Optimal Design of Eco-Industrial Parks with coupled energy networks addressing Complexity bottleneck through an Interdependence analysis

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Optimal Design of Eco-Industrial Parks with coupled

energy networks addressing Complexity bottleneck

through an Interdependence analysis

Florent Mousqué, Marianne Boix, Ludovic Montastruc, Serge Domenech,

Stéphane Négny

To cite this version:

Florent Mousqué, Marianne Boix, Ludovic Montastruc, Serge Domenech, Stéphane Négny.

Opti-mal Design of Eco-Industrial Parks with coupled energy networks addressing Complexity

bottle-neck through an Interdependence analysis. Computers & Chemical Engineering, Elsevier, 2020, 138,

pp.106859. �10.1016/j.compchemeng.2020.106859�. �hal-03116641�

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To cite this version:

Mousqué, Florent and Boix, Marianne and Montastruc, Ludovic and

Domenech, Serge and Negny, Stéphane Optimal Design of

Eco-Industrial Parks with coupled energy networks addressing

Complexity bottleneck through an Interdependence analysis. (2020)

Computers & Chemical Engineering, 138. 106859. ISSN 0098-1354

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Optimal

Design

of

Eco-Industrial

Parks

with

coupled

energy

networks

addressing

Complexity

bottleneck

through

an

Interdependence

analysis

Florent Mousqué, Marianne Boix

∗

, Ludovic Montastruc, Serge Domenech, Stéphane Négny

Laboratoire de Génie Chimique, Université de Toulouse, CNRS, INPT, UPS, 4 Allée Emile Monso, 31432 Toulouse, Cedex 4, France

a

r

t

i

c

l

e

i

n

f

o

Keywords:

Industrial Ecology Interdependence Utility System Hybrid Power System Multiobjective Optimization Network complexity Renewable Energies

a

b

s

t

r

a

c

t

BygatheringinEco-IndustrialParks(EIPs),companiesobtainbenefitsfromsynergisticcooperationbutit alsocreatesariskbyincreasinginterdependencies.Theaimofthispaperistoprovideamethodfor opti-mallydesignexchangesthattakesintoconsiderationrealstakesofcompanies.Thisresolutionmethodis assessedonamulti-periodMILPmodelofcoupledenergynetworksintegratingautilitysystemproducing steamatdifferentpressurelevelsandamutualizedon-gridHybridPowerSystem(HPS)providing elec-tricityusingRenewableEnergy(RE)sources.Designconcernsinterconnectionsbetweencompaniessuch asboilers,turbinesandpowerofREsources.Amulti-stageapproachisdeveloppedtominimizenetwork complexityand NetPresentValue (NPV)oftheoverallnetwork. Lastly,an interdependencyanalysisis proposedto choosethe optimalsolution. Testedonacasestudy involving15companies,the optimal exchangeshavebeenraisedtosatisfydemandsoverfourtimeperiods.

1. Introduction

Accordingtorecentreports(IPCC2018),facingglobalwarming and theensuing environmentalchallenges isa priority to design newwaysofgoodsproduction.Findingecologicalwaystoproduce goods andservices while ensuring economic benefits constitutes a majorresearch challenge. Asa solution,industrialecology aims to reconcile industrial and environmental constraints by drawing inspiration from natural ecosystems to design industrial systems (Frosch and Gallopoulos, 1989). Indeed, in such ecosystems, the use of resources (raw materials or energy) is optimized through transformations that minimize losses and therefore wastes. The fulfilment ofthisconceptis theimplementation ofEco-Industrial Park (EIP), in which industries gather on the same sitein order tobenefitofsynergeticadvantagesofcooperation,withtwomain goals, increasing their competitivenesswhile reducing their envi-ronmentalimpact(PCSD,1996).Todate,mostoftheseparkshave beenimplementedinindustrializedcountriessuchasNorth Amer-ica, EuropeorAustralia,butnowadaysmanyofthemarealso

be-∗ _{Corresponding author}

E-mail address: marianne.boix@ensiacet.fr (M. Boix).

ing created in developing countries; e.g. China, Brazil andKorea (Montastrucetal.,2013).

In order to design exchanges in EIPs, it is necessary to use anddevelopoptimizationapproaches.Reviewsontheoptimization ofEIP (Boix et al., 2015) andon the tools used forEIP develop-ment(Kastneretal., 2015;Afshari etal., 2016) classify the exist-ingapproachesdependingonthenetworkconsidered:water net-work, material, energy or coupled networks. These reviews have reported that in contrast to EIP material orwater flow manage-mentwherethereisarelatively largenumberofresearches,only asmallamountofpublicationsaredealingwithinterplantenergy flowmanagement.Thefollowingpartprovidesdetailsonprevious optimizationmethodsdedicatedtoEIPenergynetwork.

Lowe (2001) defines two main axes for designing sustainable energy networks, the first one consists of maximizing the effi-ciency ofenergyproduction andtransportation systems, the sec-ondoneistoharnessrenewablepowersources.Fortheformer,the recommendations include the use of large-scale inter-plant util-ity system or cogeneration sources such as Combined Heat and Power(CHP)plant. Thelatteraxisfocusesonsubstituting conven-tional fossilpower production by renewable energy(RE) sources suchassolar,windturbines,biomass,geothermalenergy,etc., de-pendingonthepotentialofthelocalarea.Tothisextent,inmost eco-industrial parks, facilities designed to meet energy demand

Nomenclature

Sets

b: boiler

f: fuel

tu: turbine

so: photovoltaic(PV)solarpanel wi: windturbine

sr: electricalsources(so;wi ∈ sr)

srAC: Alternative Current (AC) electrical power sources

(wi _∈srAC)

srDC: Direct Current (DC) electrical power sources (so

∈srDC)

C: company(c ∈ C,c∈ C,c=c) H: steamheader(h ∈ H,h∈H,h<h) T: timeperiod(t ∈ T,tm ∈T,

∀

tm≤ t)

Parameters

M: largepositivevalue

Nbtime: numberofsteptime

i: discountrate

n: projectlifespan(years)

SLh_{: percentage of steam losses by trap at}

steamheader

WLwu_{: percentageofwaterlossesatwaterunit}

Calf: fuelcalorificpower(kWh/t)

Effb,f: boilerefficiencyforeachfuel

Efftu: turbineefficiency

ConP: condensateparameterforturbine

hh: steam enthalpy depending on pressure

level(kWh/t)

hw: water enthalpie before boiler heating

(kWh/t) Ds

h,t,c: steamdemand(ton/h)

De

t,c: electricitydemand(kWh)

EConsfix_b : fixed electricity consumption for boiler (kWh)

EConsvar_b : variable electricity consumption for boiler(kWh)

PMax

b,h : maximum steamproduction atboilerb

(ton/h) Pmin

b,h: minimumsteamproduction(ton/h)

SMax

h,tu: maximumsteaminturbinetu(ton/h)

Smin

h,tu: maximumsteaminturbinetu(ton/h)

LoadFactorso,t: loadfactorforthesolarPVproduction

LoadFactorwi,t: load factor for the wind turbines

pro-duction

v_wi,t: windspeedinthetimeintervalt(m/s) vrated

wi : ratedwindspeed(m/s)

DFA: Discount factor forallocation of annual operational expenditure and resources overthelifeoftheproject.

