• Aucun résultat trouvé

Optimization of a hydrogen supply chain network design under demand uncertainty by multi-objective genetic algorithms

N/A
N/A
Protected

Academic year: 2021

Partager "Optimization of a hydrogen supply chain network design under demand uncertainty by multi-objective genetic algorithms"

Copied!
23
0
0

Texte intégral

(1)

Any correspondence concerning this service should be sent

to the repository administrator:

tech-oatao@listes-diff.inp-toulouse.fr

This is an author’s version published in:

http://oatao.univ-toulouse.fr/27269

To cite this version: Robles, Jesús

and Azzaro-Pantel,

Catherine

and Aguilar-Lasserre, Alberto Optimization of a hydrogen

supply chain network design under demand uncertainty by

multi-objective genetic algorithms. (2020) Computers & Chemical

Engineering, 140. 106853. ISSN 0098-1354

Official URL

DOI :

https://doi.org/10.1016/j.compchemeng.2020.106853

Open Archive Toulouse Archive Ouverte

OATAO is an open access repository that collects the work of Toulouse

researchers and makes it freely available over the web where possible

(2)

Optimization

of

a

hydrogen

supply

chain

network

design

under

demand

uncertainty

by

multi-objective

genetic

algorithms

Jesus

Ochoa

Robles

a

,

Catherine

Azzaro-Pantel

a,∗

,

Alberto

Aguilar-Lasserre

b

a Université de Toulouse, Laboratoire de Génie Chimique, LGC UMR CNRS 5503 INP UPS TOULOUSE INP ENSIACET 4 allée Emile Monso – BP 44362

-31432, Toulouse Cedex 4, France

b Instituto Tecnológico de Orizaba, Oriente 9, Emiliano Zapata, Orizaba 94320, Ver., Mexico

a

b

s

t

r

a

c

t

Hydrogeniscurrentlyconsideredoneofthemostpromisingsustainableenergycarriersformobility ap- plications. A model of the hydrogen supply chain (HSC) based on MILP formulation (mixed integer linear programming)in amulti-objective, multi-period formulation,implemented via the ε -constraint method togenerate the Pareto front, wasconducted in a previous workand applied to the Occitania region of France. Three objective functions have been considered, i.e., the levelized hydrogen cost, the global warm- ing potential, and a safety risk index. However, the size of the problem mainly induced by the number of binary variables often leads to difficulties in problem solution.Thefirstinnovative partofthiswork exploresthepotentialofgeneticalgorithms(GAs)via a variant of the non-dominated sorting genetic al- gorithm (NSGA-II) to manage multi-objective formulation to produce compromise solutions automatically. The values of the objective functions obtained by the GAs in the mono-objective formulation exhibit the same order of magnitude as those obtained with MILP, and the multi-objective GAyields a Pareto front of better quality with well-distributed compromise solutions. The differences observed between the GA and the MILP approaches can be explained by way of managing the constraints and their different logics. The second innovative contribution is the modelling of demand uncertainty using fuzzy concepts for HSC design.Thesolutions arecomparedwiththeoriginal crispmodelsbasedoneither MILPorGA, giving morerobustnesstotheproposedapproach.

1. Introduction

Hydrogen isone ofthe mostpromisingenergycarriers inthe

search foraresilient,sustainable energymix tobeusedin differ-ent applications,such asstationaryfuelcell systemsand electro-mobilityapplications.

The challenge of developing a future commercial hydrogen

economy involves the deployment of a viable hydrogen supply

chain (HSC), considering the most energy-efficient,

environmen-tally benign, safe and cost-effective pathways to deliver hydro-gentotheconsumer(IEA 2017).TheHSC forthemobilitymarket Acronyms: CCS, Carbon Capture and Storage; GA, Genetic Algorithm; GHG, Greenhouse Gas; GWP, Global Warming Potential; HSC, Hydrogen Supply Chain; MCDM, Multi-Criteria Decision Making; MILP, Mixed Integer Linear Programming; MINLP, Mixed Integer Nonlinear Programming; NSGA-II, Non-dominated Sorting Ge- netic Algorithm; SCND, Supply Chain Network Design; SMR, Steam Methane Re- forming; TDC, Total Daily Cost; TOPSIS, Technique for Order Preference by Similarity to Ideal Solution.

Corresponding author.

E-mail address: catherine.azzaropantel@ensiacet.fr (C. Azzaro-Pantel).

is definedas a systemof activities from suppliers to customers. The activities includethechoiceofthe energysource, production technology, storage,anddistribution untilreaching refuelling sta-tions. Hydrogen can be produced either centrally (similarto ex-istinggasolinesupplychains)ordistributedatforecourtrefuelling stations assmall-scaleunitsthatcan produceH2 closetothe use

pointinsmallquantities.

The networkdesignoftheHSC appliedtofuelcellelectric ve-hicleshasbeenstudiedinvariousworks,ashighlightedin Table1.

The mostcommonmethodology tosolving theHSC problems

in-volvesamixedintegerlinearprogramming(MILP)approach.

In the same vein, the work conducted in (De-León Almaraz

et al., 2014) solved a multi-period model using a deterministic

MILP approach embedded in a GAMS/CPLEX environment with

a multi-objective formulation implemented via the

ε

-constraint

methodto generatethe Paretofront.Thefinal choicefortheHSC wasperformedthroughamultiplecriteriadecision-makingprocess (i.e., techniquefororderofpreferenceby similaritytoideal

solu-tion, TOPSIS). The modelling approachused one economic

objec-tive based onhydrogen totaldailycost (TDC), oneenvironmental

https://doi.org/10.1016/ j.compchemeng.2020.106853

(3)

Table 1

Territorial approach of the HSC studies. Approach Territorial scale Uncertain

parameters Author(s) Time scale (periods) Mono Multi Objective(s) Energy source Observations MILP Great Britain No ( De León Almaraz, 2014 ) X Cost, Ecological,

Safety risk Natural gas, coal, biomass

ε-constraint method for the multi-period problem

( Guillén-Gosálbez et al., 2010 ) 5 (5 years) Cost, Ecological The Pareto front is obtained by the

ε-constraint method ( Ren et al., 2007 ) 9 (2020-2060) Financial Coal, Natural gas, Biomass

(CCS), renewable Development of a spatially-explicit MILP model, called SHIPMod (Spatial Hydrogen Infrastructure Mode) ( Kim et al., 2011 ) 4 (seasons) Wind, renewable sources

( Deb et al., 2002 ) x Natural gas, coal, biomass, other renewable sources ( Ebrahimnejad and

Verdegay, 2016 ) 5 (2005-2034)

Demand ( Almansoori and Shah, 2012 ) 3 (2005-2022) Demand uncertainty is modelled using scenario-based-approach

Korea ( Kim et al., 2008 ) X Natural gas, renewable

sources Demand uncertainty is modelled using scenario-based-approach Germany No ( Delgado et al., 1993 ) X Natural gas, Coal (CCS),

Biomass Jeju Island,

Korea ( McKinsey&Company, 2010 ) 12 (months) Biomass A sensitivity analysis is conducted to provide insights into the efficient management of the

biomass-to-hydrogen supply chain Midi-Pyrénées,

France ( De-León Almaraz et al., 2014 ) 4 (2010-2050) Cost, Ecological, Safety risk Natural gas, photovoltaic, wind, hydro, nuclear

ε-constraint method for the multi-period problem Regional level ( Bento, 2010 ) 5 (2004-2038) Financial,

Ecological Natural gas, coal, biomass, other renewable sources The territorial scale is not specified, only defined as a "geographical region"

China ( McKinsey and Company 2010 ) 5 (2010-2034)

Malaysia ( Almansoori and Shah, 2006 ) x Cost Natural gas, coal, biomass,

water electrolysis Two methods for demand determination: one based on the prediction of vehicle numbers and the other based on the supply of gasoline and diesel

Korea ( Murthy Konda et al., 2011 ) X Financial, Safety Natural gas, renewable

sources The relative risk index proposed is based on the relative risks of individual components of hydrogen infrastructure

Spain Fuel price ( Sabio et al., 2010 ) 8 Financial, Risk Natural gas, coal (CCS), Biomass, renewable resources

The uncertainty is associated to the operating costs

MINLP-GIS Pakistan No ( Ochoa Robles et al., 2018 ) X Financial Biomass Fuzzy multiple

objective programming

Korea ( Dagdougui et al., 2012 ) X Financial,

Ecological, Risk Natural gas (CCS), other renewable sources Genetic

Algorithms Midi-Pyrénées, France ( Kim and Moon, 2008 ) 4 (2010-2050) Natural gas, renewable sources MINLP Unspecified ( European Commission 2008 ) Financial,

(4)

objective basedon GHG(greenhouse gas) emissionsanda safety index.

