PREPRINT
1
Sensi i i y Analysis o Pho o ol aic Wa e Pumping
Sys ems: Ene ge ic and Economic S udies1
Imene Yahyaoui¹*, Ahmad A ieh², Al a o Se na³ and Fe nando Tadeo³
1Technological cen e , Uni e si y o Espi ì o San o, B azil
²Uni e si y o Jo dan, Amman, Jo dan
3Indus ial Enginee ing School, Uni e si y o Valladolid, Spain
e-mails: imene.yahyaou[email p o ec ed], aka ieh@ho mail.com, al a o.se na@au om.u a.es
e nando@au om.u a.es
*Co esponding au ho : Imene Yahyaoui
E-mail add ess: imene.yahyaoui@u es.b
Tel: 0034 983 184 859
Fax: 0034 983 423161
Abs ac — In ag icul u al emo e a eas whe e elec ical ene gy is equi ed o supply wa e pumping plan s,
pho o ol aic modules a e conside ed a good op ion o gene a e elec ici y. The eliabili y o au onomous
Pho o ol aic wa e pumping plan s depends essen ially on he sys em componen s size, which should mee he
c i e ia ela ed o he plan au onomy and he wa e olume equi ed o i iga ion. In his con ex , his
esea ch pape p oposes an app oach o size he elemen s o an au onomous pho o ol aic sys em equipped
wi h an ene gy s o age de ice (a ba e y bank), and which is used o supply a wa e -pumping plan wi h
elec ici y. The p oposed app oach de e mines he op imal su ace o he pho o ol aic modules, he op imal
capaci y o he ba e y bank and he olume o he wa e s o age ank. The op imiza ion app oach akes in o
accoun he mon hly a e age sola adia ion, he ul illmen o he wa e needed o he c ops’ i iga ion and
he numbe o he days o au onomy. Measu ed clima ic da a o 10 ha si ua ed in No he n Tunisia and
plan ed wi h oma o a e used in he op imiza ion p ocess, which is conduc ed du ing he oma o ege a i e
cycle ( om Ma ch o July). The op imal esul s achie ed o his a m a e 101.5 m² o pho o ol aic modules’
1 Funded by Mineco P ojec DPI2014-54530-R and FEDER unds
su ace, 1680 Ah/12V o he ba e y bank and 1800 m³ o he olume o he wa e s o age ank. Then, o e i y
he eliabili y o he p oposed op imiza ion app oach, he esul s o he p oposed sizing algo i hm a e
compa ed wi h hose o a comme cial op imiza ion ool named HOMER, which shows be e esul s using he
p oposed app oach. Finally, he economic eliabili y o he ob ained size is s udied and compa ed wi h
sys ems ha include a diesel gene a o , and a diesel gene a o - pho o ol aic panels, espec i ely, using
clima ic and economic pa ame e s in h ee coun ies: Tunisia, Spain and Jo dan. The economic analysis o
hese wa e pumping sys ems showed ha pho o ol aic- ba e ies/ Pump sys em is he op imum solu ion in he
h ee coun ies. Howe e , he ini ial cos o he sys em can be ecupe a ed as e in Spain han in Tunisia and
Jo dan due o high p ices o he diesel hese wo coun ies.
Keywo ds— Pho o ol aic ene gy; wa e pumping; sys em sizing; economic sensi i i y.
1. In oduc ion
Fo emo e ag icul u e a eas, i is common o use diesel gene a o s o supply au onomous ins alla ions.
Howe e , due o he ins abili y o he diesel cos and he dec ease in he pho o ol aic (PV) echnology cos s,
PV- ba e ies sys ems a e bes placed o gene a e elec ici y especially in hese a eas, whe e he con inuous
need o p o iding diesel is conside ed he mos impo an disad an age o sys ems ha use diesel gene a o s
o gene a e elec ici y. The e o e, his enewable based solu ion should be eliable and economic. Thus, sizing
and he ene gy op imiza ion o PV- ba e ies ins alla ions mus be p ope ly pe o med, since hey a e a ec ed
especially by he ene ge ic and clima ic cons ain s, namely he in e mi ence o he clima ic pa ame e s [1, 2].
