wa e
A icle
Modeling I iga ion Ne wo ks o he Quan i ica ion
o Po en ial Ene gy Reco e ing: A Case S udy
Modes o Pé ez-Sánchez 1, F ancisco Ja ie Sánchez-Rome o 2, Helena M. Ramos 3
and P. Ampa o López-Jiménez 1,*
1
Hyd aulic and En i onmen al Enginee ing Depa men , Uni e si a Poli ècnica de València, Valencia 46022,
Spain; mopesan1@up .es
2Ru al and Ag i ood Enginee ing Depa men , Uni e si a Poli ècnica de València, Valencia 46022, Spain;
[email p o ec ed].es
3Ci il Enginee ing, A chi ec u e and Geo esou ces Depa amen , CERIS, Ins i u o Supe io Técnico,
Uni e sidade de Lisboa, Lisboa 1049-001, Po ugal; [email p o ec ed]
*Co espondence: palopez@up .es; Tel.: +34-96-387700 (ex . 86106)
Academic Edi o : Ashok K. Chapagain
Recei ed: 29 Feb ua y 2016; Accep ed: 26 May 2016; Published: 1 June 2016
Abs ac :
Wa e i iga ion sys ems a e equi ed o p o ide adequa e p essu e le els in any so o
ne wo k. Qui e equen ly, his equi emen is achie ed by using p essu e educing al es (PRVs).
Ne e heless, he possibili y o using hyd aulic machines o eco e ene gy ins ead o PRVs could
educe he ene gy oo p in o he whole sys em. In his esea ch, a new me hodology is p oposed
o help wa e manage s quan i y he po en ial ene gy eco e ing o an i iga ion wa e ne wo k
wi h adequa e condi ions o opog aphies dis ibu ion. EPANET has been used o c ea e a model
based on p obabili ies o i iga ion and low dis ibu ion in eal ne wo ks. Knowledge o he lows
and p essu es in he ne wo k is necessa y o pe o m an analysis o economic iabili y. Using he
p oposed me hodology, a case s udy has been analyzed in a ypical Medi e anean egion and he
po en ial a ailable ene gy has been es ima ed. The s udy quan i ies he heo e ical ene gy eco e able
i hyd aulic machines we e ins alled in he ne wo k. Pa icula ly, he maximum ene gy po en ially
eco e ed in he sys em has been es ima ed up o 188.23 MWh/yea ) wi h a po en ial sa ing o
non- enewable ene gy esou ces (coal and gas) o CO2137.4 /yea .
Keywo ds:
sma wa e ; wa e -ene gy nexus; ene gy e iciency; sus ainable wa e managemen ;
ene gy eco e ing
1. In oduc ion
Wa e and i s managemen is one o he mo e impo an cu en and u u e global challenges.
I s a iabili y can cause cloudbu s s, making sewe s o o e low, while he sca ci y o wa e in o he
componen s in ol es public se ices and educes i iga ion [
1
]. Hence, an e icien managemen
o wa e i iga ion ne wo ks is c ucial o acing u u e challenges ela ed o he ene gy-wa e
nexus, conside ing he impo ance o i iga ion in he whole plane [
2
]. The de elopmen o he
mode niza ion o i iga ion sys ems in ag icul u e ( eplacing open channel wi h p essu ized i iga ion)
has conside ably inc eased ene gy consump ion in ecen yea s [
3
]. Ne e heless, he es ablishmen o
d ip i iga ion has made mo e e icien sys ems in wa e consump ion bu no in ene gy demand.
Spain is no an excep ion: The annual i iga ion olume consumed in Spain is 16.344 km
3
/yea [
4
]
and he global i iga ion consump ion in p essu e sys ems app oaches 3925 km
3
/yea [
5
].
Consequen ly, he heo e ical ene gy eco e able could be a signi ican amoun .
In Spain, he d ip i iga ed a ea (i.e., 1.7 o 3.54 million o hec a es a e i iga ed by p essu e
sys ems) [
6
] ep esen s 17.56% o he wo ld’s su ace i iga ed by localized d ip (app oxima ely
Wa e 2016,8, 234; doi:10.3390/w8060234 www.mdpi.com/jou nal/wa e
Wa e 2016,8, 234 2 o 26
9 million hec a es) [
7
]. The high ene gy consump ion and he ising cos o a i ha e educed p o i s o
e en he iabili y o a ms [
8
]. The need o s udy s a egies o dec ease he ene gy consump ion in hese
ins alla ions is poin ed ou in he consul ed e e ences. Rega ding his issue, Coehlo e al. es ablished
he need o s udy he eco e y in wa e dis ibu ion sys ems o inc easing he ene gy e iciency,
since he ene gy consump ion in wa e ne wo ks in ol es 7% o he global ene gy consump ion [
9
].
The objec i es o his eco e y a e: o educe he ene gy oo p in o wa e in i iga ion sys em and o
lessen g eenhouse emissions compa ed wi h o he non- enewable ene gy sou ces.
Wa e -ene gy nexus analysis has become a c ucial issue in ecen yea s [
3
,
10
–
13
]. Baki e al. [
10
]
s udied wa e -ene gy in e ac ions in wa e sys ems in A hens. Okade a e al. [
11
] and He a h e al. [
12
]
analyzed wa e oo p in s o hyd oelec ici y. Wa e managemen imp o emen in i iga ion ne wo ks
ha e also been analyzed in [14], whe e a 40% i iga ion educ ion olume was achie ed.
Sus ainable social and economic g ow h based on enewable ene gy sou ces o ces wa e
ne wo ks o wo k as mul ipu pose sys ems [
15
], whe e powe gene a ion is no he i s objec i e bu
an impo an complemen a y one [16].
Some s udies and p o o ypes o eco e ing ene gy wi h small u bines can be ound in he
li e a u e o powe less han 100 kW [
17
–
22
]. The p e ious publica ions o Ca a e a e al. [
17
,
18
]
compa e he easible egula ion sys ems o pump as u bines (PATs). These au ho s [
19
,
20
] de e mined
pe o mance o PATs ins alled in d inking sys ems. The e iciency oscilla es be ween 0.4 and 0.6.
Ramos e al. [
21
,
22
] p oposed new design solu ions o ene gy p oduc ion in wa e pipe sys ems.
These solu ions a e ocused on he ins alling o PATs wi h elec ical o hyd aulic egula ion wi hin
ne wo k. Addi ionally, o he p e ious e e enced au ho s, he a iabili y o he low along ime is
s udied as an objec i e in he p esen esea ch. He e, a deep analysis o heo e ical eco e y ene gy in
he ne wo k is p oposed (i.e., dis inguishing alues o dissipa ed ene gy, necessa y ene gy and losses
in lines and consump ion poin s).
Pa icula ly in i iga ion ne wo ks, some s udies o eco e ing ene gy in open channels
low
[23–25]
and p elimina y s udies in p essu e pipe sys ems a e desc ibed. These show he
impo ance o analyze hese ne wo ks in e ms o eco e y ene gy. An example o hese s udies
is he ne wo k o Alque a in Po ugal [
26
]. In ha con ibu ion, au ho s analyzed he eco e y
ene gy wi h a e age s eady s a e lows. A disc e ized analysis in sho ime in e als is p oposed
o de e mining he heo e ical ene gy eco e able in a pa o he Alque a dis ibu ion ne wo k.
This analysis was made wi h a e age consump ion demands.
The p esen esea ch de e mines he a iabili y o lows and p essu e in any poin o line on
he ne wo k depending on i iga ion habi s. This ad an age (de e mining ins an alues o lows
and p essu e) allows pe o ming he analysis o ene gy eco e y in any poin on he ne wo k.
The me hodology ob ains he da a pai s o low (Q) and head (H) o he wo king a ea o he hypo he ical
ins alled machine.
Fu he mo e, he me hodology de e mines he a ia ion o low in a ne wo k based on he habi s
o i iga ion in o de o pe o m ene gy analyses. The applica ion o his me hodology in i iga ion
ne wo ks aims o complemen p e ious s udies o PATs e iciency in dinking supply ne wo ks,
ex ending i s use.
The a ia ion o low is based on andom demand o he use s and he eal i iga ion alloca ions.
Depending on hese pa ame e s, he p oposed me hodology es ima es he ene gy dissipa ed by
ic ion losses, he ene gy equi ed o i iga ion, and he eco e able ene gy in he i iga ion ne wo k.
The disc e iza ion o he lows leads manage s o analyze powe gene a ion depending on i iga ion
ime pe iods. Acco dingly, he p esen analysis has he ollowing objec i es:
1)
P oposing a new me hodology o de e mining he lows h oughou he yea in an i iga ion
ne wo k demand, conside ing he need o he c op, he his o ic consump ion and he i iga ion
a me s’ habi s
2) Es ima ing he low a e and p essu es wi h he ime
Wa e 2016,8, 234 3 o 26
3)
Quan i ying he ene gy balance in p essu ized i iga ion dis ibu ion sys ems o de e mine he
ene gy oo p in o wa e in he dis ibu ion sys em, and he es ima ed eco e able ene gy
4) Applying hese p ocedu es o a eal case s udy
2. Me hods and Ma e ials
2.1. Me hodology o De e mining he Flow
In his sec ion, he p oposed me hodology o de e mine he ime-dependen low h oughou he
yea is desc ibed. In o de o analyze any p essu ized i iga ion ne wo k om he ene gy poin o iew,
he low and p essu e along pipelines a e de e minan a iables. The equi emen s o he minimum
p essu e a any consump ion poin a e also undamen al. P essu es a e di e en depending on he
loca ion o i iga ion poin s. The e o e, he spa ial and iming dis ibu ion o hese consump ions a e
impo an aspec s o ake in o conside a ion.
The lows a e a iable o e any i iga ion campaign, depending on many ac o s such as
dis ibu ion o c ops in he i iga ion a ea, c op ma u i y, wea he condi ions, soil cha ac e is ics,
e iciency o d ippe s ( anging om 0.90 o 0.95), and he habi s o a me s, among o he s.
T adi ionally, he Clemen me hodology has been used o i iga ion ne wo k sizing [
27
–
29
].
This me hodology allows de e mining he maximum low ci cula ing in a ne wo k line. This maximum
low a e is calcula ed by assuming a binomial dis ibu ion low. The ma hema ical expec a ion
and s anda d de ia ion o he binomial p obabili y dis ibu ion depends on he opening poin o
consump ion. Clemen assumed ha his p obabili y was uni o m and equal o e ime. This uni o m
p obabili y conside a ion can lead o unde es ima ing he lows. Consequen ly, he Clemen
me hodology canno be used o analyzing po en ial ene gy eco e y. P obabili y o i iga ion a
any poin is non-uni o m, and depends on he habi s o i iga ion a me s. The e o e, i a ies
h oughou he day, week, and mon h. This unde es ima ion leads o he p oposal o di e en
me hodologies o es ima ing lows in i iga ion ne wo ks. The mos common a e hose ha use
s a is ical me hods [
27
–
29
], o models based on he andom opening o i iga ion poin s by means o
compu e simula ions [30–33]. A new me hodology conside ing bo h s a egies is he e p oposed.
Flow and ene gy implica ions a e he e o e sepa a ely conside ed and desc ibed.
The majo i y o wa e dis ibu ion ne wo ks only ha e wa e me e s in each i iga ion poin
o billing and con olling he consumed olumes. Un o una ely, i is no usual ha he i iga ion
ne wo k has eadings o lows and p essu es a any ime. Fo his eason, he p oposed me hodology
simula es he ope a ion o any i iga ion ne wo k based on he andom gene a ion o consump ion in
i iga ion poin s.
The day, s a , and du a ion o i iga ions (as unc ion o he habi s o he a me s) a e conside ed
in his esea ch as ac o s o i iga ion p obabili y and lows. Fu he mo e, he eal consump ion
p obabili y weigh s (ob ained om his o ical a chi es o he i iga ion en i ies) can be assigned o
consump ions, and he ne wo k can be e y p ecisely simula ed.
Hence, o any day o he yea , consump ions can be es ima ed in any i iga ion poin by ollowing
hese s eps (Figu e 1).
1. Es ima ion o cumula i e olume consumed by he i iga ion poin
The decision o i iga e depends on he balance (V
Na
) be ween he p e ious i iga ed olume
and he consump ion assigned (needs) o he i iga ion poin (Inpu 1). I he olume o cumula i e
consump ion is posi i e, au oma ically he me hodology indica es ha his is no an i iga ion day.
Only when his olume is nega i e, i iga ion is possible. I he olume o cumula i e consump ion is
nega i e, he me hodology de e mines he i iga ion p obabili y.
2. The de e mina ion o he i iga ion p obabili y (PI)
Wa e 2016,8, 234 4 o 26
To andomly de e mine i c ops a e i iga ed o no du ing a pa icula day, wo ypes o weigh
unc ions a e assigned. These unc ions a e ob ained om in e iews wi h a me s. Acco ding o
Figu e 1, Inpu 2 de e mines he i iga ion weekly pa e n (w
dj
), p io i izing he i iga ion days pe
week. Inpu 3 de e mines he maximum days be ween i iga ions o each mon h o he yea (i). I in
p e ious days no i iga ion has been pe o med, wa e ing is o ced.
Wa e 2016, 8, 234 4 o 25
Figu e 1. Schema ic desc ip ion o he me hodology o low es ima ion.
The me hodology gene a es a andom numbe (RN) be ween ze o and one associa ed wi h an
i iga ion p obabili y. I ≤P i iga ion is assigned o his consump ion poin .
De e mina ion o he
i iga ion p obabili y
j<=365
VIR=Id穌
i
1
Inpu 4
5
Weekly end o
days be ween i iga ions
I
De e mina ion o i iga ion du a ion
i iga ions pa e ns
No
VNa=VNa(i-1) +VIR
2
I iga ion du a ion
6
Annual
No
Pa e n o maximum
Es ima ion o cumula i e olume
i=i+1
Yes
(mon h and day)
3
7
Yes
Inpu 1
Inpu 2:
VNa>0
Pa e n o
i<=n
De e mina ion o he olume i iga ed
Recalcula ion o accumula ed olume o consump ion
4
EPANET Toolki
Consump ion Pa e n
Inpu 3:
De e mina ion he s a o i iga ion (day, hou )
(a ea and amoun )
No
I iga ion Poin (i)
P <[0-1]
Random Numbe
=[1- 60 min]
Da a Read I iga ion Poin s
No
(i=1,...n)
Yes
Da a Read Day
j=j+1
Day (j) (j=1,...365)
Choice o he ime in e al
Yes
Figu e 1. Schema ic desc ip ion o he me hodology o low es ima ion.
The me hodology gene a es a andom numbe (RN) be ween ze o and one associa ed wi h
an i iga ion p obabili y. I RNjďPIi iga ion is assigned o his consump ion poin .
PI“wdj
řn“i´j`1
n“1wdn
(1)
Wa e 2016,8, 234 5 o 26
whe e:
i= numbe s o days inside o in e al;
j= day o decision making;
wdj = pa e n o i iga e one pa icula day inside he in e al;
řn“i´j`1
n“1wdn = o al addi ion o pa e ns.
3. The de e mina ion o he i iga ion du a ion
The me hodology allows de e mining he es ima ed ime based on i iga ion habi s o a me s o
sa is y i iga ion needs (Inpu 1). This alue depends on i iga ion amoun and ype o c op.
4. The s a o i iga ion
The i iga ion du a ion andomly de e mines he s a o i iga ion as a unc ion o he daily
p obabili y cu es o i iga ion ime (Inpu 4). When he me hodology de e mines ha a consump ion
poin has o be i iga ed, he s a ime o i iga ion is de e mined. The e o e, he cumula i e p obabili y
mus be used o s a ing i iga ion. This cu e is de ined by wen y- ou sec ions (one pe hou ).
When no i iga ion exis s, he i iga e weigh (wh) in his in e al is assigned o be ze o.
The p obabili y in he ime in e al (ph) is:
ph“wh
řh“23
h“0wh
(2)
whe e whis he de ined pa e n (Inpu 2) o i iga e one pa icula hou inside he in e al.
The cumula i e p obabili y (pcm) is:
pc“ÿh“m
h“0phpm“0, . . . , 23q(3)
whe e mis he numbe o in e als in one day.
A new RN is gene a ed, anging om 0 o 1. I is compa ed wi h he alues o cumula i e
p obabili y (p
cm
) and he s a i iga ion pe iod is es ablished. Fo his pa icula ime pe iod, he
me hodology selec s wi hin his pe iod he s a in e al om ze o o alue equal o
60
∆
(
whe e ∆
is
he ime in e al in which he simula ed low is disc e ized). When his s ep is comple ed, he day and
hou o s a ing i iga ion is known.
5. De e mina ion o i iga ion olume
The i iga ion supply (ag onomic known pa ame e , which depends on: amewo k plan a ion,
numbe o d ippe pe plan and low o he d ippe ) and he du a ion (Inpu 4) a e known and he
i iga ion olume can be calcula ed o ha day.
6. Calcula ion o cumula i e consump ion
When he i iga ion olume is known, he me hodology upda es he wa e olume a ailable o
he plan .
7. The p essu e and low modeled o each node in he ne wo k
They a e calcula ed o e e y i iga ion poin s and each day using Epane Toolki . Epane is
public domain so wa e [
34
] ha models wa e dis ibu ion in pipe sys ems. Di e en elemen s can be
ep esen ed: pipe ne wo ks composed by pipes, nodes (junc ions), pumps, al es, and s o age anks o
ese oi s. The model can simula e ex ended-pe iod hyd aulic analysis by simula ing by so o pipes
sys ems, compu ing ic ion and mino losses, ep esen ing a ious ypes o al es, junc ions, anks
and pumps, conside ing mul iple pa e ns a nodes consump ion wi h ime a ia ion, and sys em
ope a ion on simple ank le el, ime con ols o complex ule-based con ols.