Inthiswork, aswellasin themajorityoftheworksreported in the literature, the economic criterion is formulated as a lin-ear function that has the advantage ofsimplifying problem

solv-ing. Much progress has been made in the solution of the

sup-ply chain network design (SCND) models, as emphasized in the

work of(Eskandarpour etal., 2015),which analysedthe develop-ment of efficient multi-objective models that adequately address

the different dimensions of sustainable development. Concerning

solutiontechniques,standard andpowerfulsolvers havebeenthe

mostwidely used toolsto solveSCND models.However, the size

and particularlythe number ofbinary variables inpractical sup-plychainproblemsoftenleadtonumericaldifficultiessothatthe

initial problem must be decomposed into an upper-level master

problem,whichisaspecificrelaxationforobtainingalowerbound onthecost,beingcombinatoricallylesscomplexthantheoriginal model.Thelowerlevelplanningproblemistypicallysolvedforthe selected set of technologies, yielding an upperbound on the to-talcostofthenetworkforanyfeasiblesolutionoftheupperlevel (Guillén-Gosálbezetal.,2010).

The results reported in (De-León Almaraz et al., 2014) also

showed that the solution strategy based on the

ε

-constraint

method for a multi-objective, multi-period problem is not so

straightforward,particularlyforthecreationofthepay-off tables: thenumberof thegeneratedefficientsolutions canbe controlled

by properly adjusting the number of grid points in each of the

objective function ranges, which can be considered as an asset

comparedtotheweightingmethod(Mavrotas,2007)butdoesnot guaranteediversityinthesetofsolutions.

Over the last decade, there has been a growing interest in

genetic algorithms (GAs) to solve a variety of single and

multi-objective problems in supply chain management that are

com-binatorial and NP-hard (Dimopoulos and Zalzala, 2000, Gen and Cheng, 2000).The firstscientificchallenge ofthiswork isthusto explore the potential ofgeneticalgorithms (GAs) via a variantof NSGA II(Gomezetal., 2008) toaddress thecombinatorialnature oftheHSCdesignproblemandtoprovideanautomaticgeneration oftheParetofrontoftheresultingproblem.

The second scientific barrier is to model the uncertainty re-lated to different variables andparameters of the HSC, e.g., fuel price (Sabio et al., 2010) or hydrogen demand, whichhave been

identified as among the most significant parameters in the HSC

( Ochoa Robles et al., 2015, Ochoa Robles et al., 2017). Several

methods have generally been mentioned to model demand

un-certainty (Chen andLee, 2004, Junget al., 2004, You and Gross-mann,2008):(i)thescenario-basedapproach;(ii)the distribution-based approach;(iii)thefuzzy-based approach; (iv)the

determin-istic planning and scheduling models, with the incorporation of

safetystocklevels;and(v)thespatiallyaggregateddemandmodel. As far as HSC is concerned, significant work in thisfield was

performed by (Kim et al., 2008) who developed a steady-state,

stochastic MILPmodeltoconsidertheeffectofhydrogendemand

uncertainty. A scenario planningapproach to captureuncertainty

inhydrogendemandoveralong-termplanninghorizonwas

devel-opedin(AlmansooriandShah,2012, Nunesetal.,2015).Although stochastic methodsare traditionallyused,they are generallytime consumingandmightnotrepresentthenatureofuncertaintysince

theproblemofhydrogensupplychaindesigncan beviewedasa

deployment problemforwhichdata collectionfordemandis not

possibleforanewproductdevelopmentproblem.Thisreason

mo-tivates our choice touse an alternative approach based onfuzzy concepts(Verdegay,1982, Villacortaetal.,2017).

A comprehensivereview ofstudies in thefield of SCND

(sup-plychainnetworkdesign)andreverselogisticsnetworkdesign un-deruncertaintywasrecentlydeveloped(Govindanetal.,2017)and

showedthatafewstudiesappliedmeta-heuristicsapproaches.Due totheNP-hardnatureoftheSCNDproblemunderuncertainty, de-velopingthistypeofsolutionapproachcanbeviewedasa promis-ingalternative.Althoughmeta-heuristicscannotguaranteethe op-timal solutionforan optimizationproblem,theseapproachescan solvelarge-scaleproblemswithinanacceptablecomputationtime.

This paper first presents the methods and tools used for the

development ofan HSC designframework with uncertain

hydro-gendemand.Theadaptationofthemodelpreviouslydevelopedin

(De-LeónAlmarazetal.,2014)ispresented.Acomparisonbetween

the results is obtained by the two models for a multi-objective

casebasedontheminimizationofthetotaldailycost(TDC),global

warming potential (GWP)andsafetyrisk (Risk),measured bythe

relative risk ofhydrogenactivities proposedin(Kim etal., 2008). Forthispurpose,acasestudydevelopedfortheFrenchmarketof the Occitania region (partially corresponding to theformer Midi-Pyrénéesregion)solvedby theinitialMILPmodelisusedto

vali-datethe newmethodology. Occitania’sambitionistobecomethe

firstPositiveEnergyRegioninEurope,anditiscommittedto cut-tinginhalfitsenergyconsumptionpercapita,whichisthe equiv-alentofa40%reduction intheenergyconsumptionoftheregion andtomultiplyingbythreeitsrenewableenergyproduction,both

by 2050:the use of hydrogencould be one solution to reaching

this target. A3-echelon supplychain involvinghydrogen produc-tion,transportationandstorageintheterritory,dividedinto8 sub-regions,isconsidered.Somesignificantresultsarehighlightedand comparedwiththosepreviouslyobtainedwithcrispvalues.

2. Methodsandtools

2.1. GeneralprinciplesofHSCframeworkdesignwithuncertain demand

The generalmethodology ofthe HSC design proposed in this

workisillustratedin Fig.1.Itshowstheextendedflowdiagramof

the methodologyproposedforHSCdesignoptimization,

consider-ing boththemulti-objectiveoptimizationframeworkeitherbased onthedeterministicMILPsolutionstrategydevelopedin(DeLeón Almaraz, 2014)oronaGAandthemultiplecriteriadecision mak-ing tool selected to find the most interesting solution from the

compromise solutions obtained from the Pareto front based on

a variant of the TOPSIS method (Ren et al., 2007). The

MULTI-GEN environmentpreviously developed inourresearch group [8]

was selectedas thegenetic algorithm platform.The demand

un-certainty hasbeenmodelledusingfuzzyconceptsaspresentedin (Verdegay,1982, Villacortaetal.,2017).

2.2. CapturingtheHSCdesignmodelinaGAenvironment

Themathematicalmodelpreviouslydevelopedby(DeLeón

Al-maraz, 2014) for HSC design was solved within the GAMS 23.9

environment using CPLEX solver. This model has been adapted

to be embedded in an external optimization loop based on the

multi-objective genetic algorithm. The whole model is presented

to maintainits integrity,andthechangesthat havebeenadopted toconsidertheintegrationintotheexternaloptimizationloopare presentedinitalics.

2.2.1. HSCmodellingprinciples

Ageneralsupplychainnetwork(SCN)modelforhydrogen(see

Fig.2) isconsidered(productionplants,storageunits,distribution gridsanddemandforeachgrid).

Thefollowingassumptionshavebeenmade:

- Thenumberofgridsisknown(8);

- Thecapacityoftheproductionplantsandthestorageplantsis known;

(5)

Fig. 1. Methodology of the HSC design framework.

(6)

Table 2

Optimization variables and dependent variables. Optimization variables Dependent variables

NP pig AH ig GC PGWP TCC NSs ig DI ig GWP Tot PT ig TDC PR pig DL ig LC RP ig TGWP Q ilgg’ FC MC SGWP FCC NTU ilgg’ SP ig FOC PD ig ST ig

- Thedemandforeachone ofthegridsisfixedandknown(for thecrispmodel);

- Itispossibletoeitherimportorexporthydrogenfrom/toeach grid;

- Each grid can produce hydrogen in three different ways, i.e., steammethanereforming (SMR), electrolysis(centralized)and distributedelectrolysis (decentralized,i.e., produced onsitefor captiveuses);and

- Theaverage distancebetweenthe maincitiesisconsidered to calculatethedeliverydistancesovertheroadnetwork. Themathematicalmodelformulationinvolvesthefollowing no-tations:

- gandg’:gridsquaressuchthatg’6=g(8) - i:productphysicalform(LH2)

- l:typeoftransportationmodes(tankertruck)

- p:planttypewithdifferentproductiontechnologies(SMR, elec-trolysis,diselectrolysis)

- s:storagefacilitytypewithdifferentstoragetechnologies (LH2 stock)

- e: energy source type (natural gas, solar, wind, hydroelectric, nuclear)

The modelformulationis developedinthe Appendix.The

de-signdecisionsare basedon thenumber,type, capacity,and loca-tion ofproductionand storagefacilities, thenumberof transport

units, andthe flow rateof hydrogen betweenlocations. The

op-erational decisionsconcern the totalproduction rateofhydrogen ineachgrid,thetotalaverageinventoryineachgrid,thedemand coveredbyimportedhydrogenandlocalproduction.

Theinvolvedconstraintsarerelatedtodemandsatisfaction,the availability of energy sources, production facilities, storage units, transportationmodesandflowrates.

Thevariablesusedinthismodelaresplitintotwogroups: de-cisionvariablesthataregeneratedbytheoptimizationprocedure; anddependentvariablesthatarecalculatedfromtheequality con-straints.Theclassificationisshownin Table2.

