# Probabilistic Estimation of the Energy Consumption and

## Transcript Of Probabilistic Estimation of the Energy Consumption and

energies

Article

Probabilistic Estimation of the Energy Consumption and Performance of the Lighting Systems of Road Tunnels for Investment Decision Making

Antonio Bracale 1 , Pierluigi Caramia 1 , Pietro Varilone 2 and Paola Verde 2,* 1 Department of Engineering, Università di Napoli “Parthenope”, 80143 Naples, Italy; [email protected] (A.B.); [email protected] (P.C.) 2 Department of Electrical and Information Engineering, Università di Cassino e del Lazio Meridionale, 03043 Cassino, Italy; [email protected] * Correspondence: [email protected]; Tel.: +39-0776-299-3638

Received: 2 March 2019; Accepted: 15 April 2019; Published: 19 April 2019

Abstract: This paper presents a probabilistic model for supporting the process of decision making about the value of new lighting systems in existing road tunnels when some data and parameters are aﬀected by uncertainty. The proposed model, which we have called Probabilistic Energy Screening of Tunnel (PrEST), accounts for both the technical performance and the economic objectives of the new lighting systems. The technical performance is described on an adequate (x, y) plane that was deﬁned by two indices. The ﬁrst index measured the consumption of electricity per kilometre of tunnel lengths; the second index measured the performance of the lighting systems per unit of illuminated area. The economic results were measured by the net present value of the savings and by the payback period. Both the terms account for initial capital investments, energy and maintenance costs. PrEST was applied to two real road tunnels in service in Italy showing that the statistics of the results can support a ﬁnal decision in function of the business strategy.

Keywords: lighting systems; energy eﬃciency; light performance

1. Introduction

Adequate levels of visibility on roads allow pedestrians to walk minimizing the risk of accidents; further, in the town, they can also enjoy the space around perceiving a sense of security against aggressions or thefts [1]. The lighting systems of roads and tunnels are essential for the security of the citizens and for the safety of the drivers. Good luminosity on roads and in tunnels is strictly linked to the safety of the vehicle driving. The driver must be able to detect the presence of obstacles, to perceive any changes in driving conditions without developing a sense of uncertainty or, even worse, fear.

With reference to the safety of vehicle driving, National and International Standards, such as those of the Commission Internationale de l’Eclairage (CIE), state the requested levels of minimum illuminance within accepted boundaries for limiting other aspects like glare or the lack of vertical uniformity. In particular, the lighting systems of a tunnel (LSTs) must be designed following the minimum luminance proﬁle, as reported by the European Standard [2]. The standard gives the required values of the luminance along the longitudinal axis of the tunnel versus the travel time along the tunnel at the reference speed (the reference speed is equal to the speed limit in the tunnel; the value is provided by the operator of the road where the tunnel is in service), as Figure 1 shows.

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Figure 1. Plot of the required luminance L along the longitudinal axis x of the tunnel for diﬀerent Figure 1. Plot of the required luminance L along the longitudinal axis x of the tunnel for different reference speeds [2]. reference speeds [2].

The performance of the lighting system for a LST in terms of quantity and quality of luminosity is onlyTohnee poefrtfhoermprainncceipoafltahsepleigchtstitnogascycsotuemnt ffoorr ainLtShTeidnetseirgmnsstoafgqeu. aTnhtietyfuarntdheqruaaslpiteycot frelufemrsintoostihtye iesnoenrglyy oconnesoufmthpetiporni.ncipal aspects to account for in the design stage. The further aspect refers to the energTyhceoLnSsuTsmrpetpiorens.ent the most electricity-consuming loads for the companies that manage the primTarhyerLoaSdTss. rSeuprrveesyesntshthowe mthoasttlieglhectitnrigcictoyn-csounmsuesm3i0n%g loofatdhse feonrertghye ccoonmsupmaneidesbtyhtahtemmaencahgaenitchael panridmealreyctrroiacdals.sSyustrevmeyssisnhohwighthwaatyligtuhntinneglscoannsdumtheast3t0h%e toufnthneelenliegrhgtyincgoncosustms eadrebay tlhoessmfoecrhtaunnincaell amnadnaegleecmtreicnatldseypsatermtmseinntsh[i3g,4h]w. ay tunnels and that the tunnel lighting costs are a loss for tunnel manaTgeecmhneonltodgiecpaal ritnmnoevnatsti[o3n,4s]i.n lamps with the introduction on the market of solid state lamps using LightTEemchinttoinloggDiciaoldiensn(oLvEaDtiso)nhsasincelratmaipnslywreitdhucthede tihnetrpordoubclteimonoof nentehregymcaornkseutmopf tsioolni,dbsuttaittedliadmnpost uersainsegiLt iagthatllE. mLEitDtisngarDe isoudreelsy(cLhEaDrasc)theariszecderbtayinalnyirnecdreuacseeddtehﬃe cpireonbclyemvaolufeemneeragsyurceodnsinumlupmtieonn/,Wbauttt (itlmdi/dWn),obtuetrathsee iptaarttiaclul.laLrEaDpspalirceastiuorneslyocfhthareascetelarmizepds ibnytahne itnucnrneealssedstielflfrieciqeunicryesvtahleueinmsteaallsautrioedn ionf lsuomlidens/tWateatltam(lmps/Ww)i,thbuathtihgeh ppaorwticeur lvaarluape,pelivceantioifnlsowoferthtehsaenltahmopses oinf gthase dtuisncnhealrsgestliallmrepqsuwirieths tthhee isnasmtaelllautmioennosf. solid state lamps with a high power value, even if lower than those of gas discharge lampTshweitchotmhpe asnamiese ltuhmatemnsa.nage a large set of tunnels have the problem of sorting the LTSs for plannTihneg cionmvepsatmnieesnttshoatvemraanadgeeﬁnaeldartgime eseht oorfiztounn.neTlshehaovpetitmhealpsroorbtilnemg mofussot rctoinngsidtheer LboTtShs tfhoer ptelcahnnniicnagl rienqvueisrtemmeennttss oavnedrthaedneefeindefdortitmheerehdouricztoionn. oTfhteheopentiemrgayl csoonrtsiungmpmtiuosnt. consider both the technIincatlhreeqsupierceimaleiznetds alnitdertahteurnee,etdhefoarstpheecrteodfuectnieorngoyfctohneseunmerpgtyiocnonosfuLmSpTtsiohna.s been faced from diﬀerIenntthpeosinptescioaflivzieedwl[it5e–r9a]t.uIrne,[5th],ethaespaeuctthoofrsedneeargltywciothnstuhme pentieorngyofreLqSuTirsemhaesnbtseeonf tfhaecelidghfrtionmg dsyifsfteermenstipnoeinmtserogfevniceywco[5n–d9i]t.ioInns[5w],htehne aaunthacocrisddeneatlot cwcuitrhs.thTeheenyersghyowreqauciaresemsetnutdsyofinthwe hliigchhtitnhge seynsetregmyscionnseummerpgteionncyfocronbdaictkio-unps wanhdensaafnetayccoifdtehnet eomcceurrgse. nTchyeyligshhtoiwngaacreasceosvteurdedy ibnywmheicahnsthoef penheortgoyvoclotanicsupmanpetliso,ngefnoerrabtaicnkg-uapcaashndﬂoswafeatbyleotfo tphaeyebmacekrgtheneceyxtlriagihntvinegstmareentcoinveprheodtobvyolmtaiecasn. sThoef pcohnottroivboulttiaoinc [p6a]nperlos,pgoesnesertahteinegstaimcaastihonfloowf thaebleenteorgpyaycobnascukmthpetioexntsraofinthveesLtmSTesnitnitnhpehdoetsoigvnolstataicgse. Ttahkeincgonptrroipbuertliyonin[t6o]apcrcoopuonstetshethaedevsatnimtaagteios nofotfhtehpeoewneerrgcyoncsounmsupmtiopntiosanvsinogf sthoebtLaSinTasbilne bthyeindteesringanl slutamgientaankciengrepgruolpateirolny.into account the advantages of the power consumption savings obtainable by internPaalpleurm[7i]npanrocpeorseegsuilmatpioronv. ing the global performance of the lighting systems in a tunnel, by using new rPoaapderp[a7v]inpgrompoasteesriiamlspcrhoavriancgtetrhiezegdlobbyalapheirgfhoermr raenﬂceectoiof nthceoleigﬃhctiienngtstyhsatnemotshienr aortduinnnaerly, bayspuhsainltgs. new road paving materials characterized by a higher reflection coefficient than other ordinary asphalts.

In [8,9], the Energy Screening of Tunnel (EST) model was introduced to handle both the aspects of reducing the energy consumption and improving the lighting performance, in an integrated way.

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EnergiIens 2[081,99,]1,2t,hxeFOEnRePrEgEyRSRcErVeeIEnWing of Tunnel (EST) model was introduced to handle both the aspe3ctosf o21f

reducing the energy consumption and improving the lighting performance, in an integrated way. EST EalSloTwasllroewprsesreenptrinesgeenvtienrgy LeSvTeriyn aLSCTaritnesiaanCpalratnesei{aenlepctlrainciety{ceolencsturimciptytiocno,npseurmfoprtmioann,cep}eirnftorromduancicneg} ianptprorodpurciiantge ianpdpircoeps.riIante[9i]ntdhiecerse.sIunlt[s9o] fththeerEesSuTltms oodf ethl ewEeSreTamlsoodveelrwiﬁeerde baylsmo evaenrisfioefdebxypemriemanenstoafl emxepaesruimreemnetanltsmoenastuherermoaedn.tsTohne tEhSeTrmoaodd.eTlhweaEsSnTomt aotdoeollwfoarsdneostigantionogl nfoerwdLesSiTg.nEinSgT,ninewsteLaSdT, .wEaSsTa, vinasltueaabdl,ewmaesaan vfoarlusaobrtlienmg ethaendfoecrissoiorntinogf tthheeidnevceisstimonenotfstthoeminavkeestomnesnetvsetroalmexaiksetinogn LseSvTesrtaalkeinxigstiinntgo LacScTosutnakt ibnogthintthoeaaccvoeurangt ebolitghhtthinegavpeerrafgoermligahntcienganpdertfhoermavanercaegaenedntehregayvceornagsue menpetrigoyn.consumption.