In ac , sizing o au onomous PV sys ems is conside ed a key ac o ha allows he PV ene gy gene a ed o
be op imized and he elec ical powe equi ed o he loads supply o be p oduced du ing he needed days o
au onomy [2, 3]. Consequen ly, he op imal sizing is indeed ecognized as being c ucial o he sys em o
p o ide sa is ac o y powe o he loads. Mo e p ecisely, o ag icul u al applica ions, whe e wa e is used
p incipally o c ops i iga ion, he size o PV- ba e ies sys ems mus gua an ee he wa e olume needed
du ing he c ops ege a i e cycle [3]. In ac , he knowledge o he wa e olume equi ed, he si e’ clima ic
pa ame e s, he PV module and he ba e ies cha ac e is ics a e c ucial o he au onomous sys em design [1,
2]. Indeed, sizing op imiza ion echniques mus p o ide adequa e alues o he wa e pumping sys em
componen s, especially he PV modules’ su ace, he ba e ies bank capaci y and he ese oi olume.
In his con ex , esea che s ha e es ablished a ious me hods o op imize he size o he PV ins alla ions’
componen s [4- 6]. Fo ins ance, some esea ch wo ks ha e ocused on de eloping analy ical me hods based
on a simple calcula ion o he PV modules’ su ace and he ba e y bank’s capaci y using he ene ge ic balance
me hod, as i has been s udied in [7- 9]. O he esea ch wo ks ha e concen a ed on he cos e sus eliabili y
issue by s udying he op imum sizing o he sys em elemen s om an economic poin o iew, as i has been
epo ed by [10]. Mo eo e , some esea che s ha e p oposed sizing algo i hms based on he minimiza ion o
cos unc ions using he Loss o Load P obabili y (LLP) concep [6, 11- 12]. Addi ionally, o he esea che s
ha e combined he A i icial Neu onal Ne wo ks (ANN) and he Gene ic Algo i hms (GA) o de e mine he
op imum size o au onomous PV sys ems, as i has been epo ed by [9, 13]. De e minis ic me hods and
p obabilis ic app oaches ha e also been used o analyze he impac o he geog aphic si e on he PV modules
and he ene gy s o age design [14]. Mo eo e , mul i-objec i e op imiza ion app oach based on Fuzzy logic has
also been used o ensu e he bes comp ise be ween wo con lic ing objec i es, such as he sys em eliabili y
and cos op imiza ions, as ea ed in [15].
Al hough he e iciency o hese echniques in inding eliable sizing o he sys ems componen s, hey may
esul in an o e sized sys em o one loca ion and an unde sized one o ano he one [16]. Indeed, he
o e sized case esul s in high ins alla ion cos s. Whe eas o an unde sized case, he ins alla ion is unable o
supply he load wi h he needed ene gy [17- 18], as well as he ins alla ion li e ime is sho due o excessi e
use o he ba e ies. Thus, he sys em size mus be ca e ully selec ed o each speci ic applica ion and loca ion
[1, 16].
Consequen ly, his esea ch pape p esen s a con inua ion o p e iously published wo ks by some o he
au ho s [17, 18], whe e a sizing algo i hm o a PV- ba e y ins alla ion des ined o wa e pumping is
p oposed and e alua ed. In ac , using he d ip- i iga ion echnique o oma oes, he pumped wa e is used
he e o i iga e an ag icul u e land si ua ed in No he n Tunisia (la i ude: 36.39º; longi ude: 9.6º) du ing he
c ops ege a i e cycle, which is om Ma ch o July. The sys em consis s o PV modules, a ba e y bank, an
MPPT/ cha ge egula o , an in e e and a wa e ese oi . The egula o is used o a oid he ba e ies damage
due o o e cha ging. The MPPT acks he Maximum Powe Poin (MPP) gene a ed by he PV modules o
ha e an e icien con e sion o he sola ene gy o elec ici y. Fig. 1 shows he main componen s o he
au onomous PV sys em used o he wa e pumping in his applica ion.
The main con ibu ion o his esea ch pape is he compa ison o he algo i hm pe o mances wi h hose
ob ained using Home [1]. Then, an economic s udy is de eloped by compa ing he cos s o he adop ed
sys em o hose o wo o he possible wa e -pumping sys ems, which a e he DG/ pump and he PV/ DG/ pump
sys ems. Indeed, he economic s udy includes he componen s buying, main enance and eplacemen cos s.
The s udy has been e alua ed in h ee coun ies, Tunisia, Spain and Jo dan.
The pape is o ganized as ollows: Sec ion 2 de ails he models used o desc ibe he sys em componen s
ope a ing. The sizing algo i hm p inciple is de ailed in he hi d sec ion. Then, a case s udy o es he sizing
algo i hm pe o mance is desc ibed and explained deeply in Sec ion 4. The achie ed esul s a e compa ed wi h
hose ob ained by HOMER in Sec ion 5. Then, Sec ion 6 p esen s an economic compa ison o h ee possible
sys ems, which a e he DG/ pump, PV/ DG/ pump and he PV/ ba e ies/ pump, whe e cos s in h ee coun ies:
Tunisia, Spain and Jo dan a e compa ed. Finally, he esea ch pape is concluded in Sec ion 7.
