323
1 INTRODUCTION
Despitealltheacknowledgedadvantagesintermsof
environmental impact reduction, energy efficiency
and noise reduction, the electric mobility market is
belowexpectations,especiallyfortheelectricship.
Infact,electricvehicleshavelimitationsthatpose
several important challenges for achieving a
sustainable mobility system: among them, the
availabilit
yofan adequatechargingi nfrastructureis
recognized as a fundamental requirement and
appropriate approaches to optimize public and
privateinvestmentsinthisfieldaretobedelineated.
Asakindofpopularelectricship,thebatteryship
isappliedinsmallscalepassengertransportationand
cargo transportation system, such as touri
st ship in
environment sensitive area. For the development of
battery ship, the ship charging station location is
becoming important. The principle and requirement
of ship charging station location is different from
vehicles in land, due to the navigation environment
and ship charging demand distribution deployment
law. The energy requirement for each one of the
subareas is esti
mated in terms of the electric energy
used by the equivalent fleet of electric vehicles to
reachtheirdestination.
Hogan and ReVelle [1] introduced the idea of
backup coverage into location models.These models
were developed in the context of siting emergency
facilitiesthatarerequiredtoserveagivenpopula
tion.
Araz C [2] proposed a multi‐objective maximal
covering location model, three objectives are
maximization of the population covered by one
vehicle,maximizationofthepopulationwithbackup
Charging Station Location Optimization of Electric Ship
Based on Backup Coverage Model
W.Zhang,X.Yan&D.Zhang
IntelligentTransportationSystemResearchCenter(ITSC),Wuhan UniversityofTechnology,Wuhan,China
NationalEngineeringResearchCenterforWaterTransportSafety(WTSC),Wuhan,China
ABSTRACT:Intermsofelectric shipenergyrequirement innavigation, theshipchargingstationlocationis
especiallyimportant. Inthispaper,amulti‐periodship charging stationlocationoptimizationmodelis pro‐
posed to ma
ke location decision in overall, from initial possible station sites chosen to the capacity
determinationforthefinallocationsites.Inthefirstphase,fromtheperspectiveofexternalenvironment,find
outallpossibleshipchargingstationcandidatesitesthroughthefeasibleanalyze.Inthesecondphase,ta
king
theshipchargingdemandsintoconsideration,thefinalshipchargingstationsitescanbeselectedamongthe
candidate sites based on backup coverage model. In the last phase, regarding the cost of construction and
servicecapabilityfordifferentgradeasthemainfactorincapacitydetermination,theoptimalcapacityofeach
finalshipchargingstationaredeterminedbymea
nsofoptimizationmethod.Finally,anexampleofYanqilake
inChinaisusedtoverifythevalidityoftheproposedmethodology.Thereasonablelocationofchargingstation
couldensuretheelectricenergysupplyandavoidcongestioncausedbyshipcharginggathering.Themodel
canbeeasilygeneralizedtootherproblemsregardingfacilit
yallocationbasedonuserdemand.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 11
Number 2
June 2017
DOI:10.12716/1001.11.02.16
324
coverageandminimiz ationofthetotaltraveldistance
fromlocationsatadistancebiggerthanaprespecified
distancestandardforallzones.ZhuZH[3]proposed
a novel model for the charging station location
problem of plug‐in electric vehicles. With the
objective of minimizing the total cost, the
proposed
modelsimultaneouslyhandlestheproblemofwhere
to locate the charging stations and how many
chargers should be established in each charging
station. Xiang Y [4] develops a novel solution to
integrateelectricvehiclesandoptimallydeterminethe
siting and sizing of charging stations (CSs),
considering the interactions between
power and
transportation industries. A two‐step screening
method with the environmental factors and service
radiusofelectricvehiclechargingstationsconsidered
ispresentedtoidentifythecandidatesitesofelectric
charging stations [5]. Hamaide B [6] considers the
caseoflandheterogeneityintermsoftheriskoflarge
disturbances
that threaten species even within a
reserve, proposed a reserve site selection model. A
traffic‐flowcapturemodelintegratedwithtrafficflow
datawasproposedinreference[7]tohelplocateCSs.
Reference [8] introduced a charging traffic flow,
whichcontainsboth spatial and temporal properties
ofachargingload,
asadiscretesequencetodescribe
charging start events. Wang Sunwei [9] proposed a
multi‐objectiveoptimizationlayoutmodeltooptimize
the locations of emergency resource stations. Jinfen
Zhang,XinpingYanandZhangDi[10]focusesonthe
assessment of MSA performance in term of safety
with Belief Rule‐base (BRB)
methodology. Shanshan
Fu, Xinping Yan and Zhang Di [11] proposed a
frameworkofquantitativeriskassessmenttoestimate
thepotentialriskofLNG‐fueledvesselsleakage.
