Minimum cost solar power systems for LTE macro base stations

Contents lists available at ScienceDirect

Computer

Networks

journal homepage: www.elsevier.com/locate/comnet

Minimum

cost

solar

power

systems

for

LTE

macro

base

stations

Yi Zhang

a

, Michela Meo

a ,∗

, Raffaella Gerboni

b

, Marco Ajmone Marsan

a ,c

a_{Department of Electronics and Telecommunications, Politecnico di Torino, Italy} b_{Department of Energy, Politecnico di Torino, Italy}

c_{IMDEA Networks Institute, Leganes (Madrid), Spain}

a

r

t

i

c

l

e

i

n

f

o

Article history:

Received23September2015 Revised30March2016 Accepted8October2016 Availableonline26October2016

Keywords: Cellularnetworks Greennetworking Renewableenergy Optimization

a

b

s

t

r

a

c

t

Thispaperproposesanalgorithmfortheidentificationoftheminimumcostsolutionovera10yeartime horizontopower anLTE(Long-TermEvolution) macrobasestation,usingaphotovoltaicsolarpanel,a setofbatteries,andoptionallyalsoasecondarypowersource,whichcanbeaconnectiontoa(possibly unreliable)powergrid,orasmallDieselgenerator.TheoptimizationisformalisedasanMixedInteger Programming(MIP)problem,which,afterlinearization,canbesolvedwithCPLEX.Aheuristicalgorithm isalsoproposed,withtheobjectiveofdecreasingthecomputationalcomplexityoftheoptimization. Nu-mericalresultsshow thatahybridsolar-grid(orsolar-diesel)powersystemsavesasignificantfraction ofthetotalcost, comparedtoapuresolarsystem, andtothe traditionalpower-gridsystem,overthe investigated10-yearperiod,inasouthEuropeancity,likeTorinoinItaly,aswellasinalocationcloseto thetropic,likeAswaninEgypt.Ourproposedheuristicalgorithmcanbeusedtoobtainasolutionwithin 10–20%oftheoptimum,atacomputationalspeed200timesfasterthantheMIPsolution.

© 2016ElsevierB.V.Allrightsreserved.

1. Introduction

Energy-efficient (or green) networking has been a hot re-searchtopicinthelastdecade.Severallargeinternationalresearch projectshave beenlaunched in thisfield, like EARTH [1] ,TREND [2] , andECONET [3] ,funded by the European Commission under its 7th Framework Programme, and GreenTouch [4] , the largest industry-driven initiative so far. In addition,many smaller initia-tives,andcuriosity-driven research, have contributedto the gen-eration ofa wide body ofresults in thisarea. Researchhas con-cernedall fields of networking, from access to core, fromwired towireless, buthassurelyfocusedmostlyoncellularradioaccess networks, dueto the increased relevance of wireless access, and to the recent introduction of the LTE technology, aiming at pro-vidinghighbandwidthubiquitousInternetaccesstoanever grow-ingnumberofsmartuserterminals.Researchhasconsideredmany differentaspects,frommoreenergy-efficientcomponentsand sys-tems,tolessenergy-hungryapplicationprotocols,togreener net-workmanagementprocedures,andarchitecturalvariations [5–8] .

However,inspiteofalltheattentiongiventoenergy consump-tioninnetworks, recent dataindicate that theamount ofenergy usedby networkskeepsincreasing.Probably,energyconsumption

∗ _{Correspondingauthor.}

E-mail addresses: [email protected](Y.Zhang),[email protected]

(M.Meo),[email protected](R.Gerboni).

goesup atalowerratethanitwouldhave,withoutalltherecent researchinthefield,butupitgoes.Themainreasonsforthis con-tinuinggrowthinthecaseofcellularnetworksare(amongothers) that:i)thedeploymentofthenewandmoreenergy-parsimonious Base Station(BS) models isslowerthan expected, dueto lagging operator investments because ofthe economic slowdown; ii)the newenergy-awarenetworkmanagementprocedures,mostlybased ontheswitch-off ofpartsoftheequipmentinperiodsoflow traf-fic, are not being adopted by operators, who fear that coverage holesmaybegenerated,thatQoSmaybedegraded,andthatfaults mayoccuratswitch-on;andiii)moreandmoreBSsarenecessary tosatisfytheexplodingvolumeoftrafficrequests.

It thus becomesinteresting totackle theissue ofenergy con-sumptionincommunicationnetworksfromadifferentperspective, focusingonthetypeofenergywhichisconsumed,since,ifwecan make networks green by consumingenergy produced by renew-able sources,the amount ofconsumed energybecomesless crit-ical. Actually, the combinationof renewable energy sources with energy-efficientequipment,protocols,andalgorithms isextremely important,sinceonlythroughanoptimisedsystemintegrationthe useofrenewableenergysourcesbecomesviable.

In this paper we study the use of solar energy to power an energy-efficientLTEmacrobasestation.Bycouplingaphotovoltaic (PV)solarpanelwithbatteriesthatcanstoretheenergyproduced inhighsolarradiationperiods,tobeusedduringnights,aswellas cloudydays,solarpanelscan powerbasestations atverylimited cost,andthusprovide aninteresting optionforbothareaswhere

http://dx.doi.org/10.1016/j.comnet.2016.10.008

thepowergridisnotpresentornotreliable,andareaswherethe powergridisubiquitous,butenergycostsarehigh,andregulations maymakeitinconvenienttoconnectaBStothepowergrid.

Today,especiallyin remotelocations, anumberofBSs already operate with no connection to the power grid. The most com-monsolutionto poweroff-gridbasestationsconsistsininstalling a Diesel power generator, which requires large amounts of fuel, which is expensive in itself, but becomes extraordinarily costly whentransportisproblematic(helicoptersarenecessarywhen lo-cationsarereallyremote),andwhenfueltheftsoccur.

Intherecentliterature,PVpanelshavebeenprovedtobemuch more cost-effective than diesel generators (in some areas, differ-encesincostareashighasanorderofmagnitude [5] ).Some Mo-bileNetworkOperators(MNOs),Orangeforexample,havealready deployedover 2000solar-powered BSs serving more than3 mil-lionpeopleinAfrica,withasavingof25millionlitersoffueland 67millionkgofCO2 in2011 [9] .Theseexperiences,coupledwith increasingenergycosts,aremakingsolarenergyaninteresting op-tionalsoforcountrieswheretheaccesstothepowergridis typi-callyubiquitousandreliable.