2.3. Multi-objectiveoptimizationbyGAs

The solving method used in this investigation is based on a

multi-objective genetic algorithm. Let us recall that, in a single-objective optimization, theoptimalsolution isusually clearly

de-fined. However, this assumption is not the case for a

multi-objectiveprobleminwhichtheobjectivescanconflict.Asingle so-lution is hardly the best for all of the objectives simultaneously. Instead ofa singleoptimum,there isa set oftrade-off solutions,

which are the so-calledPareto optima solutions. The aim of the

multi-objectiveevolutionaryalgorithmistocausethesolutionset

to approachthe Paretoidealfrontierofthe problemwithawide anduniformdistributioninasinglesimulationrun.

A variant of the non-dominated sorting genetic algorithm II

(NSGA-II)(Debetal.,2002),whichisoneofthemostwidelyused

multi-objectiveevolutionary algorithmsimplemented throughthe

MULTIGENlibrarydevelopedby(Gomezetal.,2008),wasselected inthiswork.

The main featureofNSGA-II amongmulti-objective

evolution-ary techniques is the determination of individual fitness values

based ontheParetodominancerelationshipanddensity

informa-tionbetweenindividuals.

Inthiswork,theresultsobtainedfromthe

ε

-constraintmethod (DeLeónAlmaraz,2014)andGAarecomparedtoanalysethe

ad-vantages anddisadvantages ofeach technique and its impact on

the network configuration of the HSC. The set of chromosomes

representingthevariablesisillustratedin Fig.3.

The variablePR representstheproductionrateofproductiby plant type p in grid g; Q is the flow rateof product iby trans-portlbetweenthegridsgandg’.NPisthenumberofproduction plantsoftypep ofproductiingridg,whileNSisthenumberof storagefacilitiesoftype pofproductiingridg.Finally,DListhe demandsatisfiedforproductibylocalproductioningridg.Inthe

GA used,thechromosomeofthe variablesiscomplementedby a

vector containing the typeof variable(i.e.,0 forcontinuous vari-ables,1forintegervariablesand2forbinaryvariables).Theother procedures followthe NSGAII variant proposed by (Gomez etal., 2008).

2.4. Multiplecriteriadecisionmaking(MCDM)

AmodifiedTOPSIS(M-TOPSIS)evaluationisbasedonthe origi-nalconceptofTOPSIS(techniquefororderofpreferenceby similar-itytoidealsolution)andproposedby(Renetal.,2007)isused.It choosesanalternativethatshouldsimultaneouslyhavetheclosest distancefromthepositiveidealsolutionandthefarthestdistance fromthenegative idealsolution,solvingtherankreversalandthe evaluation failure problempresentedin theoriginal TOPSIS tech-nique.

2.5. Uncertaintymodelling 2.5.1. Fuzzy-constraintproblems

The review proposed by (Ebrahimnejad and Verdegay, 2016)

has reportedthat manyworkshavebeendevoted tofuzzy linear

programming (FLP) andsolution methods. These worksare

typi-callydividedintofourareas:(FLP1)linearprogramming(LP) prob-lems with fuzzyinequalities andcrisp objective function; (FLP2) LP problemswith crispinequalities andfuzzyobjective function;

(FLP3) LP problems with fuzzy inequalities and fuzzy objective

function; and (FLP4) LP problems with fuzzy parameters. In the

HSC design problem that has been mathematically formulated

(DeLeónAlmaraz,2014),hydrogendemandhasbeenidentifiedas an uncertainparameter,andtheHSCdesignproblemreferstothe simplestformoffuzzylinearprogramming,i.e.,FLP1.

Thedecisionmakercanacceptaviolationoftheconstraintsup to acertaindegreepreviously established.Thisacceptancecanbe formalizedforeachconstraintas(Villacortaetal.,2017):

aixfbi,i=1,...,m

(7)

6

Fig. 4. Uncertain demand modelling.

In thisexpression, thef indexindicates that the inferior rela-tionshipinvolvesfuzzynumbers.

Thisindexcanbemodelledusingamembershipfunction:

µ

i:R→[0,1],

µ

i

(

x

)

=

(

1 i fxb i fi

(

x

)

i fbixbi+ti 0 i fxbi+ti

where the fi are continuous, non-increasing functions. The toler-ance thatthedecisionmakeriswillingtoaccept uptoavalue of

bi+ti is given by the membership function

µ

i. For every xR,

µ

i(x)represents the degree of fulfilment of the i-th constraint.

Then,theproblemcanbesolved: maxz=cx

subjectto Axfb x≥0

Theapproachproposedby(Verdegay,1982)throughthe

repre-sentationtheoremhasprovedthattheproblemcanbe solvedvia

thefollowingparametriclinearprogrammingproblem: maxz=cx subjectto Axg

(

α

)

x≥0,

α

∈[0,1] whereg

(

α

)

=

(

g1

(

α

)

,...,gm

(

α

)

)

Rm,withg i=fi−1.

Tosimplifytheproblem,iffiarelinear: maxz=cx

subjectto Axb+t

(

1−

α

)

x≥0,

α

∈[0,1]

witht=

(

t1,...,tm

)

Rm.

Ithasbeenproved(Delgadoetal.,1993)that,whenfiislinear, a solutionforthefuzzyconstraintsproblemcan befound asifit is a modelwithnon-linearfunctions, without anygeneralityloss

when assuming linear functions for the fuzzy constraints. Some

samplevalues canbe applied to

α

inthe interval [0,1],andthen

the model can be solved forevery sample value. For example,a

stepsizeof0.25forsampling

α

canbetransformedinfive

α

-cuts for

α

=

{

0;0.25;0.5;0.75;1

}

.

2.5.2. ApplicationtodemanduncertaintymodellinginHSCNdesign

Hydrogendemandistheonlyparameterthatwillbeconsidered uncertain.Inthispaper,onlythemodificationsimplementedinthe HSCmodelarepresented(see Fig.4).

Theuncertaintyhasbeenconsideredusingthefollowing infor-mation:

- Thelowerandupperlevelsofdemandhavebeenobtainedfrom theanalysisin(DeLeónAlmaraz,2014);

- Fromthesevalues,averagedemandiscalculated;

- Thedifferencebetweenthe averageandthelow/highdemand

iscalculated,representinganacceptedtolerance;and

- Variable

α

is then introduced. This variable can take values from 1 to 0,andit represents the rateof useof tolerance. A valueof

α

equalto0.5correspondstotheaveragedemand. Theconstraintsthataremodifiedintheinitialcrispversion of themodelareconstraints2-4.

Consideringthedemandastherightsideoftheconstraints,as inVerdegays’approach (Verdegay,1982), thefuzzyrightsidecan beexpressedmathematicallyas:

g DTig=

£

DTig+PDig

(

1−

α

)

¤

(1)

Eq.(1)mustbeinsertedintoconstraints (2)-(4), whichreplace

the corresponding ones in the initial model (see (De León

Al-maraz,2014)). DLig+DIig=DTig+PDig

(

1−

α

)

i,g (2) PTig− X l,g

¡

Qilgg′−Qilggg

¢

=DTig+PDig

(

1−

α

)

i,g (3) STig

β

=DTig+PDig

(

1−

α

)

i,g (4)

PDig is the tolerance of DTig, and

α

is the rate of use

of the tolerance. Six values of

α

-cuts were considered:

α

=

{

0.16;0.33;0.5,0.66;0.83;1

}

. Foreach value of

α

-cuts, an eval-uationofthemodelwasperformed.

3. Casestudy

3.1. ParametersoftheHSC

3.1.1. Estimationofhydrogendemand

The case study refers to the design for an HSC in the

for-mer Midi-Pyrénées region in France as previously presented in

(De León Almaraz, 2014). The demand is considered

determin-istic for the first case and is calculated from the work of

(McKinsey&Company, 2010) with the same methodology as

pro-posed in (De-León Almaraz et al., 2014). The demand evolution

profile corresponds to the valuesof Dmin (Table 3) (low demand scenario studied in (De-León Almaraz etal., 2014)).The demand (for both Dmin and Dmax) includes fuel cell electric vehicles and

captivefleets(i.e.,buses,privateandlight-goodsvehicles,forklifts)

asdefined in(De León Almaraz, 2014). The market demand

sce-nariosareestablishedfrom(Bento,2010)and(McKinseyand Com-pany 2010), in which the two scenarios identifying the two lev-elsofdemandsforFCEVpenetrationweredevelopedprovidingthe

Table 3

Demand scenarios of FCEV penetration.

Scenario/year 2020 2030 2040 2050 D min 1% 7.5% 17.5% 25%

(8)

Table 4

Demand (D min , D max ) and tolerance (PD) evolution profile used in the case study (kg per day).

Period/Grid 1 2 3 4

Dmin Dmax PD Dmin Dmax PD Dmin Dmax PD Dmin Dmax PD 2020 502 995 493 843 1650 807 977 1953 976 709 1404 695 2030 3780 7440 3660 6320 12430 6110 7410 14630 7220 5320 10450 5130 2040 8850 17350 8500 14750 29030 14280 17330 34100 16770 12400 24380 11980 2050 12610 24790 12180 21100 41470 20370 24770 48730 23960 17710 34810 17100

Period/Grid 5 6 7 8

Dmin Dmax PD Dmin Dmax PD Dmin Dmax PD Dmin Dmax PD 2020 570 1136 566 639 1263 624 3221 6362 3141 437 810 373 2030 4420 8590 4170 4850 9510 4660 24180 47670 23490 3150 6250 3100 2040 10260 20030 9770 11310 22160 10850 56470 111230 54760 7420 14570 7150 2050 14610 28610 14000 16170 31660 15490 80620 158950 78330 10580 20790 10210

percentageofFCEVexpectedtoreplaceICEs(ignition combustion engines).