Prifuel_f : fuelpurchaseprice(USD/ton) Priwater_{: waterpurchaseprice(USD/ton)}

PriElecpurchase_{: electricitypurchaseprice(USD/kWh)}

PriElecsales_{: electricitysalesprice(USD/kWh)}

Fstock_b,f,t,c_safety: fuelsafetystock(ton)

CAPEX_b: capitalexpenditureforboiler(USD) OPEXb: operational expenditurefor boiler(USD

peryear)

DFI_b: discount factor for investment and re-placementcostofboiler

CAPEXtu: capitalexpenditureforboiler(USD)

OPEXtu: operational expenditure for turbine

(USDperyear)

DFItu: discount factor for investment and

re-placementcostforturbine

CAPEXfix_pipe: fixed capital expenditure for pipeline (USD)

CAPEXvar_pipe: variablecapitalexpenditureforpipeline (USD/ton/h)

OPEXpipe: operational expenditure for pipeline

(USD/ton/h))

DFI_pipe: discount factor for investment and re-placementcostofboiler

minIntercDiameter_Threshold: minimum diameter of interconnection pipes(ton/h)

MaxIntercDiameter_Threshold: Maximum diameter of interconnection pipes(ton/h)

CAPEXsr: capital expenditure for electric power

sources(USD/kW)

OPEXsr: operational expenditure for electric

powersources(USD/kWperyear) DFIsr: discount factor for investment and

re-placementcostofelectricpowersources

Effinv: inverterefficiencyforDCsources

MaxEprodTur: maximum production for turbines (kWh)

MaxInstallsr: maximumpower installed forelectrical

source(kW)

Variables

NPV: NetPresentValueoftheoverallproject CostRaw_{: raw material cost for the project lifespan}

(USD)

CostBoilers_{: boilerscostfortheprojectlifespan(USD)}

CostPipes_{: pipescostfortheprojectlifespan(USD)}

CostTubines_{: turbinescostfortheprojectlifespan(USD)}

CostElec_sources_{: electricalsourcescostfortheprojectlifespan}

(USD)

CostElec_{: electricitycostfortheprojectlifespan(USD)}

CostFuel_{: fuelcostfortheprojectlifespan(USD)}

CostWater_{: watercostfortheprojectlifespan(USD)}

Nb_interc: numberofinterconnectionintheutility sys-tem

AvgInterc_Diameter: averageofinterconnectiondiameters MaxInterc_Diameter: maximumofinterconnectiondiameters



Q1Q3Interc_Diameter: differencebetweenquartile1andquartile3 oftheinterconnectiondiameters

Ts

h,t,c,c: steam transferfromcompany cto company

c’(ton/h) Tw

t,c,c: water transferfrom companyc to company

c’(ton/h) ysel

b,c: binaryvariabletoselectboilertechnologies

yprod_b,t,c: binaryvariabletoregulateboilersteam pro-duction

ysel

tu,c: binaryvariabletoselectturbinetechnologies

ypipe_h

,c,c: binary variable to select interconnection

pipesfromcompanyctocompanyc’ Prated

sr : rated installed power of electrical power

source(kW)(so;wi _∈ sr)

IntercDiameter_h,c,c : diameterofaninterconnectionpipe(ton/h) Fb,f,t,c: fuelconsumedbyboiler(ton)

Fpurchase_b,f,t,c : fuelpurchasebyboiler(ton) Fstock

Sprod_b,h,t,c: steam production from boiler to steam header(ton/h)

S_h,h,t,c: steam flow fromheaderh’ tosteam header

h(ton/h) SIn

h,tu,t,c: steam flow from steam header to turbine

(ton/h) SOut

h,tu,t,c: steam flow from turbine to steam header

(ton/h)

Strap_h,t,c: steam losses by condensate trap at steam header(ton/h)

Svent

h,t,c: steamventedatsteamheader(ton/h)

Wh,t,c: water flow from process use to water unit

(ton/h)

W_b,t,c: waterflowfromwaterunittoboiler(ton/h) WOut

tu,t,c: water flow from turbine to water unit

(ton/h) Wstock

t,c : quantityofwaterintheutilitynetwork

dur-ingtimeintervalt(ton)

Wpurchase_t,c : waterpurchaseforwaterunitfeeding(ton) Wfeeding_t,c : waterpurchaseforwaterunitfeeding(ton) Wlosses

t,c : Waterlossesinwaterfeedboiler(ton)

Wdump_t,c : waterdumpedfromtheutilitynetwork(ton) EprodSources_t : producedelectricpowerintheHPS(kWh) Eprod_sr,t : produced electric power depending on the

electricalsource(kWh)(so;wi ∈ sr) EprodCons_t : producedelectricpowerconsumed(kWh) EprodSell_t : electricpowersoldpersteptime(USD) Epurchase_t,c : electricpowerpurchasedper steptimebya

company(USD) Eboiler

b,t,c : consumedelectricpowerbyboiler(kWh)

Eturbine

tu,t,c : electricpowerproducedbyturbine(kWh)

Esources

sr,t : electric power produced by sources in the

HPS(kWh)

are utility systems,they produce utility forprocesses (i.e.mainly heat, cold and compressed air) (Hipólito-Valencia et al., 2014), although Hybrid Power Systems (HPS) generate electricity using multiple powersources (Xu etal., 2013). Severaltechniques have been introduced to assess the economic feasibility of utility sys-tem and HPS. In most methods, the final objective is to search for the energy network design with the lowest investment cost (Kastneretal.,2015).

1.1. EnergynetworksforEIP

During the last decades, a great majority of studies deals with utility systems design and planning by the mean of eco-nomic and thermodynamic optimization. Among them, Papoulia andGrossmann(1983)developedaMixed-IntegerLinear Program-ming (MILP) modelto design the utility system atthe industrial parkscale.Inthismodel,differentconfigurationsandtechnologies (e.g.boilers,steam turbines,andgasturbines) areavailablein or-der to provide fixed demands of electricity and of steam at dif-ferentlevels ofpressure.Lateron,includingdemandvariations, a multi-periodenhancementofthismodelhasbeenproposed After-wards,Aguilaretal.(2007)developedamulti-periodMILPmodel tooptimizethedesignandoperationofindustrialutilitysystems. Thereafter,Kimetal.(2010)developedamulti-periodMILPmodel tooptimizesteam,waterandelectricitynetworksplanningandto designtheinterconnectionstoimplementregardingeconomicand environmental criteria. Most recently, Combined Heat and Power

(CHP) has been also included as a technology to design indus-trial parks. Indeed, CHP allows generating electricity while pro-ducing thermal energy (mainly steam and hot water) with heat thatwouldhavebeenwasted(ChiccoandMancarella2009). Com-paredto theseparate generationofheatandpower,cogeneration canimproveenergyefficiencybetween10and40%(Madlenerand Schmid, 2003) and thereby reduce CO2 emissions. Among these schedulingworks,Aghaetal.(2010)introduced anintegrated op-timizationapproachthatsimultaneouslyoptimizestheproduction systemandtheutilitysystem.Inaddition,Mitraetal.(2013)took intoaccountthevariationofthesellingpriceoftheelectricitywith a time-sensitive model. Later, Li et al. (2016) have developed a modelthatconsidersstorageforCHPcoupledwithwind turbines to sellit on theelectricity market. Finally, designing an EIP util-itysystem,Ramosetal.(2018)developedamodelbasedongame theoryconceptsinordertotakeintoaccountthebehaviourof par-ticipants.Theiroptimizationmethod consistsintoa multi-leader-followergame modelthat istransformed asa MO problemwith equilibriumconstraints andsolved asa Non LinearProgramming (NLP).

Hybridpowersystems(HPS)are consideredasa decentralised electric power generation system directly connected to the local distributionnetworkorclosetothepowerdemand(Paliwaletal., 2014).Theadvantagesofthesetypesofsystemsarethereduction ofthe relianceonthe external grid,the stabilityofpower prices (Gao et al., 2014), the security and power quality (Dondi et al., 2002) and the possibility to provide power in remotes region. Considering environmental aspects, the main benefits is the re-duction of carbonemissions by contributing to the development of renewable sources (Abou El-Ela et al., 2010; Bellamy et al., 2014). One of the mostused methods for HPS design and plan-ningisthe Power Pinch Analysis (PoPA).This methodintroduced by Bandyopadhyay (2011),is based on theconcepts ofmass and energy balances and integrates time dimension, allowing energy storage. Bandyopadhyay developed a model to optimally design sourcesandstoragecapacityforoff-gridsHPS.Asetofpossible op-timalsolutions is provided usinggraphic visualization where the battery capacity is a function of the size of the energy sources. Fromthismethod,WanAlwietal.(2012)developedamodelto de-signanHPSsystemwiththeminimumoutsourcedelectricity sup-plyandthe minimumstoragecapacityin on-gridcases. Address-ing this issue, mathematical optimization is an efficient solution for HPS design, as presented in HPS optimization review papers (Zhouetal.,2010;SinhaandChandel,2015)developedagenericLP modeltominimizetheminimumoutsourcedelectricitysupplyand thestoragecapacityof HPSwhiletakinginto account theenergy lossesintheallocation ofpowergeneratedfromrenewables.This modelhas been testedon a typical householdcase studyin the UK.WhereasHoetal.(2014)propose aMILPbiomass-based HPS connectedtotheresidentialdemandofIskandarIslandinMalaysia. ThereafterTheoetal.(2016) presentedaMILPmodeltooptimize cost andstorage capacityof an on-grid HPS foran EIP, compris-ingAlternativeCurrent(AC)andDirectCurrent(DC)power.Inthis paper,severalstoragetechnologiesareassessed.