IInn tthhiiss ppaappeerr,, ssttaarrttiinngg ffrroomm tthhee iinniittiiaall vveerrssiioonnss ooff EESSTT pprreesseenntteedd iinn [[88,,99]],, wwee ﬁfirrsstt iimmpprroovveedd tthhee mmooddeell bbyy iinncclluuddiinngg aann eeccoonnoommiicc mmoodduullee.. TThhiiss eeccoonnoommiicc mmoodduullee aalllloowwss ccoommppaarriinngg tthhee iinnvveessttmmeennttss rreeqquuiirreedd ffoorr iimmpprroovviinngg tthhee eenneerrggyy eefﬃficciieennccyy aanndd tthhee lliigghhttiinngg ppeerrffoorrmmaannccee ooff aannyy LLSSTT.. BByy uussiinngg tthhee eeccoonnoommiicc mmoodduuleleoonneecacnanhahvaevaen aidneaidoefathoef ctohset acsossotcaiastseodciwatiethd dwiﬀitehrendtiftfeecrhennitcatelcshonluictiaolnssoclauptiaobnles coafpimabpleroovfinimg pthroevpienrgfotrhme apnecrefoorfmthanecLeSoTfitnhteerLmSTs oinf ctoernmsusmopf tcioonnsaunmdpltiigohntianngdeﬃligchietinncgy.eTffhiceinen, wcye. Tdheaelnt,wwitehdtehaeltfuwrtihtherthperofublretmherthpartorbelaelmly cthaantcroenadlliyticoannthcoenddeictiisoionnthoef tdheeciisnivoenstomf tehnetsi:ntvheestumnceenrttsa:itnhtey uthnactearﬀtaeicnttsysothmaet oaffftehcetsdsaotamoef tohfethperodbaletamo. fTtohtehipsraoibmle,mw.eTtroanthsifserariemd,thweemtroadneslfEerSrTedonthaepmroobdabelilEisStiTc obnasaisparnodbapbriolipstoicsebPasriosbaanbdilipsrtiocpEonseerPgryobSacbreileinstiincgEonferTguynSncerle(ePnriEnSgTo)f. ITnupnnaretlic(PurlaErS, Tw).eIﬁnrpsat ratnicaulylasre, wthee fmiroststainmalpyosretatnhteEmSoTsitnipmuptodratatanat nEdSTpainrapmutetdearstathaantdrepqaurairme ethteersintthroadt urecqtiuoinreotfhreanindtormodvuacrtiioabnleosf. Trahnedno, mthevaprrioabbalebsi.liTsthicente, cthhneipqruoeboafbialnisatliycstiescihsndiqesuceriobfeadnianlydseistaiislsd. escribed in details.

TThhee ppaappeerr iiss ssttrruuccttuurreedd aass ffoolllloowwss:: EESSTT iiss rreeccaalllleedd iinn SSeeccttiioonn 22 sshhoowwiinngg tthhee aaddvvaanncceemmeennttss iinn rreessppeecctt ttootthheepprerceecdedininggpappaepresr[s8,[98],;9t]h; ethperopbraobbialibsitliicstmicodmeolldineglliPnrgESPTrEisSTpriessepnrteesdeninteSdecintioSnec3t;isoonm3e; snoummeenriucmalerreiscualltrsesaureltsshaorewsnhoinwSneicntiSoenct4iowni4thwrietfherreefnecreentocestoomsoemLSeTLsSaTcstuacatlulyalilny sinersveircveicine iIntaIltya.ly.

2. RReeccaallll aanndd Immpproveements of the Model EST

The EESSTTmmodoedleplrepsreensteendteind[8i,n9][w8,a9s] imwparsovimedpbroyviendtegbryatiinngteagsreactitniogn faorseccotinoonmfioc reveaclounatoimonisc; ethvealnueawtiovnesr;stiohne nofewESvTecrosinosnisotsf oEfStTwcoonmsoisdtus loefs,twnaommeolydtuhlest,enchamniecalyl mthoedtuecleh,nTicMal, amnoddtuhlee,eTcoMn,oamnidc tmheodeucolen,oEmMic(Fmigoudruele2,).EM (Figure 2).

Assignment of input data: Tunnel structure and installations

Technical Module “TM”

Economic Module “EM”

For each LST solution: Position on the Cartesian plane (electricity

consumption, performance). Evaluation of Net Present Value and

Pay-back period

Figure Figure

2. 2.

EESSTT

wwiitthh

tthhee

tteecchhnniiccaall

TTMM,,

aanndd

tthhee

EEccoonnoommiicc

MMoodduullee

EEMM..

TM, based on the model developed in [8,9], allows representing any LST on the same Cartesian planeTM{el,ebcatrsiecdityoncothnesummopdteilodne, vpeelrofpoerdmiann[c8e,}9.],Tahlleowobsjerecptirveeseonfttinhge aTnMy LwSaTs othnethdeersiavmateioCnarotfestiwano pinladnicees{e, loencterilcinitkyedcotnosuthmepatvioenra, gpeerlifgohrmtinagncpee}.rfTohrme aonbcjeectoifvethoefLtShTe, tThMe owthaesrtlhinekdeedritvoatthioenavofertawgoe indices, one linked to the average lighting performance of the LST, the other linked to the average power consumption. The choice of these indices was motivated by the need to represent on the same Cartesian plane {electricity consumption, performance} every LST, using the actual service conditions and in the new service conditions due to possible interventions. Such a representation on

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power consumption. The choice of these indices was motivated by the need to represent on the same Cartesian plane {electricity consumption, performance} every LST, using the actual service conditions and in the new service conditions due to possible interventions. Such a representation on the same Cartesian plane allowed comparing several LSTs with each other, and for the same LST, diﬀerent possible interventions for making decisions on a long time horizon, when several LSTs are managed by the same company. TM is not a tool for designing a LST.

EST was conceived as a tool for supporting the decisions of the manager of several LSTs about the investments for upgrading them both for the illumination performance and for the energy consumption, providing a screening of their operating conditions (current conditions and estimated future conditions linked to possible alternative interventions) without performing detailed in ﬁeld measurements. This is the great advantage of using EST according to the methods usually adopted for having information and data on the current operating conditions of several LSTs. Usually, the managing company must measure the luminance in the ﬁeld. This is a very expensive activity in time, in human resources, and indirect costs linked to the need for limiting, deviating or stopping the traﬃc. EM, added in this paper to EST, allows comparing the investments faced for improving the energy eﬃciency and the lighting performance of any LST.

2.1. The Technical Module TM

The key idea at the basis of the TM of EST was to represent any LST on the same Cartesian plane {electricity consumption, performance} by means of proper variation indices with the respect to the LST of reference, namely the LST* [10].

The choice of the LST* was eﬀected on the basis of the incentives given in Italy to promote the energy eﬃciency investments. The national authority for the regulation on the energy, Autorità di Regolazione per Energia, Reti e Ambiente (ARERA, formerly AEEG) stated with the resolution [10] in which cases ﬁnancial incentives were recognized for installing new LSTs. Note that in other countries, the LST* can be diﬀerent in function of the local regulations. For example, in [11] diﬀerent strategies for supporting the investments on energy eﬃciency in the diﬀerent USA states are listed and commented.For the primary roads, three types of structure of LST were deﬁned as baseline cases. They are the LSTs whose performance, in terms of energy consumptions and lighting, must be overcome for obtaining the incentives. Each baseline was proposed by ARERA with characteristics adequate for guarantying the respect of the European Standard [2]. The main characteristics of the baseline cases proposed by ARERA in [10] are listed below. The data common to every LST* are:

- 100 W sodium high pressure (SHP) lamps, with 14 W of auxiliary circuits, reduced power during the night to 59 W with invariant power of auxiliary circuits;

- eﬃciency equal to 61 lm/W; - the lamps have a color rendering index not greater than 60 so that the lighting category of the

road is not reduced; - 13 h of operation during the morning, 11 h of operation during the night, 365 days of

annual operation; - height of whitewashed walls equal to 3.0 m; - LSTs which have the lines of luminaires equipped with lamps placed sideways are assimilated to

the ones with luminaires equipped with lamps placed in line above the roadway: - for the short tunnels, e.g., those according to [2] of length up to 125 m, the lighting level is

assumed equal to 100% of that provided for the long galleries.

The characteristics diﬀerent for each of the baseline cases reported in [10] are:

- single central line of luminaries with 10 m of spacing, 100 luminaires/Km; - double central line of luminaries with 9 m of spacing, 222 luminaires/Km; - triple central line of luminaries with 9 m of spacing, 333 luminaires/Km.

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Starting from the baseline cases proposed by ARERA in [10], we extended the baseline cases

for covering most of the actual roads in operation, that is dual or single carriageway, single-way or

double-way road with diﬀerent speed limit values, and considering the three possible conﬁgurations

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of the lines of luminaires (single, double or central line). For all the baseline cases, comprising

ftrheoesweaprreopproosgerdambyDAiaRlEuRx A[12in], [n1o0t],awvaeilﬁarbsltelyindtehveeDloipaeludxtlhibermaroyd. eBlys fmoeraunssinogf Dthiealfurexe, wthaerleupmriongarnacme

pDrioafliulex o[1f 2e]v,enroytbaavsaeillianbelewianstvheeriDfiieadluinx laicbcroarrdy.anBcyemweitahntshoefsDtainadluaxr,dth[2e].luInmsionadnociengp,rwoﬁelereoafliezvederay

lbiabsrealriyneofwbaassveleirniﬁe ecdasiens,acLcSoTrd*,afnocrecwomithpathriensgtaanndyaLrdST[2i]n. Itnhesostduodiyngw, iwthetrheeamliz.ed a library of baseline

casesF, oLrSeTv*e, rfyorLcSoTm* poaf rtihnegbaansyelLinSeTliibnrtahrye,swtuedcyowmipthuttehdemtw. o indices of reference: LPi* and ECi*. LPi*

is theFaovreervaegreyiLllSuTm*ionfanthcee bfoarseelainceh lsiqburaarrye, wmeetceormofptuhteedLStwTio; EinCdi*ic, eiss tohfereafnenreunaclee:nLePrgi*yacnodnEsuCmi*p. tLioPni*

pisetrhkeilaovmereatgere oilfluthmeinLaSnTci*e. for each square meter of the LSTi; ECi*, is the annual energy consumption

per kWiloimtherteefreorefnthcee LtoSTFii*g.ure 2, the TM starts with the assignment of the data of the tunnel, of the

road,Wainthd roeffetrheencLeStTo.FTighuerem2a,itnhedTatMa stotaratssswiginthatrhee: alesnsiggtnhm, wenitdothf tahneddahteaigohf tthfeortutnhneelt,uonfntehle; rdouaadl,

caanrdrioafgtehweaLySsT.oTrhseinmgaleincdaarrtiaatgoeawsasiygsn, aarned: lsepnegethd, wlimiditthfaonrdthheeigrohatdfo; rstthruecttuunrnee(ls; idnugalel ccaernritargael wlianyes,

dorousibnlgelececnatrrrailaglienwe,atyrsi,palendcesnpteraeldlliinme)itafnodr tchhearroaactde;rsistrtuiccstuorfeth(seinlagmlepcsen(ptroawl leinr,ee, fdfoicuiebnlecyce, naturxaillilainrey,

stryisptleemcse)nftorarltlhineeL)SaTn.d characteristics of the lamps (power, eﬃciency, auxiliary systems) for the LST.