Wa e 2016,8, 234 6 o 26
2.2. Balance o Ene gy
Once lows and p essu es a e es ima ed along he ime in he whole ne wo k, he ene gy equa ion
(Reynolds Theo em) mus be implemen ed o conside he ene gy balance in he sys em [35].
Acco ding o Figu e 2, a gene ic i iga ion ne wo k wi h all possible elemen s ( ese oi , pumps,
u bines, and compensa ion anks) is p esen ed. The conse a ion o ene gy equa ion is de ined as:
dE
d “
“
“dQ
d `
`
`Wsha
d “d
d yCVρˆgz `u` 2
2˙dV `
`
`xCS ˆgz `u`P
ρ` 2
2˙ρˆÑ
¨d
Ñ
A˙(4)
whe e:
dE
d = exchange o ene gy pe uni ime in he con ol sys em;
dQ
d = exchange o hea pe uni o ime (hea powe );
Wsha
d = powe ansmi ed di ec ly o o om he luid (e.g., pump);
dV = di e en ial olume o con ol olume o in eg a ion;
Ñ
= eloci y ec o o luid;
d
Ñ
A= di e en ial a ea o con ol su ace o in eg a ion;
ρ= luid densi y;
gz = po en ial ene gy pe uni mass;
u= in e nal ene gy pe uni mass;
2
2= kine ic ene gy pe uni mass;
P
ρ= heigh o p essu e pe uni mass;
Wi hin he con ol sys em, he ollowing simpli ica ions can be made:
The wa e densi y is cons an .
Flow is uni o m in each in e al.
Exchange o hea be ween luid and su oundings is negligible (adiaba ic sys em).
The sha wo k is he powe ansmi ed di ec ly o/ om he luid in he case ha a pump o
u bine exis s in he ne wo k.
The e is no compensa ion ank in he ne wo k, he e o e, he ime ene gy a ia ion inside o he
con ol olume as unc ion o ime is negligible.
Wa e 2016, 8, 234 6 o 25
Once lows and p essu es a e es ima ed along he ime in he whole ne wo k, he ene gy equa ion
(Reynolds Theo em) mus be implemen ed o conside he ene gy balance in he sys em [35].
Acco ding o Figu e 2, a gene ic i iga ion ne wo k wi h all possible elemen s ( ese oi , pumps,
u bines, and compensa ion anks) is p esen ed. The conse a ion o ene gy equa ion is de ined as:

=
+
 =
󰇧++

󰇨+ 󰇧++
+
󰇨
󰇍
󰇍

∙

󰇍
󰇍


 (4)
whe e:

 = exchange o ene gy pe uni ime in he con ol sys em;

 = exchange o hea pe uni o ime (hea powe );

  = powe ansmi ed di ec ly o o om he luid (e.g., pump);
dV = di e en ial olume o con ol olume o in eg a ion;
 = eloci y ec o o luid;

󰇍
󰇍
󰇍

= di e en ial a ea o con ol su ace o in eg a ion;
ρ = luid densi y;
 = po en ial ene gy pe uni mass;
 = in e nal ene gy pe uni mass;

 = kine ic ene gy pe uni mass;

 = heigh o p essu e pe uni mass;
Wi hin he con ol sys em, he ollowing simpli ica ions can be made:
The wa e densi y is cons an .
Flow is uni o m in each in e al.
Exchange o hea be ween luid and su oundings is negligible (adiaba ic sys em).
The sha wo k is he powe ansmi ed di ec ly o/ om he luid in he case ha a pump o
u bine exis s in he ne wo k.
The e is no compensa ion ank in he ne wo k, he e o e, he ime ene gy a ia ion inside o he
con ol olume as unc ion o ime is negligible.
Figu e 2. Ene gy balance in he p essu ized i iga ion wa e ne wo k adap ed om [36].
I an i iga ion sys em ope a es by g a i y (Figu e 3), he equa ion o ene gy applied o any
con ol sys em along a ime in e al is de ined by Equa ion (5):
equi ed om F ic ion ene gy
ank Ene gy
Gene a e by
Ene gy
i iga ion
h ough
Compensa ion
TTu bine
Rese oi
leaks
Ene gy
dissipa ed
P essu e Wa e Sys em (PWS) Con ol Volume (CV)
Tu bine
Pump
Ene gy
in al es
Wa e Ne wo k CV
Figu e 2. Ene gy balance in he p essu ized i iga ion wa e ne wo k adap ed om [36].
Wa e 2016,8, 234 7 o 26
I an i iga ion sys em ope a es by g a i y (Figu e 3), he equa ion o ene gy applied o any con ol
sys em along a ime in e al is de ined by Equa ion (5):
γQDHD∆ “
n
ÿ
i“1
γQoi Hoi∆ `ρ˜n
ÿ
i“1
pQoiuoi ´QDiuDiq¸∆ (5)
whe e:
∆ = ime in e al (s);
n= o al numbe o i iga ion poin s;
i= indi idual i iga ion poin s;
γ= speci ic weigh o he luid (N/m3);
QD= o al low demanded by he ne wo k (m3/s);
HD
= piezome ic head o he ese oi . Fo a pumped sys em, he alue is he manome ic heigh ;
Qoi = low demanded by each i iga ion poin (m3/s);
Hoi = piezome ic head o he consump ion node (m);
γQDHD
= o al ene gy (kW) supplied o he sys em. This e m is equal o E
T
, which is
la e de ined;
řn
i“1γQoi Hoi
= ene gy consumed by all i iga ion poin s (kW). This e m will be de ined as E
RI
plus ETRI;
ρ`řn
i“1pQoiuoi ´QDiuDiq˘
= Exchange o in e nal ene gy. In an adiaba ic sys em, i is equal o
ic ion losses. This e m will be de ined as EFR.
Leakages a e no conside ed in his analysis because he d ip i iga ion ne wo k is s ill new
(minimum leakages), he main enance and epai plans a e usually unde aken (which educe possible
losses), and inally, hese ne wo ks a e no as au oma ed as d inking sys ems so unmeasu ed olumes
and leakages a e di icul o disce n. I an ene gy audi we e made, his olume should be conside ed
o es ima ed [
6
,
36
]. Fu he mo e, he ins alla ion o hyd aulic machines does no a ec he wa e
quali y o he inal use (i.e., i iga ion).
Wa e 2016, 8, 234 7 o 25
γ
∆=
γ


 ∆+ρ(−)

 ∆ (5)
whe e:
∆ = ime in e al (s);
n = o al numbe o i iga ion poin s;
i = indi idual i iga ion poin s;
γ = speci ic weigh o he luid (N/m3);
 = o al low demanded by he ne wo k (m3/s);
 = piezome ic head o he ese oi . Fo a pumped sys em, he alue is he manome ic heigh ;
 = low demanded by each i iga ion poin (m3/s);
 = piezome ic head o he consump ion node (m);
γ = o al ene gy (kW) supplied o he sys em. This e m is equal o ET, which is la e
de ined;
∑γ

 = ene gy consumed by all i iga ion poin s (kW). This e m will be de ined as ERI
plus ETRI;
ρ(∑ (−)