Toour knowledge,no other studyhas presentedthe coupling ofutility systemsand HPS inan EIP.Thus, thefollowing section focuseson the specific issues related to the design of a coupled energynetwork.Inthisregard,increasingthesizeoftheexchange network by coupling networks (e.g. heat, power, water, material, wastes,etc.)isa majorissuethat can beovercomeby the devel-opmentofgeneric optimizationmethodsabletosolvelarge prob-lems. Indeed, it is particularly true forEIP networks design and planning, that can involve many interconnected plants and pro-cessesandthereforemanyconstraints andvariablesincluding bi-naries.

1.2.NetworkcomplexityofanEIP

Another major issueunderlinedby Kastner et al.(2015), isto deal with the network complexity ofthe designedsolutions. In-deed, the network complexity is represented by the number of connections between the several companies involved in the EIP, namedinterconnections(NobelandAllen,2000;Avisoetal.,2011), andit is directlylinked tothe feasibility of the network ( Rubio-Castroet al., 2011). In addition, (Boix et al., 2012) have demon-stratedthat costandnetworkcomplexityareantagonists,sothey canbeconsideredasobjectivefunctionsinaMOoptimization. Fi-nally,Tianetal.(2014)highlightedthatinfrastructuresharing(e.g. boilers,wastewatertreatment,etc.)allowedbytheinterconnection networkisalsoanothermajorissuetocopewithEIPdevelopment. Therefore,interconnectionsaremorerelevant foranEIP develop-mentthan connections betweenprocesses inside the same com-pany,becausethey involveother conceptssuch asconfidenceand interdependence between companies. While network complexity has been widely analysed in the sense of technical feasibility, a lackofstudiesisfoundregardingthereliancebetweencompanies andtherefore the interdependence that interconnection between companies implies. Indeed, dependencies allow to benefitof the advantagesofsynergeticexchanges, butitisalsoawayto propa-gatefailureswithinthenetwork(Valenzuela-venegasetal.,2019). Theseorganisational aspects are addressed inthis paperthrough theinterdependenceindicatordevelopedhereafter.

The contributions of this paper are: i/ the development of a genericapproachfortheoptimaldesignofanenergynetwork cou-plingtheutilitysystemandtheHPSinanEIPandalsoii/ address-ing thecomplexity challenge through the developmentof a new procedureandindicators. Inthe first part,thisarticledetails the problemstatementaswell asthe developedsuperstructure, after whichthe mathematical formulationis presented.The resolution methodologyisthengiven.Thismethodisdiscussedinan applica-tioncasestudyofacomplexrealprobleminvolving15companies inan EIPwithenergy demandstaken fromYeosuindustrial park (Kimetal.,2010).Thefinalsectionaimsatapplyingamulticriteria decisionmaking tool to choose an optimal networkbased on an interdependenceanalysis.

2. Problemformulation

2.1.Problemstatement

Given is a set of input parameter including: energy demands (i.e.steam at differentlevels of pressure andelectricpower), ef-ficiencyandnominalpower fortheutility systemenergysources (i.e.boilers,turbines),fueltypefortheboilers,efficiencyand max-imuminstallablepowerfortheHPSenergysources.The optimiza-tionproblemhastofindthedesignof:

i. Theenergynetwork oftheEIP: the flowratesexchanged fora given time period, the power ofthe energy sources installed, andthesteamexchangedbetweencompanies.

ii. The powergenerationandexchangesplanningovertime peri-odsrepresentthedynamicsofproductionanddemand. Designvariablesarebinariesfortheboilers,turbines, intercon-nections selection and position (i.e. in which company) and for the operation of boilers (i.e. turned on or off). Continuous vari-ablesareusedtoallocatetheamountofresources(i.e.fuels,water, andoutsourcedelectricpower),thepowerinstallationofwind tur-binesandsolarPVandthediameterofinterconnections.Duetoits genericity,thismodelisapplicabletoboththegrassrootsdesignof EIPsand the retrofit design of existing industrial parks. The MO optimizationmodel consistsin minimizingtheoverall costofthe wholeenergysystem(i.e.utility systemandHPS) andminimizing

theinterconnections. This optimizationmodelis solved over sev-eraltimeperiods.

2.2. Superstructurebasedmodel

An overview of the general model description is provided in

Fig.1.It presentsthe developedenergyexchange networkmodel couplingthe utility systemto supply thesteam demand andthe on-gridHPStosupplytheelectricpower.Companiescanexchange steamusinginterconnectionpipes.Couplingtheutilitysystemand theHPS,andoptimizingthemsimultaneously, enablesamore re-alisticdesigntobeachieved,byconsideringthewholesystemand interactionbetweenheatandpower.

For both steam and electric power demands, the dynamic is taken into account. Indeed, as shown in the energy profile sec-tion, energy demand varies over time for companies depending on their production mode (i.e.batch or continuous) butalso de-pending onseasonality. Togo further,on theleft side of the fig-ure theenergysources are represented andthedynamicoftheir production ishighlighted with shortervariation steps forthe in-termittentrenewable sources thanforthe steamproductionwith boilers.Fromperiodtoperiod,continuityconstraintsareimposed, they involvethestocklevels (water andfuel).The superstructure ofthewholenetworkisrepresentedonFig.2.Itdescribesthe op-eration of the internal utility system of a company, the possible exchanges to other industries and finally the HPS for the whole EIP.Consideringtheutility system, differentlevelofpressureand temperature, between boilers andprocesses inside a single com-panyaswellasexchangeswiththeother companiesoverseveral time periods are considered. Boilers are producing the steam, to supply theheat demand of the processes.Moreover, the transfer from a higher-pressure steam header to a lower one is done by PressureReliefValves(PRV)orusingturbines.Indeed,a cogenera-tionsystemisintegratedthroughtheuseofturbinesthatconvert high-pressuresteamto alower levelofpressureorto condensed waterintoelectricpowerbydrivinggenerators.

The steam network of thismodel is a loop system. After the processesuse,thewaterreturnstothewaterunit.Thewaterstock inthewaterunit isconsidered asonehour ofconsumption.This modelincludeswaterlossesduetoevaporationinthe waterunit and steam losses in the network, through condensate traps or vents.Thelatterisusedasanexcesspurgeanditgivestothe sys-temadegree offreedom byenablingitto evacuateoverloads.To compensatethesewaterlosses,industriescanpurchasefeed-water. While designing the utility system, to supply the energy de-mand, the model selects the boilers and turbinesto be installed amongdifferent technologies.The sizing specificationsforboilers aretheirmaximumproductioncapacity,theirlevelofsteam pres-sureproduced,thefuelconsumedandthecostoftheboiler.

Inthis model,theturbines canbe single-stage ormulti-stage. Insingle-stageturbines,onlytheinletflowratecanbecontrolled, in multi-stage, the distribution betweenthe outlets is also man-ageable(Aghaetal.,2010).

Boilersand turbinesof thismodelare installed in companies. In this way, stand-alone mode (i.e. companies without intercon-nections to the sharing network, with its own production) or in EIPmode,interconnectedwithothercompanies canbereachable. Toexchangetheheatedsteam,thenetworkcomposedof intercon-nectionsbetweencompanies isalsodesigned. An interconnection isdirectional,i.e.steamcanonlyflowinonedirection.

Regarding RE sources, the model determines the power to be installed. The production of intermittent RE sources depends on their estimatedloadfactor,whichis anaverage ofprevious mea-suresrelatedtothegeographicpositionoftheEIPandtotime pe-riod.BecausetheHPSison-grid,ateachtimestep,themodelcan

Fig. 1. Schematic representation of the utility system coupled to the HPS to supply the EIP demand.

Fig. 2. Superstructure of the utility system an industry and HPS for the EIP.

decideto purchaseelectricity.Itmayalsochoosetosellthe elec-tricityproducedon-sitetotheexternalgrid.

Conversely to boilers and turbines, the location of wind tur-binesandsolarPVsourcesisnotconsideredasaparameterinthis model,whichmeansthatHPSsourcescanbelocatedatanyplace: within thesiteofa company orona dedicatedsite. Indeed,itis considered that the electricity grid alreadyexists, its installation costsarethereforenegligible.

