Minimum cost solar power systems for LTE macro base stations Computer Networks

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Computer Networks

journalhomepage: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 rt i c l e i nf o

Article history:

Received 23 September 2015 Revised 30 March 2016 Accepted 8 October 2016 Available online 26 October 2016 Keywords:

Cellular networks Green networking Renewable energy Optimization

a b s t ra 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- vidinghighbandwidthubiquitousInternetaccesstoanevergrow- ingnumberofsmartuserterminals.Researchhasconsideredmany differentaspects,frommoreenergy-efficientcomponentsandsys- tems,tolessenergy-hungryapplicationprotocols,togreener net- workmanagementprocedures,andarchitecturalvariations[5–8].

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

∗ Corresponding author.

E-mail addresses: [email protected] (Y. Zhang), [email protected] (M. Meo), [email protected] (R. Gerboni).

goesup atalowerratethanitwouldhave,withoutalltherecent researchinthefield,butupitgoes.Themainreasonsforthiscon- 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 ofpartsoftheequipmentinperiodsoflowtraf- fic, are not being adopted by operators, who fear that coverage holesmaybegenerated,thatQoSmaybedegraded,andthatfaults mayoccuratswitch-on;andiii)moreandmoreBSsarenecessary tosatisfytheexplodingvolumeoftrafficrequests.

It thus becomesinteresting totackle theissue ofenergycon- sumptionincommunicationnetworksfromadifferentperspective, focusingonthetypeofenergywhichisconsumed,since,ifwecan make networks green by consumingenergy produced by renew- able sources,the amount ofconsumed energybecomeslesscrit- 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

1389-1286/© 2016 Elsevier B.V. All rights reserved.

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(helicoptersarenecessarywhenlo- cationsarereallyremote),andwhenfueltheftsoccur.

Intherecentliterature,PVpanelshavebeenprovedtobemuch more cost-effective than diesel generators (in some areas, differ- encesincostareashighasanorderofmagnitude[5]).SomeMo- bileNetworkOperators(MNOs),Orangeforexample,havealready deployedover 2000solar-powered BSs serving more than3 mil- lionpeopleinAfrica,withasavingof25millionlitersoffueland 67millionkgofCO₂ in2011[9].Theseexperiences,coupledwith increasingenergycosts,aremakingsolarenergyaninterestingop- tionalsoforcountrieswheretheaccesstothepowergridistypi- 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;inad- 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-yearpe- 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.Section2 brieflyoverviews previous workinthefield. Section3describesthearchitectureof our proposed hybrid BS power system. Section 4 formulates the problemofoptimizing thetotalcost ofthe hybridBSpowersys- tem.Section5proposesaheuristicalgorithmtosolvetheproblem and reduce computationcomplexity. Section 6 shows simulation results,andSection7concludesthepaper.

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 ofwhicharepow- eredby RES.Forexample,the authorsof[13]propose optimalBS switch-on/off strategiestosave energywithina radio accessnet- work,whensomeoftheBSsarepoweredbyRES.In[14],theau- thorsproposean optimized methodforRES utilizationinaradio accessnetwork,based ona 2-BS model,considering hybridpow- 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 energypro- 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)weassumeanevolutionaryperspectiveforboththesys- temefficiencyandtheBStrafficload,overthe10-yearperiod;iv) weoptimizethe totalcost overthe10-yeartime spanbefore the introductionofanewerradioaccessnetworktechnology.

3. TheBSpowersystem

Thissectionintroducestheelementsofthesolarpowersystem, aswellastheoverallBSpowersystemarchitecture,anddiscusses theparametersthatareusedinourstudy.