 ) = Exchange o in e nal ene gy. In an adiaba ic sys em, i is equal o
ic ion losses. This e m will be de ined as EFR.
Leakages a e no conside ed in his analysis because he d ip i iga ion ne wo k is s ill new
(minimum leakages), he main enance and epai plans a e usually unde aken (which educe
possible losses), and inally, hese ne wo ks a e no as au oma ed as d inking sys ems so unmeasu ed
olumes and leakages a e di icul o disce n. I an ene gy audi we e made, his olume should be
conside ed o es ima ed [6,36]. Fu he mo e, he ins alla ion o hyd aulic machines does no a ec
he wa e quali y o he inal use (i.e., i iga ion).
Figu e 3. Scheme o i iga ion ne wo k.
When a global ene gy balance o he ne wo k is es ablished, i is possible o de ine di e en
e ms o ene gy. Such as lines, hyd an s and i iga ion poin s, as ollow (Figu e 4):
- To al Ene gy (ETi): po en ial o al ene gy in an i iga ion poin when he consump ion is null in
he en i e ne wo k. I co esponds o he s a ic ene gy (i.e., po en ial) o he node. Fo an
i iga ion poin along a ime in e al, he alue is:
(ℎ)=9.81
3600(−) (6)
whe e:
 is he low ci cula ing by a line ha supplies o mo e un a o able i iga ion poin (mos
disad an ageous consump ion node in e ms o need o he p essu e) (m3/s);
 is he geome y le el abo e e e ence plane o he i iga ion poin . In his case, he e e ence
is sea le el (m);
 is he geome y le el abo e e e ence plane o he ee wa e su ace o he ese oi . In his
case, he e e ence is sea le el (m);
IRRIGATION POINT
MAIN PIPE
PLOT OF CROPS
HYDRANT
RESERVOIR
SECONDARY BRANCH
HYDRANT-IRRIGATION
POINT PIPE
LEGEND
Figu e 3. Scheme o i iga ion ne wo k.
When a global ene gy balance o he ne wo k is es ablished, i is possible o de ine di e en e ms
o ene gy. Such as lines, hyd an s and i iga ion poin s, as ollow (Figu e 4):
-To al Ene gy (ETi):
po en ial o al ene gy in an i iga ion poin when he consump ion is null in he
en i e ne wo k. I co esponds o he s a ic ene gy (i.e., po en ial) o he node. Fo an i iga ion
poin along a ime in e al, he alue is:
ETipkWhq “ 9.81
3600Qipzo´ziq∆ (6)
Wa e 2016,8, 234 8 o 26
whe e:
Qi
is he low ci cula ing by a line ha supplies o mo e un a o able i iga ion poin (mos
disad an ageous consump ion node in e ms o need o he p essu e) (m3/s);
zi
is he geome y le el abo e e e ence plane o he i iga ion poin . In his case, he e e ence is
sea le el (m);
z0
is he geome y le el abo e e e ence plane o he ee wa e su ace o he ese oi . In his
case, he e e ence is sea le el (m);
∆ is he ime in e al (s).
-F ic ion Ene gy (EFRi):
o a ime in e al, i is he ene gy dissipa ed in he ne wo k by he wa e
coming om head un il he i iga ion poin .
EFRipkWhq “ 2.725¨10´3Qipzo´ pzi`Piqq ∆ (7)
whe e:
Pi
is he se ice p essu e in any poin o he ne wo k when consump ion exis s. The uni s a e
me e wa e column (m w.c.).
Mino losses (p essu e loss in pa icula ne wo k componen s like ees, al es, and simila ) a e
conside ed as a pe cen age o ic ion losses. Associa ed wi h his e m, he Ene gy Foo p in o Wa e
(EFW) can be calcula ed. Ene gy Foo p in o Wa e is de ined as he a ion be ween ene gy dissipa ed
due o ic ion losses (EFRi)o e he dis ibu ed olume on he ne wo k (kWh/m3).
-Theo e ical Ene gy Necessa y (ETNi):
i is he minimum ene gy equi ed in a hyd an o line o
ensu e he minimum p essu e o i iga ion in he mo e un a o able poin . The alue is:
ETNipkWhq “ 2.725¨10´3QiPmini∆ (8)
whe e:
Pmini
is he minimum p essu e o se ice o a line o hyd an o ensu e he minimum p essu e in
he mos disad an ageous consump ion node. The uni s a e me e wa e column (m w.c.).
-Ene gy Requi ed o I iga ion (ERIi):
du ing an in e al o ime, i is he minimum ene gy equi ed
a an i iga ion poin o ensu e he i iga ion wa e e enly. The alue is:
ERIipkWhq “ 2.725¨10´3QiPminIi∆ (9)
whe e:
PminIi
is he minimum p essu e o se ice o an i iga ion poin equi ed o ensu e he i iga ion
wa e e enly. The uni s a e me e wa e column (m w.c.).
-Theo e ical A ailable Ene gy (ETAi): i is he a ailable ene gy o eco e y in a hyd an o line. The
eco e y coe icien in a hyd an o line (C
RT
) depends on losses exis en be ween he hyd an
(o pipeline) and he mos disad an ageous consump ion node. I is equal o he sum o he
heo e ical ene gy eco e able plus he heo e ical ene gy un eco e able (E
NRT
). The alue o his
ene gy o a pa icula ime du a ion, is de ined as:
ETAipkWhq “ 2.725¨10´3Qi`Pi´Pmini˘∆ (10)
-Theo e ical Reco e able Ene gy (ETRi):
i is he maximum heo e ical eco e able ene gy in
an i iga ion poin , hyd an o line o he ne wo k, ensu ing a downs eam he minimum
p essu e o i iga ion.
Wa e 2016,8, 234 9 o 26
ETRipkWhq “ 2.725¨10´3Qi`Pi´max`Pmini;PminIi˘˘∆ “2.725¨10´3QiHi∆ (11)
whe e
Hiis he alue o head in i iga ion poin , hyd an o line (m w.c.), ob ained as:
Hi“Pi´max`Pmini;PminIi˘(12)
-Theo e ical un eco e able Ene gy (ENTRi):
i is he ene gy in a hyd an o line on he ne wo k ha
canno be eco e ed. This ene gy is necessa y o assume he losses om he line o hyd an o he
mo e un a o able i iga ion poin .
ENTRi“ETAi´ETRi(13)
-Reco e y coe icien in hyd an o line (CRTi):
i is he quo ien be ween E
TRi
and E
TAi
in an i iga ion
poin , hyd an o line o he ne wo k. I ep esen s he p opo ion o eco e y ene gy o e
a ailable ene gy.
CRTi“ETRi
ETAi
(14)
Wa e 2016, 8, 234 9 o 25
=


(14)
Figu e 4. Scheme o hyd aulic ene gies g ade line.
 (Figu e 4) is he low ci cula ing in a line o consumed by a hyd an (m3/s),  is he
geome y le el abo e e e ence plane o he line o hyd an .  is he piezome ic heigh o he
ese oi ha supplies he ne wo k. The uni s a e me e wa e column (m w.c.). I ese oi is open,
 is equal o .
When Equa ion (5) is applied in a poin o he ne wo k, i is de ined by Equa ion (15):
 =++
 (15)
When all i iga ion poin s a e conside ed (zi in Figu e 4), he annual balance o ene gy is de ined
by Equa ion (16):


 =(++
)