Inthispaperamulti‐period methodologyofship
charging station model is proposed to make the
location decision in overall, from initial possible
stationsiteschosentothecapacitydeterminationfor
the final location sites. The model can be easily
generalized to other problems regarding facility
allocationbasedonuserdemand.
2 PROPOSEDMETHODOLOGY
Theshipcharging stationlocation procedureofship
charging stations is divided into three phase. In the
first phase, from
the perspective of external
environment, find out all possible ship charging
stationcandidatesitesthroughthefeasibleanalyze.In
thesecondphase,takingtheshipchargingdemands
intoconsideration,thefinalshipchargingstationsites
can be selected among the candidate sites based on
backup location model. Lastly, regarding the
cost of
constructionandservicecapabilityfordifferentgrade
as the main factorin capacity determination of ship
charging station, the optimal capacity of each final
ship charging station are determined by means of
optimizationmethod.
2.1 Feasibleanalyzeofshipchargingstationsites
From the perspective of external environment, the
shipchargingstationsitesshouldsatisfysomecertain
basic requirements, including safety requirements,
geological condition, land planning, channel
condition,navigationcondition,andetc.Inthispaper,
6aspects ofthe requirements arechosen to evaluate
thefeasibilityofshipchargingstationsites.Itshould
benotedthat,asisdifferent
fromelectriccarcharging
stationplace,theshipchargingstationshouldbebuilt
ontheriver shoreforthe convenience.Themeaning
and evaluate criterion of the requirements are
depictedfollowed.
Safety requirements: The sites should have fairly
goodsafetytoguaranteethesafetyandstabilityof
electric supply. In
this way, the charging station
wouldgaintheelectricsourcesuccessfully.
Geologicalcondition:Thestationsitesareingood
geological condition, available for electric grid
layingandchargingpileinstallment.
Land planning: The station sites are allowed to
constructpowerstationbylocalgovernment.
Channel condition: The
channel width should
allowatleastoneshipberthingwithoutdisturbing
the other ship navigation normally, as well as
providing enough berths for ship charging. We
shouldtrytoavoidmeanderingwater areainsites
seeking.
Navigation condition:The average flow speed of
the site should not more than 5m/s.
If the site
locates in a steep river area, it’s obviously not
benefit for the ship charging, suffering from
charging disturbing. Usually, we are inclined to
selectsitesinsmoothwaters.
Surroundingpopulationandfacilitiesdeployment:
Thepeople’sdailylife,suchassmokingaswellas
cooking, may increase
the fire risk of station.
Bridge and buildings surrounding will increase
the difficulty of electric wire laying. The sites
without no population and facilities surrounding
inaradiuof10misgood.
According to the feasible analyze results, we can
findoutallshipchargingstationcandidatesitesfora
study
waterarea.
2.2 Locationmodelbasedonbackupcoverage
After feasible analyze of external environment, ship
chargingstationcandidatesitesaregained.However,
thepurposeofshipchargingstationistoprovidethe
service for ships, the ship charging demands is
especiallyimportantinthe chargingstationlocation.
Takingthe
shipchargingdemandsintoconsideration,
the final ship charging station sites can be selected
amongthe candidatesites. Inthissection,a location
model based on backup coverage is introduced to
determinetheshipchargingstationsites.
Hogan and ReVelle [1] introduced the idea of
backupcoverage into locationmodels.Here,
backup
coverage means the presence within the distance
standardofmorethanonefacility,ormoreprecisely,
thenumberoftimes ademandzoneiscovered. The
modelwasdevelopedinthecontextofsitingfacilities
thatarerequiredtoserveagivendemand.Insucha
situation,theunavailability
ofafacilitywithinatime
or distance standard would jeopardize performance
ofthesystem.