The hydrogen demandfor thetwo scenarios is obtainedfrom

Eq.(5)(AlmansooriandShah,2006),(MurthyKondaetal., 2011):

DTig=

(

FE

)

(

d

)

(

Qcg

)

(5)

wherethetotal demandineach grid(DT) isprovidedby thefuel economyofthevehicle(FE),theaveragedistancetravelled(d)and thenumberofFCEVsineachgrid(Qc).

Foruncertaindemand, Table4alsopresentsthedemandinthe

highdemand scenario caseproposed by (De-León Almarazet al.,

2014),i.e.,(Dmax).Thetolerancesarerepresentedbythedifferences

betweenDmaxandDminovertheperiods.

3.1.2. Techno-economicassumptions

Thestudyisbasedonthefollowingassumptions:

- acapitalchange factor(depreciationperiod)of12 yearsis in-troduced;

- in a multi-periodapproach, four periods were analysed, from 2020to2050,witha10-yeartimestepforeach;

- three types of technologies to produce hydrogen are

consid-ered: steam methane reforming (SMR), electrolysis and

dis-tributedelectrolysis;

- fiveenergysourcesare considered:solar, wind,hydro,nuclear andnaturalgas(OchoaRoblesetal.,2018);

- hydrogenmustbeliquefiedbeforebeingstoredordistributed;

- aminimumcapacityofproductionandstorageequalto50kg

ofH2 perdayisconsidered;

- renewableenergyisdirectlyusedonsitebecauseofgrid satu-ration,whichallowstoallocatetheCO2impactoneachsource;

- onesizeforstorageandproductionunitsisconsidered; - inter-districttransportisallowed;

- the maximum capacity of transportation is fixed at 3500 kg

liquid-H2(Dagdouguietal.,2012);

- thehydrogenisstoredinliquidform,anda10-dayLH2safety stockisconsidered;

- the risk indexis calculated by the methodology proposed by

(KimandMoon,2008);

- thenumberofplantsisinitializedatanullvalue;

- thecostofswitchingfromacurrentrefuellingstationtoH2fuel

isnotconsidered;and

- thelearningratecostreductionsdueaccumulatedexperienceis consideredas10%perperiod(McKinseyandCompany2010).

3.2. Optimizationparameters

For the mono-period andmono-objective case, a total of 500

individualsinthepopulationand1000generationsareconsidered, with0.9forthecrossoverrateand0.5forthemutationrate.These values havebeenfixedfroma preliminarysensitivityanalysis. As alreadyhighlighted,thedefinitionofvariablesisdifferentinboth

models. In the GA formulation, there are 352 decision variables

versus676intheMILPformulation.Inthecaseofmulti-periodand multi-objective formulations, 2000 individuals in the population and3000generationsareused,with1408variablesversus3319in the MILPmodel.FortheM-TOPSISanalysis(Renetal.,2007),the sameweighting factorsforcost,safety,andenvironmentalcriteria are considered.The defaultfeasibilityofCPLEXandtheoptimality tolerancesof10−6havebeenadopted.

4. Results

In Sections4.1to 4.3,thesamecostdataasthoseusedin( De-LeónAlmarazetal.,2014)areadoptedforvalidationpurposes.The

parameters oftheHSC modelarepresentedinthesupplementary

materials.Inallofthemapsprovided,thenumberofplantsis in-dicatedinsidethesymbolsusedfortechnologyrepresentation.The mapsareobtainedafterthesuccessiveuseoftheoptimization al-gorithmandtheMCDMstrategyforthemulti-objectivecase.

For themono-periodoptimization runs(Sections4.1and 4.2), thedemandscenariorelativetoperiod4isanalysed.

4.1. Mono-objectiveandmono-periodoptimization

A preliminarystudywasperformedwiththeGA approach:10

runswereperformedforeachcasetoguaranteethestochastic na-tureofthealgorithm(Table5).Thesamemethodologyisusedfor allofthecasesinwhichtheGAmethodologyisused.

Table 5

Statistical results of the runs performed in the mono-period and mono-objective GA approach.

Min (TDC) Min (GWP) Min (Risk)

TDC (M$/ day) GWP (ton CO 2

eq / day) Risk TDC (M$ / day) GWP (ton CO eq per day) 2 Risk TDC (M$ / day) GWP (ton CO eq / day) 2 Risk Mean 1.21 1552.08 496 1.32 763.42 485 1.22 1642.82 479 Standard deviation 0.0327 257.38 21.17 0.0218 167.42 22.17 0.0251 211.80 11.98

(9)

Table 6

Mono-objective and mono-period detailed optimization results.

The results of the three mono-objective optimizations (min

TDC,GWP,andRiskseparately),solvedbyCPLEX,ontheonehand, and by the GA,on the other hand,are presented in Table6. For

each criterion to be optimized, each column presents the

opti-mized values ofthe decisionvariables, some intermediate values involved inthe evaluationofthecriteria andtheoptimizedvalue of theconsidered criterion (inbold type andincolour). Foreach mono-optimizationcase,acomputationoftheothercriteriaisalso performedinparallel.

Table6alsopresentstheunitcostofH2 aswellastheamount ofemittedCO2 perkgofH2 thatisdeducedfromthevalueofthe optimizationcriteria(inthesamecolour).

It can be observed that, whichever criterion is considered,

CPLEXoutperformsGA.

Forinstance,whenTDCisminimized,alowervalueisnot

sur-prisingly obtained with CPLEX(1.18 M$/day) than with GA (1.21

M$/day),whichisexactlythesametrendwiththeothercriteria.

Let usconsideronce morethe TDC caseminimization forthe

sake of illustration. Since a better value has been obtained with

MILPforTDC,thevalue ofGWPisnowhigherthanthatobtained

withGA(respectively,10.82kgCO2-eqperkgH2withMILPvs7.83

kgCO2-eqperkgH2withGA),reflectingacompromiseamongthe

criteria. Thistype of observationis not valid inthis caseforthe riskcriterion,whichcanbeexplainedbydifferentuseoftransport betweenthegrids.

The trend observed for TDC can be generalized to the other

criteria:it meansthat,ifabetter valueissystematically obtained withMILPthan withGA foragivencriterion thathasbeen opti-mized,theperformanceofonecriterionthatisnotoptimizedcan bedegradedcomparedtotheresultsobtainedwithGAinthesame conditions.

Fig. 5 showsthe obtained networkfor the three optimization

cases.ForTDCminimization,thenetworksobtainedareveryclose

to each other with both optimization strategies, producing the

most hydrogen via SMR with some electrolysis plants. The main

difference between the approaches mostly involves the way in

whichhydrogenisdistributedthroughthegrids.

When GWP is minimized, priority is given to the production

of hydrogen via electrolysis forboth approaches. With the MILP

model,thereisnotransportbetweengrids,andhydrogen produc-tionisachievedthroughseveraldistributedplants.WithGA,fewer facilitiesareinstalled,buthydrogentransportationoccursthrough grids.

Table 7

Best trade-off solutions selected by TOPSIS for ε-constraint and AG. MILP GA Demand (t per day) 198.17 198.17 Number of total production facilities 25 39 Number of total storage facilities 214 214 Number of transport units 0 0

Capital cost

Plants and storage facilities (10 6 $) 2595.00 2480.45

Transportation modes (10 6 $) 0 0

Operating cost

Plants and storage facilities (10 3 $ per day) 1056.20 1143.28

Transportation modes (10 3 $ per day) 0 0

Total daily cost (10 6 $ per day) 1.65 1.68

Cost per kg H 2 ($) 8.32 8.48

Production facilities (t CO 2 -eq per day) 614.33 409.82 Storage facilities (t CO 2 -eq per day) 139.51 139.51

Transportation modes (t CO 2 -eq per day) 0 0

Total GWP (t CO 2 -eq per day) 753.84 549.33 Kg CO 2 -eq per kg H 2 3.80 2.77

Production facility risk 14.40 16.05 Storage facility risk 387.00 387 Transportation modes risk 0 0

(10)
(11)

Fig. 6. Maps of the two scenarios with multi-objective optimization a) with GA; b) with MILP.

Forriskminimization,hydrogenproductionisbasedexclusively

onSMRplantsfortheMILPapproachandamixofSMRand

elec-trolysis for the GA approach with transportation through grids.

Thissituationismainlyduetothesmalldifferenceintherisk val-uesbetweenthevarioustechnologiesfortheplantsizethatis con-sidered.

Itmustbeemphasizedthatthesolarsourceiseliminatedinthe optimizationprocesssincehydrogenproducedviaelectrolysiswith solar energyis themostexpensiveprocess andexhibits a higher carbonfootprint,comparedtowindandhydro.

4.2. Multi-objectiveandmono-periodoptimization

In this case, the obtained results are only slightly improved withlinearprogramming,comparedtoGAforcostandriskcriteria (Table7, Fig.6(a)and(b)).The degreeofcentralizationisalmost the same. In Fig.6 (a), relative to GA, the configurationinvolves a setofseveralplantswiththedistributedelectrolysistechnology withnotransportation;withMILPin Fig.6(b),priorityisgivento electrolysisplantsfromvarioussources,includingthenuclearone (see Table8).