FFoorr eevveerryy LLSSTTii,, wweeccoommppuuteteddththeeeneenregrygycocnosnusmumptpiotnioinndinedx,eEx,CEi,Cain, danthdetihlleumilliunmaninceanincedeixn,dLePxi,.

LFiPnia. lFlyin, caollnys,idcoenrisnigdethriengbatsheelinbeasLeSliTnie* cLoSrTrei*spcoonrrdeisnpgotnodeinvgerytoLeSvTeriny sLtuSTdyi,nitswtuadsyp,oistswibales tpoocsosimblpeuttoe

cthoemfpoulltoewthinegfovlaloriwatiinogn vinadriiacteiso:n indices:

∆ECi = ECi − ECi*

(1)

∆ECi = ECi − ECi*

(1)

∆∆LLPPIiIi== LPii −−LLPPii**

(2()2)

If ∆EECCii iiss ggrreeaatteerr tthhaann zzeerroo,, the consummppttiioonn mmuusstt be reduced; otherwiissee,, thee consumppttiioonn is acceppttaabbllee.. IInnaassiimmiillaarrwwaayy,,iiff ∆∆LLPPiiisislleesssstthhaannzzeerroo,, tthhee lliigghhttiinngg ppeerrffoorrmmaannccee hhaass ttoo be improved otherwise it is acceptable.

The importtaanntt rreessuulltt ooff the TM, which wass an intermmeeddiiaattee rreessuulltt ooff EST, is the representation of every LST on the Cartesiann plannee shoowwnn iinn Figure 3 where three LSTs were reepresented [9]. It is evident tthhaattnnooLSLTSTfalflasllisn tinhetsheecosnedcoqnudadqruaandtrwanhterwe hbeorteh tbhoethentehregyecnoenrgsuymcpotnisounmanpdtiothnealingdhttihneg lpigerhftoinrmg apnecrefoarrme aanccepatraebalec.ceptable.

Figure 3. Cartesian plan {electricityy connssuummppttiioonn,, ppeerrffoorrmmaannccee}}wwiitthhtthhrreeee LLSSTTs represented with a green triangle, red square, and blue rhombus [9].

The LST corresponding to the green triangle requires a reduction of the energy consumption, the LSTs corresponding to the red square and to the blue rhombus primarily need improved lighting performance.

Once obtained the characterization of every LST on the Cartesian plane of Figure 3, the TM allows evaluating the new values of (∆ECi)k and (∆LPi)k for any kth possible intervention aimed to

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The LST corresponding to the green triangle requires a reduction of the energy consumption, the LSTs corresponding to the red square and to the blue rhombus primarily need improved lighting performance.

Once obtained the characterization of every LST on the Cartesian plane of Figure 3, the TM allows evaluating the new values of (∆ECi)k and (∆LPi)k for any kth possible intervention aimed to reduce tEhneergeinese2r0g1y9,c1o2,nxsuFOmRpPtEioEnR RanEVdIEimWprove the lighting performance. Using Equations (1) and (2) in w6 hofic2h1 tinhewrehfiecrhenthcee vraelfuereesnLcPei*vaanludesECLiP*i*araenudnEchCai*ngaered,uitnicshpaonsgseidb,lei,tfoisr pevoessryibsleo,lufotironevkertoy ismolpulteimonenkt itno eimveprlyemLSeTnit, itnheevcoemrypLuStaTtii,otnheofcothmepnuetwatvioanluoefotfhtehneeiwndvicaelsue(∆oEfCthi)ek iannddic(e∆sL(P∆iE)kC.i)Bkyansodd(∆oLinPgi),kw. Beycasno vdeoriinfyg,iwf aencyaonfvtehreifpyoisfsaibnlye oinfttehrevepnotsisoinblceainntderrivveenetaiocnh cLaSnTidirnivteheeascehcoLnSdTqi uinadthreanste.cond quadrant.

FFiigguurree 44 iiss aann eexxaammpplleeoofftthheerreessuullttssoobbtataininaabblelefoforroonneeoof fththeeththrereeeLLSTSsTsrerperperseesnetnetdedininFiFgiugruer3e. I3n. Ipnarptiacrutilacur,lFairg, uFriegu4rseho4wsshothweseﬀtheectesfofefcttws oofditﬀweoredntififnetreernvtenintitoernvsetnhtaitonwsertehactonwseidreerceodntsoidimerperdovtoe timhepLroSvTerethpereLsSeTntreedpirnesFeingtuerde i3nwFiigthurthee3gwreitehntthreiagnrgeleen. Ttrhiaencgolnes.iTdheerecdoanlstiedrenraetdivaelstewrneraeti:ves were: -- NeNwewSHSHP:Ps:usbusbtisttuittuintigngsosdoiduimumhihgihg-hp-rpersessusruereddisicshcahragrege(S(SHHPP) )wwitihthhhiigghheerr eefﬃficciieennccyy ffoorr tthhee

exeisxtiisntginSgHSPH; P; -- LELDE:Dsu: sbusbtistutittiuntginLgELDEDlumluimnainiraeisre(SsH(SPH)Pfo)rfothretheexiesxtiinstginSgHSPH. P.

150

∆LP [lm/m2]

i

100

50

0

-50 Actual

-100

New SHP

LED -150

-200 -150 -100 -50

0

50 100 150 200

∆ECi [MWh/year*km]

Figure 4. Cartesian plan {electricity consumption, performance} with the alternative interventions on the LST represented inn Fiigguurree 33 wwiitthh tthhee ggrreeeenn ttrriiaannggllee..

IItt iisseevvidideennttfrformomFiFgiugruer4e t4hatthaaltl athlletihneteirnvteenrtvieonntsioimnspriomvpertohveeLtShTe oLpSeTraotipoenr,aitniofnac, ti,nthfeacpto, itnhtes rpeopinretssernetpatrievseenotfatthiveemoofdtihﬁeedmLoSdTisfibedeloLnSgTstobtehleonsegcotondthqeuasedcroanndt. Tqouasdurpapnot.rtTtohesﬁunpaplodrtectihseiofninoanl tdheeciisnivoenstomnetnhtetoinfvaecsetmamenont gtothfaocsee asomluotnigontsh,owsehiscohluimtiopnros,vwedhtichhe pimerpforormveadnctheeofpeearfcohrLmSaTni,cEe SoTf eruacnhs tLhSeTei,coEnSoTmruicnms tohdeuelceoEnMom, dicesmcroidbuedleinEMth,edfeoslcloriwbeindginsetchteiofno.llowing section.

22..22.. TThhee EEccoonnoommiicc MMoodduullee EEMM TThhee EEMM ssttaarrttss wwiitthh tthhee aassssiiggnnmmeenntt ooff tthhee ddaattaa ffoorr tthhee ppoossssiibbllee ssoolluuttiioonnss wwhhiicchh rreessuulltteedd iinn tthhee

TTMM aaddeeqquuaattee ffoorr iimmpprroovviinngg bbootthh tthhee ininddiicceess,, ((∆∆EECCii))kk aanndd ((∆∆LLPPii))kk.. FFoor reeaachchLLSSTTi i ssoommee ppoossssiibbllee ssoolluuttiioonnss ccaannbbeeininsstatalllilninggﬂfuluxxrergeuglualtaotrosrosnotnhetheexiesxtiinstginlagmlapms apnsdanludmliunmaiirneasi,rseusb, sstuitbusttiintugtlianmg plasmanpds launmdinluamireins awirieths hwigithherhliugmheirnoluums eiﬃnocuascyefffoircathcye efxoirsttihneg eoxniesst,inogr ionnsteasl,lionrg inneswtalllaimngpsnaenwdllaummpinsaairneds wluimthinﬂauixrersewguitlhatfolrusxorregduimlamtoerrsso. rNdoitme mtheartsi.nNtohteeftohlalotwininthge, tfoolalovwoiidngv,etroboasveonidotvaetriobnostehneostuabtisocnripthtei rseufbesrcreridpttoi rinefdeerxretduntoneinl,dwexilltunnotnbele, uwsielldn. ot be used.

FFoorr eevveerryykktthhssoolulutitoionn, ,ththeemmaianindadtaataaraer: ep:opwoewr,elru, mluimnoinuos uesﬃecfafcicya, cnyu,mnbuemr,buesre, fuuslelfifuel, ltioftea,ltcootastl ocof stht oeflathmeplsa,mthpes,luthmeinluamireinsaainredstahnedauthxeilaiaurxieilsi,acroiesst,ocfotshteomf tahientmenaainntceen, atanrcieﬀ, otafrtihffeoefntehregye,naenrgdys,oanond. so on. All these data permit the computation of the cost of the existing LST, named annual cost of the old solution (KAn)OS to face in the year n, and of the improved (LSTi)k, named annual cost of the new kth solution (KAn)k to face in the year n.

For the computation of the annual costs of the old solution and of any new solution, the

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All these data permit the computation of the cost of the existing LST, named annual cost of the old

solution (KAn)OS to face in the year n, and of the improved (LSTi)k, named annual cost of the new kth solution (KAn)k to face in the year n.