We investigate the cost of differentsolutions to power a LTE macroBS:i) the caseofaccessto thepower grid,ii)the caseof a Dieselgenerator, andiii)the caseofa PVpanel withbatteries. Inaddition,we alsoexplorehybridsolutions,whichconsistin:iv) theuseofaPVpanelwithbatteries,coupledwithagridaccess,or asmallDieselgenerator.

Inparticular,inthispaper,refiningourprevious works [10,11] , we focus on the optimization of the total cost (including CapEx and OpEx) of the solar energy systemthat is installed to power a macroLTE basestation.We consider a10-yearlife span ofthe equipment,andoversuchperiodweaccountforexpectedchanges in conditions,includingthe stronggrowth oftheend usertraffic demand,aswellastheincreaseofthegridelectricityprice;in ad-dition, we alsoconsider the evolution ofbattery technology, and thereduction ofthesolarpanelefficiencyfromyeartoyear.Two are thereasonswhywe selecta10-yearhorizon.The firstreason isthat PVpanelsare designedtolast atleast10years.Therefore, duringthe10-yearhorizon,thereisnoneedtochangePVpanels, whichwouldimplyacompletereplacementofthePVsystem.The secondreasonisthat,uptonow,newgenerationsofmobileradio accesstechnologieshadan opportunitywindowofabout10years before thedeployment ofa newertechnology, ascanbe seen by looking atthe cases ofGSM and3G. The currentlydeployedLTE BSswillprobablybereplacedby5Gtechnologyinaboutthesame time frame.Finally, predictingthe energyconsumption of5GBSs beyondyear2025isnotwithinthescopeofthispaper.

We study the system through a Mixed Integer Programming (MIP) approach,aimingatcost minimizationoverthe10-year pe-riod, and we design a heuristic algorithm that allows compu-tational complexity to be drastically reduced. Numerical results provethatminimumcostsolarenergysystemsareaviablechoice to power a LTE macro BS, and that hybrid energy systems (so-lar+gridorsolar+diesel)canbethemosteffectivechoice.

Thispaperis organizedasfollows. Section 2 brieflyoverviews previous workinthefield. Section 3 describesthearchitectureof our proposed hybrid BS power system. Section 4 formulates the problemofoptimizing thetotalcost ofthe hybridBSpower sys-tem. Section 5 proposesaheuristicalgorithmtosolvetheproblem and reduce computationcomplexity. Section 6 shows simulation results,and Section 7 concludesthepaper.

2. Relatedwork

Research on the use of renewable energy sources (RES) to powerBSs ofradioaccessnetworksstartedonlyafew yearsago.

The authorsof [12] provide quite a comprehensivesurvey of the stateoftheartinthisfield.

Severalworksfocused ontheallocation ofresources ina por-tionofanetworkcomprisinga fewBSs,some ofwhichare pow-eredby RES.Forexample,the authorsof [13] propose optimalBS switch-on/off strategiestosave energywithina radio access net-work,whensomeoftheBSsarepoweredbyRES.In [14] ,the au-thorsproposean optimized methodforRES utilizationinaradio accessnetwork,based ona 2-BS model,considering hybrid pow-eringsystems comprisingRES andaccessto the power grid.The same authorsalso investigate a green-energy-aware and latency-awareuserassociation problemin [15] .However, theseworksdo notconsiderindetailhowenergyiscapturedfromRES,storedand consumed,and how RES can be combined with power grid use. Furthermore,these works do not account for the solar radiation variationduringdifferentportionsofaday,anddifferentseasonof a year,andthus withthe corresponding variationin energy pro-duction.

Ifwe lookintothedetailsofahybridenergysystem(RESand power grid), although several works were published in the area ofenergyengineering (e.g., [16,17] ), only fewpapers appeared in the context oftelecommunications with the aimto optimize the BSpower system,includingthe variationofenergyconsumedfor variabletraffic load.A recentworkproposesa hybriddiesel-solar energysystem to power a BS [18] ,but does not try to optimize CapExandOpEx.Theauthorsof [19] propose theoptimizationof the cost ofa PV-wind hybrid systemto power a GSM/CDMABS, accountingfor wind andsolar energyvariations duringthe year, butdonotconsiderthetrafficvariationduringtheday.In [20] the authorsproposeaservice-adaptive method(i.e.,theadaptationof capacityand coverage) for managing the PV andgrid power re-sourcestopowera BS,andproposean implementation;however, theydonotinvestigatethesystemCapExandOpEx.

Thenoveltiesofourworkwithrespecttopreviouspapersare: i) we focus on the global optimizationof both CapEx and OpEx fora hybrid LTE BSpower system (with PVand power grid);ii) we consider the variation ofsolar radiation in differenttimes of theday,differentseasonsoftheyear,anddifferentlocationsofthe world;iii)weassumeanevolutionaryperspectiveforboththe sys-temefficiencyandtheBStrafficload,overthe10-yearperiod;iv) weoptimizethe totalcost overthe10-yeartime spanbefore the introductionofanewerradioaccessnetworktechnology.

3. TheBSpowersystem

Thissectionintroducestheelementsofthesolarpowersystem, aswellastheoverallBSpowersystemarchitecture,anddiscusses theparametersthatareusedinourstudy.

3.1. Photovoltaicpanels

Photovoltaic(PV)orsolarpanelsareusedtoconvertsolar radi-ationintoelectricity.ThePVpanelinstantaneousoutputpower de-pendsonthelevelofsolarradiation,ontheconversionefficiency, andonthepowerlossfactor,thataccountsforsystemlosses dur-ingthe powertransformation.Inthispaperweassume a conver-sionefficiencyequal to16%,whichistodaycommonforstandard PVpanels.

