Optimization Strategy for Improving the Energy Efficiency of Irrigation Systems by Micro Hydropower

21 Pages·2017·8.3 MB·English

water
Article
Optimization Strategy for Improving the Energy
Efficiency of Irrigation Systems by Micro
Hydropower: Practical Application
ModestoPérez-Sánchez1 ID,FranciscoJavierSánchez-Romero2 ID,HelenaM.Ramos3 ID
andP.AmparoLópez-Jiménez1,* ID
1 HydraulicandEnvironmentalEngineeringDepartment,UniversitatPolitècnicadeValència,
46022Valencia,Spain;[email protected]
2 RuralandAgrifoodEngineeringDepartment,UniversitatPolitècnicadeValència,46022Valencia,Spain;
[email protected]
3 CivilEngineering,ArchitectureandGeoresourcesDepartament,CERIS,InstitutoSuperiorTécnico,
UniversidadedeLisboa,1049-001Lisboa,Portugal;[email protected]
* Correspondence:[email protected];Tel.:[phone](ext.86106)
Received:4August2017;Accepted:16October2017;Published:17October2017
Abstract: Analyses of possible synergies between energy recovery and water management are
essentialforachievingsustainableadvancesintheperformanceofpressurizedirrigationnetworks.
Nowadays,theuseofmicrohydropowerinwatersystemsisbeinganalysedtoimprovetheoverall
energyefficiency. Inthisline,thepresentresearchisfocusedontheproposalanddevelopmentof
anoveloptimizationstrategyforincreasingtheenergyefficiencyinpressurizedirrigationnetworks
byenergyrecovering. Therecoveredenergyismaximizedconsideringdifferentobjectivefunctions,
includingfeasibilityindex: thebestenergyconvertermustbeselected,operatinginitsbestefficiency
conditionsbyvariationofitsrotationalspeed,providingtherequiredflowineachmoment. These
flows(previouslyestimatedthroughfarmers’habits)arecomparedwithregisteredvaluesofflow
inthemainlinewithverysuitablecalibrationresults,gettingaNash–Sutcliffevalueabove0.6for
differenttimeintervals,andaPBIASindexbelow10%inalltimeintervalrange. Themethodology
was applied to a Vallada network obtaining a maximum recovered energy of 58.18 MWh/year
(41.66%oftheavailableenergy),improvingtherecoveredenergyvaluesbetween141and184%when
comparingtoenergyrecoveryconsideringaconstantrotationalspeed. Theproposalofthisstrategy
showstherealpossibilityofinstallingmicrohydropowermachinestoimprovethewater–energy
nexusmanagementinpressurizedsystems.
Keywords: irrigationsystems;optimizationstrategy;water–energynexus;pumpworkingasturbine
1. Introduction
Modernsocietyisincreasinglyawareoftheneedtoimproveenergyefficiencyacrossallindustrial
sectorsandprocesses. Increasedsustainabilitycanbeachievedthroughthedevelopmentofrenewable
energysourcessuchasphotovoltaic,wind,tidalorhydropower. Toreachthissustainablegrowth,
deepmanagementisnecessary[1]. Waterdistributionsystems,particularlyirrigationsystems,have
not been included in this trend, considering that these infrastructures are high energy consumers
regarding the captation, distribution and reuse of water resources. The importance of hydraulic
systems as energy consumers is shown through the worldwide consumption of energy, in which
theenergyconsumptionforwatersupplynetworksrepresents7%ofthetotalconsumedenergy[2].
Ifthisvalueisdiscretized,thedistributionisapproximatelyone-third(2–3%)ofthisconsumption[3].
Therefore, consideringtheneedtodevelopsustainablegrowthinwatersystems[4]sincethe
distributionofwaterisanintensiveenergyprocess[5],newstrategiesshouldbeintroducedforwater
Water2017,9,799;doi:10.3390/w9100799 www.mdpi.com/journal/water
Water2017,9,799 2of21
managementsystems. Theaimofthesestrategieshastobetheimprovementoftheenergyefficiency
andthedecreaseofthecarbonfootprint[6], consideringthebasicprinciplesfortheintegrationof
the water and carbon footprints cost into the resource and environmental costs respectively [7–9],
aswellasnewlyavailabletechnologiesthatimprovethewatermanagementoftheresourcesandtheir
feasibility[10,11].Thesestrategiesmustconsidertheflowvariationovertimeinextendedperiodssince
theanalysisofthelong-extendedperiodenablesustoanalysethebehaviourofthemicrohydropower
systemswhentheflowchanges[12]. Hence,theinstallationofrecoverysystemsisoneofthemost
effectivestrategiestobeusedinplaceswheretheenergyhastobedissipated(e.g.,pressurereduction
valves(PRVs)orhydraulicjumps[13–15]),withhighfeasibilityindexes[16].