The Pareto solutions proposed by the GA include the Pareto

space, which was identified as using the MILP methodology

(Fig.7).Asmallvariation(2%)isobservedintheunitcost($8.32of MILPvs$8.48perkgH2ofGA)betweenthetwoTOPSISsolutions.

From the environmental viewpoint, a significant improvement is

observed withtheGA:GWPexpressedinkgCO2 eqper kgH2 in

the GA approach is 27% lower than the value obtained withthe

Table 8

Use ratio of energy sources for hydrogen production (multi- objective and mono-period case).

Energy source MILP GA Wind 60% 69% Hydraulic 32% 31% Nuclear 8% 0%

MILPapproach.Thisdifferencecanbeexplainedbytheuseof dis-tributedplantsinsteadofelectrolysisplants.The differenceinthe riskcriteriabetweentheapproachesisnotsignificant.

The computation time for MILP withCPLEX (Intel R

°

Xeon R

°

CPU 2.10GHz) is approximately3 hours versus 4 hours with GA,

withasetof174ParetopointsobtainedwiththeGAapproachand 43withtheMILPapproach.

4.3.Multi-objectiveandmulti-periodoptimization

Fig. 8 is a projection of the Pareto surface onto the

two-dimensional plane corresponding to cost and environmental

im-pact. Forthese two criteria, better compromise solutions are ob-tainedwiththeGAthanwithCPLEX.Thiscaseisnottruewiththe riskindex,whichcanbehigher.

TheTOPSISsolutions(see Table9)providelowervaluesforboth

costandGWP.The unitcost ofhydrogenislower withGA(8.00)

thanwithMILP(8.27),despitea slightlyhigherrisk (838vs873). Thisoutcomecanbeexplainedbythewayinwhichtheplantsare distributedthroughtheperiods.

IntheMILPapproach(Fig.9),priorityisgiveninthefirstperiod tothe establishmentofdistributedplants,mainlydueto thelow

value of the demand. In the three other periods, the demand is

satisfiedmainlywiththeelectrolysisplantssothatGWPandrisk remainnotashigh.

IntheGAapproach(Fig.9),thefirstperiodisdedicatedtothe installationofdistributedelectrolysisplantsandoneSMR, signifi-cantlyincreasingCO2emissions.Forthesecondperiod,some

elec-trolysis plantsare added. The CO2 emissions remain higherthan withMILP, andbecause of transport betweengrids, therisk also increases.Forthethirdandfourthperiods,transportbetweengrids remains,buttheSMRplantsdisappearfromdistribution, decreas-ingtheCO2emissions.

Finally,forthisexampleandwithoutprovidingafeatureof gen-eralitytotheobtainedresults,comparedtoMILP,GApromotesthe deployment of hydrogen by favouring cost objectives inthe first period.Inthelasttwoperiods,bettervaluesforGWPareobtained withtheGAapproachratherthanwithMILPbecauseofthe

(12)

instal-Fig. 7. Pareto fronts for the optimization carried out by MILP and GA.

Fig. 8. Projection of the Pareto fronts onto the two-dimensional plane corresponding to cost and environmental impact for the optimization run carried out by MILP and GA for a multi-objective and multi-period approach.

lationof asmaller numberofproductionfacilities. Thisapproach

leads againto the implementationof transport between grids to

satisfy the demand. Finally, fromthe safety point of view (risk), theMILPmodelpresentsbetterresults,mostlyduetotheabsence oftransport betweenthegrids. Table10showsthepercentageof

energy sources used by each methodology. Regarding the

mono-objective case, the solarsource is eliminated in theoptimization process.

4.4. Multi-objectiveandmulti-periodoptimizationwithnewcosts

Inadditiontohydrogendemand,oneofthemostsignificant pa-rametersisfeedstockcost(OchoaRoblesetal.,2017),(Ochoa Rob-les et al., 2017). In the original model (De-León Almaraz et al., 2014),the unit production cost(UPC) of electricity remains fixed for all of the periods regardless of the technology, which was a severesimplification.Inwhatfollows,anevaluationofUPCis con-sideredwithfixedfacilitycosts(maintenance,labourcost),aswell aselectricityandfeedstockcosts.

Table 11presentsthepriceofelectricityproducedfrom differ-ent energysources andthe priceofnaturalgas forconditionsin France(2013).

In the original model,UPC is a fixed parameter (De León Al-maraz, 2014) (SMR: $3.36 per kg; electrolysis: $4.69per kg; dis-electrolysis $6.24per kg), whichis only dependenton the size of the productionunit ($per kgH2). However, asmentionedinthe (McKinsey&Company,2010)report,abettervisionofUPCisto con-siderthefixed,electricityandfeedstockcosts.Thefixedcostis re-latedtolabourandmaintenance.

Allofthecontributionsarereflectedin Eq.(6),wheretheUPC calculation($perkgH2)isgivenbytheadditionofthefixedcost

ofaproductionplantoftypepandsizejintimeperiodt(FCPept,

$per kgH2),theelectricitycostforgeneralusageinaproduction plantoftypepprojectedfortimeperiodt(ECept,$perkgH2)and

the feedstockecostfora productionplantofthe ptype (FSCept).

The FSCept isobtainedbymultiplying thefeedstockeefficiencyin

the process p intime t (kWhelec/kg H2) by thefeedstock e price

(13)

consid-Table 9

Multi-objective and multi-period optimization results.

MILP GA

Year 2020 2030 2040 2050 2020 2030 2040 2050 Demand (t per day) 7.90 59.43 138.79 198.17 7.90 59.43 138.79 198.17 Number of total production facilities 17 34 47 69 17 28 30 41 Number of total storage facilities 12 66 150 214 12 66 150 214

Number of transport units 0 0 0 0 0 4 2 3

Capital cost

Plants and storage facilities (10 6 $) 681.01 765.69 707.92 185.42 737.93 520.31 443.72 153.42

Transportation modes (10 6 $) 0 0 0 0 0 0.80 0.28 0.41

Operating cost

Plants and storage facilities (10 3 $ per day) 49.35 321.64 748.23 1066.00 48.14 332.99 786.41 1133.53

Transportation modes (10 3 $ per day) 0 0 0 0 0 1.31 0.46 0.46

Total daily cost (10 3 $ per day) 91.68 525.60 1127.00 1600.25 83.17 476.53 1116.65 1557.90

Cost per kg H 2 ($) 11.61 8.84 8.12 8.08 10.53 8.02 8.05 7.86

Production facilities (t CO 2 -eq per day) 24.58 185.23 430.25 613.33 42.20 220.70 287.02 409.82 Storage facilities (t CO 2 -eq per day) 5.56 41.84 96.71 139.51 5.56 41.84 97.71 139.51 Transportation modes (t CO 2 -eq per day) 0 0 0 0 0 2.60 2.19 1.44 Total GWP (t CO 2 -eq per day) 30.14 226.07 526.96 752.84 47.76 265.13 386.91 550.77

Kg CO 2 -eq per kg H 2 3.81 3.80 3.79 3.79 6.05 4.46 2.79 2.78

Production facility risk 4.05 6.30 12.45 16.05 3.96 4.68 9.60 13.50 Storage facility risk 20.7 118.8 272.7 387 20.7 118.8 272.7 387 Transportation modes risk 0 0 0 0 0 20.8 6.5 14.3 Total Risk 24.75 125.10 285.15 403.05 24.66 144.28 288.80 414.80

Global TDC (M$ per day) 3.34 3.23

Global unit cost ($ per kg H 2 ) 8.27 8.00

Global GWP (T CO 2 eq per day) 1536 1251

Global Kg CO 2 -eq per kg H 2 3.80 3.09

Global Risk 838 879

Table 10

Use ratio of energy sources for hydrogen production (multi-objective and multi-period case).

Energy source MILP GA

2020 2030 2040 2050 2020 2030 2040 2050 Natural gas 0% 0% 0% 0% 6% 11% 0% 0% Hydro 53% 71% 70% 64% 53% 67% 70% 64% Wind 41% 24% 30% 36% 41% 22% 30% 36% Nuclear 6% 6% 0% 0% 0% 0% 0% 0% Table 11

Prices of natural gas and costs of electricity from different sources (2013).

Energy source (Price/unit) 2020 2030 2040 2050 Reference

European price of natural gas ($2010/kg) 0.587 1.300 1.750 ∗ 2.200 For 2030 and 2050: [48]

Cost of electricity (nuclear) in France

( $2013/kWh ) 0.0439 0.0665 0.089

0.112 For 2020: [49]

For 2030: [50] Cost of electricity (PV) in France ( $2013/kWh ) 0.328 0.101 0.060 ∗ 0.053 For 2020: [49]

For 2030 and 2050: [51] Cost of electricity (Wind) in France ( $2013/kWh ) 0.073 0.068 ∗ 0.063 0.058 For 2020: [49]

For 2050: [51] Cost of electricity (Hydro) in France ( $2013/kWh ) 0.018 0.044 ∗ 0.071 0.098

Calculated by interpolation.

erediselectricity,andtheenergysourcecostvariesdependingon thetype,e.g.,fossilvsrenewable(Table11).