The peak output power of a PV panel, usually measured in “kilowatt-peak” (kWp), is directlyproportional to the panel size. A 1 kWp PV panel is defined as a PV module. The instanta-neousoutput powerofa 1kWp PVmoduleisdirectly relatedto the corresponding solar radiation, and can be expressed as P=

G

1000A

η(

G,Tm

)

, whereA is the module area in m2, G is the so-larradiationinW/m2_,and

η

_(G,T

thevariationoftheinstantaneouspowerproductionofaPVpanel isthesameasthetrendofthevariationoftheinstantsolar radi-ation(althoughthe relationisnon-linear). Theamount ofenergy producedby a PVpanel alsodependson thelocation, which de-termines the amountof solar radiation, dueto latitude, tilt, and weatherconditions.TheNationalRenewableEnergyLaboratory of the United States has made available online a software named “PVWatts” [21] ,which allows the estimation ofthe different en-ergyproductionpatternsofPVpanelslocatedindifferentpositions oftheearth.Weusethesoftware“PVWatts” toobtaintheamount ofenergyproduced duringatypical meteorologicyear,andselect twolocationsasexamples:TorinoinItalyandAswaninEgypt.The climateandsolar radiationpatterns inthese two citiesare quite different.Torino has a typical cycle of four different seasons; in winteritisrainyandcold,whileduringthesummeritishotand sunny. Aswanlocates nearthe Tropic ofCancer; itis usually hot anddry duringthe whole year, with limitedseasonal variations. Oursolarpowersystemistestedinthesetwocitiestoanalysethe mostsuitableconditionsofthedifferentpoweroptions.

3.2.Batteries

Batteries are used to store the energy which is not immedi-atelyusedtorun theBS, butbecomesnecessaryatnightor dur-ing the days when solar radiation is too low (i.e., rainy days or cloudydays,or daysofshort solarradiation inwinter) toobtain enoughelectricityto powertheBS. InouroptimizationoftheBS power system, we simulate the battery charge and discharge to compute how many batteries are needed to avoid energy short-ageattheBS.Weconsiderapowerlossfactorequalto85%,which meansthat15%ofthepowerislostduringthetransitionof charg-ing/dischargingbatteries.Usually,thebatterychargelevel(i.e.,the percentageofenergyinsidethebatterieswithrespecttothe max-imum)needstostayabove30%tokeep thebatteries inahealthy conditionforthelead-acidbatteriesweuseinthispaper.

WedefineaparameternamedPT,asthepercentageoftime dur-ingthe wholeyearwhenthe batteriescharge level isabove30%. Forpure solarBSpowersystems,weneed PT= 100%.Forhybrid solar-gridorsolar-dieselsystems,wecanconsiderlowervaluesof

PT, since we assume that the BS can obtain energy from either thepowergridorasmallDieselgeneratorwhenthebatteriesare empty(i.e.,theirchargelevelreaches0%).Inthispaper,we inves-tigatethreehybridscenarios,withPTequalto70%,80%,and90%.

An additional issue to be considered in the study of the BS power system over a 10-year period is the battery life. We as-sumethat the system uses traditional lead-acidbatteries, whose lifeisaround 500cycles [22] .Thismeans thata batterymustbe replaced when the cumulative depth of discharge of the battery reaches500timesitscapacity.Weaccountfortheimprovementof batterytechnologyduringthe10-yearperiod.Thelifetimeof bat-teriesimproveswhennewbatteriescometothemarket.According to [23] ,batterylifeispredictedtoimprovefrom500cyclesatthis momentto3000cyclesin2030.

3.3.ThearchitectureoftheBSpowersystem

Fig. 1 shows the high-level architecture of the BS power sys-tem.A controllermanagestheenergyflow fromthethree power sources(i.e.,PVpanel,batteries,andpossiblygrid/dieselasan ad-ditionalpowersource) tothe two power consumers(i.e., BSand batteries). The algorithm running on the controller dynamically switches the energy intake from the PV panel to the batteries to the additional power source, ifpresent. Whenever the power generated by the PV panel is more than what needed to oper-atethe BS, the extra power issent tothe battery. When the PV panel produces less power than needed by the BS, some energy

is taken from batteries. If batteries are depleted, and the power generatedby thePVpanelisnot sufficienttooperatethe BS,the additionalpowersourceisused,ifpresent;otherwise,theBSmust be switchedoff.Inaddition,iftheBSpowersystemisconnected to the power grid, it may be possible to sell back the extra en-ergy which is generatedby the PV panel when the batteries are full(100%charge).

3.4. PowermodeloftheLTEbasestation

The powerconsumption of theLTE macroBScan be approxi-mated asa function of theoutput power ofthe power amplifier withintheRadioFrequency(RF)module, [1] :

P

(ρ

)

=NTX

(

P0+

pPmax

ρ

)

0≤

ρ

≤1, (1)

whereNTXisthenumberofantennas,Pmaxisthemaximumpower outoftheRFpoweramplifier,P0isthepowerconsumedwhenthe RFoutputisnull,

p istheslopeoftheemission-dependent con-sumption.ThepoweroutoftheRFpoweramplifierisproportional tothetrafficloadoftheBS.

To reduce the power consumption of LTE base stations, one effective technological choice consists inthe adoption of Remote Radio Units (RRU), i.e., in the placement of radio units close to antennas, so as to reduce the power losses inherent in long an-tenna feed cables. In this paper, we use the power model of a LTE macro base station with RRU, as reference to conduct our study.

3.5. Trafficprofileofthemobileusers

Adetaileddailyprofileofthetrafficgeneratedbymobileusers is necessaryto compute, together with the BSpower model,the daily energy consumption of the BS. This quantity and the PV power generation duringthe day allow usto obtain the amount of energy which can be stored in the batteries, or needs to be drained frombatteries (dependingifthebalance betweenthePV panelgeneration andtheBSconsumptionispositiveornegative). Fig. 2 showsthenormalizedtrafficprofilemeasuredonacellofan Italianmobilenetworkoperator,distinguishingbetweenweekends andweekdays.Theprofile refersto aresidential area,withpeaks duringtheevening.

3.6. Evolutionoftheparametersover10years

Fig.1. ArchitectureoftheBSpowersystem.

Table1

PredictionofthevaluesoftheparametersoftheBSpowersysteminthe10-yearperiod.