 (16)
In he case o lines and hyd an s (zh in Figu e 4), he annual balance o ene gy is de ined by
Equa ion (17): =++
 =++
+ (17)
The ene gy oo p in o wa e and he heo e ical eco e able ene gy a e c ucial o he ene gy
balance. The ene gy oo p in on he ne wo k dis ibu ion can be ob ained along he yea and
compa ed wi h a e age alues analyzed in o he dis ibu ion sys ems. Some o hese alues a e: 0.31
kWh/m3 in injec ed i iga ion ne wo k [36], 0.18–0.32 kWh/m3 acco ding o Cali o nia Ene gy
Commission [37], 0.081 kWh/m3 in Bangkok, 0.5 kWh/m3 in Delhi and 0.13 kWh/m3 in Tokyo [38].
Rega ding he heo e ical eco e able ene gy in a ne wo k, i mainly depends on he o og aphy
o he i iga ion a ea. The ne wo ks wi h la ge g adien s be ween he supply and he consump ion
poin s ha e g ea e possibili y o eco e ene gy, i he app op ia e machine is selec ed. The ene gy
eco e y can be analyzed in di e en pa s o he ne wo k:
i) In plo o cul i a ion—in his case, he p i a e use needs o educe p essu e down o 30 m w.c.
o ca y ou d ip i iga ion. Gene ally, he use ins alls a p essu e educe o dissipa e he excess
ene gy. This elemen can be eplaced by a pico- u bine o gene a e ene gy o sel -consump ion.
This ene gy can be used in emo e-con ol sys em, cleaning o il e s, ligh ing and o he s simila
consump ions.
ii) In he hyd an pipe—when he hyd an supplies o la opog aphy, educ ion o p essu e can
be done. In an ope a ing ne wo k, his educ ion is ca ied ou wi h a p essu e educing al e.
This eco e y could po en ially be done i a sui able u bine could be ins alled.
Figu e 4. Scheme o hyd aulic ene gies g ade line.
Qh
(Figu e 4) is he low ci cula ing in a line o consumed by a hyd an (m
3
/s),
zh
is he geome y
le el abo e e e ence plane o he line o hyd an .
H0
is he piezome ic heigh o he ese oi ha
supplies he ne wo k. The uni s a e me e wa e column (m w.c.). I ese oi is open,
H0
is equal o
z0
.
When Equa ion (5) is applied in a poin o he ne wo k, i is de ined by Equa ion (15):
ETi “EFRi `ERIi `ETRi (15)
When all i iga ion poin s a e conside ed (z
i
in Figu e 4), he annual balance o ene gy is de ined
by Equa ion (16):
n
ÿ
i“1
ETi “
n
ÿ
i“1
pEFRi `ERIi `ETRiq(16)
In he case o lines and hyd an s (z
h
in Figu e 4), he annual balance o ene gy is de ined by
Equa ion (17):
ET“EFRh `ETA `ETN “EFRh `ERI `ETR `ENTR (17)
Wa e 2016,8, 234 16 o 26
Wa e 2016, 8, 234 15 o 25
4. Dis ibu ion o i iga ion s a p obabili y: a me s end o i iga e in ce ain pa icula hou s o
he day. This aspec is conside ed in his me hodology by using he pa e ns o he p obabili y
o s a ing i iga ion in he di e en schedules. The wa e ing schedule be ween 10 A.M. and 4
P.M. is chosen in he mon hs o Janua y, Feb ua y, Ma ch, Ap il, Oc obe , No embe and
Decembe . Howe e , a me s i iga e in di e en ligh hou s in summe mon hs o a oid
wa me hou s and nigh . The e o e, h ee pa e ns ha e been de eloped o de ine he p obabili y
(see Figu e 1, s ep 4).
A i s pa e n is assigned o he win e mon hs om Oc obe o Ap il and conside s ha he
i iga ion s a s be ween 8 A.M. and 6 P.M. A second pa e n is assigned o he summe mon hs, om
May o Sep embe , whe e he i iga ion a oids hou s o day wi h highe empe a u es. The wa e ing
schedule s a s be ween 4 A.M. and 12 P.M. and om 6 P.M. o 12 A.M. Finally, a hi d pa e n
unc ion is de ined o i iga ing plo s wi h mo e o wo sec o s, a any ime o he day along he yea .
4. Resul s
4.1. Basic Cha ac e is ics
Following he me hodology, an analysis o lows and p essu es is necessa y o ene gy
conside a ion in he ne wo k based on hyd aulic simula ions. These simula ions ha e been un wi h
he so wa e EPANET.
The model o he ne wo k de eloped by means o he so wa e EPANET, has been un o each
day along one yea . In his case, hese calcula ions ha e been epea ed 20, 40 and 60 imes wi h
di e en scena ios ep esen ed. Ne e heless, compa ing hese simula ions, he a iabili y ob ained
when he low in he main line is compa ed o he a e age low is smalle han 5%. As his de ia ion
emains simila , no mo e epe i ions a e conside ed.
This me hodology has been calib a ed in o he ne wo ks by he au ho s. The calib a ion has been
pe o med wi h measu ed low e e y i e minu es. The esul s ha e been sa is ac o y wi h Nash-
Su cli e index uppe o 0.40, oo ela i e squa ed mean e o below 0.7 and pe cen bias below 5%,
as indica ed in [47].
Figu es 12 and 13 depic he opology o he ne wo k o be conside ed and analyzed in u he
sec ions.
Figu e 12. Iden i ica ion o pipes in he i iga ion ne wo k.
Figu e 12. Iden i ica ion o pipes in he i iga ion ne wo k.
Wa e 2016, 8, 234 16 o 25
Figu e 13. Iden i ica ion o hyd an s in he i iga ion ne wo k.
4.2. Flows in he Ne wo k
Flow and p essu e ha e been ob ained along he ime, based on he his o ical se ies o eco ds
egis e ed be ween 2003 and 2014, in any line o he sys em, acco ding o he i iga ion ends. These
ime se ies o da a collec ed in hose 12 yea s (17,808 eco ds), low in he main line (see Figu e 12,
line 1) and hyd an 201 (see Figu e 13, H201) a e depic ed in Figu e 14.
(a) (b)
Figu e 14. Flow in he main line (pipe 1) along he yea (a); Flow and p essu e a ia ion in he hyd an
(H201) o e ime (b).
The equency his og am (Figu e 15) displays he la ge a iabili y o lows along he yea . Hence,
i iga ion ne wo ks beha e in a di e en way han d inking sys ems: mon hly seasonal a ios ange
be ween 0.8 and 1.2 in d inking ne wo ks (excep o ou is ic ci ies) and i s a iabili y o lows du ing
he day a ies be ween 0.7 and 1.5 o he a e age alue. Opposi e o his, he low seasonali y ac o
in i iga ion sys ems is much la ge han in d inking sys ems. In he case o ci us, seasonali y ac o
a ies be ween 0.14 and 2.36 imes ela i e o he annual a e age consump ion olume. Acco ding o
his, he es ima ed a iabili y in his ne wo k case s udy anges be ween 0.1 and 2.54 imes he
a e age low.
Addi ionally, he e is a e y high equency o e y low lows (Figu e 15). Flows below 0.05 m3/s
(25% o he maximum low a e) a ise up o 80% imes in he main line o he ne wo k. These small
lows will become o u mos impo ance o be used o ene gy eco e y.
Figu e 13. Iden i ica ion o hyd an s in he i iga ion ne wo k.
4.2. Flows in he Ne wo k
Flow and p essu e ha e been ob ained along he ime, based on he his o ical se ies o eco ds
egis e ed be ween 2003 and 2014, in any line o he sys em, acco ding o he i iga ion ends. These
ime se ies o da a collec ed in hose 12 yea s (17,808 eco ds), low in he main line (see Figu e 12,
line 1) and hyd an 201 (see Figu e 13, H201) a e depic ed in Figu e 14.