3.1. Photovoltaicpanels

Photovoltaic(PV)orsolarpanelsareusedtoconvertsolarradi- ationintoelectricity.ThePVpanelinstantaneousoutputpowerde- pendsonthelevelofsolarradiation,ontheconversionefficiency, andonthepowerlossfactor,thataccountsforsystemlossesdur- ingthe powertransformation.Inthispaperweassume aconver- 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,Tm)isthemoduleefficiency,which}

dependsonradiationandtemperature[10].Therefore,thetrendof

thevariationoftheinstantaneouspowerproductionofaPVpanel isthesameasthetrendofthevariationoftheinstantsolarradi- ation(althoughthe relationisnon-linear). Theamount ofenergy producedby a PVpanel alsodependson thelocation, whichde- 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, butbecomesnecessaryatnightordur- 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%ofthepowerislostduringthetransitionofcharg- ing/dischargingbatteries.Usually,thebatterychargelevel(i.e.,the percentageofenergyinsidethebatterieswithrespecttothemax- imum)needstostayabove30%tokeep thebatteries inahealthy conditionforthelead-acidbatteriesweuseinthispaper.

WedefineaparameternamedPT,asthepercentageoftimedur- 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,weinves- 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.Thelifetimeofbat- 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/dieselasanad- 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) whereN_TXisthenumberofantennas,Pmaxisthemaximumpower outoftheRFpoweramplifier,P₀isthepowerconsumedwhenthe RFoutputisnull,p istheslopeoftheemission-dependentcon- 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.2showsthenormalizedtrafficprofilemeasuredonacellofan Italianmobilenetworkoperator,distinguishingbetweenweekends andweekdays.Theprofile refersto aresidential area,withpeaks duringtheevening.

3.6. Evolutionoftheparametersover10years

Inthis paper,we focuson thecomputationof thecost ofthe BS power system, including CapEx and OpEx for a period of 10 years;duringsuch alongtime span,manyofthe keysystempa- rametersareboundtochange,somebyasignificantamount.Itis thusnecessarytoaccountforthesevariationsinthecostcomputa- tion,inordertoachievea carefulassessmentoftherelative mer- its ofthe possible alternativesolutions. The priceof solarpanels andbatteriescanbeestimatedfromarecentreportbyNREL[24], concludingthatthepriceofalead-acidbattery(12 V,200Ah)is approximately150€,andthe priceof1kWp PVpanel isaround 800 €. We collected data from reports and forecasts about the current levels andthe predicted future evolution ofPV andbat- teryprices,trafficprofiles,electricityprices,dieselfuelprices,bat- terytechnologiesandPVpanelefficiency,etc.,inbothAswanand Torino.Table1showstheforeseenevolutionoftheBSpowersys- temparameters.Weassumethatthetrafficloadwillfollowa50%

CAGRfrom2%inthefirstyearto76.8%inthe10thyear[25];the PV efficiency is known to degrade 1% each year [26]; the elec- tricity anddieselprices are forecastedtoincrease 3% per yearin Torino[27]and20%per yearinAswan[28].Thegapbetweenthe actualandthepredictedelectricityanddieselpricesbetweenthe twocitiescomesfromthefactthatEgypthasrichoilstorageand

Fig. 1. Architecture of the BS power system.

Table 1

Prediction of the values of the parameters of the BS power system in the 10-year period.

Year Peak traffic load PV efficiency reduction Electricity price [€ /kWh] Diesel price [€ /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. Traffic profiles measured on an operational cellular network.

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 thisinter- 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];S_iismeasuredinWh.

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

• B:Capacityofenergystorageforonebattery;Bismeasuredin Wh.

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

• C_batt:Costofonebattery;C_batt ismeasuredinEuros.

• C_grid:Costof1 Whofelectricityobtainedfromthepowergrid.

Alternatively,wecanuseC_diesel:Costof1 Whofelectricityob- tainedfromaDieselgenerator.C_gridandC_diesel aremeasuredin Euro/Wh.

Variables:

• x_i:ChargeofbatteriesnormalizedtothecapacityB,x_i∈[0,1], i∈[1,T].

• y_i:Variableusedtodefine thebatterycharge andpossibleen- ergy deficitafterthegenerationandconsumption intimeslot i,i∈[1,T].y_iismeasuredinWh.

• n:Numberofbatteries,n>0.