For the computation of the annual costs of the old solution and of any new solution, the economic

model of the CIE [13] deﬁnes the hourly cost of an LST taking into account all the components of cost

arising during the annual operation from the costs for installation to those for the maintenance. This

model of the cost is very valuable when the cost and saving estimation is performed on a one-year basis.

When the ﬁnancial analysis is extended in a time period longer than one year, the economic

model of the annual cost of the old solution and of any new solution is more eﬀective if the costs of the

investments are separated from the other costs. This choice allows for estimating the cash ﬂow taking

into account the time value of the money. With this choice, the annual cost (KAn)OS and (KAn)k faced in the year i are:

(KAn)os = (KAIn)os + (KAOn)os

(3)

(KAn)k = (KAIn)k + (KAOn)k

(4)

where (KAIn)os and (KAIn)k are the costs for acquiring and installing the lamps CLampn os and the luminaires (CLumn)os of the old solution, and of any new k solution CLampn k and (CLumn)k, respectively; (KAOn)os and (KAOn)k are the other costs to face in each year for the old solution and for any new k solution.

The costs (KAOn)os and (KAOn)k are derived from the hourly costs (KAOnh)os and (KAOnh)k as:

(KAOn)os = (KAOnh)os ∗H

(5)

(KAOn)k = (KAOnh)k ∗H

(6)

where H is the number of operation hours during each year n. The expression of the hourly cost in the year n, (Knh)j for any j solution is given by:

(Kih)j = (CMatih)j + (CEnih)j + (CMaintih)j + (CFih)j

(7)

with j =

os for the old solution k for any new solution

In Equation (7) (CMatnh)j is the hourly cost in the year n of all the materials with the exclusion of the lamps and luminaires, (CEnnh)j is the hourly cost in the year i of the electric energy consumptions, (CMaintnh)j is the hourly cost in the year n of the maintenance, (CFnh)j is the hourly cost of further possible interventions. The Appendix A presents the expressions of the terms in the Equation (7).

Considering the Equations (3) and (4) with the position (5), the general expressions of the annual

cost of the year n of the old solution and of any new k solution are:

(KAn)os = (KAIn)os + (KAOnh)os ∗H;

(8)

(KAn)k = (KAIn)k + (KAOnh)k ∗H.

(9)

Starting from the knowledge of the annual cost of the old solution, (KAn)OS, and of each kth new solution, (KAn)k, EM allows performing the ﬁnancial analysis. In the actual version, EM evaluates two main ﬁnancial quantities for the alternative k. They are the net present value of the total savings,

NPVSk and the discounted payback period, PBk.

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The NPVSk is the current worth of the future saving of money or stream of cash ﬂow, given a speciﬁed rate of return α. Considering a period of N years in which we perform the ﬁnancial evaluation. For every new solution k, the NPVSk is given by:

N DKAn + DCEnn ∗ (1 + β)n−1

NPVSk =

n−1

(10)

n=1

(1 + α)

where is variation rate of the energy cost, DCEnn is the variation of the cost of electric energy of each

year n given by:

DCEnn = (CEnn)os − (CEnn)k

(11)

with (CEnn)os = (CEnnh)os∗ H and (CEnn)k = (CEnnh)k∗ H.

In (10), DKAn is the variation of the annual costs between the old solution and the new kth

solution given by:

DKAn = (KAn)os − (KAn)k

(12)

where (KAn)os and (KAn)k are the annual cost, other than the annual energy cost, to be incurred in each year n for the old solution and for the new solution, respectively.

The values of (KAn)os and (KAn)k depends on the year n since in each year we must include the cost of all the replacements, if any. For the old solution, we considered the cost of only the replacements

of the existing lamps when they end their life; for the new solution we considered to replace all the

materials only at the ﬁrst year; for the successive years, we assumed to replace only the lamps. For any

solution j, this implies that:

LLamphj

LLampj ≤ N; LLampj = 8760 ,

(13)

LLumhj

LLumj > N; LLumj = 8760 ,

(14)

Lmathj

LMatj > N; LMatj = 8760 ,

(15)

where LLampj, LLumj, LMatj are the nominal life in years of lamps, luminaires and materials of the jth solution, respectively, and LLamphj , LLumhj , Lmathj are the corresponding lives expressed in hours.

Let’s consider the number of substitution to face in the period N for the old solution, NSos, and

for any new solution k, NSk; they are given by:

N NSos = LLampos (16)

N NSk = LLampk (17)

where the symbol x represents the ceiling function which maps x to the least integer greater than or equal to x.

Taking into account the relation (16), for the old solution, the following considerations are valid in function of the value of n. For the ﬁrst year and for every year in which no substitution takes place, the expression of (KAn)os is:

(KAn)os = H∗[(CMaintnh)os + (CFnh)os]

for n = 1, . . . , N

n

p ·LLampos

(18)

p = 1, . . . , pmosax

pmosax = NSos − 1

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For every year during which the lamps are replaced, the expression of (KAn)os is:

(KAn)os = CLampn os + H∗[(CMaintnh)os + (CFnh)os ]

for n = p ·LLampos

(19)

p = 1, . . . , pmosax

pmosax = NSos − 1

Taking into account the relation (17), for any new solution k, we added in the ﬁrst year also the cost of the replaced components of the lighting system (lamps, luminaires and other materials), therefore the following expression of KAi k is valid:

(KAn)k = CLampn k + (CLUmn)k + H∗[(CMaintnh)k + (CMatnh)k + (CFnh)k ]

(20)

for n = 1.

For every year in which no substitution takes place, the expression of (KAn)k is:

(KAn)k = H∗[(CMaintnh)k + (CFnh)k]

for n = 2, . . . , N

n

1 + p ·LLampk

(21)

p = 1, . . . , pmk ax

pmk ax = NSk − 1

For every year during which the lamps are replaced, the expression of (KAn)k is:

(KAn)k = CLampn k + H∗[(CMaintnh)k + (CFnh)k ]

for n = p ·LLampk

(22)

p = 1, . . . , pmax

pmk ax = NSk k− 1

The term PBk gives the number of years it takes to break even from undertaking the initial expenditure, by discounting future cash ﬂows and recognizing the time value of money.

Considering the previous relations, we computed the PBk as the minimum value of the year m such that the following relation is satisﬁed:

m DCEnn ∗ (1 + β)n−1

m DKAn

−

≥ 0 m = 1, 2, . . . , N

(23)

n=1

(1 + α)n−1

n=1

(1

+

α)n−1

2.3. Intermediate and Final Outputs of EST

Summarizing, the intermediate and ﬁnal outputs are:

(i) representation on the same Cartesian plane of all EST, with reference to a set of LSTs, ar the LSTs of interest in the actual state of service;

(ii) identiﬁcation on the same Cartesian plane which LST is in an acceptable state of service (second quadrant), which LST needs intervention for reducing the energy consumptions and/or improving the lighting performance;

(iii) representation on the same Cartesian plane of the eﬀect of the interventions on every LST adopting one of the possible alternatives (substituting the luminaries and/or integrating luminosity regulation);

(iv) economic evaluation of every intervention on each LST; (v) sorting of the alternative solutions by means of the economic quantities NPVSk or PBk.

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It is evident that the decision maker can prioritize the interventions and make the best choice based on business policies and on the available initial capital costs.

3. Probabilistic Energy Screening of Tunnel, PrEST

The decision on the investments both for improving the lighting performance and for reducing the energy consumptions of an existing LST can be taken using EST when all the data of the model are known without uncertainty. In reality, however, several data and many parameters can be uncertain or assigned with a diﬀerent grade of conﬁdence.

The most adequate way to take into account the uncertainties is to express the input data by random variables and to apply probabilistic techniques of analysis. In the following, we ﬁrst analyze the most important EST input data and parameters that require the introduction of random variables. Then, we describe the probabilistic analysis technique.

3.1. Lamp and Luminaires

When we deal with the installation of devices one parameter is strongly uncertain: the useful life. This is particularly true when the devices are characterized by signiﬁcant technological innovation, as is the case of the luminaires with the solid state lamps like the LEDs [14–16]. The value of life inﬂuences the annual cost of any solution, and therefore both the economic quantities in Equations (10) and (23).

The “standard” or “default” useful life of a lamp depends on its technology [17]. For all the lamps with the exception of the LED, the useful life is a number of hours of operation at which half the product population, B50, fails; it is the median life of the lamps.

For the LEDs, it was deﬁned in terms of lumen output and speciﬁed as the time when light output of half the product population, B50, has fallen below 70% of average initial light output, L70, for any reason [18]. For some applications, also the colour shift of the LED may be considered a failure. For these cases, the lifetime can consider also when light output of half the product population B50 has shifted colour beyond a speciﬁed limit that depends on the needs of the speciﬁc application.

Reference [19] proposed a life prediction methodology for L70 life of LEDs based on the Kalman ﬁlter and the extended Kalman ﬁlter models. Both the proposed models were able to predict the lumen degradation as well as the chromaticity shift. It is interesting to evidence that the estimated mean value of L70 for the considered LEDs ranged from about 26,000 to about 40,000 h depending on the underlying degradation mechanism. The standard deviation ranged from about 6% to about 30% of the mean value. Such a large variation of the LED life surely has a large impact on the evaluation of the investments.

A further variable that can be aﬀected by uncertainty is the luminous eﬃcacy, ε, of the lamp and luminaire. This is valid both for the existing devices and for those to install for upgrading the LST.

The luminous eﬃcacy (lm/Watt) is the ratio between the lumens associated with a given optical power, that is the integral of eye response V(λ) over wavelength, and the electrical source power (pe) used to create the optical power:

ε = po(λ)V(λ)dλ (24) pe

The luminous eﬃcacy in Equation (24) is linked to the eﬃciency of all the subsystems or components which collectively make up the luminaire. In [20], the luminous eﬃcacy of a warm-white LED luminaire was linked to the thermal eﬃciency droop, the eﬃciency of the driver, of the ﬁxture/optical, of the overall luminaire. In particular, for the real value of the luminous eﬃcacy, the operating temperature of the LED package is critical and is variable, for a given thermal design of a luminaire, mainly with the ambient temperature and with the operating current.