Theassumptionsforthismodelare:

– Whendesigninginterconnections,theirlengthisnottakeninto account.Thisispossiblebecauseallcompaniesareexpectedto belocatedonthesameEIPsite,closeenoughthatthedistances betweenthemarerelativelyshort.

– Power andheatlossesare nottakenintoaccount, indeeditis consideredasaninsignificantamountincomparisontoenergy exchangesflows(Kim,etal.,2010;Theoetal.,2016).

– The transitory behaviour of elementssuch aswarm andcold start-ups,shutdownsforboilersarenottakenintoaccount be-causethis modelis dedicatedto long termdesignand notto shorttermscheduling.

– The HPSdoesnot includeenergystorage,ascurrent technolo-gies are considered uneconomic, particularly when connected totheexternalnetworkasprovenby(Mousqué etal.,2018).

3. Mathematicalformulation

This section details the mathematical formulation resulting fromthesuperstructurepresentedabove.

3.1.Objectivefunctions Economicobjective:

TheeconomicobjectiveusedistheminimizationofNPV,which isthe discounted value of the designedenergy network over its lifetime.Itcomprisesthecosts ofrawmaterials,boilers, intercon-nections,turbinesandpowergenerationsources(1).

minNPV=CostRaw+CostBoilers+CostPipes+CostTubines

+CostElec_sources ₍₁₎

The cost of raw materials includes fuel, electricity and water

(2).

CostRaw₌



_CostFuel_+CostElec_+CostWater



₍₂₎

Aswithotherrawmaterialsandoperationalcosts,thefuelcost iscalculatedover theduration oftheproject.Thus, toobtain the fuelcost, thetotal quantity offuel purchased overall time steps ismultipliedby thepurchasepriceofthe fuel(3).Depending on theirspecifications,boilerscanoperateasmulti-fuelboilers.

CostFuel₌ 

b,f,t,c



Fpurchase_b,f,t,c × Prifuel f



× DFA (3)

The cost of electricity is determined from the electricity pur-chasedfromthegridminustheelectricitysold(4).

CostElec₌





t,c

Epurchase_t,c × PriElecpurchase₋ t

EprodSell_t

×PriElecsales



× DFA (4)

Purchasedwateristheamountofwaterrequiredtooperatethe steamsystemplus thewater tocompensate lossesandleaks (5). Wpurchase_t,c representspurchases forthe waterstock,whileWfeeding_t,c standsforthereplacementofwaterlossesthroughouttheduration oftheproject.Moreover,thepriceofthepurchasedwater encom-passesthetreatmentcost.

CostWater₌



 t,c Wpurchase_t,c + t,c Wfeeding_t,c



× Priwater_{× DFA (5)}

The cost of the boilers (6) covers both the investment (i.e. CAPEX)andtheoperationalcost(i.e.OPEX). Thebinariesysel

b,c and

yprod_b,t,c representrespectively if a boiler is selected and if it is in operationatthegiventimestep.DFI allowsthereplacementofa boilertobe takenintoaccount ifits averagelifetimeis lessthan thedurationoftheproject.

CostBoilers₌ b,c ysel b,c× CAPEXb× DFIb+  b,t,c

yprod_b,t,c× OPEXb× DFA

(6)

Similarly,ifaturbineispurchased

(

ysel

tu =1

)

,itscostconsistsof

theinvestmentandtheoperationalcost(7).

CostTurbines₌ tu,c

ysel

tu,c×

(

CAPEXtu× DFItu+OPEXtu× DFA

)

(7)

Theinterconnectioncostincludesthefixedinvestmentcostand the variable cost proportional to the pipe diameter. This diame-tercorrespondstothemaximumflow-rateflowingthroughthe in-terconnection. Moreover, the operating cost dependson the pipe section (8).ypipe_h,c,cisa binaryvariabletoselectan interconnection fromcompanyctocompanyc’(candc’aresubsetsofC,andcis differentfromc’). CostPipes₌  h,c,c ypipe_h,c,c× CAPEXfix pipe+  h,c,c IntercDiameter h,c,c ×CAPEXvar pipe× DFIpipe+  h,c,c IntercDiameterh,c,c

× OPEXpipe× DFA

(

∀

c



=c

)

(8)

For the cost of electricity production, investment and opera-tionalcostsdependonthenominalinstalledcapacityPrated

sr (9).

CostElec_sources₌ sr



Prated

sr ×

(

CAPEXsr× DFIsr+OPEXsr× DFA

)



(9)

TheDiscountFactorforAllocationofannualexpenditures(DFA)

(10)isusedtocalculatetheNPV ofan operatingorresourcecost that lasts for the duration of the project. Here n represents the numberofyearsoftheprojectandiisthediscountrate.

DFA=

(

1+i

)

n_{− 1}

i

(

1+i

)

n (10)

Connectionsinthenetwork

Theinterdependenceindicatorisassessedinafirststep,thanks tothenumberofinterconnections(11):

Nbinterc=



h,c,c

ypipe_h,c,c

(

∀

c



=c

)

(11)

Three other sub-criteria, detailed in section 4.2 will be stud-iedinthemulti-criteriadecisionmakingstepfurtherinthisstudy. Theyare representativeof thedistribution ofthe diameterof in-terconnectionsinthenetwork.

3.2. Constraints

The constraints of the optimization problem are the physical andthermodynamicconstraints oftheenergynetwork aswellas themassandenergybalances. Theconstraintsare formulatedfor eachelementofthesuperstructure:steamheaders,processes, wa-ter unit, fuel stocks,turbines,boilers and finally theHPS divided intoelectricitygrid,demandandsourcesofelectricpower produc-tionandfinallytheinterconnections.

Steamheaders:

Theinletofasteamheadercomesfromthesteamproducedby theboilers,fromturbinesoutletorfromthePressureReleaseValve (PRV). The outletstreams ofthe steam header feed the turbines andthedemandoftheprocesses.ItcanalsoflowthroughthePRV togofromone headerh’toanotherheader hwithalower pres-sure(withhandh’subsetsofsteamheadersH,h’havinga higher-pressurelevelthanh).Inaddition,apartofthesteamislostinthe traporcanexitfreelythroughthevent.Finally,steamtransfersare possiblefromonecompanytoanother(12).

 b Sprod_b,h,t,c+ h Sh_,h,t,c+  tu SOut_h,tu,t,c+ c Ts_h,t,c_,c

=Ds h,t,c+  h Sh,h,t,c +Straph,t,c+S vent h,t,c+  tu SIn h,tu,t,c + c Ts h,t,c,c

(

∀

c



=c, h<h



(12)

Condensatelossesthroughthetrapsareapercentageofthe to-tal steamflowinginthe steamutility system. Thesesteam losses include trap lossesin pipes andheaders aswell asprocess trap losses(13). Strap_h,t,c=SLh×



 b Sprod_b,h,t,c+ h Sh,h,t,c+  tu SOut_h,tu,t,c+ c Ts_h,t,c,c



×

(

∀

c



=c,h<h



)

(13)

Processsteamdemands:

The water that is released afterprocesses use isequal to the steamdemand(14).

Ds

h,t,c=Wh,t,c (14)

Waterunit:

The waterflowingintothewaterunit comesfromother com-panies, from turbines, from processes, and from water feeding to compensate waterlosses. The water that exits,corresponds to thewaterthatflows toboilers,other companiesandwaterlosses

(15).  c Tw t,c,c+  tu WOut tu,t,c+  h Wh,t,c +Wfeedingt,c = b Wb,t,c +Wlossest,c +  c Tw t,c,c

(

∀

c



=c, h<h

)

(15)

Waterlossesareapartofthewaterflowingintothewaterunit

(16). Wlossest,c =WLwu×



 tu WOuttu,t,c+  h Wh,t,c



(16)

Thewaterfeedingthelossesisthesumofallthelosses,atthe trapsbutalsoattheventsthatevacuatetheexcess(17).

Wfeeding_t,c =Wlossest,c +  h



Strap_h,t,c+ Svent h,t,c



(17)

The quantityofwaterinthesystemWstock

t,c corresponds tothe

quantityconsumedbytheboilersduringatimestept(18).

Wstockt,c =  b Wb,t,c (18) Multi-periodconstraints: Waterstock:

Thequantityofwaterinthenetworkattimesteptdependson the quantity ofwaterpurchasedanddumped duringcurrentand previous timesteps tm(tandtmare subsetsofT,andtmisless thanorequaltot)(19). Wstock t,c = tm  t=0



Wpurchase_t,c − Wdump t,c



(

∀

tm≤ t

)

(19) Fuelstock:

Thefuelstockisequaltothestockinitiallypresentplusthefuel purchased,minusthefuelconsumedbytheboiler.Eachboilerhas itsownfuelstockforeachfueltowhichitisadapted.(20).