Fig.1 Block diag am o he PV wa e pumping sys em used o he c ops i iga ion
2. Modeling o he sys em componen s
2.1 PV module
A PV module is composed o PV cells connec ed in se ies. Then hese modules a e connec ed in pa allel,
which esul s in a PV a ay. Nowadays, he mos common solu ion o c ys alline PV echnology is made o 60
cells in se ies [19]. Thus, modeling a PV module can be based on modelling a PV cell [19, 20]. In ac , a
simple app oach o model a PV module consis s in using a ma ix whe e he sola adiance G and he ambien
empe a u e
a
T
o a pa icula loca ion a e linked, and used o de e mine he co esponding PV powe
p
P
,
and he e o e o ming he ma ix
p
P
(G;
a
T
) [21]. Despi e he simplici y o his me hod, i emains p ac ical
only o he s udied echnology and he PV module, and he e o e, i canno be gene alized. Mo eo e , some
o he esea che s use non-linea models o cha ac e ize he PV modules. These nonlinea models use one diode
o wo diodes based model, which associa es a cu en sou ce in pa allel wi h he diodes, o desc ibe he PV
cu en gene a ed by he sola cell [22, 23]. In his model, losses ela ed o he PV cells connec ion a e
p esen ed by he se ies esis ance
s
R
. Howe e , losses caused by he cha ge ca ie s, namely, losses by
di usion, a e modeled by a pa allel esis ance
p
R
[1, 23, 24].
Addi ionally, he yield based PV module model has also been used o cha ac e ize he PV module
ope a ion [1]. In ac , his model is e alua ed using he sola cell pa ame e s alues, namely he Nominal
Ope a ing Cell Tempe a u e (NOCT), as well as he empe a u e coe icien o he module yield and he
module yield a he e e ence empe a u e. The yield model is simple o use, adap able o he si e
cha ac e is ics and he PV module echnology. Mo eo e , i has expe imen ally been alida ed in a p e ious
published wo k [1]. The e o e, in his esea ch pape , he yield model is chosen o model he PV modules. I is
desc ibed by he ollowing equa ions [1, 36]:
( ) ( )
()( )
e c
p
p T T −−=
β
ηη
1
(1)
whe e:
η
: he module e iciency a he e e ence condi ions, STC (S anda d Tes Condi ions),
p
β
: he empe a u e coe icien o he module yield (
1−
°C
),
( )
T
c
: he PV cell empe a u e (ºC),
e
T
: he empe a u e o he PV cell e e ence (°C).
The e a e many simple models o calcula e he cell empe a u e
()
T
c
, s a ing om he ambien ope a ing
condi ions, he one ha is based only on he he mal pa ame e , NOCT, p o ided by he PV modules
manu ac u e is he ollowing [1, 25, 36]:
( ) ( ) ( )
800
,
e a
ac
TNOCT
d H T
T −
+=
(2)
whe e:
a
T
: he ambien empe a u e (°C),
( )
d H
,
: he sola adia ion on a il ed PV module (W/m²),
NOCT: he No mal Ope a ing Cell Tempe a u e (ºC),

e a
T
: he e e ence ambien empe a u e (°C).
Finally, he PV powe
( )
P
p can be e alua ed as ollows, whe e only he he mal losses ha e been
conside ed; he op ical, misma ch and joule losses o he PV a ay will be conside ed wi h sepa a ed
e iciencies [1, 36]:
( ) ( ) ( )
d HS P
p p
η
,=
(3)
whe e S is he PV module su ace (m²).
2.2 Ba e y bank
The in e mi ence o he sola adia ion and he gene a ion o he PV powe only du ing he day ime make
using s o age ene gy componen s namely he ba e ies, necessa y. Thus, ba e y bank is gene ally used o
supply he equi ed powe o he load on one hand and o s o e he PV ene gy gene a ed in excess, on he o he
one [1, 24]. In his esea ch pape , a non-linea model, based on he ba e y bank’ cu en and ol age, is used
o model he ba e y ope a ion. The model pe o mance is e alua ed by he ba e ies dep h o discha ge (dod),
which is exp essed as ollows [1, 24, 26, 36]:
( )
( )
p
R
k
C
C
dod k
−=1
(4)
whe e he s o ed cha ge in he ba e y
R
C
is gi en by [36]:
( ) ( )
( )
p
k
k
ba
k
R
k
RI
k
CC 3600
1∂
+= −
(5)
whe e:
k∂
: he ime be ween ins an k-1 and k,
p
k
: he Peuke coe icien ,
p
C
: he Peuke capaci y (Ah),
( )
k
ba
I
: he ba e y bank cu en , which is conside ed cons an (A).