• p:Sizeofthesolarpanel;pismeasuredinkWp.

• a_i: Variable that indicates if the battery charge is above 0.3;

neededtodefinetheconstraintonPTforhybridsystems.

• b_i:AmountofenergytakenfromthegridortheDieselgenera- torintheithinterval,i∈[1,T];b_iismeasuredinWh.

Objectivefunction:

minimize: (2)

C_total=C_PV× p+C_batt× n+C_grid/diesel×

T i=1

b_i (3)

Constraints:

y_i=min

{

^{B× n× x}i−1+p× Si− Ei,B× n

}

⁽⁴⁾

B× n× xi=max

{

^yi,0

}

⁽⁵⁾

b_i=max

{

−yi,0

}

⁽⁶⁾

x1=1 (7)

0≤ xi≤ 1,i∈[2,T] (8)

a_i=



0 ifxi<0.3

1 ifx_i≥ 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 thatallvariablesa_iareequalto0,i.e.,x_i ≥ 0.3.This meansalsothaty_iisneverbelow0,andb_iisalways0.Indeed,in thepure PVcase, no energyis boughtfrom thegrid orsupplied bythedieselgenerator;thebatterychargeisneverbelow30%.In- stead,inthecaseofa hybridBSpowersystem, some variablesa_i cangoto0,meaningbatterychargebelow30%,andinsomecases thevariables y_i become negative, meaning that the batteries are depleted(x_i=0)andsomeenergycorrespondingtob_iispurchased 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,thisimpliessomesacrificeintheac- curacyofthefinal results.Toinvestigatethesensitivityoftheop- timization solutionto thechosen time granularity, in Table2 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,withdif- 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-yearpe- riod, the system parameters must be modified year by year, ac- cordingto theevolution oftheparameters that wasdescribedin Section3andreportedinTable1.Tooptimallydimensionthesys- 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 thedimensioningobtainedforagivenyearisnotsufficientforan- 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 astheapplica- ble one withthe minimum total cost, taking intoaccount initial investment,batteryreplacements,andenergypurchase(ifany).

ForthecaseofTorino,whosedetailedresultswillbediscussed in Section 6, we found that the system dimensioningis possible only whenthe one-yearoptimization isperformed usingthe pa- rameters ofthe 9thor10thyear. Inorder tobetter explain why, consider an example.Assume that thesystem dimension isopti- mizedusingtheparametersforthefirstyear.Whena10-yearlong period issimulated, astime goes by,the PVpanel efficiency de- grades andthe traffic load increases to such an extent that the requested constraint onPT cannot be met inthe years following thefirst.Forthisreason,moreconservativeassumptionsonthepa- rameters(suchasvaluescorrespondingtothe9thor10thyear)are neededtoguaranteethattheconstraintonPTismetforthewhole period.Whenconsideringthetotal cost,thedimensioningforthe

Table 2

Impact of time granularity , case of Torino.

Time granularity [ hour ] PV size [kWp] No. batt. PV+batt. cost [k€ ] Total cost [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 makesthecomputationtimeforoneinstanceoftheoneyearopti- mizationaslowasaboutaquarterofanhour,thetotalcomputa- tiontime necessarytoobtainsolutions usingCPLEXremains very long.Indeed,each probleminstancehastobesolved50timesfor each of the admissiblevalues ofthe number ofbatteries, dueto thenon-linearconstraintsresultingfromtheproductsoftwovari- 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 Algorithm1.

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 maximumconsid- eredPVpanelsizeinkWp.Themostinternalloopspansthecon- 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,accordingtothelowestvalueofto- 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:themaximumPVpanelsizeinkWpmulti- pliedbythemaximumnumberofbatteries,andbythenumberof timeintervalsinayear.Inpractice,thisamounts,intheworstcase andforthefinerconsideredtimegranularity,to20× 50× 17,520,

Table 3

Dimension of PV panel and batteries from 1st year to 10th year, case of Torino with PT = 100% and PT = 90% , one-year optimization done with CPLEX for parameters of the 9th year.