Fstock

b,f,t,c=Fbstock,f,t−1,c+F purchase

b,f,t,c − Fb,f,t,c

(

∀

t>0

)

(20)

Thefuelstockmustbegreaterthantheminimumsafetystock

(21).

Fstock b,f,t,c≥ F

stock_safety

b,f,t,c (21)

Foritsinitialization,thefuelstockatthefirsttimestepisequal tothestockattheendofthepreviouscycle(22).

Fstock

b,f,t=0,c=Fstockb,f,t=Nbtime,c (22)

Turbines:

Theamountofsteam enteringinthe turbines,SIn

h,tu,t,c,hasan

upperandlowerlimitthreshold(23).

Smin

h,tu× yseltu,c≤ SInh,tu,t,c≤ SMaxh,tu× yseltu,c (23)

Anupperlimitthresholdisalsoappliedtotheamountofsteam leavingthe turbinesSOut

h,tu,t,c (24).Inthe casethat an outletis not

connectedtoasteamheader,thisthresholdisfixed atzero.Thus, forasingle-stageturbine,allbutoneoftheoutputsareconnected toasteamheader.

Smin

h,tu× yseltu,c≤ SOuth,tu,t,c≤ SMaxh,tu× yseltu,c (24)

Intheturbines,thesteamenteringthroughhigherpressure in-leth’isdistributedattheoutletsbetweenthedifferentlower pres-surelevelshandthecondensedwater(25).

SIn h,tu,t,c=  h SOut h,tu,t,c+WOuttu,t,c

(

h<h



)

(25)

Theelectricity produced dependson the efficiencyofthe tur-bines but also on the pressure of the steam at the inlet andits pressureattheoutlets(26)(Aghaetal.,2010).

Eturbinetu,t,c =Efftu×



SIn_h,tu,t,c× hh−  h SOut_h,tu,t,c× hh− WOuttu,t,c× hw



(

h<h



)

(26)

AproportioncorrespondingtoConP ofthesteamentering the turbineiscondensed(27).

WOut

tu,t,c= ConP × ShIn,tu,t,c (27)

Boilers:

The steam production of the boilers is betweenits minimum powerproductionPmin

b,h anditsmaximumcapacityP Max b,h (28). Pmin_b,h × yprod b,t,c≤ S prod b,h,t,c≤ P Max b,h × y prod b,t,c (28)

Boilerscanbemulti-fuelboiler(Aguilaretal.,2007),steam pro-ductiondependsontheenthalpy differencebetweenthewaterat theinletandthesteamattheoutlet, onthequantity offuel con-sumed,onthecalorificvalueofthefuel,andalsoontheefficiency oftheboiler(29). Sprod_b,h,t,c= fCalf × Fb,f,t,c × Effb,f

(

hh − hw

)

(29)

The amount of water entering the boilers corresponds to the amountofsteamproduced(30).

Sprod_b,h,t,c=Wb,t,c (30)

The electricity consumed by the boilers is described by

equation(31).

Eboiler_b,t,c =EConsfixb × yselb,c+ECons var b × S

prod

b,h,t,c (31)

Ifaboilerisstartedatleastoncethenitisselected,thatmeans purchased(32).

ysel b,c≥ y

prod

b,t,c (32)

HybridPowerSystem:

The electricity produced by the energy sources in the HPS is equal to theelectricity produced by the turbines,by the AC (i.e. windturbines)andDC(i.e.solarPVpanels)sourcesmultipliedby theefficiencyoftheconverter(33).

EprodSourcest =  sr∈srAC Eprodsr,t +  tu,c Eturbinetu,t,c +  sr∈srDC Eprodsr,t ×Effinv (33)

The electricityproduced on-site isdistributedbetweenthe lo-calconsumptionoftheindustrialsiteandthepotentialsaletothe externalgrid(34).

EprodSources_t =EprodCons_t +EprodSell

t (34)

Theelectricityconsumedbythedifferentindustriesisproduced bytheinstalledsourcesorpurchasedfromthegrid(35).

 c Det,c=E prodCons t +E purchase t (35)

The productionofsolar PVpanelsandwind turbinesdepends ontheinstalledcapacityandtheloadfactorduringthetimeperiod

(36)(37).

Eprod_so,t=Prated

so × LoadFactorso,t (36)

Eprod_wi,t=Prated

wi × LoadFactorwi,t (37)

The maximum power that can be installed for an electrical sourceislimited,thisconstraintdependsontheresourceavailable onthesite(38).

Pratedsr ≤ MaxInstallsr (38)

Theelectricpowerproductionoftheturbinesisalsolimited de-pendingonthepossibilityofinstallationonsite(39).

Eturbine

tu,n,t,c≤ MaxEproTur (39)

Interconnectionpipes:

Anexchange ofsteam,T_h,t,c,c,betweenindustriesisonly pos-sibleiftheinterconnectionexists

(

ypipe_h,c,c=1

)

(40).Misabig pos-itivevalueusedtosatisfytheexistenceconstraintofapipe.

ypipe_h,c,c/M≤ Ts h,t,c,c≤ y

pipe

h,c,c× M

(

∀

c



=c

)

(40)

If an interconnection exists, its diameter must be larger than the threshold, minIntercDiameter_Threshold, that represents the minimum technicallyfeasiblesectionofpipes(41).

IntercDiameter_h,c,c ≥ ypipe

h,c,c× minInterc Diameter

Threshold

(

∀

c



=c

)

(41)

Fromthelinearbehaviourofthesystemsoftheenergynetwork andtheuseofbinariestoselectthedesignedfacilities,thismodel isaMILPsolvedwithCPLEX®.

4. Resolutionprocedure

4.1.Optimizationprocedure

Whiletakingintoaccountan economiccriterionandthe inter-dependenceofcompaniesthroughthenumberofinterconnections, theoptimizationmodelcanbe hardtosolve,especiallywhenthe industrialparkconsideredislarge.

Inthispartofthestudy,aclassicMOoptimizationmethod(i.e. epsilon-constraint)has been tested in orderto justify the devel-opment of the optimization procedure detailed further. Epsilon-constraint(Marglin,1967)methodisalexicographicapproachthat consists in minimizing one criterion, while slicing the research spaceofthe other criteria usingconstraints andfinally finding a solutionforeachslice.Inthiscase,thenumberofinterconnections issettledasaconstraintandNPVisminimized.

Applied on the case study detailed hereafter (15 companies, specificitiesdescribedinsection5),thismethodcouldnotachieve anoptimalsolutionduetoan importantcombinatoryoftheMILP problem.Indeed,duringthe optimizationstage ofCPLEX® solver, branch-and-cuttreeofpossibilitiessizeisexceeding theavailable computingmemory. Withthisformulation, theconstraint onthe super-variables used by the epsilon-constraintmethod to setthe numberofselected interconnections isimportant.This remarkis

particularlyrelevant forsuper-variables, that isto say, bottleneck variables for the calculation time which has been identified as thebinaryvariabletoselectinterconnections.Indeed,when super-variables are binaries, it can be difficult for thesolver to handle themappropriatelyandtoreachconvergence.Thenumberofthese variables is increasing exponentially with the numberof compa-nies in the network. Hence, the principle of the procedure is to reduce the number of super-variables by designing the network step bystep witha limitednumberofinterconnections. This ap-proachisthenintended toprovideresultsclosetotheglobal op-timum whileensuringshortercalculation time.Consequently, be-causethisproblemcannotbesolvedbyclassicalMOmethods(i.e. epsilon-constraint)anoptimizationprocedurehasbeendeveloped to overcomethesedifficulties andits schematic representationis presentedinFig.3.Thedifferentstepsachievedandtheir motiva-tionsaredetailedhereafter.