UPCe,p,t=FCPe,p,t+ECe,p,t+FSCe,p,t (6)

The feedstock cost is likely togain importance becauseit de-pendsontheenergytransitionscenarioandinducesacostchange

in renewable energy impacting the hydrogen cost overthe

long-timehorizonfrom2020to2050.

ThenewUPCcalculatedforthemodelispresentedin Table12, in which hydrogenproduced via electrolysiswith solarenergyis

the most expensive, while hydrogen produced with electrolysis

fromahydraulicsourceislessexpensive.

Theoptimizationrunsareperformedwiththesenewcosts,and the resultsare compared withthe previous ones (see Fig. 10). A

strong decrease in GWP is observed for the range of these new

costs,globallyleadingtobettersolutionsforallcriteria.

In the first period (see Fig. 11 and Table 13), the distributed plantsarethemainsourcesofproduction,whileintheother peri-ods,the electrolysisplantsstartedto beinstalled inthe different grids. Additionally, there is no transport between grids, and the CO2 emissions for the plants installed remain very low. Most of

(14)

Fig. 9. Maps of the four scenarios for the optimization run carried out by MILP and GA for a multi-objective and multi-period approach.

Table 12

UPC calculated with the new costs. Production technology Fixed cost of production ($ per kg H 2 ) Electricity usage of production plant ($ per kg H 2 ) Feedstock cost for production plant ($ per kg H 2 ) Electrical need to produce a kg of H 2 kWh elec /kg H 2

Cost of energy source ($ per kg H 2 ) ∗ UPC ($ per kg H 2 )

2020 2030 2040 2050 2020 2030 2040 2050 SMR 0.16 0.02 4.02 ¥ 3.71 2.61 3.46 4.62 3.89 2.79 3.64 4.80 Electrolysis PV 0.39 0.06 55 18.04 5.56 3.30 2.93 18.49 6.01 3.75 3.38 Wind 0.39 0.06 55 4.00 3.72 3.45 3.17 4.45 4.17 3.90 3.62 Hydro 0.39 0.06 55 0.98 2.44 3.90 5.36 1.43 2.89 4.35 5.81 Nuclear 0.39 0.06 55 2.41 3.66 4.90 6.14 2.86 4.11 5.35 6.59 Dis Electrolysis PV 0.75 0.11 55 18.04 5.56 3.30 2.93 18.90 6.42 4.16 3.79 Wind 0.75 0.11 55 4.00 3.72 3.45 3.17 4.86 4.58 4.31 4.03 Hydro 0.75 0.11 55 0.98 2.44 3.90 5.36 1.84 3.30 4.76 6.22 Nuclear 0.75 0.11 55 2.41 3.66 4.90 6.14 3.27 4.52 5.76 7.00

[Energy source cost ($/KWh)x Electrical need to produce a kg of H

2 (kWh elec /kg H 2 )].

(15)

Fig. 10. Pareto fronts obtained with the original GA and the GA with the new cost.

(16)

Table 13

Multi-objective and multi-period results for actualised costs. GA new costs

Year 2020 2030 2040 2050

Demand (t per day) 7.90 59.43 138.79 198.17 Number of total production facilities 25 62 92 110 Number of total storage facilities 12 66 150 214 Number of transport units 0 0 0 0

Capital cost

Plants and storage facilities (10 6 $) 304.47 401.53 263.71 43.44

Transportation modes (10 6 $) 0 0 0 0

Operating cost

Plants and storage facilities (10 3 $ per day) 43.44 307.15 708.68 1013.16

Transportation modes (10 3 $ per day) 0 0 0 0

Total daily cost (10 3 $ per day) 80.12 489.34 1036.96 1446.56

Cost per kg H 2 ($) 10.14 8.23 7.47 7.30

Production facilities (t CO 2 -eq per day) 8.27 61.35 142.51 201.91

Storage facilities (t CO 2 -eq per day) 5.56 41.84 97.71 139.51 Transportation modes (t CO 2 -eq per day) 0 0 0 0

Total GWP (t CO 2 -eq per day) 13.73 103.18 240.22 341.42

Kg CO 2 -eq per kg H 2 1.74 1.74 1.73 1.72

Production facility risk 7.20 9.00 12.45 20.55 Storage facility risk 20.7 118.8 272.7 387.0 Transportation modes risk 0 0 0 0 Total Risk 27.90 127.80 285.15 407.55 Global TDC (M$ per day) 3.05

Global unit cost ($ per kg H 2 ) 7.55 Global GWP (T CO 2 eq per day) 698

Global Kg CO 2 -eq per kg H 2 1.73

Global Risk 848

Table 14

Use ratio of energy sources for hydrogen production (with new costs).

Energy sources 2020 2030 2040 2050 Hydro 22% 30% 22% 33% Wind 78% 70% 78% 67%

theenergysources usedstemfromwind,withalmost 70%ofthe

electricityproduced(Table14).

4.5. Multi-objectiveGAapproachunderuncertaindemand

In thiscase, the demand can vary betweenlow andhigh

de-mand(DminandDmax,respectively, in Table4).The toleranceis

thedifferencebetweenthetwolevelsofdemand,and

α

isthe per-centageoftolerancethatisaddedtothebasedemand(Dmin). Sev-eralvaluesof

α

areused(see Table15),andthedemandusedfor each

α

-cutdependsonthetolerancelevel.

For each

α

-value, a tri-criterion optimization procedure with

the GA procedure is implemented, leading to the set of

solu-tions constituting theParetofront, towhichthe M-TOPSIS proce-dure is then applied. The criteria (average values over the peri-ods) relative tothe compromise solution ofthe HSCN finally ob-tainedarepresentedin Table16,andtheinstancesobtainedfor

α

equal to 0; 0.16;0.33;and 0.50are shownin Table 17,in which the relative deviation relative to the case

α

equal to 0 case is presented.

Table 15

(17)

Table 16

Results of HSCN solutions the different α-cuts (average values over the period).

Table 17

(18)

Table 18

Robustness analysis of the optimal configurations.

α= 0.33 α= 0.66 α= 1

2020 2030 2040 2050 2020 2030 2040 2050 2020 2030 2040 2050 TDC (M$ per day) 89.24 514.66 1083.21 1494.42 93.31 554.59 1193.17 1614.67 98.93 593.65 1292.13 1729.73

Relative deviation (reference α= 0) 11% 5% 4% 3% 16% 13% 15% 12% 23% 21% 25% 20%

Unit cost ($ per kg H 2 ) 11.30 8.66 7.80 7.54 11.81 9.33 8.60 8.15 12.52 9.99 9.31 8.73

relative deviation (reference α= 0) 11% 5% 4% 3% 16% 13% 15% 12% 24% 21% 25% 20%

GWP (T CO 2 eq per day) 13.83 103.19 240.22 341.42 13.85 103.51 241.02 341.98 13.74 102.96 240.52 341.55

relative deviation (reference α= 0) 0% 0% 0% 0% 0% 0% 0% 0% 1% 0% 0% 0%

GWP (kg CO 2 eq per kg H 2 ) 1.74 1.74 1.73 1.72 1.75 1.74 1.74 1.73 1.74 1.73 1.73 1.72

relative deviation (reference α= 0) 0% 0% 0% 0% 1% 0% 0% 0% 0% 0% 0% 0%

Risk 45.25 278.12 602.26 821.36 70.31 326.36 749.19 1064.64 94.76 373.11 764.79 1099.59

relative deviation (reference α= 0) 62% 118% 111% 102% 152% 155% 163% 161% 240% 192% 168% 170%

Fig. 12. Cost of hydrogen in 2050 ($ per kg H 2 ). As expected, the operating cost and the capital cost increase

with hydrogen demand.Although the TDC is higherwhen

α

in-creases,theunit costdecreases,mostlyduetotheeffectofscale. For example, in the first period (2020), with a value of

α

equal to0(respectively0.5),theunitcostofH2 is$10.14/kgH2

(respec-tively$6.98/kgH2).Thesamesituationisobservedoverthewhole

period.Conversely,GWPandriskincreasewithhydrogendemand.

Thenumberoffacilitiesalsoincreasesas

α

-valueincreases, ex-cept for

α

equal to0.5, forwhich priorityisgiven toelectrolysis plantsinsteadofdistributedones,allowing forgreatercapacityto beavailable.

Arobustness studycanthus beperformedfromthe

optimiza-tion resultspresentedin Table18.LetusconsidertheHSCN con-figurationobtainedwith

α

equalto 0.33.Thenetwork,whichhas beenobtained fromthesuccessiveuse ofthemulti-objective

op-timization procedures andMCDM techniques, is perfectly

consis-tentwiththecorrespondingdemand.However,ifthedemanddoes

notreachthemaximalexpectedvalue,itwillresultinhigher val-uesfor allcriteria. Tocheck whetheran acceptable rangeforthe criteria valuescan still be obtained even if the network is over-dimensionedforthisdemandlevel,apost-optimalanalysisisthen

performed using the given network and the lowest value of the

demand. Table18comparestheresultsobtainedinbothscenarios.