Year Peaktrafficload PVefficiencyreduction Electricityprice[€ /kWh] Dieselprice[€ /liter]

Torino Aswan Torino Aswan

1 0.020 1 0.217 0.070 1.600 0.490

2 0.030 0.99 0.223 0.084 1.648 0.588

3 0.045 0.98 0.230 0.098 1.696 0.686

4 0.067 0.97 0.236 0.112 1.744 0.784

5 0.101 0.96 0.243 0.126 1.792 0.882

6 0.151 0.95 0.249 0.140 1.840 0.980

7 0.227 0.94 0.256 0.154 1.888 1.078

8 0.341 0.93 0.262 0.168 1.936 1.176

9 0.512 0.92 0.269 0.182 1.984 1.274

10 0.768 0.91 0.275 0.196 2.032 1.372

0 4 8 12 16 20 24

0 0.2 0.4 0.6 0.8 1

Time(hour)

Normalized traffic load

Weekdays Weekends

Fig.2. Trafficprofilesmeasuredonanoperationalcellularnetwork.

exploitation, while Italyimports fromother countriesmost ofits oil and electricity. However, because of the economic globaliza-tion, the gapis forecastedto become smaller andsmaller inthe next years,thereforethepricesinAswanfollowahigherincrease rate.

4. Mathematicalformulation

4.1. Optimizationoftheyearlycost

Forstarters, weformulate thecostminimization problemover one year(the systemparameters are kept constant in this inter-val),andthen we extendour optimizationtothe 10-yearperiod, accountingfortheevolutionofthesystemparameters.

The time granularityis definedby the parameter

,which is used to calculate energy production and consumption. Since the trafficandtheenergyproductionprofilesthatweusecontaindata forevery halfhour,thefinesttime granularitythatwe canuseis

=30min.Withthischoice,thenumberofintervalsinoneyear, thatis denotedby T,becomesT=17,520. Ifwereduce the time granularityto

=120 min,we getT=4380.Foreachinterval

wedefineappropriatevariablesinthemathematicalformulation.

Thefollowingisthedefinitionoftheproblem. Parameters:

• S_i:Energyproductionof1kWpsolarpanelintheithinterval,i

∈[1,T];SiismeasuredinWh.

• Ei:EnergyconsumedbytheBSintheithinterval,i ∈[1,T];Ei ismeasuredinWh.

• B:Capacityofenergystorageforonebattery;Bismeasuredin Wh.

• CPV: Cost of 1 kWp PV solar panel; CPV is measured in Euro/kWp.

• Cgrid:Costof1 Whofelectricityobtainedfromthepowergrid. Alternatively,wecanuseCdiesel:Costof1 Whofelectricity ob-tainedfromaDieselgenerator.CgridandCdiesel aremeasuredin Euro/Wh.

Variables:

• xi:ChargeofbatteriesnormalizedtothecapacityB,xi∈[0,1],

i∈[1,T].

• y_i:Variableusedtodefine thebatterycharge andpossible en-ergy deficitafterthegenerationandconsumption intimeslot

i,i∈[1,T].yiismeasuredinWh. • n:Numberofbatteries,n_>0.

• p:Sizeofthesolarpanel;pismeasuredinkWp.

• ai: Variable that indicates if the battery charge is above 0.3; neededtodefinetheconstraintonPTforhybridsystems. • bi:AmountofenergytakenfromthegridortheDiesel

genera-torintheithinterval,i∈[1,T];biismeasuredinWh.

Objectivefunction:

minimize: (2)

Ctotal=CPV×p+Cbatt×n+Cgrid/diesel× T

i=1

bi (3)

Constraints:

yi=min

{

B×n×xi−1+p×Si−Ei,B×n

}

(4)

B×n×xi=max

{

yi,0

}

(5)

bi=max

{

−yi,0

}

(6)

x1=1 (7)

0≤xi≤1,i∈[2,T] (8)

ai=

0 ifxi<0.3

1 ifxi≥0.3

(9)

T

i=1

ai/T≥PT (10)

Constraint (4) imposes that each battery cannot be charged aboveitscapacityB; (5) ,instead,definestheactualbatterycharge. Inthe case ofa pure solarBS powersystem (i.e., noconnection to the grid, andno Diesel generator), PT₌100%, and constraint (10) imposes thatallvariablesaiareequalto0,i.e.,xi ≥0.3. This meansalsothatyiisneverbelow0,andbiisalways0.Indeed,in thepure PVcase, no energyis boughtfrom thegrid orsupplied bythedieselgenerator;thebatterychargeisneverbelow30%. In-stead,inthecaseofa hybridBSpowersystem, some variablesai cangoto0,meaningbatterychargebelow30%,andinsomecases thevariables y_i become negative, meaning that the batteries are depleted(xi=0)andsomeenergycorrespondingtobiispurchased fromthegrid.

4.2.Analysisofcomputationalcomplexityandlinearisation

The complexityof solving this MIPproblem is very high, be-causeof thelarge numberofvariablesandconstraints,especially whenafinegranularity(smallvaluesof

)ischosen.

The formulation above contains two kinds of non-linearities. One stems from the min and max functionsthat appear in the equations.Forinstance,constraint (4) includesamin functionthat defines a limit forthe battery charge. CPLEX can deal with this kindof nonlinearities, as long asthe solution set is convex. The

other non-linearity derivesfrom theproduct of two variables. In ourcase,thetermn×xiinconstraint (4) istheproductoftwoof theproblemvariables.CPLEXcannothandlethiskindofnon-linear constraints.Itis thusnecessaryto introducealinearization, orto use a fixed point approach.We decided touse the latteroption, fixing thevalueofn andsolving theMIPproblemforthe chosen value,andthenchangingthevalueofnandagainsolvingtheMIP problem. Welet thevalue ofnvary intherange[0, 50],andwe selectthevalueofnthat providesthebestresult(i.e.,thelowest totalcost)asthefinaloptimalsolution.

ForaPCwithInteli5dual-coreCPUand4GBofmainmemory, the process of finding thesolution in the case

=30 mintakes 2–3h.Inthe case

=120min,the computationtime reducesto around10–15min.Obviously,thisimpliessomesacrificeinthe ac-curacyofthefinal results.Toinvestigatethesensitivityofthe op-timization solutionto thechosen time granularity, in Table 2 we show an example ofthe resultsobtained withthe two valuesof time granularityinthe caseofTorino,underfull traffic load,and pure solarsystem.The resultsshow thatthesacrifice inaccuracy isonlyaround1%,whichseems acceptable.Othercases,with dif-ferentchoicesoftheload,presented similaraccuracy.Inthe next sections,wewillreporttheresultsofCPLEXforatimegranularity equalto

₌120min.