Deepknowledgeofthewater–energynexusinhydraulicsystemsisessentialtodefineandto
introducenewactionlinesfortheirmanagementinordertodefineperformanceindicators[17,18].
Theanalysisofthewater–energynexus,whichdependsontheintrinsicfactorsofthehydraulicsystems,
definesthepotentialenergyrecoveryinanyhydraulicsystem.Oncethewater–energynexusisdefined,
theperformanceindicatorscanbeestablished,quantifyingtheenergysavingsandcontributingto
theimprovementofthesustainable,environmental,economic,andmanagementcomponents[19–22].
Theimprovementoftheseindicatorswastackledforwatersystemsusingoptimizationanalysesfor
thelocationsofthehydropowersystems[23,24],aswellasdevelopingcomparisonsbetweendifferent
algorithms[25].
Thepresentresearchisfocusedoncontributingtotheknowledgepertainingtotheoperating
modeofenergyrecoverysystems,whentheyareinstalledinpressurizedwaternetworks(particularly
in irrigation networks). The aim of this research is centred on the proposal and development of
amethodologytoimproveenergyefficiencyinpressurizedirrigationnetworks. Theimprovementis
achievedthroughtheinstallationofmicrohydropowerturbines,whichtakeadvantageofthehigh
pressureinsomezonesofthenetworkbyrecoveringtheexcessofthepressure-generatinggreenenergy.
Thisisachievedbyreplacingpressurereductionvalves,currentlyinstalledinthewatersystemsto
reducethepressurebymicrohydropower,reducing,asaconsequence,leakages[26,27].
2. MethodsandMaterialsintheOptimizationStrategy
Thedevelopmentofamethodologytooptimizetheenergyrecoveryinpressurizedwatersystems
iscarriedout,andthestrategyisparticularlyappliedtoirrigationnetworks. Therefore,theresearchis
definedbyanensembleofmethodologiesandmaterials,inwhichtheresultsandtheircorrelations
constitutethemethodologytooptimizeenergyrecoveryinpressurizedwatersystems.
2.1. Methods
Theusedmethodswerefocusedon(i)thedefinitionoftheanalyticalmodeltodeterminetheflow
overtime;(ii)thestrategytovalidatethemethodologytoestimatetheflowineachlineofthenetwork;
(iii)theoptimizationoftherecoveredenergybyananalyticalstrategy; (iv)thestudyofanalytical
models to know the efficiency in quasi-steady flow conditions when the demand changes using
affinitylawsformachineoperatingconditions;and(v)simulationoftheanalyticalmethodbyusing
ahydraulicnumericalmodeltoknowthepressureandflowovertimeineachline.
The definition of the analytical model to determine the flow over time was focused on the
determination of the opening or closing irrigation points, depending on the balance between
theirrigationneedsandtheirrigationcumulatedvolume. Theopeningofanirrigationpointwas
establishedondifferentpatternsthatshowtheirrigationtrendsoffarmers,suchastheweeklytrend,
themaximumdaysbetweenirrigation,andtheirrigationduration. Thedefinitionofthesepatterns
enablesustodeterminethetimeforthestartofirrigation.
Thecalibrationstrategywasbasedonkeyperformanceindicators(KPIFs),comingfromtraditional
hydrological models [28,29]. The KPIFs were Nash–Sutcliffe (E), root relative square error (RRSE)
andpercentofbias(PBIAS).Thesecalibrationindicatorsenableustodeterminethegoodness-of-fit
betweenestimatedandregisteredflows.
Water2017,9,799 3of21
Thedevelopedoptimizationwascarriedoutintwophasesbyananalyticalstrategy. Thefirstwas
focused on the integral balance of the energy in a control volume [30]. The energy terms were
defined, distinguishing between recoverable and non-recoverable energy. The estimation of these
termsdependedontherequiredenergyforirrigation. Thesecondphasewasproposedtodevelop
anoptimizationstrategythroughaheuristicalgorithmthatwasbasedontheanalogywiththephysics
processoftheannealingofmetalsandwhichinspiredtheMonte-Carlomethod[31]. Basedonthis
algorithm,preliminarystudieswereusedtoallocatethreemachines[32]. However,therecovered
energy in a recovery system depended on the efficiency of the implemented hydraulic machine.