4.6. Resultsanddiscussion

Thehydrogenpriceevolutionisdirectlydependenton produc-tion anddistribution costs. The differentstudies have shownthe

hydrogencost evolutionwiththegradualintroductionofdemand

fromthemobilitysector. Acomparativestudyofthe different re-sults considering different FCV market penetration rates, consid-ering differenthydrogen production technology choices, was car-ried out,andeven forthehighestdemand,theresultsshow (see

Fig. 12)that hydrogencosts for2050remainexpensivecompared

to the Hyways roadmaptargets (European Commission 2008) for

thebestcompromisesolutionsobtainedusingtheproposed multi-objective-MCDM framework. Forthe sake ofillustration, the best solutionobtainedforhydrogencostminimization ($4.18/kgofH2)

and GWP minimization ($7.30/kg H2) has also been reported. A

consistent approach wouldbe to find acompromise solution

be-tweentheseboundssincetheGWPisconsistentwiththetargeted values(Mobilité HydrogèneFrance2016)(see Fig.13).

Fig.13 comparesthewell-to-wheel CO2 emissionsper km

ob-tained withFCEVs obtainedby the useof theproposed

method-ology and those related to ICE vehicles equipped with

gasoline-ordiesel-fuelledengines(HydrogenCouncil2017)forthe2050 pe-riod.Currently,on-roadfueleconomyisapproximately1kgof

hy-drogen per 100 kmtravelled, andtheemissionsexpected forICE

vehiclesareapproximately60gCO2/km(IEA2015).Withthecosts

used intheoriginal models,theemissionsareinthe rangeof28 - 38gCO2/kmfortheMILPandGAapproaches,respectively.With thenewUPCcost,theemissionsarelessthan20gCO2/km.Itmust

be emphasized that FCEV emissionsareexpected tobe lessthan

23 g CO2/km (Mobilité Hydrogène France 2016) in 2030, which

means thattheHSCN obtainedwiththe newcosts iscompetitive

(19)

Fig. 13. Comparison of emissions by sector in 2050 (g CO 2 /km). Data from [59].

5. Conclusion

This paperhas presentedthe coremethodology forHSCN

de-sign, combining multi-objective optimization tools and multiple

criteriadecision-makingtechniques.Thescientificchallengeofthis work was to use the potential of genetic algorithms asan

alter-native to the current methodologies in the optimization of the

HSCdesign,particularlyasacomplementaryapproachtotheMILP frameworkpreviouslydevelopedin(De-LeónAlmarazetal.,2014): the size andparticularlythenumber ofbinary variableshave of-ten led to difficulties for problem solution in (De-León Almaraz et al., 2014). Inthis work, a variantof NSGA-II previously devel-oped in(Gomezet al., 2008) was explored toaddress the

multi-objective formulation sothat compromise solutions can be

auto-maticallyproduced.

The case study of the hydrogen mobility market in the

for-merMidi-Pyrenéesregionhasbeenconsideredsinceitwasalready studiedin(De-LeónAlmarazetal.,2014)forvalidationpurposesof theproposedmethodology:itisforeseentobethefastestgrowing

and most important market in the horizon of 2025 – 2030 and

thusisclearlyrelevanttothecontextofa“greenhydrogen” study. The objectivefunctionsobtainedbyGAexhibit thesameorder

of magnitudeasthose obtainedwithMILPin themono-criterion

problem, andthe multi-objectiveGAyields a Paretofrontof bet-ter qualitywithabetterdistributionofthecompromisesolutions. However, inourview,bothstrategiesdo nothavetobe opposed,

butthemaximumuseoftheirpotentialbenefitsmustbemade.

Severalexperimentswere developedwithafixeddemand and

for mono- and multi-objective cases. In the multi-objective

in-stances, the GAoutperformsthe

ε

-constraintstrategy. Itmust be emphasized thattheGA prioritizestheTDC cost,providingbetter resultsthanthe

ε

-constraintmethod,aswellasthetransportation ofhydrogenbetweenthegrids.Thedifferencesinthedistributions

andthe resultsbetweentheGAandthe MILPapproachescan be

explained bywayofmanaging the constraintsandtheir different logics.

In the original model(De-LeónAlmaraz etal., 2014), the unit productioncost(UPC)ofelectricityremainsfixedforallofthe pe-riods, regardlessofthe hydrogentechnology, whichwas a severe simplification. Theunit production cost involvesthe fixed facility costs (maintenance, labourcost), as well as electricity and feed-stockcosts,whicharemorerelevanttotherealityofcosts.

Hydrogen demand was identified as one the most significant

parameters forHSCNdesign,andaGAmodelwasdevelopedwith

demanduncertaintymodelledusingfuzzyconcepts.

Since hydrogen demand was simply involved through

con-straints in the HSCN model formulation, the HSC design

prob-lem refers to the simplest form offuzzy linear programming, as

proposedby (Verdegay,1982),(EbrahimnejadandVerdegay,2016,

Delgadoetal., 1993).Thesolutionstrategycanthusbe easily

im-plementedby varying

α

,whichcanbeconsidered thepercentage

of tolerance added to the base demand. This sensitivity analysis has allowed for identifying more robust solutions. The solutions arecomparedwiththeoriginalcrispmodels,basedoneitherMILP orGA,givingmorerobustnesstotheproposedapproach.

Anextension could be todevelop a fuzzyoptimization model

for supplychain design that considers demand andprice

uncer-tainties.Themodelcould beformulated asafuzzymixed-integer

linear programming model, in which the data are poorly known

andmodelledbytriangularfuzzynumbers.Thesynergeticeffectof

geneticalgorithmsandfuzzydemandmodellingcouldbethus

ex-ploredsothat thefuzzymodelwouldprovidethedecisionmaker

withalternativedecisionplansfordifferentdegreesofsatisfaction. Finally,thisstudyhasrevealedthat iftheeconomicand envi-ronmentalcriteriacanbeformulatedbyprovenmethodologies,the safetyriskisperhapsmoredifficulttoformulateandcalibrate.

Theuseoftheframeworkcould beusefulindeploying

hydro-gensolutionssincetheintroductionofhydrogenasanenergy car-rierisnotonlyatechnologychallenge,butitalsorequiresthe con-vergenceofmanyeconomic,environmentalandsocialfactors.

DeclarationofCompetingInterest

Allauthors have participatedin (a)conception anddesign, or analysisandinterpretationof thedata; (b)draftingthe articleor revisingitcriticallyforimportantintellectualcontent;and(c) ap-proval of the final version.This manuscripthas not been submit-tedto,norisunderreviewat,anotherjournalorotherpublishing venue.Theauthorshavenoaffiliationwithanyorganizationwitha directorindirectfinancialinterestinthesubjectmatterdiscussed inthemanuscript

Supplementarymaterials

Supplementary material associated with this article can be

found, in the online version, at doi:10.1016/j.compchemeng.2020. 106853.

(20)

Appendix

Indices

g and g’ Grid squares such that g’ 6 = g (8)

I Product physical form

L Type of transportation mode

P Plant type with different production technologies

S Storage facility type with different storage technologies

E Energy source type Parameters

B Storage holding period - average number of days’ worth of stock (days)

γepj Rate of utilization of primary energy source e by plant type p and size j (unit resource/unit product)

AD gg’ Average delivery distance between g and g’ by transportation l (km per trip)

Adj gg’ Road risk between grids g and g’ (units)

CCF Capital change factor payback period of capital investment (years) DT ig Total demand for product form i in grid g (kg per day)

DW l Driver wages for transportation mode l (dollars per hour)

FE l Fuel economy of transportation mode l (km per litre)

FP l Fuel price of transportation mode l (dollars per litre)

GE l General expenses of transportation mode l (dollars per day)

GWProd p Production GWP by plant type p (g CO 2 -eq per kg of H 2 ) GWStock i Storage global warming potential form i (g CO 2 -eq per kg of H 2 ) GWTrans l Global warming potential of transportation mode l (g CO 2 per ton-km)

LUT l Load and unload times of product for transportation mode l (hours per trip)

ME l Maintenance expenses of transportation mode l (dollars per km)

NOP Network operating period (days per year)

Qmax il Maximum flow rate of product form i by transportation mode l (kg per day)

Qmin il Minimum flow rate of product form i by transportation mode l (kg per day)

PCapmax pi Maximum production capacity of plant type p for product form i (kg per day)

PCapmin pi Minimum production capacity of plant type p for product form i (kg per day)

PCC pi Capital cost of establishing plant type p producing product form i (dollars)

RP p Risk level of the production facility p (units)

RS s Risk level of the storage facility s (units)

RT l Risk level of the transportation mode l (units)

SCapmax si Maximum storage capacity of storage type s for product form i (kg)

SCapmin si Minimum storage capacity of storage type s for product form i (kg)

SCC si Capital cost of establishing storage type s storing product form i (dollars)

SP l Average speed of transportation mode l (km per hour)

SSF Safety stock factor of primary energy sources within a grid (%)

TCap il Capacity of transportation mode l transporting product form i (kg per trip)

TMA l Availability of transportation mode l (hours per day)

TMC il Cost of establishing transportation mode l for product form i (dollars)

UPC pi Unit production cost for product i produced by plant type p (dollars per kg)

USC si Unit storage cost for product form i at storage type s (dollar per kg-day)

W l Weight of transportation mode l (tons)

WFP g Weigh factor risk population in each grid (units)

