
2.2.1 Workersdemand
The workers demand necessary to carry out the
maintenancetasksintheOWFdependsofhowmany
wind turbines had PPMS at the same time. In this
paperwe
useanempiricalfunctiontodeterminatethe
workersdemandaccordingtoPPMSproposedforthe
PowerSystemintheLevelIproblem.
The model proposed to determinate the workers
demandWD
tisdefinedbelow:
1, ,
1
2, ,
1
,,
1
if 1
if 2
for 1, 2, ,
if
WT
WT
WT
WT
N
tit
i
N
tit
i
t H
N
Nt it WT
i
WN x
WN x
WD t N
WN x N
(21)
where WN
i workers number necessary to carry out
themaintenancetasksintheoffshorewindfarm,N
WT
number of offshore wind turbines, N
H number of
hoursintheyear,x
i,t[0,1]isabinaryvariable,sois
equal to 1 when the offshore wind turbine i have a
maintenance tasks at instant of time t, and 0
otherwise.
2.3 Workerscapacity
On another hands, the workers capacity depends of
the vessel fleet size. It’s typically found vessels and
bases,
each one has different capacity and the
selection depends on maintenance tasks and
necessary workers Alcoba et al., 2017; but we can
defineageneralmodelasshownbelow:
,, , ,
11
for 1, 2, ,
VB
N
N
titititit H
ii
WD WC x VC x BC t N
(22)
whereWCworkersnumbercapacitytocarryoutthe
maintenance tasks in the offshore wind farm, N
V
numberofvessels,N
Bnumberofbases,NHnumberof
hours in the year, VC
i,t workers number capacity in
thevesseliatinstantoftimet ,BC
i,tworkersnumber
capacityinthebaseiatinstantoftimetandx
i,t[0,
1]isabinary vectorwiththearrayx
1,x2,…,xNV,xNV+1,
x
NV+2, …, xNV+NB, so is equal to 1 when the vessel or
828
base i is necessary at instant of time t, and 0
otherwise.
2.3.1 Optimizationmodel
The optimization model objective (23) is to
determine the optimum vessel fleet size support
system that guarantee to minimize the workers
numberneededtocarryoutthemaintenancetasksin
the offshore wind farm.
The input is described by a
set of decision‐making combination x
1, x2, …, xNV,
x
NV+1,xNV+2,…,xNV+NBdefinedinxi,t[0,1].Penalties
areintroducedwhenthefleetisnotablesuppliedthe
workersdemand.
22
min for 1, 2, ,
subject to :
tt H
tt
WC WD t N
WC WD t
(23)
3 RESULTSANDDISCUSSIONS
The Power System energy matrix analyzed is
composedofdieselandfuelthermalgeneratingunits
oftheTable1andoffshorewindfarmoftheTable2.
TheOWFhasacapacityof2,75MWandoperatesin
base load throughout the year; therefore, two‐
state
Markov model is used to simulate the wind farm
stochastic capacity. However, in the case of fuel or
dieselgeneratingunits,itisdifferent.
The Power System analyzed has a maximum
demandof18MWandastaticcapacityinstalledof21
MW distributed in small capacity generating units.
This
characteristic condition the Power System
operation. To satisfy the demand, fuel and diesel
generating units are rotated according to the
operating times, therefore, these units operate
intermittently. For this reason, four‐state Markov
model is used for the simulation of diesel and fuel
generating units. The offshore wind farm
mathematical
model needs other considerations for
thesimulation.Weassumeawindmeanμ
sw= 5.4m/s
and standard deviation σ
sw = 2.3, and with these
valueswecalculatetheshapeandscaleparametersof
theWeibullprobabilitydistributiondensityfunction.
The inverse of cumulative probability distribution
functionallowstosimulatethewindspeedbehavior
generatingu uniformlydistributedrandom numbers
[0, 1]. The wind turbine used in this paper has
a
nominalpower Prof275 kW,thecut‐in speedwind
V
ciis4m/s,theratedspeedwindVris10m/sandthe
cut‐out wind speed V
co is 25 m/s. For each wind
turbine,theMTTFandMTTRdataareshowninTable
2. In the investigation, load curve forecast of the
systemusedisshowninFigure3.