ThestrategiesofregulationthatweredefinedbyCarravettaetal.[33],wereconsideredtodetermine
the recovered energy since the flow varies over time in any water system. This management was
based on the affinity laws and characteristic parameters of the hydraulic machines. The objective
wastoanalysethevariationofheadandefficiencycurvesasafunctionoftherotationalspeedwhen
themachineoperatesundersteadystateconditions.
Oncetheanalyticalmethodhadproposedtheconsumptionpatternscurves,simulationswere
developedtobeappliedtodifferentcasestudies. ThesoftwareusedwasEPANET[34]software,which
isapublicdomainsoftwarethatmodelswaterdistributioninpipesystems. Differentelementscan
be represented: pipe networks, nodes (junctions), pumps, valves, and storage tanks or reservoirs.
Themodelcananalyseextended-period,computingfrictionandminorlosses;representvarioustypes
ofvalves,junctions,tanksandpumps;considermultiplepatternsofnodeconsumptionovertime;and
operatethesystemofasimpletanklevel,timercontrolsorcomplexrule-basedcontrols.
2.2. Materials
Inthisparticularcase,thematerialsaretheexperimentaldata,whichwereobtainedalongthe
development of this research. These materials were collected through different strategies: (i) the
developmentofinterviewstogettoknowthefarmers’habits. Thedatawereusedasinputdatain
theanalyticalmodelthatwasdevelopedtoestimatetheflowovertime;(ii)thedataforregistered
flowoverthetimeoftheirrigationnetwork;(iii)theexperimentalcurvesbasedonthecharacteristic
parameters(dischargeandheadnumber)asafunctionofthespecificspeed.
Theinterviewswithfarmersweredevelopedintheirrigationcommunitythatisrelatedtothecase
study. Theresultswereafterwardsusedtodeterminethepatternstoestimatetheflowbytheproposed
methodology in the case study. The registered flow data were used to carry out the calibration
strategy. Thedatawereobtainedbyaflowmeter,whichwasinstalledinthemainlineoftheanalysed
irrigationnetwork.
The final materials used were the head-flow characteristic curve (Q-H) and the efficiency as
a function of the flow (Q-η). However, other methodologies to model this performance have
been implemented, since there were no available experimental values for the recovered head and
theefficiencyasafunctionoftheflowfordifferentrotationalspeedstobeusedformodelling. Hence,
thePATwillbecharacterizedthroughthespecificspeed,theimpellerdiameterandtherotationalspeed.
Asanovelty,thenextsectiondescribesthecharacterizationofthishydraulicmachine. Theproposed
methodconsidersthebestefficiencyline(BEL)andthebestefficiencyhead(BEH)asthestrategyused
tooptimizetheenergy-recoveringactions. BEL(Figure1)isthelinethatestablishesthemaximum
efficiencyofonemachineforadeterminedrotationalspeedandflow. BEHisthelinethatisassociated
with BEL and represents the recovered head when the efficiency is maximum for each rotational
speed[35].
Water2017,9,799 4of21
Water 2017, 9, 799 4 of 21

FiFgiugruere1 .1.B BEELLa anndd BBEEHH ooppeerraattiioonn sscchheemme.e .
Characterization of the Hydraulic Machine
CharacterizationoftheHydraulicMachine
The characterization of the hydraulic machine is necessary in the optimization strategy. In this
Thecharacterizationofthehydraulicmachineisnecessaryintheoptimizationstrategy. Inthis
research, a synthetic PAT module is proposed based on characteristic parameters (head number (ψ)
research,asyntheticPATmoduleisproposedbasedoncharacteristicparameters(headnumber(ψ)
and discharge number () [36]) that are shown in Figure 2. These characteristic numbers are defined
anddischargenumber(ϕ)[36])thatareshowninFigure2. Thesecharacteristicnumbersaredefined
by Equations (1) and (2):
byEquations(1)and(2):
Q(cid:1843)
ϕφ== (1) (1)
N(cid:1840)D(cid:1830)(cid:2871)3
Hg
ψ= (2)
N(cid:1834)2D(cid:1859)2
ѱ= (2)
whereQistheflowinm3/s;Nistherotationalsp(cid:1840)e(cid:2870)e(cid:1830)d(cid:2870)ofthemachineinrpm;andDistheimpeller
diameterinm.
where Q is the flow in m3/s; N is the rotational speed of the machine in rpm; and D is the impeller
Theturbinecharacterization(Figure3)isdevelopedbythefollowingthenextsteps:
diameter in m.