These quantities are typically not known with precision at the stage of the planning of the investments for upgrading existing LSTs, even if they were, they would be variable during the time in

Article

Probabilistic Estimation of the Energy Consumption and Performance of the Lighting Systems of Road Tunnels for Investment Decision Making

Antonio Bracale 1 , Pierluigi Caramia 1 , Pietro Varilone 2 and Paola Verde 2,* 1 Department of Engineering, Università di Napoli “Parthenope”, 80143 Naples, Italy; [email protected] (A.B.); [email protected] (P.C.) 2 Department of Electrical and Information Engineering, Università di Cassino e del Lazio Meridionale, 03043 Cassino, Italy; [email protected] * Correspondence: [email protected]; Tel.: +39-0776-299-3638

Received: 2 March 2019; Accepted: 15 April 2019; Published: 19 April 2019

Abstract: This paper presents a probabilistic model for supporting the process of decision making about the value of new lighting systems in existing road tunnels when some data and parameters are aﬀected by uncertainty. The proposed model, which we have called Probabilistic Energy Screening of Tunnel (PrEST), accounts for both the technical performance and the economic objectives of the new lighting systems. The technical performance is described on an adequate (x, y) plane that was deﬁned by two indices. The ﬁrst index measured the consumption of electricity per kilometre of tunnel lengths; the second index measured the performance of the lighting systems per unit of illuminated area. The economic results were measured by the net present value of the savings and by the payback period. Both the terms account for initial capital investments, energy and maintenance costs. PrEST was applied to two real road tunnels in service in Italy showing that the statistics of the results can support a ﬁnal decision in function of the business strategy.

Keywords: lighting systems; energy eﬃciency; light performance

1. Introduction

Adequate levels of visibility on roads allow pedestrians to walk minimizing the risk of accidents; further, in the town, they can also enjoy the space around perceiving a sense of security against aggressions or thefts [1]. The lighting systems of roads and tunnels are essential for the security of the citizens and for the safety of the drivers. Good luminosity on roads and in tunnels is strictly linked to the safety of the vehicle driving. The driver must be able to detect the presence of obstacles, to perceive any changes in driving conditions without developing a sense of uncertainty or, even worse, fear.

With reference to the safety of vehicle driving, National and International Standards, such as those of the Commission Internationale de l’Eclairage (CIE), state the requested levels of minimum illuminance within accepted boundaries for limiting other aspects like glare or the lack of vertical uniformity. In particular, the lighting systems of a tunnel (LSTs) must be designed following the minimum luminance proﬁle, as reported by the European Standard [2]. The standard gives the required values of the luminance along the longitudinal axis of the tunnel versus the travel time along the tunnel at the reference speed (the reference speed is equal to the speed limit in the tunnel; the value is provided by the operator of the road where the tunnel is in service), as Figure 1 shows.

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Figure 1. Plot of the required luminance L along the longitudinal axis x of the tunnel for diﬀerent Figure 1. Plot of the required luminance L along the longitudinal axis x of the tunnel for different reference speeds [2]. reference speeds [2].

The performance of the lighting system for a LST in terms of quantity and quality of luminosity is onlyTohnee poefrtfhoermprainncceipoafltahsepleigchtstitnogascycsotuemnt ffoorr ainLtShTeidnetseirgmnsstoafgqeu. aTnhtietyfuarntdheqruaaslpiteycot frelufemrsintoostihtye iesnoenrglyy oconnesoufmthpetiporni.ncipal aspects to account for in the design stage. The further aspect refers to the energTyhceoLnSsuTsmrpetpiorens.ent the most electricity-consuming loads for the companies that manage the primTarhyerLoaSdTss. rSeuprrveesyesntshthowe mthoasttlieglhectitnrigcictoyn-csounmsuesm3i0n%g loofatdhse feonrertghye ccoonmsupmaneidesbtyhtahtemmaencahgaenitchael panridmealreyctrroiacdals.sSyustrevmeyssisnhohwighthwaatyligtuhntinneglscoannsdumtheast3t0h%e toufnthneelenliegrhgtyincgoncosustms eadrebay tlhoessmfoecrhtaunnincaell amnadnaegleecmtreicnatldseypsatermtmseinntsh[i3g,4h]w. ay tunnels and that the tunnel lighting costs are a loss for tunnel manaTgeecmhneonltodgiecpaal ritnmnoevnatsti[o3n,4s]i.n lamps with the introduction on the market of solid state lamps using LightTEemchinttoinloggDiciaoldiensn(oLvEaDtiso)nhsasincelratmaipnslywreitdhucthede tihnetrpordoubclteimonoof nentehregymcaornkseutmopf tsioolni,dbsuttaittedliadmnpost uersainsegiLt iagthatllE. mLEitDtisngarDe isoudreelsy(cLhEaDrasc)theariszecderbtayinalnyirnecdreuacseeddtehﬃe cpireonbclyemvaolufeemneeragsyurceodnsinumlupmtieonn/,Wbauttt (itlmdi/dWn),obtuetrathsee iptaarttiaclul.laLrEaDpspalirceastiuorneslyocfhthareascetelarmizepds ibnytahne itnucnrneealssedstielflfrieciqeunicryesvtahleueinmsteaallsautrioedn ionf lsuomlidens/tWateatltam(lmps/Ww)i,thbuathtihgeh ppaorwticeur lvaarluape,pelivceantioifnlsowoferthtehsaenltahmopses oinf gthase dtuisncnhealrsgestliallmrepqsuwirieths tthhee isnasmtaelllautmioennosf. solid state lamps with a high power value, even if lower than those of gas discharge lampTshweitchotmhpe asnamiese ltuhmatemnsa.nage a large set of tunnels have the problem of sorting the LTSs for plannTihneg cionmvepsatmnieesnttshoatvemraanadgeeﬁnaeldartgime eseht oorfiztounn.neTlshehaovpetitmhealpsroorbtilnemg mofussot rctoinngsidtheer LboTtShs tfhoer ptelcahnnniicnagl rienqvueisrtemmeennttss oavnedrthaedneefeindefdortitmheerehdouricztoionn. oTfhteheopentiemrgayl csoonrtsiungmpmtiuosnt. consider both the technIincatlhreeqsupierceimaleiznetds alnitdertahteurnee,etdhefoarstpheecrteodfuectnieorngoyfctohneseunmerpgtyiocnonosfuLmSpTtsiohna.s been faced from diﬀerIenntthpeosinptescioaflivzieedwl[it5e–r9a]t.uIrne,[5th],ethaespaeuctthoofrsedneeargltywciothnstuhme pentieorngyofreLqSuTirsemhaesnbtseeonf tfhaecelidghfrtionmg dsyifsfteermenstipnoeinmtserogfevniceywco[5n–d9i]t.ioInns[5w],htehne aaunthacocrisddeneatlot cwcuitrhs.thTeheenyersghyowreqauciaresemsetnutdsyofinthwe hliigchhtitnhge seynsetregmyscionnseummerpgteionncyfocronbdaictkio-unps wanhdensaafnetayccoifdtehnet eomcceurrgse. nTchyeyligshhtoiwngaacreasceosvteurdedy ibnywmheicahnsthoef penheortgoyvoclotanicsupmanpetliso,ngefnoerrabtaicnkg-uapcaashndﬂoswafeatbyleotfo tphaeyebmacekrgtheneceyxtlriagihntvinegstmareentcoinveprheodtobvyolmtaiecasn. sThoef pcohnottroivboulttiaoinc [p6a]nperlos,pgoesnesertahteinegstaimcaastihonfloowf thaebleenteorgpyaycobnascukmthpetioexntsraofinthveesLtmSTesnitnitnhpehdoetsoigvnolstataicgse. Ttahkeincgonptrroipbuertliyonin[t6o]apcrcoopuonstetshethaedevsatnimtaagteios nofotfhtehpeoewneerrgcyoncsounmsupmtiopntiosanvsinogf sthoebtLaSinTasbilne bthyeindteesringanl slutamgientaankciengrepgruolpateirolny.into account the advantages of the power consumption savings obtainable by internPaalpleurm[7i]npanrocpeorseegsuilmatpioronv. ing the global performance of the lighting systems in a tunnel, by using new rPoaapderp[a7v]inpgrompoasteesriiamlspcrhoavriancgtetrhiezegdlobbyalapheirgfhoermr raenﬂceectoiof nthceoleigﬃhctiienngtstyhsatnemotshienr aortduinnnaerly, bayspuhsainltgs. new road paving materials characterized by a higher reflection coefficient than other ordinary asphalts.

In [8,9], the Energy Screening of Tunnel (EST) model was introduced to handle both the aspects of reducing the energy consumption and improving the lighting performance, in an integrated way.

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EnergiIens 2[081,99,]1,2t,hxeFOEnRePrEgEyRSRcErVeeIEnWing of Tunnel (EST) model was introduced to handle both the aspe3ctosf o21f

reducing the energy consumption and improving the lighting performance, in an integrated way. EST EalSloTwasllroewprsesreenptrinesgeenvtienrgy LeSvTeriyn aLSCTaritnesiaanCpalratnesei{aenlepctlrainciety{ceolencsturimciptytiocno,npseurmfoprtmioann,cep}eirnftorromduancicneg} ianptprorodpurciiantge ianpdpircoeps.riIante[9i]ntdhiecerse.sIunlt[s9o] fththeerEesSuTltms oodf ethl ewEeSreTamlsoodveelrwiﬁeerde baylsmo evaenrisfioefdebxypemriemanenstoafl emxepaesruimreemnetanltsmoenastuherermoaedn.tsTohne tEhSeTrmoaodd.eTlhweaEsSnTomt aotdoeollwfoarsdneostigantionogl nfoerwdLesSiTg.nEinSgT,ninewsteLaSdT, .wEaSsTa, vinasltueaabdl,ewmaesaan vfoarlusaobrtlienmg ethaendfoecrissoiorntinogf tthheeidnevceisstimonenotfstthoeminavkeestomnesnetvsetroalmexaiksetinogn LseSvTesrtaalkeinxigstiinntgo LacScTosutnakt ibnogthintthoeaaccvoeurangt ebolitghhtthinegavpeerrafgoermligahntcienganpdertfhoermavanercaegaenedntehregayvceornagsue menpetrigoyn.consumption.