The proposed method consists then inan iterativeprocedure, startingfromtheeconomicminimumsolutionandobtaininga so-lutionforeach numberofinterconnectionsuntilthereisnomore interconnection, the minimum for interdependence indicator be-ing reached. Severalsteps are carried out: the first consists in a mono-objectiveoptimizationbyminimizingNPV.Then,a multiob-jectiveoptimizationconsideringNPV andinterconnectionnumber isachieved.Thisstepleadstobuild theParetofrontwhichis ob-tained by using an epsilon-constraintapproach for two objective functions. After obtaining all the optimal solutions, the multicri-teria analysis is conducted through AHPmethod to evaluate the interdependenceofthedifferentcompaniesintheEIP byusing4 differentcriteria:

• 1rst_{stepoftheprocedure}

During the procedure, the first step consists in a mono-objectiveoptimizationtoobtaintheoptimaldesignbyminimizing theeconomiccriterion (1).Theresultofthisstepisthedesignof thenetworkthatminimizesthecostsoitinvolvesusuallyalotof interdependencies.

• 2nd_{stepoftheprocedure}

From thesolutionobtained duringthe firststep,a limitedlist ofinterconnectionsavailable forthenextstepoftheprocedureis determined.Thisisdonebysettingtheselectionbinaryofthe un-used interconnection (the corresponding flow isequal to 0) as a parameterequalto0(i.e.theinterconnectionisnotselected).The numberoftheselectedinterconnectionsisnowequalton.

Another important parameter is also constrained during this step: the diameter of an interconnection (directly dependant of the exchanged flow). It is considered as an indicator of the in-terdependence betweencompanies. In this way,a large flow be-tween companies corresponds to a high degree of interdepen-dence. The maximumthreshold for the diameterof interconnec-tions

(

MaxIntercDiameterThreshold

)

is constrainedtobe inferiororequal to

thevalueofthemaximumdiameterofinterconnectionspresentin theresultofthefirststep(42).

IntercDiameterh,c,c ≤ ypipeh,c,c× MaxInterc Diameter

Threshold

(

∀

c



=c

)

(42)

Afterwards, the procedure is iterative. At each iteration, the principle is to reduce by one (n₌n-1) the number of intercon-nectionsinthedesignednetworkandtoselectninterconnections among the initial limitedlist. Then the problem is economically optimized. As shown in Fig. 4, throughout the resolution proce-dure, while removing interconnections, this constraint allows to limitthemaximumdiameterofinterconnectionsandthereforethe average diameter. Whereas without this constraint, interconnec-tiondiametertendsto increasebecauseproductionflows are dis-tributedinfewerconnections.

Fig. 3. Schematic representation of the procedure.

Fig. 4. Influence of the maximum diameter constraint throughout the resolution procedure.

Fig. 5. Figurative case study representing the distribution of interconnections and interdependence sub-criteria.

4.2. Multi-CriteriaDecisionMaking(MCDM):Interdependence trade-off

FromtheMOoptimizationpreviouslyproposed,asetofoptimal solutionsisbuilt,neartheParetofront.Amongthesesolutions,an innovativeevaluationofinterdependenceisdevelopedforchoosing asolution.

Toevaluateflowexchangesovertheentirenetwork,the distri-bution of the diameter of the interconnections is taken into ac-count. As an illustration, Fig. 5 presents the defined interdepen-dencetrade-off subdividedintofoursub-indicators:

- Thenumberofinterconnections(Nb_interc):evenifan EIPseeks to enhance collaboration, inter-companies exchanges will be used becausethey allow to minimize thecosts. Thisindicator has to be minimized in order to limit the interdependencies which are a bottleneck to participateinto an EIP. In addition, the moreinterconnectionsthereare inthenetwork,the more management constraints it implies for companies. The num-berofinterconnectionsisalsolinkedtotopologicalconstraints andthereforetothefeasibilityoftheexchangenetwork( Rubio-Castroetal.,2011).

- Theaveragediameterofinterconnections

(

AvgInterc_Diameter

)

:is con-sidered to minimize flows over the whole network (lowflow interconnections being considered as connections with fewer interdependencies). Thus, while interconnection allows eco-nomicsynergeticadvantage,thefinalgoalofthisapproachisto give prioritytointerconnectionswithlowflowsbyminimizing theiraverageflowsbutwithhigheconomicgainbyminimizing globalcost.

- The maximum diameter of interconnections

(

MaxIntercDiameter

)

, is

minimized to avoid an interconnection with a large flow-rate relatively to others. Thatis to say, an interconnection witha strong dependence,because ifthisinterconnection isremoved ithasastrongimpactonthenetwork.

- Thedifferencebetweenthefirstandthirdquartileof intercon-nection diameters

(

Q1Q3Interc_Diameter

)

,to beminimized, withthe aim of grouping interconnection diameters. This allows a fair distributionoftherisksincurredbycompaniesbyavoidingthat some companies areleftwithsmallinterconnection flowsand otherswithlargeones.

Fig. 6. Developed AHP structure for the design of the energy exchange network of an EIP.

Inordertoevaluateallthesolutionsobtainedattheendofthe resolutionprocedure,MCDMtoolscanbeused.Amongtheearliest andthemostbasicMCDMtoolsistheweightedsummethod,also calledthedecisionmatrixapproach(BhushanandRai,2007).One ofthe mainbiasesofthismethodistheuseofcriteriaforwhich unitscannot beaddedinabalancedway.Oneofthecriteriamay takeprecedenceoverthe others.Toovercomethis, the weighted-productmethod isa dimensionlessmethodusing thesame prin-ciple,except that each termisnormalized. Anotherbiasof these methods is the subjectivity and the prejudice in assigning the weightsthatcannot beeliminated orassessedusingthismethod. Addressingthisissue,theAnalyticalHierarchyProcess(AHP) devel-opedby(Saaty,2002)isusingtheweighted-productmethodbutit allowstoorganiseandprioritizethecriteriainastructuredwayby givingaweightbetweeneachpairofcriteria.Forthisreason,itcan help assign weights with several decision-makers. In the mean-time,theconsistencyoftheseweights ischecked,validatingtheir choiceinordertoassesseachsolutionandselecttheoptimalone (FormanandGass,2001).Nevertheless,AHPisthemethodchosen becausein this MOstudy, prioritizing the criteriabetween com-plexityandcostbutalsoselectandverifytherelevanceofweights arethemajorissues.

AHPdetailedprocedureisdescribedhereafter:

- Step1:aspresentedinFig.6,theproblemisdecomposedinto goal,criteriaandsub-criteria;

- Step2:decision-makersorexpertssetaweightforeachpairof criteriaorsub-criteria;

- Step 3: theseweights are plottedinto a comparison pairwise squarematrixwhereeachcriterionisrepresentedbyalineand a column.The (i,j)value representingthepairwise weight be-tweenthecriteriaintheith_{rowandtheoneinthej}th_column;

- Step 4: previous weights are normalized in the standardized matrixandaglobalweightforeachcriterioniscalculatedfrom thesumofpreviouspairwisenormalizedweightdividedbythe numberofcriteria;

- Step 5: the consistency of the matrix is assessed using the developed consistency index (Saaty, 2002). This indicator as-sesseswhetherthereisnoinconsistentweightassignmentdue totransitivity.Forexample,ifcriterionweightAishigherthan BandBishigherthanC,thenAshouldbehigherthanC.Saaty suggestsavalue higherthan 0.1forthisindex.Ifitislower it isrecommendedtoreconsiderpairwisecomparison;

- Step6: aweightedsumisrealizedforeachsolutionbasedon thenormalizedvalueofcriterionmultipliedbytheweight ob-tained with AHPmethod. A ranking betweenthe solutions is thenobtained,withthesolutionswiththehighestscoresbeing thebest.

Table 1

Steam properties in the Yeosu EIP of the case study ( Kim et al., 2010 )

Properties VHP HP MP LP

Temperature ( °C) 525 370 270 195

Pressure (atm) 121.5 40.0 15.0 3.5

Enthalpy (kJ/kg) 3422 3156 2982 2858

Thus, Fig.6 showstheAHPstructure developed todesign the energy exchange network of an EIP. The two objective functions oftheoptimizationstepareNPVandinterdependence.Finally,the solutionsarecomparedandanalyzedusinganormalizedweighted sumwiththe differentindicatorspreviously developed, the solu-tion with the highestscore is the selected one forthe designed energynetwork.

5. Casestudy:resultsanddiscussion

5.1. Casestudydescription

Theprocedurepreviouslydevelopedisappliedonacasestudy composed of 15 industries and four operating periods are taken into account, one per season. The dataare taken fromYeosu in-dustrialparkinChina(Kimetal.(2010).