Year PT = 100% PT = 90%

PV size [kWp] No. batt. PV size. [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. Comparison of PV size and number of batteries between the solution ob- tained with CPLEX and the heuristic algorithm; PT = 100%, case of Torino.

whichisabout17million.Thesearchfortheglobaloptimumwith thisheuristicapproachrequiresabout1minute.

5.3.GapbetweenCPLEXandalgorithm

Wenowassesstheaccuracyoftheheuristicalgorithmbycom- paringtheresultswiththoseweobtainthroughtheMIPformula- tion.

Table3showstheevolutionofthesystemsizeoverthe10-year periodforthecaseofTorinoandPT=100% orPT=90%; there- 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 arein- stalled.Thenumberofbatteries,instead,increasesyearbyyearto sustaintheincreasedneedforenergyduetogrowingload. Inthe caseof PT=100%, the systemneeds larger panel size andmore batteries,duetothetighterconstraint.

Toshow thedifferencebetweenthesolutionobtainedthrough theMIPformulationandtheheuristicapproach,Fig.3reportsthe chosenPVsizeandnumberofbatteriesinthe10-yearperiod,for PT= 100%. The results for CPLEX have smaller size ofPV panel

Algorithm1 Pseudocodeoftheheuristicalgorithm:Findthecom- binationofPVsizeandnumberofbatteriesthatminimizestheto- 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%areshowninFig.4. AlthoughthedimensionforPT=90%ismuchsmallerthanthedi- mensionforPT=100%,thecomparisonofCPLEXandalgorithmis thesame:CPLEXresultsrequiresmallerPVsizebutlargernumber ofbatteries.

Fig. 4. Comparison of PV size and number of batteries between the solution ob- tained with CPLEX and the heuristic algorithm; PT = 90%, case of Torino.

Fig. 5. Comparison between CPLEX and the heuristic algorithm in the case of Torino with no energy sell-back.

Wenowconsiderthedifferencebetweenthesolutionsinterms ofthetotal costofthe system. Thetotalcost iscomputedasthe sumof theinitial investment,including thecost of thePV panel andbatteries, and theadditional cost that occurs duringthe 10- yearperiodto increasethenumberofbatteries,ifneeded,andto replacethebatteriesoncetheyareexhausted.Inordertocompute whenthebatteriesareexhausted,thebatterychargestatusissim- ulatedoverthewholeperiod.Adetaileddiscussionofthiswillbe providedinSection 6.Moreover, whenPT<100%,somecostdue toenergypurchasefromthepowergridisalsotakenintoaccount.

Fig.5showsthecomparisonbetweenthetotalcostfortheso- lutionsobtainedwithCPLEXandtheheuristic algorithm.Thegap forPT=90%iswithin10%,whilethegapforPT=100%iswithin about20%.Largergapsappearfromthemomentinwhichthebat- teries are being replaced, e.g., from the 8th year for PT=100%, andthe3rdyearforPT=90%.Forthesolutionobtainedfromthe heuristics, thenumberofbattery replacementsis higherthanfor theCPLEXsolution.Thisisbecausetheheuristicsreturns alarger PVpanel size andlowernumberof batteries,which meansmore batterycyclesandmorefrequent batteryreplacements.Note that sometimesthe resultsoftheheuristicsaremore convenientthan those ofCPLEX. This isdueto two reasons:1) the CPLEXresults are calculated by relaxed granularity, i.e. 2h, which reduces the accuracyoftheoptimumsolution;2)theoptimizationisonlydone foroneyearandnotoverthewhole10-yearperiod,because,asal-

Fig. 6. Comparison between CPLEX and the heuristic algorithm in the case of Torino with energy sell-back.

Fig. 7. Comparison between CPLEX and the heuristic algorithm in the case of Aswan, no energy sell-back.

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

Fig.6showsthecomparisonbetweentheresultsofCPLEXand 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,showninFig.5.