The turbine characterization (Figure 3) is developed by the following the next steps:
1. Selectionoftheoperationparameters: differentparametersmustbedefined. Toestablishadatabase
1.o fsSyenletchtieotni cofP tAheT osp(eirnatitohni spapraamrteicteurlsa: rdicfafesreen8t8 p93ardamiffeetreersn mtPuAstT bsew deerfiendede.fi Tnoe eds)t.aTblhisehd aa dtaatbaabsaesew as
devoefl osypnetdhetthicro PuAgThsc (hina rtahciste priasrttiiccucluarrv ceasseth 8a8t9a3r deisffheorewnnt PinAFTisg wureere2 d(Ienfipnuedt)1. )Tahsew dealtlaabsasceh wanags ing
thedfeovlleolowpiendg tphraoruamghe ctehrasr:acteristic curves that are shown in Figure 2 (Input 1) as well as changing
the following parameters:
a. Specificspeed(n ): definedaccordingtoEquation(3):
s
a. Specific speed (ns): defined according to Equation√ (3):
P
(cid:1866) =n(cid:1840)s =(cid:3493)(cid:1842)N(cid:3019) H1.2R5 (3) (3)
(cid:3046) (cid:1834)(cid:2869).(cid:2870)(cid:2873) R
(cid:3019)
whereNistheratedrotationalspeed(rpm);P istheratedpower(kW);H istherated
where N is the rated rotational speed (rpm); PR is tRhe rated power (kW); HR is the rRated head
h(ema dw(.cm.);w b.eci.n);gb ‘Rei’n tghe‘ Rp’utmhep pduesmigpn dpeosinigt norp tohien bteosrt tehffeicbieenstcye fcfiocnidenitcioync. ondition.
TThheer raannggee ooff ssppeecciiffiicc ssppeeeedd ooscsiclillaltaetse bsebtewteweene 1n4 1a4ndan 7d9 r7p9mrp (mm, (kmW,)k. W).
b. b. RRotoattaitoionnaall ssppeeeedd ((NN)):: tthhee rraannggee ooff tthhee rroottaatitoionnaal lspspeeede dosocsilclialtleadte bdebtwetewene e5n105, 1100,2100, 2200,402,0 40,
24204000,,a anndd2 2990000 rrppmm..
c. Impeller Diameter (D): the range of the defined impeller was between 0.04 and 0.6 m.
c. ImpellerDiameter(D):therangeofthedefinedimpellerwasbetween0.04and0.6m.
d. Variation of the rotational speed: when the machine operates with a different rotation speed
d. Variationoftherotationalspeed:whenthemachineoperateswithadifferentrotationspeedas
as a function of the flow, the coefficient (α) that is defined by Equation (4) can vary between
afunctionoftheflow,thecoefficient(α)thatisdefinedbyEquation(4)canvarybetween
0.5 and 1.5.
0.5and1.5.
N
α= t (4)
N
0
where Nt istherotationalspeedforeachtimeinrpm; and N0 isthenominalrotational
speedinrpm.
Water 2017, 9, x FOR PEER REVIEW 5 of 21
(cid:1840)
(cid:3047)
α = (4)
(cid:1840)
(cid:2868)
where (cid:1840) is the rotational speed for each time in rpm; and (cid:1840) is the nominal rotational
(cid:3047) (cid:2868)
Water2017,9,799 5of21
speed in rpm.

Figure2.Characteristiccurvesbasedonexperimentaltestsandaffinitylaws[35,37,38].
Figure 2. Characteristic curves based on experimental tests and affinity laws [35,37,38].