4.3. Dimensioningovera10-yearperiod

In the previous section, we have discussed the minimization problemover aone-yearperiod.Whenlookingatthe10-year pe-riod, the system parameters must be modified year by year, ac-cordingto theevolution oftheparameters that wasdescribedin Section 3 andreportedin Table 1 .Tooptimallydimensionthe sys-temfora10-yearperiodofoperation, weproceedasfollows.We repeatthesystemdimensioningprocessupto10times,usingthe parametersreferringtoeachyear,fromthe10-th,downtothe1-st. Oncethedimensioningisobtainedforasetofparameters’values corresponding to a given year,the systemevolution is simulated forthe10-yearperiod.Duringthissimulation,itmayhappenthat thedimensioningobtainedforagivenyearisnotsufficientfor an-otheryear(forexample,becauseoftheviolationoftheconstraint on PT).This typicallyhappens whenthe parameters refer to one of the first years ofthe 10-year period,where traffic is low and the PV panel is atthe peak of its efficiency, so that the system dimensioningis not sufficient for a later year withhigher traffic andlowerPVpanel efficiency.Thisiswhywe startwithyear10, andwe godownuntilwefindayearforwhichthedimensioning isinsufficient.Whenthishappens,thedimensioningforsuchyear (sayyeark),aswellasforallotherpreviousyears(allyearsi≤k) canbeconsideredinapplicable.Duringthissimulation,thepossible cost of batteryreplacements, due to batteries reaching the max-imum number of charge and discharge cycles,is also taken into account. Finally,thebest dimensioningisdecided asthe applica-ble one withthe minimum total cost, taking intoaccount initial investment,batteryreplacements,andenergypurchase(ifany).

Table2

Impactoftimegranularity,caseofTorino.

Timegranularity[hour ] PVsize[kWp] No.batt. PV+batt.cost[k€ ] Totalcost[k€ ] Gap[%]

0.5 4.5 15 5.807 8.115 1.34%

2 4.8 14 5.853 8.007 0

9thyearresultsmoreconvenientthanthedimensioningbasedon 10thyear parameters.The bestdimensioningis thusthe one ob-tainedby runningtheone-yearoptimizationwiththeparameters ofthe9thyear.

In thecaseof Aswan,the second location we considerin this paper, the optimizationwith the parameters of the 10th year is theonly onethat guaranteesthat theconstrainton PTis metfor thewhole10yearperiod.

5. Aheuristicalgorithm

Although the reduction of the time granularity in the MIP makesthecomputationtimeforoneinstanceoftheoneyear opti-mizationaslowasaboutaquarterofanhour,thetotal computa-tiontime necessarytoobtainsolutions usingCPLEXremains very long.Indeed,each probleminstancehastobesolved50timesfor each of the admissiblevalues ofthe number ofbatteries, dueto thenon-linearconstraintsresultingfromtheproductsoftwo vari-ables,aswementionedintheprevioussection.Therefore,thetotal computationtimetoobtaintheglobaloptimumisoftheorderof severalhours.Whilethiscanbeacceptableforthefinaltuningof the selected option,itis clearlytoo longfor thewhat-if analysis that isnecessary toexplore possiblevariablesettings intermsof RANtechnology,networkdeployment,BSlayout(e.g.,smallcells), resourceallocationalgorithms(e.g.,sleepmodes),serviceoffering, etc. Withtheobjectiveof aconsistent reductionofthe computa-tion time, we propose a heuristic algorithm forthe approximate solutionoftheoptimizationproblem.

5.1. Pseudocode

The pseudo code of the heuristic algorithm is reported in Algorithm 1 .

The heuristic can handle both the pure solar and the hybrid solar-grid (or solar-diesel) BS power systems. The algorithm in-cludes 3layersofnestedloops.The mostexternalloop spansthe size ofthePVpanel,startingfrom0uptothe maximum consid-eredPVpanelsizeinkWp.Themostinternalloopspansthe con-siderednumberoftimeslotsintheyear.Thethirdloopspansthe numberof batteries,startingfrom0up to themaximum consid-erednumber.Duringtheloopexecution,ifthebatterychargedoes not meet the PT constraint, the program jumps out of the most inner loop and one more battery is considered. The middle and mostexternalloopsstop whentheminimumnumberofbatteries is found.Thus, forthe differentadmissible valuesofPV size,the minimum required number ofbatteries is calculated.Finally, the bestPVpanelsizeisselected,accordingtothelowestvalueof to-talcost.

5.2. Computationalcomplexity

The proposed heuristic has much lower complexity as com-paredwiththeMIPsolutionthroughCPLEX.Intheworstcase,the heuristic algorithm examines each value of the 3 loop layers, so that the total numberof examined casesis equal tothe product ofthreeintegervalues:themaximumPVpanelsizeinkWp multi-pliedbythemaximumnumberofbatteries,andbythenumberof timeintervalsinayear.Inpractice,thisamounts,intheworstcase andforthefinerconsideredtimegranularity,to20×50×17,520,

Table3

DimensionofPVpanelandbatteriesfrom1styearto10thyear,case ofTorinowith PT =100%and PT =90%,one-yearoptimizationdone withCPLEXforparametersofthe9thyear.

Year PT =100% PT =90%

PVsize[kWp] No.batt. PVsize.[kWp] No.batt.

1 12.8 36 7.6 10

2 12.8 36 7.6 10

3 12.8 38 7.6 11

4 12.8 41 7.6 12

5 12.8 41 7.6 12

6 12.8 42 7.6 12

7 12.8 43 7.6 12

8 12.8 44 7.6 12

9 12.8 45 7.6 13

10 12.8 47 7.6 15

Fig.3. ComparisonofPVsizeandnumberofbatteriesbetweenthesolution ob-tainedwithCPLEXandtheheuristicalgorithm;PT =100%,caseofTorino.

whichisabout17million.Thesearchfortheglobaloptimumwith thisheuristicapproachrequiresabout1minute.

5.3.GapbetweenCPLEXandalgorithm

Wenowassesstheaccuracyoftheheuristicalgorithmby com-paringtheresultswiththoseweobtainthroughtheMIP formula-tion.