IInn tthhiiss ppaappeerr,, ssttaarrttiinngg ffrroomm tthhee iinniittiiaall vveerrssiioonnss ooff EESSTT pprreesseenntteedd iinn [[88,,99]],, wwee ﬁfirrsstt iimmpprroovveedd tthhee mmooddeell bbyy iinncclluuddiinngg aann eeccoonnoommiicc mmoodduullee.. TThhiiss eeccoonnoommiicc mmoodduullee aalllloowwss ccoommppaarriinngg tthhee iinnvveessttmmeennttss rreeqquuiirreedd ffoorr iimmpprroovviinngg tthhee eenneerrggyy eefﬃficciieennccyy aanndd tthhee lliigghhttiinngg ppeerrffoorrmmaannccee ooff aannyy LLSSTT.. BByy uussiinngg tthhee eeccoonnoommiicc mmoodduuleleoonneecacnanhahvaevaen aidneaidoefathoef ctohset acsossotcaiastseodciwatiethd dwiﬀitehrendtiftfeecrhennitcatelcshonluictiaolnssoclauptiaobnles coafpimabpleroovfinimg pthroevpienrgfotrhme apnecrefoorfmthanecLeSoTfitnhteerLmSTs oinf ctoernmsusmopf tcioonnsaunmdpltiigohntianngdeﬃligchietinncgy.eTffhiceinen, wcye. Tdheaelnt,wwitehdtehaeltfuwrtihtherthperofublretmherthpartorbelaelmly cthaantcroenadlliyticoannthcoenddeictiisoionnthoef tdheeciisnivoenstomf tehnetsi:ntvheestumnceenrttsa:itnhtey uthnactearﬀtaeicnttsysothmaet oaffftehcetsdsaotamoef tohfethperodbaletamo. fTtohtehipsraoibmle,mw.eTtroanthsifserariemd,thweemtroadneslfEerSrTedonthaepmroobdabelilEisStiTc obnasaisparnodbapbriolipstoicsebPasriosbaanbdilipsrtiocpEonseerPgryobSacbreileinstiincgEonferTguynSncerle(ePnriEnSgTo)f. ITnupnnaretlic(PurlaErS, Tw).eIﬁnrpsat ratnicaulylasre, wthee fmiroststainmalpyosretatnhteEmSoTsitnipmuptodratatanat nEdSTpainrapmutetdearstathaantdrepqaurairme ethteersintthroadt urecqtiuoinreotfhreanindtormodvuacrtiioabnleosf. Trahnedno, mthevaprrioabbalebsi.liTsthicente, cthhneipqruoeboafbialnisatliycstiescihsndiqesuceriobfeadnianlydseistaiislsd. escribed in details.

TThhee ppaappeerr iiss ssttrruuccttuurreedd aass ffoolllloowwss:: EESSTT iiss rreeccaalllleedd iinn SSeeccttiioonn 22 sshhoowwiinngg tthhee aaddvvaanncceemmeennttss iinn rreessppeecctt ttootthheepprerceecdedininggpappaepresr[s8,[98],;9t]h; ethperopbraobbialibsitliicstmicodmeolldineglliPnrgESPTrEisSTpriessepnrteesdeninteSdecintioSnec3t;isoonm3e; snoummeenriucmalerreiscualltrsesaureltsshaorewsnhoinwSneicntiSoenct4iowni4thwrietfherreefnecreentocestoomsoemLSeTLsSaTcstuacatlulyalilny sinersveircveicine iIntaIltya.ly.

2. RReeccaallll aanndd Immpproveements of the Model EST

The EESSTTmmodoedleplrepsreensteendteind[8i,n9][w8,a9s] imwparsovimedpbroyviendtegbryatiinngteagsreactitniogn faorseccotinoonmfioc reveaclounatoimonisc; ethvealnueawtiovnesr;stiohne nofewESvTecrosinosnisotsf oEfStTwcoonmsoisdtus loefs,twnaommeolydtuhlest,enchamniecalyl mthoedtuecleh,nTicMal, amnoddtuhlee,eTcoMn,oamnidc tmheodeucolen,oEmMic(Fmigoudruele2,).EM (Figure 2).

Assignment of input data: Tunnel structure and installations

Technical Module “TM”

Economic Module “EM”

For each LST solution: Position on the Cartesian plane (electricity

consumption, performance). Evaluation of Net Present Value and

Pay-back period

Figure Figure

2. 2.

EESSTT

wwiitthh

tthhee

tteecchhnniiccaall

TTMM,,

aanndd

tthhee

EEccoonnoommiicc

MMoodduullee

EEMM..

TM, based on the model developed in [8,9], allows representing any LST on the same Cartesian planeTM{el,ebcatrsiecdityoncothnesummopdteilodne, vpeelrofpoerdmiann[c8e,}9.],Tahlleowobsjerecptirveeseonfttinhge aTnMy LwSaTs othnethdeersiavmateioCnarotfestiwano pinladnicees{e, loencterilcinitkyedcotnosuthmepatvioenra, gpeerlifgohrmtinagncpee}.rfTohrme aonbcjeectoifvethoefLtShTe, tThMe owthaesrtlhinekdeedritvoatthioenavofertawgoe indices, one linked to the average lighting performance of the LST, the other linked to the average power consumption. The choice of these indices was motivated by the need to represent on the same Cartesian plane {electricity consumption, performance} every LST, using the actual service conditions and in the new service conditions due to possible interventions. Such a representation on

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Energies 2019, 12, 1488

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power consumption. The choice of these indices was motivated by the need to represent on the same Cartesian plane {electricity consumption, performance} every LST, using the actual service conditions and in the new service conditions due to possible interventions. Such a representation on the same Cartesian plane allowed comparing several LSTs with each other, and for the same LST, diﬀerent possible interventions for making decisions on a long time horizon, when several LSTs are managed by the same company. TM is not a tool for designing a LST.

EST was conceived as a tool for supporting the decisions of the manager of several LSTs about the investments for upgrading them both for the illumination performance and for the energy consumption, providing a screening of their operating conditions (current conditions and estimated future conditions linked to possible alternative interventions) without performing detailed in ﬁeld measurements. This is the great advantage of using EST according to the methods usually adopted for having information and data on the current operating conditions of several LSTs. Usually, the managing company must measure the luminance in the ﬁeld. This is a very expensive activity in time, in human resources, and indirect costs linked to the need for limiting, deviating or stopping the traﬃc. EM, added in this paper to EST, allows comparing the investments faced for improving the energy eﬃciency and the lighting performance of any LST.

2.1. The Technical Module TM

The key idea at the basis of the TM of EST was to represent any LST on the same Cartesian plane {electricity consumption, performance} by means of proper variation indices with the respect to the LST of reference, namely the LST* [10].

The choice of the LST* was eﬀected on the basis of the incentives given in Italy to promote the energy eﬃciency investments. The national authority for the regulation on the energy, Autorità di Regolazione per Energia, Reti e Ambiente (ARERA, formerly AEEG) stated with the resolution [10] in which cases ﬁnancial incentives were recognized for installing new LSTs. Note that in other countries, the LST* can be diﬀerent in function of the local regulations. For example, in [11] diﬀerent strategies for supporting the investments on energy eﬃciency in the diﬀerent USA states are listed and commented.For the primary roads, three types of structure of LST were deﬁned as baseline cases. They are the LSTs whose performance, in terms of energy consumptions and lighting, must be overcome for obtaining the incentives. Each baseline was proposed by ARERA with characteristics adequate for guarantying the respect of the European Standard [2]. The main characteristics of the baseline cases proposed by ARERA in [10] are listed below. The data common to every LST* are:

- 100 W sodium high pressure (SHP) lamps, with 14 W of auxiliary circuits, reduced power during the night to 59 W with invariant power of auxiliary circuits;

- eﬃciency equal to 61 lm/W; - the lamps have a color rendering index not greater than 60 so that the lighting category of the

road is not reduced; - 13 h of operation during the morning, 11 h of operation during the night, 365 days of

annual operation; - height of whitewashed walls equal to 3.0 m; - LSTs which have the lines of luminaires equipped with lamps placed sideways are assimilated to

the ones with luminaires equipped with lamps placed in line above the roadway: - for the short tunnels, e.g., those according to [2] of length up to 125 m, the lighting level is

assumed equal to 100% of that provided for the long galleries.

The characteristics diﬀerent for each of the baseline cases reported in [10] are:

- single central line of luminaries with 10 m of spacing, 100 luminaires/Km; - double central line of luminaries with 9 m of spacing, 222 luminaires/Km; - triple central line of luminaries with 9 m of spacing, 333 luminaires/Km.

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Starting from the baseline cases proposed by ARERA in [10], we extended the baseline cases

for covering most of the actual roads in operation, that is dual or single carriageway, single-way or

double-way road with diﬀerent speed limit values, and considering the three possible conﬁgurations

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of the lines of luminaires (single, double or central line). For all the baseline cases, comprising

ftrheoesweaprreopproosgerdambyDAiaRlEuRx A[12in], [n1o0t],awvaeilﬁarbsltelyindtehveeDloipaeludxtlhibermaroyd. eBlys fmoeraunssinogf Dthiealfurexe, wthaerleupmriongarnacme

pDrioafliulex o[1f 2e]v,enroytbaavsaeillianbelewianstvheeriDfiieadluinx laicbcroarrdy.anBcyemweitahntshoefsDtainadluaxr,dth[2e].luInmsionadnociengp,rwoﬁelereoafliezvederay

lbiabsrealriyneofwbaassveleirniﬁe ecdasiens,acLcSoTrd*,afnocrecwomithpathriensgtaanndyaLrdST[2i]n. Itnhesostduodiyngw, iwthetrheeamliz.ed a library of baseline

casesF, oLrSeTv*e, rfyorLcSoTm* poaf rtihnegbaansyelLinSeTliibnrtahrye,swtuedcyowmipthuttehdemtw. o indices of reference: LPi* and ECi*. LPi*

is theFaovreervaegreyiLllSuTm*ionfanthcee bfoarseelainceh lsiqburaarrye, wmeetceormofptuhteedLStwTio; EinCdi*ic, eiss tohfereafnenreunaclee:nLePrgi*yacnodnEsuCmi*p. tLioPni*

pisetrhkeilaovmereatgere oilfluthmeinLaSnTci*e. for each square meter of the LSTi; ECi*, is the annual energy consumption

per kWiloimtherteefreorefnthcee LtoSTFii*g.ure 2, the TM starts with the assignment of the data of the tunnel, of the

road,Wainthd roeffetrheencLeStTo.FTighuerem2a,itnhedTatMa stotaratssswiginthatrhee: alesnsiggtnhm, wenitdothf tahneddahteaigohf tthfeortutnhneelt,uonfntehle; rdouaadl,

caanrdrioafgtehweaLySsT.oTrhseinmgaleincdaarrtiaatgoeawsasiygsn, aarned: lsepnegethd, wlimiditthfaonrdthheeigrohatdfo; rstthruecttuunrnee(ls; idnugalel ccaernritargael wlianyes,

dorousibnlgelececnatrrrailaglienwe,atyrsi,palendcesnpteraeldlliinme)itafnodr tchhearroaactde;rsistrtuiccstuorfeth(seinlagmlepcsen(ptroawl leinr,ee, fdfoicuiebnlecyce, naturxaillilainrey,

stryisptleemcse)nftorarltlhineeL)SaTn.d characteristics of the lamps (power, eﬃciency, auxiliary systems) for the LST.