Wa e 2016,8, 234 17 o 26
Wa e 2016, 8, 234 16 o 25
Figu e 13. Iden i ica ion o hyd an s in he i iga ion ne wo k.
4.2. Flows in he Ne wo k
Flow and p essu e ha e been ob ained along he ime, based on he his o ical se ies o eco ds
egis e ed be ween 2003 and 2014, in any line o he sys em, acco ding o he i iga ion ends. These
ime se ies o da a collec ed in hose 12 yea s (17,808 eco ds), low in he main line (see Figu e 12,
line 1) and hyd an 201 (see Figu e 13, H201) a e depic ed in Figu e 14.
(a) (b)
Figu e 14. Flow in he main line (pipe 1) along he yea (a); Flow and p essu e a ia ion in he hyd an
(H201) o e ime (b).
The equency his og am (Figu e 15) displays he la ge a iabili y o lows along he yea . Hence,
i iga ion ne wo ks beha e in a di e en way han d inking sys ems: mon hly seasonal a ios ange
be ween 0.8 and 1.2 in d inking ne wo ks (excep o ou is ic ci ies) and i s a iabili y o lows du ing
he day a ies be ween 0.7 and 1.5 o he a e age alue. Opposi e o his, he low seasonali y ac o
in i iga ion sys ems is much la ge han in d inking sys ems. In he case o ci us, seasonali y ac o
a ies be ween 0.14 and 2.36 imes ela i e o he annual a e age consump ion olume. Acco ding o
his, he es ima ed a iabili y in his ne wo k case s udy anges be ween 0.1 and 2.54 imes he
a e age low.
Addi ionally, he e is a e y high equency o e y low lows (Figu e 15). Flows below 0.05 m3/s
(25% o he maximum low a e) a ise up o 80% imes in he main line o he ne wo k. These small
lows will become o u mos impo ance o be used o ene gy eco e y.
Figu e 14.
Flow in he main line (pipe 1) along he yea (
a
); Flow and p essu e a ia ion in he hyd an
(H201) o e ime (b).
The equency his og am (Figu e 15) displays he la ge a iabili y o lows along he yea . Hence,
i iga ion ne wo ks beha e in a di e en way han d inking sys ems: mon hly seasonal a ios ange
be ween 0.8 and 1.2 in d inking ne wo ks (excep o ou is ic ci ies) and i s a iabili y o lows du ing
he day a ies be ween 0.7 and 1.5 o he a e age alue. Opposi e o his, he low seasonali y ac o
in i iga ion sys ems is much la ge han in d inking sys ems. In he case o ci us, seasonali y ac o
a ies be ween 0.14 and 2.36 imes ela i e o he annual a e age consump ion olume. Acco ding
o his, he es ima ed a iabili y in his ne wo k case s udy anges be ween 0.1 and 2.54 imes he
a e age low.
Addi ionally, he e is a e y high equency o e y low lows (Figu e 15). Flows below 0.05 m
3
/s
(25% o he maximum low a e) a ise up o 80% imes in he main line o he ne wo k. These small
lows will become o u mos impo ance o be used o ene gy eco e y.
Wa e 2016, 8, 234 17 o 25
Figu e 15. His og am o low in he main line.
4.3. Wa e -Ene gy Nexus Es ima ion
This sec ion analyzes he es ima ion o ene gy dissipa ed in he ne wo k as a esul o ic ion
losses. Figu e 16 shows he a ia ion o he ene gy oo p in based on ime. The ne wo k is wo king
5943 h du ing o he yea . Figu e 16 shows he ene gy oo p in du ing he dis ibu ion o lows in
he wa e ne wo k. As shown in he his og am, 99.7% o he ime he ne wo k has an ene gy oo p in
below 2 kWh/m
3
. The maximum alue ob ained is 2.87 kWh/m
3
o a July day. Howe e , 58.5% o he
ime he ne wo k has an ene gy oo p in below 0.1 kWh/m
3
.
Figu e 16. Ne wo k ene gy oo p in o wa e .
Figu e 15. His og am o low in he main line.
4.3. Wa e -Ene gy Nexus Es ima ion
This sec ion analyzes he es ima ion o ene gy dissipa ed in he ne wo k as a esul o ic ion
losses. Figu e 16 shows he a ia ion o he ene gy oo p in based on ime. The ne wo k is wo king
5943 h du ing o he yea . Figu e 16 shows he ene gy oo p in du ing he dis ibu ion o lows in he
wa e ne wo k. As shown in he his og am, 99.7% o he ime he ne wo k has an ene gy oo p in
below 2 kWh/m
3
. The maximum alue ob ained is 2.87 kWh/m
3
o a July day. Howe e , 58.5% o
he ime he ne wo k has an ene gy oo p in below 0.1 kWh/m3.
Wa e 2016,8, 234 18 o 26
Wa e 2016, 8, 234 17 o 25
Figu e 15. His og am o low in he main line.
4.3. Wa e -Ene gy Nexus Es ima ion
This sec ion analyzes he es ima ion o ene gy dissipa ed in he ne wo k as a esul o ic ion
losses. Figu e 16 shows he a ia ion o he ene gy oo p in based on ime. The ne wo k is wo king
5943 h du ing o he yea . Figu e 16 shows he ene gy oo p in du ing he dis ibu ion o lows in
he wa e ne wo k. As shown in he his og am, 99.7% o he ime he ne wo k has an ene gy oo p in
below 2 kWh/m
3
. The maximum alue ob ained is 2.87 kWh/m
3
o a July day. Howe e , 58.5% o he
ime he ne wo k has an ene gy oo p in below 0.1 kWh/m
3
.
Figu e 16. Ne wo k ene gy oo p in o wa e .
Figu e 16. Ne wo k ene gy oo p in o wa e .
4.4. Theo e ical Reco e able Ene gy
I he esul s a e analyzed in i iga ion poin s, he o al heo e ical eco e able ene gy is
188.23 MWh/yea (i.e., 68.7% o he o al ene gy supplied o he ne wo k). In hese nodes, he
heo e ical coe icien o eco e y (CRT) is equal o one, as ERT is equal o ETA.
Figu e 17 shows a de ail o ins an aneous powe along da a egis e ed o he mon h o July o he
analyzed ime se ies, and he dis ibu ion o ins an powe equencies o e ime o an i iga ion poin .
In hese poin s, he equency a which he alue o ins an aneous powe appea s is p ac ically
cons an because he consump ion low is uni o m and only p essu e a ies due o he use o
p essu e-compensa ing d ippe s.
As an example, in i iga ion poin 303, he annual ope a ing ime is 2957 h. The ins an aneous
powe oscilla es be ween 9.96 kW and 11.64 kW. The maximum powe occu s 44.2% o ime, and he
heo e ical o al ene gy is 33.80 MWh/yea (Figu e 17).
In he case o hyd an s, he esul is simila whe e he sum o he heo e ical eco e able ene gy
is 178.1 MWh/yea . Figu e 18 shows analogous esul s o hose exposed in he i iga ion poin s.
Pa icula ly, a maximum ins an aneous powe o 4.64 kW is achie ed in hyd an H201, wi h an annual
ope a ing ime o 1460 h and o al ene gy o 1.59 MWh/yea . The a e age weigh ed coe icien o
eco e y in his hyd an is 0.68 (i.e., 9.68% o he o al ene gy could be eco e ed i u bines had 100%
e iciency). The maximum eco e y occu s in he hyd an H045 wi h 16.12 MWh/yea , wi h a eco e y
a e o 0.83 (Figu e 18).
The alues o heo e ical ene gy eco e able in all hyd an s a e de ailed in Table 1, as well as hei
eco e y coe icien s. The heo e ical maximum eco e able ene gy is ob ained in hyd an H042 wi h
a o al ene gy o 33.73 MWh/yea , and a coe icien o eco e y o 0.80. The heo e ical ene gy anges
be ween 0.01 (H056) and 33.73 MWh/yea . The eco e y coe icien anges be ween 0.14 (H055) and
0.84 (H053). The weigh ed a e age eco e y coe icien is 0.75.
Wa e 2016,8, 234 19 o 26
Wa e 2016, 8, 234 18 o 25
4.4. Theo e ical Reco e able Ene gy
I he esul s a e analyzed in i iga ion poin s, he o al heo e ical eco e able ene gy is 188.23
MWh/yea (i.e., 68.7% o he o al ene gy supplied o he ne wo k). In hese nodes, he heo e ical
coe icien o eco e y (C
RT
) is equal o one, as E
RT
is equal o E
TA
.
Figu e 17 shows a de ail o ins an aneous powe along da a egis e ed o he mon h o July o
he analyzed ime se ies, and he dis ibu ion o ins an powe equencies o e ime o an i iga ion