Variables

A Rate of utilization of the tolerance AH ig Available hydrogen in grid g

DL ig Demand for product i in grid g satisfied by local production (kg per day)

DI ig Imported demand for product form i in grid g (kg per day)

FC Fuel cost (dollars per day) FCC Facility capital cost (dollars)

FOC Facility operating cost (dollars per day) GC General cost (dollars per day)

GWPTot Total global warming potential of the network (g CO 2 -eq per day)

LC Labour cost (dollars per day) MC Maintenance cost (dollars per day)

NPp ig Number of plants of type p producing product form i in grid g

NSs ig Number of storage facilities of type s for product form i in grid g

NTUil gg’ Number of transport units between g and g’

PD ig Tolerance of the demand in grid g

PGWP Total daily GWP in production facility p (g CO 2 -eq per day)

PR pig Production rate of product i produced by plant type p in grid g (kg per day)

PT ig Total production rate of product i in grid g (kg per day)

Qil gg’ Flow rate of product i by transportation mode l between g and g’ (kg per day)

RP ig Received hydrogen in grid g

SGWP Total daily GWP in the storage technology s (g CO 2 -eq per day) SP ig Overproduction of hydrogen in grid g

ST ig Total average inventory of product form i in grid g (kg) TCC Transportation capital cost (dollars)

TDC Total daily cost of the network (dollars per day) TGWP Total daily GWP in transportation mode l (g CO 2 -eq per day) TOC Transportation operating cost (dollars per day)

TotalRisk Total risk of this configuration (units) TPRisk Total risk index for production activity (units) TSRisk Total risk index for storage activity (units) TTRisk Total risk index for transport activity (units)

(21)

Modelformulation

The modelis based on an optimization formulationinvolving

theeobjectivefunctions(minimizationcaseconsideredinisolation orsimultaneously)andasetofconstraints.Theconstraintsare ex-pressedforthewholetimehorizondividedintoseveraltperiods

Costobjective

Thecostobjectiveinvolvesthetotaldailycost(TDC), represent-ing thecost in $ per dayof the entireHSC, in whichFCC isthe facility capital cost ($), TCCis the transportation capitalcost ($), andNOPisthenetworkoperatingperiod(daysperyear)relatedto thecapitalchargefactor(CCF,inyears).Then,thefacilityoperating cost(FOC,$perday)andthetransportationoperatingcost(TOC,$ per day)arealsoassociated.Inaddition,thecostofimported en-ergy (UICasthe unitary imported cost andIPES asthe imported energy)isadded. TDC=

³

FCC+TCC

(

NOP

)

CCF

´

+FOC+TOC+X eg UICeIPESeg (A.1)

whereFCCisrelatedtotheestablishmentofproductionand stor-agefacilities.Itiscalculatedbytheproductoftheproductionand storageplants(NPandNS,respectively)andtheircapitalcosts(PCC

andSCC,respectively),dividedbythelearningrate,whichisacost reduction fortechnologyandmanufacturers thatresultsfromthe accumulationofexperienceduringatimeperiod.

FCC=X i,g

Ã

1 LearnR

Ã

X p PCCpiNPpig+ X s SCCsiNSsig

!!

(A.2)

Thetransportcost(TCC)dependsontheflowratebetween dif-ferent grids (Q), the transportation mode availability (TMA), the distance betweengrids (AD) (round trip), the averagespeed (SP), the loading/unloadingtime (LUT) and the cost for transportation mode(TMC). TCC=X i,l

(

"

X i,l,g,g

µ

Q ilggTMAlTCapil

µ

2 ADggSPl +LUTl

¶¶#

TMCil

)

(A.3) FOC refers tothecost forproductionandstorageplant opera-tion,dependingonunitproductionandstoragecosts(UPCandUSC, respectively)andonthequantityofhydrogenproducedandstored (PRandST,respectively). FOC=X i,g

Ã

X p UPCpiPRpig+ X s USCsiSTig

!

(A.4)

Finally,TOCconsiders:

• fuelcost(FC),givenbythefuelpriceandthedailyfuelusage; • labourcost(LC),givenbythedriverwageandthetotaldelivery

time;

• maintenancecost(MC),representedbythemaintenanceofthe

transportationbydistancetravelled;and

• andgeneralcost(GC),consistingoftransportationinsurance,

li-censesandregistrations,andoutstandingfinances.

TOC=FC+LC+MC+GC (A.5)

Globalwarmingpotentialobjective

The global warming potential (GWPTot, in g CO2 per day) is givenbythetotaldailyproductionGWP(PGWP,ingCO2 perday),

thetotaldailystorageGWP(SGWP,ingCO2perday)andthetotal dailytransportGWP(TGWP,ingCO2perday).

GWPTOT=PGWP+SGWP+TGWP (A.6)

TheGWPrelatedtotheproductioniscalledPGWPandisgiven by the quantity of hydrogenproduced (PR) and the emissionsof CO2 associatedwiththeproductionfacilities(GWiprod.

PGWP=X pig

¡

PRpigGWiprod

¢

(A.7)

The GWPassociated withthe storage isthe SGWP,where the

hydrogenproduced(PR)isrelatedtotheGWPforthestorage tech-nology(GWstock i ). SGWP=X pig

¡

PRpigGWistock

¢

(A.8)

The GWP associated with transport (TGWP) is given by the

distance (AD) and the flow rate of hydrogen (Q) between grids, theglobalwarmingpotential(GWiptrans)associatedwiththe trans-portationmodeanditsweight(Wl).

TGWP=X ilgg

µ

2AD lggQilggTCapil

GWTrans i wl (A.9) Riskobjective

Thetotalrelativerisk(TR)(A.10)compilesTPRisk,thetotalrisk ofproductionfacilities(A.11),TSRisk,thetotalriskofstorage facil-ities(A.12),andTTRisk,thetotalriskoftransportationunits(A.13).

TR=TPRisk+TSRisk+TTRisk (A.10)

Eachiscomputedbytheproduct ofthenumberofproduction

plants(NP) (or the storageunits (NS) orthe transportation units (NTU))byariskfactor(RP,RS,andRT,respectively)andbythe pop-ulationweightfactorineachgridinwhichtheproductionor stor-agefacilityislocated(WFP)ortheroadriskbetweengrids(Adj). TPRisk=X pig

¡

NPpigRPpWFPg

¢

(A.11) TSRisk=X sig

¡

NSsigRSsWFPg

¢

(A.12) TTRisk=X ilggNTUilggRTlAdjgg′ (A.13) Constraints

ForinteroperabilitypurposeswiththeMULTIGENplatform,the inequality constraints have been coded in Matlab R

°

and formu-latedfollowingthe“lower orequalthanzero” structure(≤0). All of the demand (DT) must be satisfied with the local production (DL)andthehydrogenimportedfromothergrids(DI)

DTig=DLig+DIig

i,g (A.14)

Basedonthe conservationofmass,thetotalflow ofhydrogen leavingthegridg(Q,fromgtog’)andthetotalproductionratein thesamegrid(PT)mustbeequaltotheflowofhydrogenentering thegridg(Q,fromg’tog)andtotaldemandrequiredbythesame grid(DT): PTig= X l,g

¡

Qilgg′−Qilg′g

¢

+DTig

i,g (A.15)

Toguaranteetheavailabilityoftheproduct,avariableisadded. Duringsteady-stateoperation,thetotalinventoryofproductform

iingridg(ST)isequaltoafunctionofthecorrespondingdemand (DT)multipliedbythestorageperiod(

β

):

Figure

Fig.  1. Methodology of the HSC design framework.
Fig.  4. Uncertain demand modelling.
Table 6 also presents the unit cost of H 2 as well as the amount of emitted CO 2 per kg of H 2 that is deduced from the value of the optimization criteria (in the same colour).
Fig.  6. Maps of the two scenarios with multi-objective optimization a) with GA; b) with MILP
+5

Références

Documents relatifs

Les nouvelles incitations ont statistiquement contribué à renforcer l’agriculture productiviste, mais il y a eu (ébauche de) réflexion entre agriculteurs, au sein des institutions

• Francesca Arcelli Fontana, University of Milano Bicocca (Italy) • Xavier Devroey, Delft University of Technology (Netherlands) • Benoît Frenay, University of Namur (Belgium).

Les films à base de caséinate de sodium présentent des bonnes propriétés barrière à l'oxygène quand ils sont utilisés dans un environnement sec.. La présence d'

Overall, the results presented in this section tend to dismiss the alternative explana- tions of the channels of local public goods and social interactions as explanations for

We also interpret classical control politics for an irrigation canal (local upstream and distant downstream control) using automatic control tools, and show that our method enables

PACIFIC: SiPM Readout Introduction PACIFIC Preamplifier Shaper Integrator Digitizer Prototypes PACIFICr0/1 PACIFICr2/3 Outlook 8 / 15 PACIFICr1: Linearity.. Good Preamplifier

ANTENNAS TRANSMITTING RECEIVING VARIABLE LINE ATTENUATOR STRETCHER STABILIZED OSCILLATOR LOCAL OSCILLATOR STABILIZED IF IF STRIP STRIP PHASE COMPARATOR

Samples powered at the higher current density experienced larger decreases in bond strength. It is suggested that high current densities not be used in the field. The loss of