2. Tointerpolatecharacteristiccurves:whenthespecificspeedisdefinedandthen curveisnotknown,
s
2. Tthoe ivnatelurpeoslaotfe hcehaadranctuemrisbteicr (cψurinvte)s:a nwdheefnfi ctiheen csyp(eηciinfti)c fsopreeeadc hisd idsecfhianregde annudm tbheer vnas lcuuer(vφei nits) anroet
kesntoimwant,e tdhbe yvlailnueeasr oinf theerpadol antuiomnber (ψint) and efficiency (ηint) for each discharge number value
3. (Tϕoingt)e nareera etsethimeaadteadn dbyef filicnieenarc yinctuerrvpeoslaatsioanf unction of flow: when the characteristic numbers are
3. Tdoe figneenderafoter heaeacdh adniad mefefitceirenacnyd cruortvaetsi oansa al sfupneectdio(nN o0f) ftlhoawt: awrehseenl etchtee dchinarsatectperoinstei,c tnhuemhebaedrsa narde
defefifcinieendc yfocru eravceha dreiadmeetetermr ainnedd rboytaEtiqounaatli ospnese(d5 )(tNo0()7 t)h:at are selected in step one, the head and
efficiency curve are determined by Equations (5) to (7):
Q =ϕ ND3 (5)
int

ψ N2D2
H = int (6)
g
η=η (ϕ ) (7)
int int
Water 2017, 9, 799 6 of 21
(cid:1843) = (cid:1840)(cid:1830)(cid:2871) (5)
(cid:3036)(cid:3041)(cid:3047)
 (cid:1840)(cid:2870)(cid:1830)(cid:2870)
(cid:3036)(cid:3041)(cid:3047)
(cid:1834) = (6)
Water2017,9,799 (cid:1859) 6of21
η= ( ) (7)
Thepolynomicequationsarefittedtotheob(cid:3036)t(cid:3041)a(cid:3047)ine(cid:3036)(cid:3041)d(cid:3047)values(themaximumconsidereddegreeis
four)throughlinearregressionbyEquations(8)and(9):
The polynomic equations are fitted to the obtained values (the maximum considered degree is
four) through linear regression by Equations (8) and (9):
Hα=1 = AQ4+BQ3+CQ2+DQ+E (8)
(cid:1834) =(cid:1827)(cid:1843)(cid:2872)+(cid:1828)(cid:1843)(cid:2871)+(cid:1829)(cid:1843)(cid:2870)+(cid:1830)(cid:1843)+(cid:1831) (8)
(cid:2880)(cid:2869)
η = FQ4+GQ3+HQ2+IQ+J (9)
α=1
 =(cid:1832)(cid:1843)(cid:2872)+(cid:1833)(cid:1843)(cid:2871)+(cid:1834)(cid:1843)(cid:2870)+(cid:1835)(cid:1843)+(cid:1836) (9)
(cid:2880)(cid:2869)
Thesecurvescanbeusedwhentheflowisbetweentheinterpolatedrange,whereA,B,C,Dand
EareTchoeesfefi cciuernvtesso cfatnh ebeQ u-Hsedch warhaecnt etrhies tfilcocwu risv ebeatnwdeFen,G th,eH i,nItearnpdolJaatered croaenfgfiec,i ewnhtseroef Ath, eB,e Cffi, cDie anncdy
cEu arrvee .coTehfefiflcioewntsli mofi tthoef Qth-eHt ucrhbairnaectiesrdisetfiicn ceudrbvye aanmdi nFi, mGu, Hm, eIf afincide nJ cayrec oconedfiftiicoinen,wts hoifc hthies epfrfoicpioensecdy
tcourbvee0. .T3hfeo rfltohwis lciamsiet sotfu tdhye. turbine is defined by a minimum efficiency condition, which is proposed
to be 0.3 for this case study.
1. Definition of the operation Characteristic curves
parameters: Head number; =fn()
ns, N, D , min, max ymin. Efficiency;  =fn()
Yes Isnsknown
exactly?
No
2. Interpolatethe
characteristiccurves
int-int-int
3. Generatehead and
efficiencycurves for=1
Q=intND3
H= intN2D2
4. ObtainRunawaycurve
5. DevelopBEH/BEL pointsfor
= range(min, max)
Are theremore Yes
turbine togenerate?
No
END
The recovery machine can be
used in the optimization strategy

FFiigguurree 33.. SScchheemmee ooff tthhee ooppeerraattiioonn ooff tthhee ttuurrbbiinnee ((PPAATT)) mmoodduullee..
3. To obtain runaway curve: the runaway curve is generated by second polynomic equation curve
4. tThoaot bctoanintariunns atwhea yfoclulorvwei:ntgh eporuinntasw: caoyorcduirnvaeteiss ogreingeinra atnedd tbhye smecionnimdupmol yvnaloume iocbetaqiunaetdio tnhrcouurgvhe
Ethqautactoionnta (i8n)s. thefollowingpoints: coordinatesoriginandtheminimumvalueobtainedthrough
Equation(8).