Similar towhatwe dowithTorino, wecomparetheresultsof CPLEXand theheuristic algorithm forthecase ofAswan;results are reportedinFig.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., without grid power), during the 9th year under the residential traffic profile, in Torino.

thedifferencesbetweenthesolutionsbecomerathersmall.Wecan concludethat theheuristicapproachleads,inshortertime, toso- 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.Table4re- 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%)savesalotintermsofcostandPVpaneldimensionwithre- 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. 8shows thesimulation ofthe battery charge statusforthe pure solarsystem(PT=100%). Thered part ofthecurverefers totheamountofenergythat cannotbestored insidethebatteries.Thispartofenergyissoldbacktothepower grid,ifthisispossible,anditiswastedotherwise.

The green part in Fig. 8 represents the battery charge status.

Thebatterystatusiskeptabove30%,whichisathresholdthatpro- videsasafetymargininthe design.Thefigurealsoclearlyshows that theenergyproduction bottleneckis inwinter(at thebegin- ningandtheendofthe year)wherethedischargeofthebattery is much deeper. Therefore,to satisfy the requirementduring the winterseason,morebatteriesandlargerPVpanelshavetobein- stalled,andthisleadsto alargerenergywastageduringsummer.

Byintegratingthepercentageofbatterycharginganddischarging,

Table 4

Size and cost of the powering system for the 9-th year dimensioning case, in Torino.

PT PV size [kWp] No. batt. PV+batt. cost [k€] Grid cost [k€ /y] Pay back [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. Example of battery status for a system with kWp = 4.3, 5 batteries, PT = 70%, during the 9th year under the residential traffic profile, in Torino.

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

Fig. 9showsthebatterystatusofthehybridsolar-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)andthelargernumberofbatteryreplace- mentsdoesnotimpairtheadvantageofthehybridsystem.Wewill discussthecoston10yearperiodsinthenextsection.

6.1.2. Capexandopexina10yearperiod

Nowwefocusonthesystemcostduringthewhole10yearpe- riod.Fig.10reportsthecaseinwhichenergysell-backisnotpos- 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 thetradi- tionalpowergrid.

Fig. 10. Total cost for some values of PT , no energy sell-back, in Torino.

Fig. 11. Total cost for some values of PT , with extra-energy sell-back, in Torino.

Fig.11showstheresultsforthecasewithenergysell-back.In thesecases,hybridsystemsreducecostfromthe6thyearwithre- specttothepowergrid.Thepuresolarsystem,beingdimensioned withlarger panels, results moreconvenient than the hybrid sys- tems.However, thepuresolarsystemsareusuallydeployedinru- ralareaswherethereisnoaccesstothepowergrid,sothatextra- energy cannot be soldback. Therefore, forcomparison purposes, we also show the pure solarenergy systemwithout energysell- back.Thehybridsystemwithsell-backsavesabout70%to80%of thecostbythe10thyearcomparedtothepuresolarsystemwith- outsell-back.

Table 5

Size and cost of the powering system for the 10th year dimensioning case, in Aswan.

PT PV size [kWp] No. batt. PV+batt. cost [k€] Grid cost [k€ /y] Pay back [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. Battery status, PT = 100%, in Aswan.

Fig. 13. Battery status, PT = 70%, in Aswan.

6.2. Aswanresults

6.2.1. Systemdimensioning

Aspreviouslymentioned,inthecaseofAswan,the10-yeardi- mensioningleadstochoosetheparameters’settingcorresponding to the 10th year (it was the 9thyear in the caseof Torino). In- deed,onlytheconservativecaseofthe10thyearparametersleads toasystemthatcanguaranteetheconstraintonPTforthewhole period.Table 5showsthe 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%), whileFig. 13 showsthe battery statusof thehybrid system (PT=70%). Comparing thesetwo figures withFigs. 8 and 9,observethatthebatteryhasdeepercharginganddischargingin the Aswan casethan in the Torino case. In Aswan, the solarra-

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. Total cost for different values of PT in Aswan, no energy sell-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. Total cost for different values of PT in Aswan, with extre energy sell-back.