Table 3 showstheevolutionofthesystemsizeoverthe10-year periodforthecaseofTorinoandPT=100% orPT=90%; the re-sultsareobtainedusing CPLEXtosolvethe MIPformulation.The one-year optimization is performed, aspreviously explained, us-ing the 9thyear parameters. The panel size is constant over the 10-yearperiodbecausepanelsarenot changed,oncethey are in-stalled.Thenumberofbatteries,instead,increasesyearbyyearto sustaintheincreasedneedforenergyduetogrowingload. Inthe caseof PT₌100%_, the systemneeds larger panel size andmore batteries,duetothetighterconstraint.

Toshow thedifferencebetweenthesolutionobtainedthrough theMIPformulationandtheheuristicapproach, Fig. 3 reportsthe chosenPVsizeandnumberofbatteriesinthe10-yearperiod,for

Algorithm1 Pseudocodeoftheheuristicalgorithm:Findthe com-binationofPVsizeandnumberofbatteriesthatminimizesthe to-talcostoftheBSpowersystem.

1: %%%%%Startinitialization

2: PT=70%or80%or90%or100%;

3: length=17520;

4: Battery_capacity=2.4

(

kWh

)

;

5: Max_PV =20

(

kWp

)

;

6: Max_battery₌50_;

7: ArrayUnit_production[length]arepre-calculated;

8: ArrayConsumption[length]arepre-calculated;

9: Sum_PT[p]₌0_;

10: Grid_energy=0;

11: %%%%%Endinitialization

12: %%%%%Main loop:Try differentvaluesofPVsize,foreach PV sizefindminimumno.ofbatteries

13: forp=0;p<Max_PV∗10;p++do

14: PV_size[p]₌p_∗0_.1_;

15: Number_o f_batteries[p]=1;

16: whileNumber_o f_batteries[p]<Max_batterydo

17: Battery_status[p][0]=Number_o f_batteries[p]∗

Battery_capacity;

18: fori=0;i<length;i++do

19: ifBattery_status[p][i]/Battery_status[p][0]<0.3then

20: PT_f lag[p][i]₌1_;

21: else

22: PT_f lag[p][i]=0;

23: endif

24: Sum_PT[p]=sum_PT[p]+PT_f lag[p][i];

25: ifSum_PT>=

(

1−PT

)

∗lengththen

26: Flag_f easible₌0_;

27: else

28: Battery_status[p][i+1]=MIN

{

(

Battery_status[p][i]+

PV_size[p]∗Unit_production[i]−Consumption[i]

)

,

Battery_status[p][0]

}

;

29: Flag_f easible=1;

30: endif

31: ifBattery_status[p][i]_<0then

32: Grid_energy[p]=Grid_energy[p]−Battery_status[p][i];

33: endif

34: endfor

35: ifFlag_f easible==0then

36: Number_o f_batteries[p]=Number_o f_batteries[p]+1;

37: else

38: Break;

39: endif

40: endwhile

41: cost[p]=Cost_PV∗PV_size[p]+Cost_battery∗

Number_o f_batteries[p]+Cost_grid_energy∗Grid_energy[p];

42: endfor

43: %%%%%Endmainloop

44:%%%%%Among thefoundsolutionslookfortheminimumcost one

45: form₌0_;m_<Max_PV_∗10_;m₊₊do

46: Findthesmallestcost[m];

47: endfor

48:return cost[m],Grid_energy[m],PV_size[m]andNumber_o f_

batteries[m];

(y-axison theleft),butlargernumber ofbatteries(y-axis on the right).SimilarresultsforthecaseofPT=90%areshownin Fig. 4 . AlthoughthedimensionforPT=90%ismuchsmallerthanthe di-mensionforPT=100%,thecomparisonofCPLEXandalgorithmis thesame:CPLEXresultsrequiresmallerPVsizebutlargernumber ofbatteries.

Fig.4. ComparisonofPVsizeandnumberofbatteriesbetweenthesolution ob-tainedwithCPLEXandtheheuristicalgorithm; PT =90%,caseofTorino.

Fig.5. ComparisonbetweenCPLEXandtheheuristicalgorithminthecaseofTorino withnoenergysell-back.

al-Fig.6. ComparisonbetweenCPLEXandtheheuristicalgorithminthecaseofTorino withenergysell-back.

Fig. 7. Comparisonbetween CPLEX and the heuristic algorithm inthe case of Aswan,noenergysell-back.

readydiscussed,theparameterevolutionandbatteryreplacements maketheformulationnon-linearandinfeasible.Hence, theCPLEX results are not always the trueoptimum over the whole 10-year period.

Fig. 6 showsthecomparisonbetweentheresultsofCPLEXand the results of heuristics, with energy sell-back (PT=100% and 90%). This means that when energy is produced that cannot be storedbecausethebatteryisfullycharged,theenergycanbesold backtothepowergrid.Weassumethatthesellingpriceishalfthe costatwhichenergyispurchasedfromthepowergrid.Thefigure showsthat thegaps betweenCPLEXandheuristicsaresimilar to thoseofthecasewithoutenergysell-back,shownin Fig. 5 .

Similar towhatwe dowithTorino, wecomparetheresultsof CPLEXand theheuristic algorithm forthecase ofAswan;results are reportedin Fig. 7 ,assuming that energycannot besold-back. Thelargestgap,inthiscase,isaround 30%,butthedifferencesat the endofthe10-yearperiodare within 15%.The resultsforthe casewith energysell-back are very similar andomittedhere for thesakeofbrevity.

The results show that while the solutions obtained with the two approaches are similar, there isa systematic difference with the heuristic solutions selecting largerPV panel size andsmaller number ofbatteries. However, when the totalcost is considered,

Fig. 8. Example of battery status for a system with kWp=16.6, 27 batteries, PT =100%(i.e.,withoutgridpower),duringthe9thyearundertheresidentialtraffic profile,inTorino.

thedifferencesbetweenthesolutionsbecomerathersmall.Wecan concludethat theheuristicapproachleads,inshortertime, to so-lutionswhosecostiscomparablewiththesolutionsobtainedwith CPLEX.Hence,inthefollowing,wewillusetheheuristicapproach.