We can set up the ship charging station location
model based on backup coverage. I (
iI
)and J
(
j
J
)are sets of demand zones and potential
325
facility sites, respectively, The decision variables in
thelocationmodelareY
i,Ui,Xj.subjectto
1 if demand zone i is covered at least once,
0otherwise,
i
Y
1 if demand zone i is covered at least twice,
0otherwise,
i
U
1 if a charging station is located in region ,
0otherwise,
j
j
X
1if ,
0otherwise,
ij
ij
dS
a
1
2
,
,
0 ,
. . 0 ,
ii
i
ii
i
ij j i i
j
ii
j
j
Max Z hY
Max Z hU
aX Y U i I
s
tU Y i I
XC
(1)
where:Sisthemaximumcoveragedistance,d
ijisthe
traveldistanceortimefromjtoi,Cisthenumberof
location sites,h
i is the number of ships in demand
zonei.
Thegoaloflocationistorealizethemaximumof
thefirstcoveragenumberandtheadditionalcoverage
numberofchargingstation.Thefirsttwoconstraints
of this model work in tandem to determine which
zones receive backup coverage. The
first constraint
determines the number of facilities within the
distance standard of a zone while the second
constraintensures that backupcoverage can onlybe
provided if first coverage is already in place.
Availablenumberofstationstobelocatedislimited
bythelastconstraint.
The maximum coverage distance S
can be
expressed as the endurance mileage. Based on the
principlethattheoutputenergyofthebatteryisequal
to the energy consumed by the ship, the endurance
mileageofshipcanbecalculatedbytheformula:
=
B
S
M
E
SV
P
(2)
where V
s is the shipping average speed; E is the
energy of the battery pack, can be denoted by
=
RR
E
CU
,CR is the rated capacity, U R is the Rated
voltage;η
Bisthe dischargeefficiency ofshipbattery
pack;
M
M
PP
,PMisthetotalpowerconsumption
of electric motor, P is the rated power, η
M is the
propulsionefficiencyoftheelectricmotor.
2.3 Capacitydeterminationmodelforshipcharging
stations
The goal of the capacity determination model is to
minimize total travel distance and the total
constructioncostofshipchargingstation.
3
4
min
min
1,,
..
1
mjm
jm
iij jmij
ij
ij jm
j
iij jm m jm
im
jm
m
jm
jm
ZFX
ZhaXd
aX i I j Jm M
ha X C X j J
st
XjJ
XC
(3)
1 if a charging station of grade is located in region ,
0otherwise,
jm
mj
X
The Decision variables are X
jm.Where hi is the
number of ship in demand of charging in demand
zonei;F
mistheconstructioncostofchargingstationof
grade m; C
m is the service capabilities of charging
stationofgradem.Mmeansthenumberofcharging
stationgrade.
Thefirst constraintindicatesthatthe shipsin the
demandzoneshouldgotothesamechargingstation
ofa fixgrade inacertain time; the second indicates
that the ship charging
requirement the must be
satisfied; the third constraint represents only one
charging station of a grade can be constructed in
candidatesite.
3 NUMERICALEXAMPLE
Theproposedmethodologyofshipchargingstationis
adoptedintheBeijingYanqilake,whichisthevenue
ofthe2014APECmeeting.
3.1 Step1:
candidateshipchargingstationsites
Accordingtothe external environment requirements
depicted in section 2.1, altogether 5 charging station
sites are selected as candidate charging sites. The
feasible ship charging station sites along the Yanqi
lakeisshowninFigure1.
Figure1.Thefeasibleshipchargingstationsites
326
3.2 Step2:Optimallocationofshipchargingstations
Supposingthechargingdemands isdistributedalong
thelakeevenly,the6demandsareshowninfigure2.
Figure2theshipchargingdemands.
Infactthenumberofshipindemandofcharging
isinfluencedbymanyfactors,suchasthedeadweight
andtheshipnavigationcondition.Inthissection,we
focus on the location method, the demand situation
are seen as known before.The parameters in the
location model based on backup coverage are
given,C=3,h
1=2, h2=1, h3=4, h4=2, h5=4,
h
6=3.Moreover,thedistancebetweentheblacklinesis
defined as unit interval(about 0.15 kilometers) in
figure1. So,thedistance d
ij betweendemandzone i
andlocationsitesjisshownintable2.
Table2.dij
___________________________
CS1 CS2 CS3 CS4 CS5
___________________________
D1 0 4 6.5 9.5 11
D
2 4 0 2.5 5.5 8
D
3 8 4 1.5 1.5 4
D
4 11 8 5.5 2.5 0
D
5 7 11 9.5 6.5 4
D
6 3 7 9.5 10.5 8
___________________________
Take all the parameters into the model location
model (1),we can solve the model by matlab7.0.The
optimal ship charging station(CS) sites are
CS
1,CS4,CS5.ThechargingstationsiteCS4isnearCS5，
whichisfarfromCS
1.