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

6.2.2. CapExandOpExina10yearperiod

Fig.14showsthecomparisonofdifferentpoweringsystems(for thecasesofpuresolar,hybridsolar-grid,gridonlyanddieselgen- erator)inAswan,withoutenergysell-back,whileFig.15showsthe results withenergy sell-back. Bycomparing thetwo figures, ob- servethattheamountofenergythatissold-backissosmallthat

thetwofiguresarealmostthesame.Thisisduetothedimension- 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.

TodiscusstheeffectivenessoftheinvestigatedBSpoweringsys- 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 alsore- 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 thesolarsolutionevenmoreattrac- tiveintheyearstocome.

Acknowledgment

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

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Yi Zhang received his B.E. and Ph.D. degree both from Department of Electronic Engineering, Tsinghua University, Beijing, China, in 2007 and 2012, respectively. He was a visiting Ph.D. student at University of California, Davis, U.S.A. from September 2008 to August 2010. He was a postdoctoral researcher at Politecnico di Torino, Italy from November 2012 to May 2015. From June 2015 he has been a postdoctoral researcher at Trinity College Dublin, Ireland. His research interest includes energy-efficient wireless networks and optical networks. He has co-authored over 5 IEEE and Elsevier journal papers. He has served as a Technical Program Committee member for over 10 IEEE and ACM conferences.

Michela Meo received the Laurea degree in Electronic Engineering in 1993, and the Ph.D. degree in Electronic and Telecommunications Engineering in 1997, both from the Politecnico di Torino, Italy. Since November 2006, she is associate professor at the Politecnico di Torino. She co-authored about 200 papers and edited a book with Wiley and six special issues of international journals, including ACM Monet, Performance Evaluation, and Computer Networks. She chairs the Steering Committee of IEEE OnlineGreenComm and the International Advisory Council of ITC. She was program co-chair of several conferences among which ACM MSWiM, IEEE Online GreenComm, IEEE ISCC, IEEE Infocom Miniconference, ITC. Her research interests include the field of performance evaluation and modeling, green networking and traffic classification and characterization.

Raffaella Gerboni received the MSc in Energy Nuclear Engineering in 20 0 0 and a PhD in Energy Engineering in 2006 both from the Politecnico di Torino. She received a five year contract as a Researcher at the Energy Department of Politecnico where she has been also a Post Doc Fellow Researcher for more than five years. She has authored a book chapter with Woodhead–Elsevier and co-authored a book chapter with Springer. She is member of the Editorial Board of the International Journal of Contemporary Energy and serves as a reviewer for 3 Elsevier Journals. Her expertise is focused on energy systems analysis and on clean and efficient energy technologies. She has been responsible for MSc and Specializing Master Courses.

Marco Ajmone Marsan holds a double appointment as Full Professor at the Department of Electronics and Telecommunications of the Politecnico di Torino (Italy), and Research Professor at IMDEA Networks Institute (Spain). He earned his graduate degree in Electrical Engineering from the Politecnico di Torino in 1974 and completed his M.Sc. in Electrical Engineering at the University of California at Los Angeles (USA) in 1978. In 2002, he was awarded a “Honoris Causa” Ph.D. in Telecommunication Networks from the Budapest University of Technology and Economics. From 2003 to 2009 he was Director of the IEIIT–CNR (Institute for Electronics, Information and Telecommunication Engineering of the National Research Council of Italy). From 2005 to 2009 he was Vice-Rector for Research, Innovation and Technology Transfer at Politecnico di Torino. Marco Ajmone Marsan is involved in several national and international scientific groups: He was Chair of the Italian Group of Telecommunication Professors (GTTI); the Italian Delegate in the ICT Committee and in the ERC Committee of the EC’s 7th Framework Programme. He is a Fellow of the IEEE and he is listed by Thomson-ISI amongst the highly-cited researchers in Computer Science. He has been principle investigator for a large number of research contracts with industries, and coordinator of several national and international research projects.