Steamandpowerdemands areprovided inAppendixA1.Four pressurelevels aretakenintoaccount forsteam:VeryHigh Pres-sure (VHP), High Pressure (HP), Medium Pressure (MP) andLow Pressure(LP),thepressurelevelsaredetailedinTable1.

Steam is produced by natural gas boilers installed in compa-nies.Ninedifferenttechnologiesareavailable:VHP,HPorMPand foreachone,maximumcapacitycanbe settledat50t/h,100t/h or500 t/h. Boiler capacityrangeis between50 and100 % of its maximum powerbecause within its rangeboiler has a relatively constantefficiency(Aguilaretal.,2007)andinseasonaloperation, itwouldbeasignificantlosstooperatetheboileratalow capac-ity,whichmeansatalowerefficiencylevel.

The VHP cannot be exchanged using interconnections due to thehighsteampressure andto thetechnicalconstraintsinvolved

(43).Forthisreason,theinterconnectionsonlyconcernHP,MPand LPsteam.

ypipe_{h=vhp,c,c}=0 (43)

TheelectricpowersourcesarewindturbinesandsolarPV pan-els, corresponding load factor per season are given in Table 2. Theseloadfactorsareestimatedforapotential locationinFrance, fromaverageclimateconditionsofpreviousyears(RTE-Réseaude transportd’électricité,2018). Byconnectingto theexternalpower grid,powercanbeboughtandexcessproductioncanbesold. Tur-bines are multi-stage andthreetechnologies canbe selected (i.e.

Fig. 7. Repartition of the flowrates in the network with the method without constraint.

Fig. 8. Results for the method developed with constraint.

Table 2

Load factors per season for solar PV and wind turbines

Winter Spring Summer Autumn

Wind Load Factor ( LoadFactor wi,t )

0.317 0.171 0.145 0.247

Solar PV Load Factor

( LoadFactor so,t )

0.1 0.2 0.195 0.093

500 kW, 3 MW,and 15 MW).Price for naturalgas isset at 280 €/tonandelectricity purchased priceis fixedat 0.07€/kWhwhile itssalepriceis0.1_€/kWh.

Themathematicalmodelformulatedincludes7864constraints, 7281variablesincluding1328binaryvariables.

5.2. Analysisoftheinfluenceofmaximumdiameterconstraint

Thisstudyaimsatdiscussingtheinfluenceofmaximum diam-eter constraintintroduced in the optimizationprocedure (second

stepoftheprocedure).Theproceduredevelopediscomparedtoa secondmethodwithouttheconstraintonthemaximumdiameter ofthe interconnections. Procedures are referred to“method with constraint” (i.e.developed procedure) and “method without con-straint” in the following.

The distributionof all the exchangesinthe network obtained foreachsolutionisshowninFigs.7and8forbothmethods (with-outandwithconstraint,respectively).Resultsarepresentedasbox plots for each solution including values of the minimum, maxi-mumandtheaverageflow.

Obtained solutions are presented from the point of the first step,themono-objectiveeconomicminimum(i.e.33 interconnec-tions). Then, according to the procedure previously introduced, fromthe initiallistofselectedinterconnections,ateach iteration, asolutionisobtainedbyreducingthenumberofinterconnections inthedesignednetworkuntiltherearenomoreinterconnections (i.e.stand-alonemode)(Fig.9).

Fig. 9. Pareto front obtained with both methods (with and without constraint).

One can observe that flow rates increases while the number ofinterconnectionsdecreaseswiththemethodwithoutconstraint. Regarding the maximum diameter, it goes fromthe initial point with71.6 ton/hto 297.8 ton/h(i.e. with4 interconnections).The averageexchangedflow-rate alsoincreasesfrom28.2ton/hto192 ton/h(i.e.with2interconnections).Finally,thedifferencebetween Q1andQ3isincreasinginanirregularlyway,fromtheinitialpoint witha difference of 26.7ton/h to the point with 3 interconnec-tions, with a difference of 105.9 ton/h. At some points, this dif-ference is smaller than the initial point (12.9 ton/h with20 and 19 interconnections and 14.7 ton/h with 9 interconnections). It should be noted that the point with one interconnection is dif-ferentfromtheseobservations,indeed,theflows decreaseatthis point.

With respect to the method with constraint, the maximum flow-ratelimitedtothevalueoftheinitialpoint,i.e.71.6ton/h re-mainsconstant throughoutthe resolutionprocedure. Theaverage value increaseswhile removing interconnections from28.2 ton/h tothemaximumflow-rate of71.6ton/h(with3interconnections) andthedifferencebetweenQ1andQ3decreases.

The increase of diameters of interconnections while reducing the number of interconnections is explained because the same amountproducedbywide cost-effectiveboilersorturbinesneeds tobesharedwithfewerinterconnectionshaving,therefore,a big-ger flow. In regards to these results, main evidence is that ex-changedflowsarewidelyreducedwiththemethodwithconstraint incomparisontothemethodwithoutconstraint.Therefore,the in-terdependenceofdesignedsolutionsisalsoreducedwiththe con-strainedmethod.Nevertheless,theeconomiccriterionofsolutions forbothmethodneedstobeanalysedtoconclude.Comparisonof NPV accordingtothe numberofinterconnectionsforboth meth-odsisgiveninFigure.

Theevolutionprofiles oftheNPV curvesforbothmethods are similar, i.e. the cost increases with the decrease in the number of interconnections. However, from15 to 2 interconnections, the methodwithconstraintachieve aslightdecline ineconomic per-formancewith0.2%moreexpensivesolutions.Amainpostulateof thisdevelopedprocedureisthat thecounterpartoftheconstraint limiting the diameter is that best economic solutions cannot be achievedwithfew interconnectionspossibilities, nevertheless, in-terdependenceishighlyimproved.

In conclusion of this section, the developed resolution proce-dure has proven to be able to solve large MILP network design problems.Furthermore, usingthis approach,the constraint limit-ing theinterconnection diameterallowsproducing solutionswith better value for interdependence criterion while slightly increas-ing the cost. This means that this procedure provides exchange networkswiththemostinteresting interconnectionsaccordingto industrials, i.e. interconnections with low interdependencies and high economic gain. The continuation of this studyanalyses the obtainedresultsonthiscasestudy.

5.3. Designofenergyexchangenetwork

Thissectiongivesan analysisofthe evolutionoftheexchange network designed throughout the procedure, from the EIP with maximuminterdependence(i.e.maximuminterconnections)tothe stand-alone situation. The selected optimal solution is then de-scribed.

Fig. 11. Values of criteria and AHP rank (a) or NPV (b) for each solution of the developed procedure. 5.3.1. Technologyselectionanalysis

The evolution of the design of the network according to the numberof interconnectionsisgivenin Fig.10. Foreach solution, thestackedbarchartrepresentsthecostsforboilers,pipes,steam turbines,windturbinesandthecostforresources,i.e.fuel,water, electricitypurchasedandsold.Formoreclarityinthegraph,only the variablepart ofthe fuel cost isshown. Indeed, apart ofthe fuel costsdoesnot dependon thedesignchoice. Thispart corre-sponds to the fuel used to produce steam to meet demand ifit isproducedwiththemostenergy-efficienttechnology.Inaddition, overa20-yearsproject,operatingcosts,andmoreparticularlyfuel costs, representthe bulk of thecost. Thus, the sumof these de-tailedcostsisrepresentedastheGlobalCostcurve.

NPV for wind turbines is then of 57 891K_{€ with} 30 MW in-stalled, itisthe maximumlimitforthistechnology.The installed powerreachedtheupperlimitbecauseitisprofitable.Besides,the installed power for solar panels is null, this technology has not beenselected.Indeed,itisnotprofitablewiththiscasestudythat isnotincludedsubsidies.Waterandelectricitypurchasedarealso

relatively constant. Moreover, naturally, the cost of the pipes re-duceswiththenumberofpipes.Themainvariationsasthe num-berofinterconnectionsdecreasesareobservedforthecostof boil-erswhichincreaseswhilethecostofsteamturbinesdecreases.

This last observation led to the following explanation of the operation of the exchange network. First of all, thanks to pipes, boilers are shared, andlarge boilers are selected (i.e. 500 t/h of productioncapacity). Whereas, without these pipes, large boilers arenotprofitabletosupplyasinglecompanybecausetheydonot haveenough steamdemand tosupply.According to theturbines, thelogicis similar,producingpower thankstoturbines is partic-ularlyprofitabletoexpand steam froma higherlevelof pressure toalowerone,andthereforetoconsumetheoutletsteamin pro-cesses.Intheabsenceofinterconnections,thisisnotenoughsteam demandinstand-alonecompaniestobesuppliedbyaturbine.