FFoorr eevveerryy LLSSTTii,, wweeccoommppuuteteddththeeeneenregrygycocnosnusmumptpiotnioinndinedx,eEx,CEi,Cain, danthdetihlleumilliunmaninceanincedeixn,dLePxi,.

LFiPnia. lFlyin, caollnys,idcoenrisnigdethriengbatsheelinbeasLeSliTnie* cLoSrTrei*spcoonrrdeisnpgotnodeinvgerytoLeSvTeriny sLtuSTdyi,nitswtuadsyp,oistswibales tpoocsosimblpeuttoe

cthoemfpoulltoewthinegfovlaloriwatiinogn vinadriiacteiso:n indices:

∆ECi = ECi − ECi*

(1)

∆ECi = ECi − ECi*

(1)

∆∆LLPPIiIi== LPii −−LLPPii**

(2()2)

If ∆EECCii iiss ggrreeaatteerr tthhaann zzeerroo,, the consummppttiioonn mmuusstt be reduced; otherwiissee,, thee consumppttiioonn is acceppttaabbllee.. IInnaassiimmiillaarrwwaayy,,iiff ∆∆LLPPiiisislleesssstthhaannzzeerroo,, tthhee lliigghhttiinngg ppeerrffoorrmmaannccee hhaass ttoo be improved otherwise it is acceptable.

The importtaanntt rreessuulltt ooff the TM, which wass an intermmeeddiiaattee rreessuulltt ooff EST, is the representation of every LST on the Cartesiann plannee shoowwnn iinn Figure 3 where three LSTs were reepresented [9]. It is evident tthhaattnnooLSLTSTfalflasllisn tinhetsheecosnedcoqnudadqruaandtrwanhterwe hbeorteh tbhoethentehregyecnoenrgsuymcpotnisounmanpdtiothnealingdhttihneg lpigerhftoinrmg apnecrefoarrme aanccepatraebalec.ceptable.

Figure 3. Cartesian plan {electricityy connssuummppttiioonn,, ppeerrffoorrmmaannccee}}wwiitthhtthhrreeee LLSSTTs represented with a green triangle, red square, and blue rhombus [9].

The LST corresponding to the green triangle requires a reduction of the energy consumption, the LSTs corresponding to the red square and to the blue rhombus primarily need improved lighting performance.

Once obtained the characterization of every LST on the Cartesian plane of Figure 3, the TM allows evaluating the new values of (∆ECi)k and (∆LPi)k for any kth possible intervention aimed to

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The LST corresponding to the green triangle requires a reduction of the energy consumption, the LSTs corresponding to the red square and to the blue rhombus primarily need improved lighting performance.

Once obtained the characterization of every LST on the Cartesian plane of Figure 3, the TM allows evaluating the new values of (∆ECi)k and (∆LPi)k for any kth possible intervention aimed to reduce tEhneergeinese2r0g1y9,c1o2,nxsuFOmRpPtEioEnR RanEVdIEimWprove the lighting performance. Using Equations (1) and (2) in w6 hofic2h1 tinhewrehfiecrhenthcee vraelfuereesnLcPei*vaanludesECLiP*i*araenudnEchCai*ngaered,uitnicshpaonsgseidb,lei,tfoisr pevoessryibsleo,lufotironevkertoy ismolpulteimonenkt itno eimveprlyemLSeTnit, itnheevcoemrypLuStaTtii,otnheofcothmepnuetwatvioanluoefotfhtehneeiwndvicaelsue(∆oEfCthi)ek iannddic(e∆sL(P∆iE)kC.i)Bkyansodd(∆oLinPgi),kw. Beycasno vdeoriinfyg,iwf aencyaonfvtehreifpyoisfsaibnlye oinfttehrevepnotsisoinblceainntderrivveenetaiocnh cLaSnTidirnivteheeascehcoLnSdTqi uinadthreanste.cond quadrant.

FFiigguurree 44 iiss aann eexxaammpplleeoofftthheerreessuullttssoobbtataininaabblelefoforroonneeoof fththeeththrereeeLLSTSsTsrerperperseesnetnetdedininFiFgiugruer3e. I3n. Ipnarptiacrutilacur,lFairg, uFriegu4rseho4wsshothweseﬀtheectesfofefcttws oofditﬀweoredntififnetreernvtenintitoernvsetnhtaitonwsertehactonwseidreerceodntsoidimerperdovtoe timhepLroSvTerethpereLsSeTntreedpirnesFeingtuerde i3nwFiigthurthee3gwreitehntthreiagnrgeleen. Ttrhiaencgolnes.iTdheerecdoanlstiedrenraetdivaelstewrneraeti:ves were: -- NeNwewSHSHP:Ps:usbusbtisttuittuintigngsosdoiduimumhihgihg-hp-rpersessusruereddisicshcahragrege(S(SHHPP) )wwitihthhhiigghheerr eefﬃficciieennccyy ffoorr tthhee

exeisxtiisntginSgHSPH; P; -- LELDE:Dsu: sbusbtistutittiuntginLgELDEDlumluimnainiraeisre(SsH(SPH)Pfo)rfothretheexiesxtiinstginSgHSPH. P.

150

∆LP [lm/m2]

i

100

50

0

-50 Actual

-100

New SHP

LED -150

-200 -150 -100 -50

0

50 100 150 200

∆ECi [MWh/year*km]

Figure 4. Cartesian plan {electricity consumption, performance} with the alternative interventions on the LST represented inn Fiigguurree 33 wwiitthh tthhee ggrreeeenn ttrriiaannggllee..

IItt iisseevvidideennttfrformomFiFgiugruer4e t4hatthaaltl athlletihneteirnvteenrtvieonntsioimnspriomvpertohveeLtShTe oLpSeTraotipoenr,aitniofnac, ti,nthfeacpto, itnhtes rpeopinretssernetpatrievseenotfatthiveemoofdtihﬁeedmLoSdTisfibedeloLnSgTstobtehleonsegcotondthqeuasedcroanndt. Tqouasdurpapnot.rtTtohesﬁunpaplodrtectihseiofninoanl tdheeciisnivoenstomnetnhtetoinfvaecsetmamenont gtothfaocsee asomluotnigontsh,owsehiscohluimtiopnros,vwedhtichhe pimerpforormveadnctheeofpeearfcohrLmSaTni,cEe SoTf eruacnhs tLhSeTei,coEnSoTmruicnms tohdeuelceoEnMom, dicesmcroidbuedleinEMth,edfeoslcloriwbeindginsetchteiofno.llowing section.

22..22.. TThhee EEccoonnoommiicc MMoodduullee EEMM TThhee EEMM ssttaarrttss wwiitthh tthhee aassssiiggnnmmeenntt ooff tthhee ddaattaa ffoorr tthhee ppoossssiibbllee ssoolluuttiioonnss wwhhiicchh rreessuulltteedd iinn tthhee

TTMM aaddeeqquuaattee ffoorr iimmpprroovviinngg bbootthh tthhee ininddiicceess,, ((∆∆EECCii))kk aanndd ((∆∆LLPPii))kk.. FFoor reeaachchLLSSTTi i ssoommee ppoossssiibbllee ssoolluuttiioonnss ccaannbbeeininsstatalllilninggﬂfuluxxrergeuglualtaotrosrosnotnhetheexiesxtiinstginlagmlapms apnsdanludmliunmaiirneasi,rseusb, sstuitbusttiintugtlianmg plasmanpds launmdinluamireins awirieths hwigithherhliugmheirnoluums eiﬃnocuascyefffoircathcye efxoirsttihneg eoxniesst,inogr ionnsteasl,lionrg inneswtalllaimngpsnaenwdllaummpinsaairneds wluimthinﬂauixrersewguitlhatfolrusxorregduimlamtoerrsso. rNdoitme mtheartsi.nNtohteeftohlalotwininthge, tfoolalovwoiidngv,etroboasveonidotvaetriobnostehneostuabtisocnripthtei rseufbesrcreridpttoi rinefdeerxretduntoneinl,dwexilltunnotnbele, uwsielldn. ot be used.

FFoorr eevveerryykktthhssoolulutitoionn, ,ththeemmaianindadtaataaraer: ep:opwoewr,elru, mluimnoinuos uesﬃecfafcicya, cnyu,mnbuemr,buesre, fuuslelfifuel, ltioftea,ltcootastl ocof stht oeflathmeplsa,mthpes,luthmeinluamireinsaainredstahnedauthxeilaiaurxieilsi,acroiesst,ocfotshteomf tahientmenaainntceen, atanrcieﬀ, otafrtihffeoefntehregye,naenrgdys,oanond. so on. All these data permit the computation of the cost of the existing LST, named annual cost of the old solution (KAn)OS to face in the year n, and of the improved (LSTi)k, named annual cost of the new kth solution (KAn)k to face in the year n.

For the computation of the annual costs of the old solution and of any new solution, the

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All these data permit the computation of the cost of the existing LST, named annual cost of the old

solution (KAn)OS to face in the year n, and of the improved (LSTi)k, named annual cost of the new kth solution (KAn)k to face in the year n.