5. TodevelopBEL/BEH:thebestefficiencypointisestimatedforeachrotationalspeed(α),adjusting

byregressionthecurvesdefinedbyEquations(10)and(11):
H = HQ4+IQ3+JQ2+KQ+L (10)
BEH
Water2017,9,799 7of21
η = MQ4+NQ3+OQ2+PQ+R (11)
BEL
whereH,I,J,KandLcharacterisethebestefficiencyheadandM,N,O,PandRarecoefficients
thatdefinethebestefficiencyline.
2.3. OptimizationStrategy
When the previously-cited material and methods are implemented, the development of the
optimizationstrategytoimprovetheenergyefficiencyinpressurizedirrigationnetworksispossible.
Thedevelopmentofthisstrategymakessensesincetherearenotanysimilarstrategiesforpressurized
waterdistributionnetworkspublishedintheexpertliterature. Thedevelopedoptimizationstrategy
fortheenergyefficiencyimprovementisdefinedbydifferentsteps. Thismethodologyneedsdifferent
inputs. Theprocedureisshowedinthefollowingflowchart(Figure4).
1. Theknowledgeoftheflowovertimeisthestartingpointintheoptimizationstrategy. Theflow
canbeknownwhenthewatermanagerhasflowmetersinthepipes. However,theknowledge
of the flow in all lines over time is almost impossible, and therefore, the flow has to be
estimatedineachline. Inthissortofirrigationwaterdistributionnetwork,theflowdependson
consumptionflowpatternswhichmustbedeterminedasafunctionoftheagronomistparameters.
Toestimatetheconsumptionflowpatterns,theusedmethodologyconsidersthefarmers’habits
andthecharacteristicsofthenetwork[39]. Thismethodologyisabletoestimatetheflowover
timeinanylineofthesystems,dependingonthenetworkcharacteristics(Input1)andthefarmers’
habits(Input2). Thefarmers’habitsareirrigationneeds,irrigationduration,maximumdays
between irrigation and the irrigation volume. The knowledge of the farmers’ habits allows
the determination of the opening or closing in consumption nodes over time. The state of
theirrigationpointdeterminestheflow(Output1)ofthestrategy. Thisoutputisaninputfor
thenextstep: Input3.
2. Thesecondstagestandsonthecalibrationstrategy. Ituseskeyperformanceindicators(KPIFs)
thatareadaptedfromthetraditionalhydrologicalmodels(Input4)[40]. Thecharacterizationof
thegoodness-of-fitisdividedintoverygood,good,satisfactory,andunsatisfactory,depending
ontheKPIFvalues(Table1). Thecomparisonisdevelopedwiththeregisteredflowdata(Input5)
todeterminethesuccessofthefit. Ifthecalibrationissatisfactory,theenergybalance(Step3)can
bedone.
Table1.Classificationofthegoodness-of-fit(adaptedfrom[40]).
Goodness-of-Fit E RRSE PBIAS(%)
VeryGood E>0.6 0.00≤RRSE≤0.50 PBIAS<±10
Good 0.40<E≤0.60 0.50<RRSE≤0.60 ±10≤PBIAS<±15
Satisfactory 0.20<E≤0.40 0.60<RRSE≤0.70 ±15≤PBIAS<±25
Unsatisfactory E<0.20 RRSE>0.70 PBIAS>±25
Water2017,9,799 8of21
Water 2017, 9, 799 8 of 21
Network’s 1. Determination
Farmer’s habits
characteristics ofconsumption
(Input 1)
(Input 2) patterns
Estimated flows
overtime
(Output 1// Input 3)
Registeredreal flows
Proposed KPIF 2. Calibration
overtime
(Input 4) Strategy
(Input 5)
Goodness No
fitof KPIFs
Minimum irrigation Yes
pressure in
3. Energy Balance
consumption point
(Input 6)
Estimated pair
data (Q, H)
(Output 2// Input 7)
4. Selection of the machine
Experimental values No Are
(Head and Efficiency) machines
curves
(Input 8) known?
Yes
5. Modifiedaffinitylaws
Turbine BEL; BEH
module (Output 4// Input 9)
Economical
6. Energy
feasibility index
Maximization Strategy
(Input 10)
OPTIMIZATION STRATEGY
Final Outputs:
- Optimal number of machines
- Optimal rotational speed depending
on flow
- Real energy recovered
- Efficiencyparameterstoanalysethe
energy improvement

FFiigguurree4 4.. SScchheemmee ooff tthhee ooppttiimmiizzaattiioonn ssttrraatteeggyyt tooi immpprroovveet thheee enneerrggyye effiffcicieiennccyy..