poin . In hese poin s, he equency a which he alue o ins an aneous powe appea s is p ac ically
cons an because he consump ion low is uni o m and only p essu e a ies due o he use o
p essu e-compensa ing d ippe s.
As an example, in i iga ion poin 303, he annual ope a ing ime is 2957 h. The ins an aneous
powe oscilla es be ween 9.96 kW and 11.64 kW. The maximum powe occu s 44.2% o ime, and he
heo e ical o al ene gy is 33.80 MWh/yea (Figu e 17).
Figu e 17. Po en ial Powe in he i iga ion poin 303.
In he case o hyd an s, he esul is simila whe e he sum o he heo e ical eco e able ene gy
is 178.1 MWh/yea . Figu e 18 shows analogous esul s o hose exposed in he i iga ion poin s.
Pa icula ly, a maximum ins an aneous powe o 4.64 kW is achie ed in hyd an H201, wi h an
annual ope a ing ime o 1460 h and o al ene gy o 1.59 MWh/yea . The a e age weigh ed coe icien
o eco e y in his hyd an is 0.68 (i.e., 9.68% o he o al ene gy could be eco e ed i u bines had
100% e iciency). The maximum eco e y occu s in he hyd an H045 wi h 16.12 MWh/yea , wi h a
eco e y a e o 0.83 (Figu e 18).
The alues o heo e ical ene gy eco e able in all hyd an s a e de ailed in Table 1, as well as
hei eco e y coe icien s. The heo e ical maximum eco e able ene gy is ob ained in hyd an H042
wi h a o al ene gy o 33.73 MWh/yea , and a coe icien o eco e y o 0.80. The heo e ical ene gy
anges be ween 0.01 (H056) and 33.73 MWh/yea . The eco e y coe icien anges be ween 0.14
(H055) and 0.84 (H053). The weigh ed a e age eco e y coe icien is 0.75.
Figu e 17. Po en ial Powe in he i iga ion poin 303.
Wa e 2016, 8, 234 19 o 25
Figu e 18. Po en ial Powe in hyd an H201.
Table 1. Theo e ical ene gy eco e able in hyd an s on he i iga ion ne wo k.
HYDRANT E
RT
C
RT
HYDRANT E
RT
C
RT
MWh
/
Yea MWh
/
Yea
H024 1.99 0.66 H065 0.80 0.63
H025 1.56 0.76 H066 0.13 0.57
H026 0.48 0.59 H067 0.22 0.53
H027 1.92 0.67 H070 1.40 0.69
H028 0.12 0.46 H071 0.40 0.72
H029 2.27 0.72 H072 0.28 0.35
H030 0.77 0.80 H073 0.22 0.45
H031 1.36 0.81 H074 0.64 0.40
H032 3.94 0.73 H075 0.31 0.54
H033 4.19 0.81 H076 1.34 0.55
H035 3.57 0.79 H077 0.52 0.64
H036 2.50 0.76 H078 3.68 0.69
H037 1.12 0.69 H079 0.76 0.53
H038 3.54 0.71 H080 1.41 0.66
H039 0.64 0.69 H081 0.40 0.72
H040 3.57 0.65 H082 1.28 0.71
H042 33.73 0.80 H083 0.87 0.72
H043 9.13 0.81 H084 0.80 0.67
H044 5.60 0.78 H085 1.50 0.58
H045 16.12 0.83 H086 0.48 0.52
H046 5.14 0.72 H087 0.27 0.58
Figu e 18. Po en ial Powe in hyd an H201.
Wa e 2016,8, 234 20 o 26
Table 1. Theo e ical ene gy eco e able in hyd an s on he i iga ion ne wo k.
HYDRANT ERT CRT HYDRANT ERT CRT
MWh/Yea MWh/Yea
H024 1.99 0.66 H065 0.80 0.63
H025 1.56 0.76 H066 0.13 0.57
H026 0.48 0.59 H067 0.22 0.53
H027 1.92 0.67 H070 1.40 0.69
H028 0.12 0.46 H071 0.40 0.72
H029 2.27 0.72 H072 0.28 0.35
H030 0.77 0.80 H073 0.22 0.45
H031 1.36 0.81 H074 0.64 0.40
H032 3.94 0.73 H075 0.31 0.54
H033 4.19 0.81 H076 1.34 0.55
H035 3.57 0.79 H077 0.52 0.64
H036 2.50 0.76 H078 3.68 0.69
H037 1.12 0.69 H079 0.76 0.53
H038 3.54 0.71 H080 1.41 0.66
H039 0.64 0.69 H081 0.40 0.72
H040 3.57 0.65 H082 1.28 0.71
H042 33.73 0.80 H083 0.87 0.72
H043 9.13 0.81 H084 0.80 0.67
H044 5.60 0.78 H085 1.50 0.58
H045 16.12 0.83 H086 0.48 0.52
H046 5.14 0.72 H087 0.27 0.58
H047 5.03 0.80 H088 0.51 0.26
H048 13.37 0.80 H089 0.73 0.59
H049 0.26 0.82 H090 0.59 0.69
H050 1.93 0.77 H100 0.89 0.65
H051 2.67 0.59 H101 1.05 0.63
H052 0.86 0.77 H123 1.78 0.79
H053 11.05 0.84 H126 0.47 0.68
H055 0.04 0.14 H140 0.73 0.74
H056 0.01 0.28 H148 0.32 0.82
H057 0.55 0.26 H152 2.47 0.72
H058 0.99 0.60 H188 2.81 0.68
H059 0.46 0.61 H200 1.35 0.77
H062 2.32 0.57 H201 1.58 0.68
H064 0.22 0.28 H202 2.08 0.76
The line ha p esen s he maximum eco e able ene gy is depic ed in Figu e 19 and Table 2.
This condi ion is se on line 38, wi h maximum eco e able ene gy o 89.99 MWh/yea and an a e age
weigh ed eco e y a e o 0.64. The maximum ins an aneous powe is 63.7 kW. The his og am
p esen ed in Figu e 19 shows ha du ing 918 h o he ope a ing ime (17.1%), he ins an aneous powe
a ises up o 10 kW.
Table 2shows ha he maximum eco e able ene gy is ob ained in line 38 wi h o al ene gy o
89.99 MWh/yea and a coe icien o eco e y 0.64. The es ima ed ene gy (E
RT
) anges be ween 0.12
(line 21) and 89.99 MWh/yea , he ange o eco e y coe icien can be ound be ween 0.15 (line 74)
and 0.84 (line 58) and he weigh ed a e age coe icien is 0.48.
The pai s o low, Q
i
, and head, H
i
, de ined in Equa ion (11) o any poin o he ne wo k a e
c ucial o de e mine ene ge ic aspec s. Wi h hese da a ( low and head), he es ima ed a ea o ope a ion
o he u u e selec ed machine could be de e mined. This cloud o poin pai s is depic ed in Figu e 20
o an i iga ion poin , a hyd an and wo o he lines wi h he maximum heo e ical eco e able ene gy.
Figu e 20 shows ha no all lines ha e na ow ope a ing poin in e als. Line 59 has a la ge
dispe sion o ope a ing poin s in he low ange. Simila ci cums ances occu in hyd an H201 wi h
a wide ange o low, making he choice o a unique u bine di icul . In he case o eco e y in
Wa e 2016,8, 234 21 o 26
i iga ion poin s, he low is cons an wi h an in e al o p essu e acco ding o he demand o he
ne wo k. This becomes an addi ional ad an age in which he pe o mance o he chosen machine
could be easily op imized.
Wa e 2016, 8, 234 20 o 25
H047 5.03 0.80 H088 0.51 0.26
H048 13.37 0.80 H089 0.73 0.59
H049 0.26 0.82 H090 0.59 0.69
H050 1.93 0.77 H100 0.89 0.65
H051 2.67 0.59 H101 1.05 0.63
H052 0.86 0.77 H123 1.78 0.79
H053 11.05 0.84 H126 0.47 0.68
H055 0.04 0.14 H140 0.73 0.74
H056 0.01 0.28 H148 0.32 0.82
H057 0.55 0.26 H152 2.47 0.72
H058 0.99 0.60 H188 2.81 0.68
H059 0.46 0.61 H200 1.35 0.77
H062 2.32 0.57 H201 1.58 0.68
H064 0.22 0.28 H202 2.08 0.76
The line ha p esen s he maximum eco e able ene gy is depic ed in Figu e 19 and Table 2.
This condi ion is se on line 38, wi h maximum eco e able ene gy o 89.99 MWh/yea and an a e age
weigh ed eco e y a e o 0.64. The maximum ins an aneous powe is 63.7 kW. The his og am
p esen ed in Figu e 19 shows ha du ing 918 h o he ope a ing ime (17.1%), he ins an aneous
powe a ises up o 10 kW.
Figu e 19. Po en ial Powe in line 38.
Table 2 shows ha he maximum eco e able ene gy is ob ained in line 38 wi h o al ene gy o
89.99 MWh/yea and a coe icien o eco e y 0.64. The es ima ed ene gy (E
RT
) anges be ween 0.12
(line 21) and 89.99 MWh/yea , he ange o eco e y coe icien can be ound be ween 0.15 (line 74)
and 0.84 (line 58) and he weigh ed a e age coe icien is 0.48.
Figu e 19. Po en ial Powe in line 38.
Table 2. Es ima ed ene gy eco e able in lines on he i iga ion ne wo k.
PIPE ERT CRT PIPE ERT CRT
MWh/yea MWh/yea
1 4.29 0.16 44 55.58 0.64
2 17.56 0.29 45 48.35 0.63
3 18.64 0.23 46 5.14 0.72
4 0.55 0.26 47 16.12 0.83
5 26.83 0.26 48 32.61 0.62
6 26.41 0.25 49 28.13 0.60
7 1.40 0.69 50 5.03 0.80
8 25.85 0.25 51 14.49 0.60
9 24.84 0.29 52 2.24 0.81
10 41.64 0.40 53 1.93 0.77
11 0.80 0.63 54 12.88 0.58
12 41.10 0.33 55 12.70 0.59
13 40.96 0.28 56 12.62 0.72
14 40.96 0.28 57 0.86 0.77
15 40.96 0.25 58 11.05 0.84
16 40.42 0.24 59 10.56 0.46