6. Comparingpoweringsystems

In this section, we compare the effectiveness of the different considered powering systems forboth Torino andAswan. As we mentioned in previous sections, the two considered cities have quitedifferentsolarradiationpatternsthatleadto quitedifferent results. Giventhe good accuracy provided by the heuristic algo-rithmanditslowercomputationalcomplexity,inwhatfollowswe deriveallresultsusingtheheuristicalgorithm.

6.1. ThecaseofTorino

6.1.1. Systemdimensioning

Westart byconsidering thecaseofTorinofordifferentvalues of PT, focusing on the one year optimization, that, for Torino, is performedusingthesystemparametersofthe9thyear. Table 4 re-portsthePVpanel size,theinitialnumberofbatteries,theinitial cost,thecostduetotheamountofenergyboughtfromthepower grid (when PT_< 100%) andthe reward dueto sold-back energy. The resultsshow that the hybrid solar-gridenergy system(PT< 100%)savesalotintermsofcostandPVpaneldimensionwith re-specttothepurePVcase(PT₌100%);savingsarefrom50%to70%. If1kWpPVpanelroughly correspondsto 5 m2 _{[21] ,thesizeof} thePVpanelofthehybridsystemwithPT=70%isaround20 m2_, whichis muchmore feasible forinstallationthan the sizeof the PVpanelforthepuresolarenergysystemthatisabout80 m2_.

Forthe samecase, Fig. 8 shows thesimulation ofthe battery charge statusforthe pure solarsystem(PT=100%). Thered part ofthecurverefers totheamountofenergythat cannotbestored insidethebatteries.Thispartofenergyissoldbacktothepower grid,ifthisispossible,anditiswastedotherwise.

Table4

Sizeandcostofthepoweringsystemforthe9-thyeardimensioningcase,inTorino.

PT PVsize[kWp] No.batt. PV+batt.cost[k€] Gridcost[k€ /y] Payback[k€ /y]

70% 4.3 5 4.07 0.16 0.240

80% 4.3 7 4.38 0.12 0.229

90% 9.1 7 8.07 0.05 0.850

100% 16.6 27 16.92 0 1.832

Fig.9. ExampleofbatterystatusforasystemwithkWp=4.3,5batteries, PT =70%, duringthe9thyearundertheresidentialtrafficprofile,inTorino.

we compute how many battery cycles are consumed duringthe year.Then, the time whenthe battery isexhausted can be com-puted.

Fig. 9 showsthebatterystatusofthehybridsolar-grid energy system (the case PT=70% is shown as an example). Similar to Fig. 8 ,theredpartonthetopstandsforthewasted(or,ifpossible, soldback)energyandthegreenpartrepresentsthebatterystatus. ForPT₌70% the percentageof time in which the battery status isabove 30% is 70% of the entire year. The red part at the bot-tomstandsfortheamountofenergythatistakenfromthepower grid.WeassumethattheBSusesenergyfromthepowergridonly whenthebatteryisempty.Thebatterydischargeinthisfigure is morebalanced duringthewhole yearwithrespect to Fig. 8 .The discharging of the battery is much deeper, leading to a shorter life time of the battery. However, the savings of the dimension-ingofthesystemislargeduetosmallerCapEx(smallerPVpanel sizeandfewerbatteries)andthelargernumberofbattery replace-mentsdoesnotimpairtheadvantageofthehybridsystem.Wewill discussthecoston10yearperiodsinthenextsection.

6.1.2. Capexandopexina10yearperiod

Nowwefocusonthesystemcostduringthewhole10year pe-riod. Fig. 10 reportsthecaseinwhichenergysell-backisnot pos-sible,i.e.,theenergythatisproduced,butcannotbestoredinthe batteryorconsumed,iswasted.Thefigureshowsthecomparison betweenthe cases ofpure solar,hybrid solar-grid, grid only and dieselgenerator.Thebreak-evenpointbetweenthehybridsystems withPT=80% and90%andthe gridonly caseisaround the8th year,meaningthattakingall costsintoaccount (CapExandOpEx) the hybrid system starts being cheaper than the grid-only pow-eringfrom the 8th year. As previously observed, hybrid systems costmuchlessthanthepure solarsystem,withsavingsfrom50% to70%.Thecasewithdieselgeneratoristhemostexpensiveone, evenmoreexpensivethanthepuresolarsystemfromthe5thyear. Theseresults demonstrate that the proposed hybrid systems not onlyhavethe advantageof renewableenergy whichisclean and sustainable,but are also cost effective withrespect to the tradi-tionalpowergrid.

Fig.10. TotalcostforsomevaluesofPT ,noenergysell-back,inTorino.

Fig.11. Totalcostforsomevaluesof PT ,withextra-energysell-back,inTorino.

Table5

Sizeandcostofthepoweringsystemforthe10thyeardimensioningcase,inAswan.

PT PVsize[kWp] No.batt. PV+batt.cost[k€] Gridcost[k€ /y] Payback[k€ /y]

70% 3.8 5 3.69 0.019 0.017

80% 3.9 5 3.76 0.014 0.024

90% 3.9 6 3.92 0.012 0.024

100% 5 15 6.15 0 0.109

Fig.12. Batterystatus,PT =100%,inAswan.

Fig.13. Batterystatus, PT =70%,inAswan.

6.2. Aswanresults

6.2.1. Systemdimensioning

Aspreviouslymentioned,inthecaseofAswan,the10-year di-mensioningleadstochoosetheparameters’settingcorresponding to the 10th year (it was the 9thyear in the caseof Torino). In-deed,onlytheconservativecaseofthe10thyearparametersleads toasystemthatcanguaranteetheconstraintonPTforthewhole period. Table 5 showsthe resultsofthe optimizationonyear10. Observethatthesystem,intermsofPVpanelsizeandnumberof batteries,ismuch smallerthanforthecaseofTorino.Thisisdue to both thefacts that inAswanthe solarradiation ishigher and the seasonalvariationsaresmaller thaninTorino. Moreover,also thegapbetweenhybridsystemsandthepuresolarsystemismuch smallerthanthecaseofTorino.