Inthecaseofvesselfleetsizesupportsystem,we
assumed10workersdemandforeachwind turbine
to
carry out the maintenance tasks in time, and a fleet
with4vesselswith8,12,16and30workerscapacity
and3baseswith12,24and36workerscapacity.
Table1.Dieselandfuelunits’indicators.
_______________________________________________
Unit Capacity(MW) MTTF MTTR D T Ps
_______________________________________________
1 1.88150 100 5 20 0.0150
2 1.8875 10 2 30 0.0090
3 1.88190 60 2 15 0.0020
4 3.85550 15 55 20 0.0225
5 3.85850 25 65 15 0.0095
6 3.85520 10 50 30 0.0085
7 3.85720 15 35 15 0.0055
_______________________________________________
Note:TheparametersMTTF,MTTR,DandTareexpressed
inhours.
Table2.Offshorewindturbinesindicators.
_______________________________________________
Windturbine Capacity(kW)MTTF MTTR
_______________________________________________
12752500 485
22751200 670
32751550 380
42751750 190
52752500 990
6275550 350
72752950 580
82752450 450
92751700 590
102752580 200
_______________________________________________
Note:TheparametersMTTFandMTTRareexpressedin
hours.
3.1 Influenceofpredictive‐preventivemaintenance
scheduling.
IntherealPowerSystemanalyzed,thePPMS ofthe
generatingunitsreduceconsiderablythesystemstatic
capacity,increasingconsequentlytherisklevels.This
condition is critical in the system because forced
output of a generating unit causes damages to the
customers electric service.
In this investigation, it is
identifiedthatthecriticalconditionisassociatedwith
the generating units PPMS improper coordination.
Thepaperproposestocoordinatethegeneratingunits
PPMSwithanonlinearstochasticoptimizationmodel
thataimstoimprovethePowerSystemrisklevelsas
much as possible (Platform concept). The
paper
showshowusingtheproposedmodelitispossibleto
coordinatethePPMSandimprovethePowerSystem
risklevels.TheinfluenceofPPMSisconsideredinthe
estimates of risk indicators. Therefore, stochastic
variables and PPMS are considered in the Power
System static capacity simulation. The maintenance
quantity and
duration, and the moment when they
areexecutedintheyear,influencesthePowerSystem
riskindicators.Conveniently,maintenanceshouldbe
spacedintheyear.Thisconditionguaranteesthatthe
Power System static capacity is not greatly affected.
The PPMS problem solution is complex because the
search spaces dimension is
large. Therefore, it is
necessary to use computational optimization models
to solve this problem. Figure 3 show a PPMS
improper coordination because every maintenance
taskstartsinthebeginningoftheyear,andFigure4
showtheproposedresultsfortheproblemsolution.
829
Figure3. Static capacity with PPMS, failures and repairs
timeofall thermalgeneratingunitsandtheoffshorewind
farminasimulateyear.
Figure4. Static capacity with PPMS, failures and repairs
timeofall thermalgeneratingunitsandtheoffshorewind
farminasimulateyear(Problemsolution).
3.2 Optimalvesselfleetsizesupport system
Eachmaintenancetaskhasseveralworkersassociate,
in this paper we assuming that each wind turbine
needs10workerstocarryoutintimethemaintenance
task coordinated in the first problem (Level I). The
objective function proposal to determinate the best
vessel fleet
size based on workers demand is a no‐
linear stochastic function. Bellow we show in the
Figure5thebestvesselfleetsizeforaPPMS improper
coordination,andFigure6showthebestvesselfleet
sizetotheproblemsolution.
Figure5.Bestvesselfleetsize.
Figure6.Bestvesselfleetsize(Problemsolution).
4 CONCLUSIONS
Theworkshowsthattheproposedplatformconcept
based on risk assessment allows to schedule the
PPMSofthermalgeneratingunitsandoffshorewind
farmatthesame timeinthe first levelproblem.We
have presented a model to determine an optimal
vessel fleet size for operation and
maintenance
activities at offshore wind farms in the second level
problem. This paper has described a potential
practical application for risk‐based maintenance of
offshorewindturbine.
ACKNOWLEDGEMENT
The work has been financially supported by the Polish
MinistryofScienceandHigherEducation.
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