Wa e 2016,8, 234 22 o 26
Table 2. Con .
PIPE ERT CRT PIPE ERT CRT
MWh/yea MWh/yea
17 0.77 0.42 60 10.18 0.43
18 0.48 0.59 61 0.85 0.39
19 39.40 0.27 62 0.31 0.54
20 38.64 0.35 63 5.79 0.21
21 0.12 0.46 64 0.22 0.45
22 83.51 0.57 65 5.27 0.17
23 82.51 0.52 66 0.89 0.65
24 1.99 0.66 67 4.90 0.16
25 79.32 0.50 68 3.01 0.47
26 78.15 0.50 69 0.76 0.53
27 77.67 0.49 70 3.29 0.66
28 2.08 0.76 71 1.96 0.66
29 76.15 0.48 72 0.40 0.72
30 9.88 0.48 73 0.40 0.72
31 2.84 0.52 74 3.08 0.15
32 1.12 0.69 75 2.90 0.16
33 7.68 0.57 76 0.59 0.69
34 4.83 0.59 77 2.78 0.16
35 0.64 0.69 78 2.51 0.17
36 4.20 0.64 79 1.50 0.58
37 3.57 0.65 80 1.78 0.19
38 89.99 0.64 81 1.60 0.21
39 8.86 0.75 82 0.51 0.26
40 7.59 0.72 83 2.98 0.59
41 3.94 0.73 84 0.73 0.59
42 4.19 0.81 85 2.81 0.68
43 82.74 0.64 – – –
Wa e 2016, 8, 234 22 o 25
Figu e 20 shows ha no all lines ha e na ow ope a ing poin in e als. Line 59 has a la ge
dispe sion o ope a ing poin s in he low ange. Simila ci cums ances occu in hyd an H201 wi h a
wide ange o low, making he choice o a unique u bine di icul . In he case o eco e y in i iga ion
poin s, he low is cons an wi h an in e al o p essu e acco ding o he demand o he ne wo k. This
becomes an addi ional ad an age in which he pe o mance o he chosen machine could be easily
op imized.
Figu e 20. Rep esen a ion o low e sus head o ideal u bine cha ac e is ics in i iga ion poin ,
hyd an and lines 38 and 55.
4.5. Global Ene gy Balance
The global ene gy ne wo k analysis in his case s udy, shows ha wi h a o al o 274.00
MWh/yea o he ne wo k (ET), he ene gy dissipa ed by ic ion (EFR) is 11.25 MWh/yea (4.10%), he
ene gy equi ed o i iga ion (ERI), is 74.52 MWh/yea and he heo e ical ene gy eco e able (ETR) is
188.23 MWh/yea (conside ing he sum o o al indi idual eco e y in all i iga ion poin s).
I o al ene gy balance in hyd an s is calcula ed, he dis ibu ion o ene gy in he ne wo k is
de ined by Figu e 21. This g aphic shows ha in he case o ca ying ou ene gy eco e y a all
hyd an s, heo e ical ene gy eco e able would be 75.2 MWh/yea (27.4% compa ed o he o al
ene gy ET).
Figu e 21. Annual Balance Ene gy in hyd an s.
Figu e 20.
Rep esen a ion o low e sus head o ideal u bine cha ac e is ics in i iga ion poin ,
hyd an and lines 38 and 55.
Wa e 2016,8, 234 23 o 26
4.5. Global Ene gy Balance
The global ene gy ne wo k analysis in his case s udy, shows ha wi h a o al o 274.00 MWh/yea
o he ne wo k (E
T
), he ene gy dissipa ed by ic ion (E
FR
) is 11.25 MWh/yea (4.10%), he ene gy
equi ed o i iga ion (E
RI
), is 74.52 MWh/yea and he heo e ical ene gy eco e able (E
TR
) is
188.23 MWh/yea (conside ing he sum o o al indi idual eco e y in all i iga ion poin s).
I o al ene gy balance in hyd an s is calcula ed, he dis ibu ion o ene gy in he ne wo k is
de ined by Figu e 21. This g aphic shows ha in he case o ca ying ou ene gy eco e y a all
hyd an s, heo e ical ene gy eco e able would be 75.2 MWh/yea (27.4% compa ed o he o al
ene gy ET).
Wa e 2016, 8, 234 22 o 25
Figu e 20 shows ha no all lines ha e na ow ope a ing poin in e als. Line 59 has a la ge
dispe sion o ope a ing poin s in he low ange. Simila ci cums ances occu in hyd an H201 wi h a
wide ange o low, making he choice o a unique u bine di icul . In he case o eco e y in i iga ion
poin s, he low is cons an wi h an in e al o p essu e acco ding o he demand o he ne wo k. This
becomes an addi ional ad an age in which he pe o mance o he chosen machine could be easily
op imized.
Figu e 20. Rep esen a ion o low e sus head o ideal u bine cha ac e is ics in i iga ion poin ,
hyd an and lines 38 and 55.
4.5. Global Ene gy Balance
The global ene gy ne wo k analysis in his case s udy, shows ha wi h a o al o 274.00
MWh/yea o he ne wo k (ET), he ene gy dissipa ed by ic ion (EFR) is 11.25 MWh/yea (4.10%), he
ene gy equi ed o i iga ion (ERI), is 74.52 MWh/yea and he heo e ical ene gy eco e able (ETR) is
188.23 MWh/yea (conside ing he sum o o al indi idual eco e y in all i iga ion poin s).
I o al ene gy balance in hyd an s is calcula ed, he dis ibu ion o ene gy in he ne wo k is
de ined by Figu e 21. This g aphic shows ha in he case o ca ying ou ene gy eco e y a all
hyd an s, heo e ical ene gy eco e able would be 75.2 MWh/yea (27.4% compa ed o he o al
ene gy ET).
Figu e 21. Annual Balance Ene gy in hyd an s.
Figu e 21. Annual Balance Ene gy in hyd an s.
Finally, he i ual possibili y o eco e ing all o he es ima ed ene gy in all i iga ions poin s
is 188.23 MWh/yea . In his case, he en i onmen al impac e sus gene a ion wi h non- enewable
esou ces (e.g., coal and gas) would be a heo e ical educ ion o 137.4 o CO
2
/yea o 216.2 o
CO2/yea wi h uels.
4.6. Economic Feasibili y
In a i s economical app oach, he maximum heo e ical eco e y line is analyzed (line 38).
The co esponding PAT p oposed o line 38 would ha e a PSR alue o 5.9 yea s and EI o 0.22
€
/kWh
(Equa ions (18) and (21)). In his case, hese esul s a e es ablished by conside ing a machine o 30 kW
peak powe wi h e iciency o 50% and he economic pa ame e s de ined in Sec ion 2.2.
5. Conclusions
In his esea ch, a me hodology o quan i ying he po en ial eco e ed ene gy o an a e age
yea in an i iga ion ne wo k has been p esen ed. E en nowadays, some i iga ion ne wo ks do no
ha e lowme e s. In hese cases, a low es ima ion me hod mus be implemen ed: he low is assigned
o pipes along ime depending on egis e ed olumes, i iga ion ends, and consump ion pa e ns.
Once lows a e known, he EPANET oolki is used o es ima ing p essu es in di e en scena ios
along he yea in o de o de e mine p essu e and ene gy balance o each poin . Hence, i is possible
o disc imina e he ene gy needed o i iga ion, ic ion head losses, non- eco e able ene gy, and
po en ially eco e able ene gy in any line o hyd an in a ne wo k.
The me hod was demons a ed as applied o a eal case. Conside ing consump ion eco ds om
2003 o 2014, an i iga ion ne wo k in Valencia (Spain) has been analyzed in o de o de e mine he
dissipa ed and eco e able ene gy, obse ing ha he ene gy oo p in achie es maximum alues
o 2.85 kWh/m
3
, being 79.7% o ime unde 0.3 kWh/m
3
. The po en ial eco e able ene gy, ins an
powe , eco e ing coe icien s ela ing o al wi h eco e able ene gy and equency his og am o powe
a e s udied o any i iga ion poin , hyd an o line.
Wa e 2016,8, 234 24 o 26
The maximum es ima ed po en ial eco e able ene gy sums o 188.23 MWh/yea conside ing all
he consump ion poin s, and 178.1 MWh/yea conside ing all he hyd an s. I only one u bine we e
o be ins alled, he mo e con enien loca ion is line 38, wi h a po en ial eco e y o 89.99 MWh/yea .
Fu u e wo ks should be unde aken o analyze he pe o mance o eal u bines in lines in o de o
p opose a me hod o op imize he selec ion o u bines and he echnical and economic in ol emen s
o such ins alla ions in di e en i iga ion ne wo ks.
Acknowledgmen s:
This pape has been possible wi h he ee collabo a ion o he “Comunidad de Regan es
Vi gen de G acia”. No addi ional unds ha e been ecei ed o his esea ch. Au ho s hank he e iewe s o
hei aluable commen s, which ha e g ea ly con ibu ed in he imp o emen o he documen .
Au ho Con ibu ions:
All he au ho s ha e pa icipa ed in any s ep o his esea ch. Pa icula ly a b ie
desc ip ion is a ached: The au ho Helena M. Ramos has con ibu ed supe ising he s a e o he a desc ip ion,
low assigna ion and ene gy implica ions o he p esen s udy. The au ho F ancisco Ja ie Sánchez-Rome o has
been in ol ed in he concep ion o he me hodology o low assigna ion and compu a ional p og amming o
EPANET Toolki . The au ho Modes o Pé ez-Sánchez has analyzed he low da a o p oposing he inal low
dis ibu ion, has implemen ed he da a o EPANET Toolki and analyzed he esul s o ene gy de e mina ion.
The au ho P. Ampa o López-Jiménez has supe ised he whole esea ch and documen and has been in ol ed in
inal ene gy analysis o esul s and conclusions.
Con lic s o In e es :
The au ho s decla e no con lic o in e es . The ounding sponso s had no ole in he design
o he s udy; in he collec ion, analyses, o in e p e a ion o da a; in he w i ing o he manusc ip , and in he
decision o publish he esul s.
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Kahil, M.; Albiac, J.; Dina , A. Imp o ing he pe o mance o wa e policies: E idence om d ough in Spain.
Wa e 2016,8, 34. [C ossRe ]
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Llop, M.; Ponce-Al onso, X. Wa e and ag icul u e in a Medi e anean egion: The sea ch o a sus ainable
wa e policy s a egy. Wa e 2016,8, 66. [C ossRe ]
3.
Co ominas, J. Agua y Ene gía en el iego en la época de la sos enibilidad. Ing. Agua
2010
,17, 219–233.
[C ossRe ]
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