For the computation of the annual costs of the old solution and of any new solution, the economic

model of the CIE [13] deﬁnes the hourly cost of an LST taking into account all the components of cost

arising during the annual operation from the costs for installation to those for the maintenance. This

model of the cost is very valuable when the cost and saving estimation is performed on a one-year basis.

When the ﬁnancial analysis is extended in a time period longer than one year, the economic

model of the annual cost of the old solution and of any new solution is more eﬀective if the costs of the

investments are separated from the other costs. This choice allows for estimating the cash ﬂow taking

into account the time value of the money. With this choice, the annual cost (KAn)OS and (KAn)k faced in the year i are:

(KAn)os = (KAIn)os + (KAOn)os

(3)

(KAn)k = (KAIn)k + (KAOn)k

(4)

where (KAIn)os and (KAIn)k are the costs for acquiring and installing the lamps CLampn os and the luminaires (CLumn)os of the old solution, and of any new k solution CLampn k and (CLumn)k, respectively; (KAOn)os and (KAOn)k are the other costs to face in each year for the old solution and for any new k solution.

The costs (KAOn)os and (KAOn)k are derived from the hourly costs (KAOnh)os and (KAOnh)k as:

(KAOn)os = (KAOnh)os ∗H

(5)

(KAOn)k = (KAOnh)k ∗H

(6)

where H is the number of operation hours during each year n. The expression of the hourly cost in the year n, (Knh)j for any j solution is given by:

(Kih)j = (CMatih)j + (CEnih)j + (CMaintih)j + (CFih)j

(7)

with j =

os for the old solution k for any new solution

In Equation (7) (CMatnh)j is the hourly cost in the year n of all the materials with the exclusion of the lamps and luminaires, (CEnnh)j is the hourly cost in the year i of the electric energy consumptions, (CMaintnh)j is the hourly cost in the year n of the maintenance, (CFnh)j is the hourly cost of further possible interventions. The Appendix A presents the expressions of the terms in the Equation (7).

Considering the Equations (3) and (4) with the position (5), the general expressions of the annual

cost of the year n of the old solution and of any new k solution are:

(KAn)os = (KAIn)os + (KAOnh)os ∗H;

(8)

(KAn)k = (KAIn)k + (KAOnh)k ∗H.

(9)

Starting from the knowledge of the annual cost of the old solution, (KAn)OS, and of each kth new solution, (KAn)k, EM allows performing the ﬁnancial analysis. In the actual version, EM evaluates two main ﬁnancial quantities for the alternative k. They are the net present value of the total savings,

NPVSk and the discounted payback period, PBk.

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The NPVSk is the current worth of the future saving of money or stream of cash ﬂow, given a speciﬁed rate of return α. Considering a period of N years in which we perform the ﬁnancial evaluation. For every new solution k, the NPVSk is given by:

N DKAn + DCEnn ∗ (1 + β)n−1

NPVSk =

n−1

(10)

n=1

(1 + α)

where is variation rate of the energy cost, DCEnn is the variation of the cost of electric energy of each

year n given by:

DCEnn = (CEnn)os − (CEnn)k

(11)

with (CEnn)os = (CEnnh)os∗ H and (CEnn)k = (CEnnh)k∗ H.

In (10), DKAn is the variation of the annual costs between the old solution and the new kth

solution given by:

DKAn = (KAn)os − (KAn)k

(12)

where (KAn)os and (KAn)k are the annual cost, other than the annual energy cost, to be incurred in each year n for the old solution and for the new solution, respectively.

The values of (KAn)os and (KAn)k depends on the year n since in each year we must include the cost of all the replacements, if any. For the old solution, we considered the cost of only the replacements

of the existing lamps when they end their life; for the new solution we considered to replace all the

materials only at the ﬁrst year; for the successive years, we assumed to replace only the lamps. For any

solution j, this implies that:

LLamphj

LLampj ≤ N; LLampj = 8760 ,

(13)

LLumhj

LLumj > N; LLumj = 8760 ,

(14)

Lmathj

LMatj > N; LMatj = 8760 ,

(15)

where LLampj, LLumj, LMatj are the nominal life in years of lamps, luminaires and materials of the jth solution, respectively, and LLamphj , LLumhj , Lmathj are the corresponding lives expressed in hours.

Let’s consider the number of substitution to face in the period N for the old solution, NSos, and

for any new solution k, NSk; they are given by:

N NSos = LLampos (16)

N NSk = LLampk (17)

where the symbol x represents the ceiling function which maps x to the least integer greater than or equal to x.

Taking into account the relation (16), for the old solution, the following considerations are valid in function of the value of n. For the ﬁrst year and for every year in which no substitution takes place, the expression of (KAn)os is:

(KAn)os = H∗[(CMaintnh)os + (CFnh)os]

for n = 1, . . . , N

n

p ·LLampos

(18)

p = 1, . . . , pmosax

pmosax = NSos − 1

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For every year during which the lamps are replaced, the expression of (KAn)os is:

(KAn)os = CLampn os + H∗[(CMaintnh)os + (CFnh)os ]

for n = p ·LLampos

(19)

p = 1, . . . , pmosax

pmosax = NSos − 1

Taking into account the relation (17), for any new solution k, we added in the ﬁrst year also the cost of the replaced components of the lighting system (lamps, luminaires and other materials), therefore the following expression of KAi k is valid:

(KAn)k = CLampn k + (CLUmn)k + H∗[(CMaintnh)k + (CMatnh)k + (CFnh)k ]

(20)

for n = 1.

For every year in which no substitution takes place, the expression of (KAn)k is:

(KAn)k = H∗[(CMaintnh)k + (CFnh)k]

for n = 2, . . . , N

n

1 + p ·LLampk

(21)

p = 1, . . . , pmk ax

pmk ax = NSk − 1

For every year during which the lamps are replaced, the expression of (KAn)k is:

(KAn)k = CLampn k + H∗[(CMaintnh)k + (CFnh)k ]

for n = p ·LLampk

(22)

p = 1, . . . , pmax

pmk ax = NSk k− 1

The term PBk gives the number of years it takes to break even from undertaking the initial expenditure, by discounting future cash ﬂows and recognizing the time value of money.

Considering the previous relations, we computed the PBk as the minimum value of the year m such that the following relation is satisﬁed:

m DCEnn ∗ (1 + β)n−1

m DKAn

−

≥ 0 m = 1, 2, . . . , N

(23)

n=1

(1 + α)n−1

n=1

(1

+

α)n−1

2.3. Intermediate and Final Outputs of EST

Summarizing, the intermediate and ﬁnal outputs are:

(i) representation on the same Cartesian plane of all EST, with reference to a set of LSTs, ar the LSTs of interest in the actual state of service;

(ii) identiﬁcation on the same Cartesian plane which LST is in an acceptable state of service (second quadrant), which LST needs intervention for reducing the energy consumptions and/or improving the lighting performance;

(iii) representation on the same Cartesian plane of the eﬀect of the interventions on every LST adopting one of the possible alternatives (substituting the luminaries and/or integrating luminosity regulation);

(iv) economic evaluation of every intervention on each LST; (v) sorting of the alternative solutions by means of the economic quantities NPVSk or PBk.

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It is evident that the decision maker can prioritize the interventions and make the best choice based on business policies and on the available initial capital costs.

3. Probabilistic Energy Screening of Tunnel, PrEST

The decision on the investments both for improving the lighting performance and for reducing the energy consumptions of an existing LST can be taken using EST when all the data of the model are known without uncertainty. In reality, however, several data and many parameters can be uncertain or assigned with a diﬀerent grade of conﬁdence.

The most adequate way to take into account the uncertainties is to express the input data by random variables and to apply probabilistic techniques of analysis. In the following, we ﬁrst analyze the most important EST input data and parameters that require the introduction of random variables. Then, we describe the probabilistic analysis technique.

3.1. Lamp and Luminaires

When we deal with the installation of devices one parameter is strongly uncertain: the useful life. This is particularly true when the devices are characterized by signiﬁcant technological innovation, as is the case of the luminaires with the solid state lamps like the LEDs [14–16]. The value of life inﬂuences the annual cost of any solution, and therefore both the economic quantities in Equations (10) and (23).

The “standard” or “default” useful life of a lamp depends on its technology [17]. For all the lamps with the exception of the LED, the useful life is a number of hours of operation at which half the product population, B50, fails; it is the median life of the lamps.

For the LEDs, it was deﬁned in terms of lumen output and speciﬁed as the time when light output of half the product population, B50, has fallen below 70% of average initial light output, L70, for any reason [18]. For some applications, also the colour shift of the LED may be considered a failure. For these cases, the lifetime can consider also when light output of half the product population B50 has shifted colour beyond a speciﬁed limit that depends on the needs of the speciﬁc application.

Reference [19] proposed a life prediction methodology for L70 life of LEDs based on the Kalman ﬁlter and the extended Kalman ﬁlter models. Both the proposed models were able to predict the lumen degradation as well as the chromaticity shift. It is interesting to evidence that the estimated mean value of L70 for the considered LEDs ranged from about 26,000 to about 40,000 h depending on the underlying degradation mechanism. The standard deviation ranged from about 6% to about 30% of the mean value. Such a large variation of the LED life surely has a large impact on the evaluation of the investments.

A further variable that can be aﬀected by uncertainty is the luminous eﬃcacy, ε, of the lamp and luminaire. This is valid both for the existing devices and for those to install for upgrading the LST.

The luminous eﬃcacy (lm/Watt) is the ratio between the lumens associated with a given optical power, that is the integral of eye response V(λ) over wavelength, and the electrical source power (pe) used to create the optical power:

ε = po(λ)V(λ)dλ (24) pe

The luminous eﬃcacy in Equation (24) is linked to the eﬃciency of all the subsystems or components which collectively make up the luminaire. In [20], the luminous eﬃcacy of a warm-white LED luminaire was linked to the thermal eﬃciency droop, the eﬃciency of the driver, of the ﬁxture/optical, of the overall luminaire. In particular, for the real value of the luminous eﬃcacy, the operating temperature of the LED package is critical and is variable, for a given thermal design of a luminaire, mainly with the ambient temperature and with the operating current.

These quantities are typically not known with precision at the stage of the planning of the investments for upgrading existing LSTs, even if they were, they would be variable during the time in