3.3 Step3:Capacitydeterminationforshipcharging
stations
Supposing there are two kinds of ship charging
station, the station of large scale is in grade 1, the
stationofsmallscaleisingrade2.Theparametersin
the capacity determination model for ship charging
stationsaregiven,F
1=160,F2=100,C1=10,C2=5.Then,we
can get the grade of each ship charging station, the
gradeofCS
4is1,thegradeofCS1andCS5is2.Itmeans
that, according to the demand situation of ship
charging,onelargescalestationandtwosmall scale
stationshouldbebuilt.Inoverall,thechargingstation
locateddispersedly.
4 CONCLUSION
In this paper, a multi‐period ship charging station
locationoptimizationmodelisproposedtosolvethe
location problem in overall, from initial possible
stationsiteschosentothecapacitydeterminationfor
the final location sites. In the first phase, from the
perspective of external environment, find out all
possibleshipchargingstationcandidatesitesthrough
the feasibleanalyze.Inthesecondphase, taking the
ship charging demands
into consideration, the final
shipchargingstationsitescanbeselectedamongthe
candidate sites based on backup location model.
Lastly,regardingthecostofconstructionandservice
capability for different grade as the main factor in
capacity determination of ship charging station, the
optimal capacity of each final ship
charging station
are determined by means of optimization method.
Finally,anexampleofYanqilakeinChinaisusedto
verifythevalidityoftheproposedmethodology.The
reasonable location of charging station could ensure
the electric energy supply and avoid congestion
causedbyshipcharginggathering.Themodelcanbe
easilygeneralizedtootherproblemsregardingfacility
allocationbasedonuserdemand.
ACKNOWLEDGEMENT
TheauthorswouldliketothanktheNationalNatural
Science Foundation of China (NSFC) (No. 51209165)
andtheNationalKeyTechnologySupportProgramof
China (No.2015BAG20B01 and No.2015BAG20B05)
fortheirfinancialsupportinthisresearch.
REFERENCE
[1]Hogan K, ReVelle C. Concepts and applications of
backupcoverage.ManagementScience1986;32:1434–44
[2]Araz C, Selim H, Ozkarahan I. A fuzzy multi‐objective
covering‐based vehicle location model for emergency
services[J]. Computers & Operations Research, 2007,
34(3):705‐726.
[3]Zhu Z H, Gao Z Y, Zheng J F, et
al. Charging station
location problem of plug‐in electric vehicles[J]. Journal
ofTransportGeography,2016,52:11‐22.
[4]XiangY,LiuJ, LiR,etal.Economicplanningofelectric
vehicle charging stations consideringtraffic constraints
and load profile templates[J]. Applied Energy, 2016,
178:647‐659.
[5]Liu Zhipeng, Wen Fushuan,
Xue Yusheng, et al. The
Optimal Location and Constant Capacity of Electric
Vehicle Charging Station [J]. Automation of Electric
PowerSystems,2012,36(3):54‐59.
[6]Hamaide B, Albers H J, Busby G. Backup coverage
models in nature reserve site selection with spatial
spread risk heterogeneity[J]. Socio‐Economic Planning
Sciences,2014,48(2):158
‐167.
[7]Cruz‐ZambranoM,CorcheroC,Igualada‐GonzalezL,et
al. Optimal location of fast charging stations in
Barcelona:Aflow‐capturingapproach[C]// International
327
Conference on the European Energy Market. IEEE,
2013:1‐6.
[8]Yang S, Wu M, Yao X, et al. Load Modeling and
Identification Based on Ant Colony Algorithms for EV
Charging Stations[J]. IEEE Transactions on Power
Systems,2015,30(4):1997‐2003.
[9]WangSunwei,ZhouRonggui,ZhangGaoqiang,Li Wei,et
al.A Method of optimizing the locations
of Flooding
Emergency Resource Stations: Journal of Transport
Information&Safety,2015.33(5):119‐127.
[10]Zhang J, Yan X, Zhang D,Haugen S,Yang X. “Safety
management performance assessment for Maritime
SafetyAdministration(MSA)byusinggeneralizedbelief
rule base methodology”[J]. Safety Science, 2014,
63(4):157‐167.
[11]Fu S, Yan X, Zhang D,C
Li,E Zio. Framework for the
quantitative assessment of the risk of leakage from
LNG‐fueledvessels by an event tree‐CFD[J]. Journalof
Loss Prevention in the Process Industries, 2016,
43,pp.42–52.