Fig. 12 shows the battery status of the pure solar system (PT=100%), while Fig. 13 showsthe battery statusof thehybrid system (PT=70%). Comparing thesetwo figures with Figs. 8 and 9 ,observethatthebatteryhasdeepercharginganddischargingin the Aswan casethan in the Torino case. In Aswan, the solar

ra-1 2 3 4 5 6 7 8 9 10

0 2 4 6 8 10 12

Total cost [kEuro]

Year

PT=70% (Hybrid) PT=80% (Hybrid) PT=90% (Hybrid) PT=100% (Off-grid) Grid-only Diesel Generator

Fig.14. Totalcostfordifferentvaluesof PT inAswan,noenergysell-back.

1 2 3 4 5 6 7 8 9 10

0 2 4 6 8 10 12

Total cost [kEuro]

Year

PT=70% (Hybrid, with energy sellback) PT=80% (Hybrid, with energy sellback) PT=90% (Hybrid, with energy sellback) PT=100% (Off-grid, without energy sellback) PT=100% (Off-grid, with energy sellback) Grid-only

Diesel Generator

Fig.15. TotalcostfordifferentvaluesofPT inAswan,withextreenergysell-back.

diationis almostconstant duringthewhole year;hence,there is nobottleneckeffectinwinter.Theleastenergyproductiontimein AswanisinMayandDecember,whenrainismorefrequentthan inothermonths.Deeperbatterycharginganddischargingleadsto morebatterycycles.

6.2.2. CapExandOpExina10yearperiod

thetwofiguresarealmostthesame.Thisisduetothe dimension-ingofthePVsystemthatwellfitstheenergyneedoftheBS.

Fromthetwofigures,wealsoseethatthehybridsystemsaves withrespect to the pure solar system, as in the caseof Torino, anditisalmostequivalentincosttothedieselgenerator(consider howeverthatweonlyaccountforthecostoffuel,whichinEgypt isverylow,excludingtransport,etc).Thecost forthehybrid sys-temsisinsteadhigher(about10%higherattheendofthe10-year period)thanfortheconnectiontothepowergrid;thisisbecause inEgyptthepriceofgridpowerisquitelow.Again,considerthat wedonotincludethecostofconnectingtheBStothepowergrid, whichcanbe marginalwithinthecityofAswan,butveryhighin thesurroundingruralareas.

The increaseofcost forthepowergridwithtime inAswanis faster than in Torino (see Figs. 10 and11 ), because the price in-creaserate(20%per year)ismuch higherthanthe oneinTorino (3%peryear).

7.Conclusion

In thispaperwe studiedpowering systemsforLTE macroBSs thatmakeuseofsolarenergy,eitherrelyingonrenewableenergy only, orusing a mix of renewable energyand traditionalsupply. Weformulated theproblemoftheoptimalchoiceofthePVpanel sizeand numberof batteries witha MixedInteger Programming problemofcost minimization.Wealsoproposed aheuristic algo-rithmwhichismuchmorecomputationallyefficientthantheMIP problemsolution,whilebeingreasonablyaccurate.

TodiscusstheeffectivenessoftheinvestigatedBSpowering sys-tems,weconsidered two locations,Torino andAswan,withquite differentsolar energy generation patterns. The results show that hybrid systems are much more effective than pure solar energy system.Inaddition,inthecaseofTorino,hybridsystems also re-duce cost with respect to the traditional power-grid system and toa diesel generator. In Aswan, hybrid systems areeconomically equivalent to diesel generators, and somewhat more expensive thanan existing connection to thepower grid,because the elec-tricityanddieselpricesarebothverylowinAswan.

Our study shows that powering BSs with renewable energy sourcesistodaynot onlypossibleatreasonablecosts, butalsoin manycaseslessexpensivewithrespecttomoretraditionalpower supplyapproaches.Theforecasttechnologyadvancesinbothsolar cellsandbatterieswillmake thesolarsolutionevenmore attrac-tiveintheyearstocome.

Acknowledgment

This work wassupported by the European Union throughthe Xhaulproject(H2020-ICT-671598).

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YiZhangreceivedhisB.E.andPh.D.degreebothfromDepartmentofElectronicEngineering,TsinghuaUniversity,Beijing,China,in2007and2012, respectively.HewasavisitingPh.D.studentatUniversityofCalifornia,Davis,U.S.A.fromSeptember2008toAugust2010.Hewasapostdoctoral researcheratPolitecnicodiTorino,ItalyfromNovember2012toMay2015.FromJune2015hehasbeenapostdoctoralresearcheratTrinityCollege Dublin,Ireland.Hisresearchinterestincludesenergy-efficientwirelessnetworksandopticalnetworks.Hehasco-authoredover5IEEEandElsevier journalpapers.HehasservedasaTechnicalProgramCommitteememberforover10IEEEandACMconferences.

MichelaMeoreceivedtheLaureadegreeinElectronicEngineeringin1993,andthePh.D.degreeinElectronicandTelecommunicationsEngineering in1997,bothfromthePolitecnicodiTorino,Italy.SinceNovember2006,sheisassociateprofessoratthePolitecnicodiTorino.Sheco-authored about200papersandeditedabookwithWileyandsixspecialissuesofinternationaljournals,includingACMMonet,PerformanceEvaluation,and ComputerNetworks.ShechairstheSteeringCommitteeofIEEEOnlineGreenCommandtheInternationalAdvisoryCouncilofITC.Shewasprogram co-chairofseveralconferencesamongwhichACMMSWiM,IEEEOnlineGreenComm,IEEEISCC,IEEEInfocomMiniconference,ITC.Herresearch interestsincludethefieldofperformanceevaluationandmodeling,greennetworkingandtrafficclassificationandcharacterization.

RaffaellaGerbonireceivedtheMScinEnergyNuclearEngineeringin2000andaPhDinEnergyEngineeringin2006bothfromthePolitecnico diTorino.ShereceivedafiveyearcontractasaResearcherattheEnergyDepartmentofPolitecnicowhereshehasbeenalsoaPostDocFellow Researcherformorethanfiveyears.ShehasauthoredabookchapterwithWoodhead–Elsevierandco-authoredabookchapterwithSpringer.She ismemberoftheEditorialBoardoftheInternationalJournalofContemporaryEnergyandservesasareviewerfor3ElsevierJournals.Herexpertise isfocusedonenergysystemsanalysisandoncleanandefficientenergytechnologies.ShehasbeenresponsibleforMScandSpecializingMaster Courses.