3. The energy balance is able to discretize different energy terms (e.g., total, irrigation, friction)
3. The energy balance is able to discretize different energy terms (e.g., total, irrigation, friction)
differentiatingthetermsfortheavailableenergybetweenthetheoreticallyrecoverableenergy
differentiating the terms for the available energy between the theoretically recoverable energy
andtheoreticallynon-recoverableenergy,consideringtheminimumirrigationpressureateach
and theoretically non-recoverable energy, considering the minimum irrigation pressure at each
consumptionpoint(Input6)[39]. Theavailableenergyenablesustodeterminethetheoretical
consumption point (Input 6) [39]. The available energy enables us to determine the theoretical
recoverycoefficientatanyline,hydrantorconsumptionpoint. Inaddition,theenergybalance
recovery coefficient at any line, hydrant or consumption point. In addition, the energy balance
enablesustoestimatetherecoveredheadforeachflowovertime. Knowingthesepairsofdata
enables us to estimate the recovered head for each flow over time. Knowing these pairs of data
(Q, H), the most suitable machine at each study point can be selected. The formula used to
(Q, H), the most suitable machine at each study point can be selected. The formula used to
determinetheannualbalanceofthenetworkisdefinedbyEquations(12)to(18):
determine the annual balance of the network is defined by Equations (12) to (18):
E = E +E + E +E (12)
(cid:1831)T=(cid:1831) FR+(cid:1831) R+I (cid:1831) T+R (cid:1831) N TR (12)
(cid:3021) (cid:3007)(cid:3019) (cid:3019)(cid:3010) (cid:3021)(cid:3019) (cid:3015)(cid:3021)(cid:3019)
9.81
E (kWh) = Q (z −z )∆t (13)
Ti 9.386100 i o i
(cid:1831) (kWh)= (cid:1843)((cid:1878) −(cid:1878))(cid:1986)(cid:1872) (13)
E (kW(cid:3021)(cid:3284)h) =2.72356·1000−3(cid:3036)Q ((cid:3042)z −(cid:3036)(z +P))∆t (14)
FRi i o i i
Water2017,9,799 9of21
E (kWh) =2.725·10−3Q P ∆t (15)
RIi i minIi
E (kWh) =2.725·10−3Q H∆t (16)
TRi i i
E (kWh) =2.725·10−3Q (cid:0)P −P (cid:1)∆t (17)
TAi i i mini
E = E −E (18)
NTRi TAi TRi
whereE isthetotalprovidedenergyinthenetwork(kWh/year);E isthetotalfrictionenergy
T FR
inthenetwork(kWh/year);E isthetotalrequiredenergytoirrigatecorrectlyallconsumption
RI
points (kWh/year); E is the total theoretical recovered energy in the network (kWh/year);
TR
E isthetotalunrecoverableenergyinthenetwork(kWh/year);E isthepotentialenergyin
NTR Ti
eachirrigationpointwhentheconsumptioninthenetworkisnull(kWh);E isthedissipated
FRi
frictionenergyuntiltheirrigationpoint(kWh);E istherequiredenergyattheconsumption
RIi
pointtoensuretheirrigation(kWh);E istheavailableenergyforrecoveryinahydrantorline
TAi
(kWh); E isthemaximumtheoreticalrecoverableenergyinanirrigationpoint,hydrantor
TRi
lineofthenetwork,ensuringtheminimumpressureofirrigationdownstream(kWh);E is
NTRi
theenergythatcannotberecoveredinahydrantorlineonthenetwork(kWh);Q istheflowby
i
aline(m3/s);z isthegeometrylevelabovereferenceplaneoftheirrigationpoint,considering
i
the reference datum level (m); z is the geometry level above the reference plane of the free
o
watersurfaceofthereservoir(m); P istheservicepressureinanypointofthenetworkwhen
i
consumption exists (m w.c.); P is the minimum pressure of service of an irrigation point
minIi
requiredtoensuretheirrigationwaterevenly;and H isthevalueoftheheadofanirrigation
i
point,hydrantorline(mw.c.). Thisheadisobtainedas H = P −max(cid:0)P ;P (cid:1);and∆tis
i i mini minIi
thetimeinterval(s).