Togofurtherontheunderstandingofthecouplingofheatand powernetworks, theseinterpretations show that the energy pro-ductionofturbinesisstronglylinked tosteamdemandandboiler productioncapacity.Inaddition tothat,pilotable turbine

produc-Fig. 12. Utility system and HPS of the final designed solution

tioncouldcomplete theintermittentREproductiontosupplythe demand.Finally,withregardtotheHPS,thismodelisbasedonan off-gridmodel,inwhichcasetheproductionofREislinkedtothe pricesoftheelectricitygrid,asthelackandsurplusofproduction canbeboughtandsoldrespectively.

5.3.2. Exchangenetworkdesign:usingMCDMtool

Henceforth, once the differentsolutions of the developed MO optimizationmethod havebeenobtained,the continuationofthe methodconsistsinusingtheMCDMtoolAHPtodeterminethe op-timalfinal solution.Thisprocessconsistsofselectingaweightfor eachpair ofcriteria. In thiscase, theweights were chosen tobe equallybalancedbetweentheNPV andtheinterdependence. Con-sideringthe NPV, the criterion applied in this casestudy is the percentageofloss of solutions inrelation tothe economic mini-mum(i.e.the initialpoint oftheprocedure). Thischoice ismade inordertoaccentuatetheNPVcriteriadifferencethatisoriginally thinbetweenEIP andstandalone mode.Indeed,a particularityof utility systems is that on a 20 years duration project, the oper-ationalcost tends totake over theinvestment costs. Whereas in thiscase study, the differenttechnologies for naturalgas boilers implantedhaveathinoperationalcostdifference.Tocontinue,the criteriaarenormalized usinglinearmax technic,whichhas been demonstrated to be the mostappropriate for AHP (Vafaeiet al., 2017).

TheAHPmethodledtoaweightof18.9%forthenumberof in-terconnections,49%forNPVcriteriaandfinally10.7%forthe max-imum and the average diameter of interconnections and forthe differencebetween Q1 andQ3. The aim wasto attribute equiva-lentweightsfor eachlevel ofFig. 6:NPV andthe package of in-terdependenceindicators.At thelower level,forinterdependence

indicators,allthecriteriahavethesameweight.Theresultsofthe AHPmethodforpairwisecomparisonaresummedupintable3.

This approach remains available for different strategies as weightscouldbechangedaccordinglytothepreferencesofthe de-cision maker. Indeed, inthis casestudy, equivalentweights have beenattributedto thedifferentclassesof criteriabutit could be adjustedasafunctionofthepreferredcriterion,ifthiscriterionis identified. In thiscase, the consistencyratio which evaluates the absenceof contradictionsinthe pairwise comparisonis1.3%. Ac-cordingtotheindicationsof(Saaty2002),itisvalidatingthe con-sistency ofweight allocation,because it islower than 10%. Then, theseweightswere appliedtothesetofsolutionsobtainedusing the developed procedure.Thus, Fig. 11 presentsthe value of cri-teriaforeach solutionobtainedandthe rakingattributedto each onewithAHP.

Therefore,the optimal solutionselected using AHPis the one with19 interconnections, its NPV is 0.12% higher than the mini-mum economicsolution,whilethe averageflowrateis48.5ton/h comparedto28.2ton/h.Asdescribedearlier,themaximum flow-rateisequivalentto thelimitedconstraint(i.e.71.6ton/h).Lastly, thedifference betweenQ1 andQ3 is significantlyreducedto the valueof4.8ton/hfrom34.3ton/hfortheinitialpoint.Thismeans that most interconnections are close in diameter in the selected solutionand thereforethat theinterdependence implied bymost oftheinterconnectionsisrelativelybalanced.

The corresponding designed network is provided below in

Fig.12.Forthesake ofclarity,some interconnectionstothesame companyhavebeenlinked,buttheyareindeeddifferent intercon-nections.Itistonotethatwiththismodelcompaniescanoperate instand-alonemode,ascompany4does.Withregard totheHPS,

Table 3

Standardized matrix for AHP method.

NPV Nb Interc Avg Interc Diam. Max Interc Diam. ࢞Q1Q3 Interc Diam. Weight

NPV 0,50 0,62 0,44 0,44 0,44 49,0%

Nb Interc 0,13 0,15 0,22 0,22 0,22 18,9%

Avg Interc Diam. 0,13 0,08 0,11 0,11 0,11 10,7%

Max Interc Diam. 0,13 0,08 0,11 0,11 0,11 10,7% ࢞Q1Q3 Interc Diam. 0,13 0,08 0,11 0,11 0,11 10,7%

thesolarPVhasnotbeenselected,whilesteamturbinesandwind turbinesaresetattheir maximumcapacity.Inthiscaseofan on-grid HPS, the selection of electrical sources is dueto their prof-itability,whichdependsonthepurchaseandsalepriceofexternal electricity(Mousqué etal.,2019).

Inconclusiontothissectionontheresults,theseanalysesshow theimportanceofusingaMOmethodwithcomplexsystemssuch as EIP exchange networks. Indeed, includinginterdependence in-dicator, the designed solution is significantly different from the mono-objectivesolutiononcost.

6. Conclusion

A model to optimally design an energy exchange network of an EIP, couplingautility systemcarrying steamandan HPS pro-vidingelectricpowerhasbeenpresented.Itallowstosize energy sourcesfortheutilitysystem(i.e.boilersandturbines)andtosize renewable energy sources such assolarPV panelsand wind tur-bines. It optimizesthe planningto supplythe energydemand as wellastheresources purchasetooperatetheenergynetwork(i.e. fuels, waterto producethesteamandoutsourcedelectricpower) withdatavarying overperiods.Theoptimizationisdone through aneconomiccriterion(i.e.NPV)andaninnovativeinterdependence indicator.

This interdependence indicator is representative to company stakes whenengaging intoEIP,i.e.they want tokeep their inde-pendencetomaintaincontrolovertheirownindustrialsite.

The objectives of thisMO optimizationprocedure are then to provide exchange networks with maximum economic gain and minimum dependencebetween companies andthereforerisks to engage.Thisindicatoris takingintoaccount thenumberof inter-connectionsandthewholeexchangeflowsinthenetworkby mea-suringtheirdistribution.

Finally,aniterativeprocedurefortheoptimizationofthe inter-dependenceofcompaniesandforsolvinglargeMILPproblemshas been provided. This procedure consists of obtaining a set of so-lutions byremoving one interconnectionfromtheminimum eco-nomic solution to the minimum of interdependence (i.e. stand-alonemode). Inordertocontaintheinterdependencesub-criteria of flow distribution inthe whole network, the principle isto fix amaximumdiameterofinterconnectionconstraint.Thefinal solu-tionisthenselectedusingtheAHPtool.

As a result, this developed resolution procedure hassolved a large case study of 15 companies taken from Yeosu EIP while classicaloptimizationmethodcouldnot solveit(i.e.lexicographic method).Resultsshowthatthismethodprovidessignificantly im-proved resultsintermsofinterdependencewitha slightlyhigher cost.

Perspectives for this research work that addresses the inter-dependence ofcompanies were identified asthe integrationof a flexibilityindicator(i.e.theabilitytowithstandflowvariations)as wellasaresilientindicator(i.e.thecapacitytosupportthe depar-ture ofa company fromthe network withminimal impact). Fur-thermore,thisstudyfocuseson thewhole EIP optimization,next

studiescouldconsiderindividualplantobjectives,forthispurpose, amongmethods,gametheoryisparticularlysuitable.

DeclarationofCompetingInterest

Theauthorsdeclarethattheyhavenoknowncompeting finan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

CRediTauthorshipcontributionstatement

Florent Mousqué: Methodology, Formal analysis, Writing -originaldraft,Methodology.MarianneBoix:Investigation,Writing - review& editing.Ludovic Montastruc: Formal analysis, Valida-tion,Formal analysis.Serge Domenech:Supervision, Supervision.

StéphaneNégny: Supervision, Data curation, Writing - review & editing,Supervision.

Aknowledgements

ThisworkwassupportedbyagrantoverseenbytheFrench Na-tionalResearchAgency (ANR)aspart oftheprogram DS0302for theGREENSCOPEproject(ANR-16-CE10-0001).

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