4. Knowingtheflow(Q)andrecoverablehead(H)overtimefromtheenergybalance(Output2,
i i
thatisInput7),enablestheselectionofthehydraulicmachinetype(e.g.,radial,axial)according
to the frequency histogram of the power generated among other conditions. To develop
a guaranteed estimation of the recovered energy, the head and efficiency curve as a function
of flow should be known for different rotational speeds (Input 8). If this information is not
provided by the manufacturer, experimental tests are recommended to obtain the efficiency
variationdependingontheflowandfordifferentrotationalspeeds. However,ifexperimental
tests cannot be carried out, the experimental curves are determined using the characteristic
numbers (discharge and head number, Figure 1) to select a machine considering its specific
speed[41]usingtheturbinethatwasdescribedintheprevioussection(Figure2).
5. Whenthetestsarecarriedorthecharacteristiccurvesareused,themodifiedclassicalaffinitylaws
basedonthevariationofthespecificparameters(dischargecoefficient,q;headcoefficient,h;and
velocitycoefficient,n)canbeused[33,42]. TheseparametersaredefinedbyEquations(19)to(21):
H
h = (19)
H
0
Q
q = (20)
Q
0
N
n = (21)
N
0
where H is the recovered head in m w.c.; Q is the flow through the turbine in m3/s when
therotationalspeedofthemachineisN;andH andQ areheadandflow,respectively,when
0 0
themachineoperatesinitsbestefficiencypoint(BEP),fortherotationalspeedN .
0
Based on modified classical similarity laws (when there are not experimental data), two new
concepts(thebestefficiencyline, BELandbestheadline, BEH)areproposed(Output4). TheBEL
adaptstherotationalspeedasafunctionoftheflow,adjustingthemaximumefficiencyateachtime
Water2017,9,799 10of21
pointandmaximisingtheenergyrecovered.TheBEHrelatesthebestefficiencypointforeachrotational
speedwiththerecoveredheadasafunctionoftheflow[35]. TheknowledgeoftheBELand/orBEH
(Input9)makespossibletheuseofthesecurvestodeveloptheoptimizationoftheenergyrecoveryon
awatersystemthroughthevariationoftherotationalspeedasafunctionoftheflow. Theclassical
lawsaredefinedbyEquations(22)to(24)[36]:
Q (cid:18)D (cid:19)3N
1 = 1 1 (22)
Q D N
0 0 0
H (cid:18)D (cid:19)2(cid:18)N (cid:19)2
1 = 1 1 (23)
H D N
0 0 0
P (cid:18)D (cid:19)2(cid:18)N (cid:19)3
1 = 1 1 (24)
P D N
0 0 0
whereQ istheflowinthenewconditionsoftherotationalspeedinm3/s;D isthediameterofthe
1 1
impellerinthenewN statusinm; D isthenominaldiameteroftheimpellerinm; N isthenew
0 1
rotationalspeedinrpm;H istheheadinthenewNstatusinmw.c.;P istheshaftpowerforeachN
1 1
inkW;andP istheshaftpowerinthenominalconditioninkW.
0
6. ThisnewstrategytomaximizetheenergyrecoveredwasdevelopedbyusingPATsoranytype
ofturbine. Thetheoreticallyrecoveredenergyandtheeconomicfeasibilityindexes(Input10),
particularlythesimplepaybackperiodareconsidered(PSR)[39]. Thisstrategymakesuseof
asimulatedannealingalgorithmtocarryouttheoptimization,selectingthebestlinestoinstall
turbinesasafunctionofthenumberofinstalledturbinesinthewatersystem. Theoptimization
canbedevelopedwithtwodifferentfunctions: thefirstfunctiononlyconsiderstherecovered
energy,whilethesecondoneanalysestheratiobetweenrecoveredenergyandPSR[35]. Thefinal
output results of the optimization strategy are the optimal number of machines to install in
thenetworkaccordingtotheobjectivefunction; theoptimalrotationalspeedasafunctionof
theflow;therealrecoveredenergy;aswellastheefficiencyparameterstoanalysetheenergy
improvementinthenetwork.
3. ResultsandDiscussion
The previously-described methodology was implemented in a real case study for an existing
irrigationnetwork. ThisnetworkwaslocatedinVallada(Valencia,Spain)andthewatermanagerknew
thevolumemeasurementsforthefinaluserpointsaswellasmainlineflowmeasurementsovertime.
3.1. CaseStudyDescription
TheValladanetworkisabranchedagronomicpressurizedwaterdistributionnetwork,inwhich
30mw.c. shouldbeguaranteedateachirrigationpoint,sothatfarmersreceivedqualitywaterservice
(Figure5). Thedrippednetworkhadseventyhydrants,whichsupply371irrigationpoints. These
irrigationpointswereconnectedbypipelineswithdiametersbetween150and500mm.