2.3 Wa e olume o Toma oes i iga ion
In his esea ch pape , he PV wa e pumping sys em is used o pump wa e o oma oes i iga ion. Hence, i
is necessa y o s udy he need o wa e o he c ops based on he clima ic and he si e pa ame e s.
In ac , Toma oes is ha es ed in Tunisia du ing he summe pe iod. Indeed, hey a e sown in nu se y plan s
du ing Feb ua y. The seedlings a e ansplan ed in Ma ch in he ields. Eigh o en weeks a e sowing,
lowe ing occu s in he middle o May. A he end o his mon h and a he beginning o June, ui s ipening
occu . In July, he ui s a e eady o be ha es ed [27]. Hence, he g owing s eps o Toma oes will be conside ed
he e as a base o de e mine he op imum sys em sizing o he PV ins alla ion componen s, which mus p o ide
he wa e olume equi ed o he c ops i iga ion, by aking in o accoun o he op imal equency and iming o
i iga ion, which co espond o a speci ic i iga ion schedule [28]. Indeed, pa ame e s ela ed o he c ops a e
used he e o model he wa e olume needed o he c ops i iga ion, namely he e e ence c op
e apo anspi a ion (
o
ET
) and he ain all
m
, which can be expec ed o a gi en 10-days pe iod [29, 30]. In ac ,
in he li e a u e, many models ha e been used o desc ibe Toma oes’ e apo anspi a ion. Fo ins ance, some
esea che s used he Penman Me hod, which depends essen ially on he ne adia ion a he c op su ace, he
mean ai empe a u e, and he wind speed [31]. O he wo ks p esen ed he e apo anspi a ion as a unc ion o he
sunligh du a ion and he ai empe a u e [1, 32]. Fo ins ance, he Blaney-C iddle model o he
e apo anspi a ion modelling includes he seasonal c op coe icien
c
k
, in addi ion o he a io o he mean daily
day ime hou s o a gi en mon h o he o al day ime hou s in he yea p and he mean mon hly ai empe a u e T
o he co esponding mon h [27]. The e by, his model p o ides good pa e ns o he wa e olume equi ed o
Toma oes’ i iga ion [27]. Hence, in his esea ch, i is used o desc ibe he Toma oes’ e apo anspi a ion [27]:
( )
13
8460 .
T.p
KETo+=
(6)
whe e K is he co ec ion ac o , which is exp essed by:
K..K 240030 +=
(7)
To ob ain he necessa y g oss wa e , i is essen ial o es ima e he i iga ion losses. Thus, an addi ional
wa e olume mus be pumped, o compensa e he possible losses. Consequen ly, he inal wa e olume V
needed o i iga e Toma oes is gi en by [1, 27, 33]:
( )
( )








−
−−
+−=
R
R
moc
Ll
Ll
ETkV 1
11
1
(8)
whe e:
m
: he a e age mon hly ain olume (m³),
l
: he leaching e iciency coe icien as a unc ion o he i iga ion wa e applied (%),
R
L
: he leaching ac ion gi en by he humidi y ha emains in he soil exp essed in (%) and gi en by:
we
w
R
EC
EC
EC
L−
=5
(9)
whe e:
w
EC
: he elec ical conduc i i y o he i iga ion wa e (dS.
1−
m
),
e
EC
: he c op sal ole ance (dS.
1−
m
).
3. Sizing Algo i hm P inciple
A good op imiza ion o he wa e pumping sys em should ul ill he elec ical powe equi ed o supply
he wa e pump du ing he necessa y pumping du a ion [34]. Hence, he main objec i e o he sizing
algo i hm is o ensu e ha he pump is supplied h oughou he day, while p o ec ing he ba e y bank agains
deep discha ge o excessi e cha ge, and gua an eeing he wa e olume needed o oma oes’ i iga ion. The
inpu s, ou pu s, objec i es and c i e ia o he sizing algo i hm a e p esen ed in Fig. 2. Indeed, he algo i hm
depends on:
• he wa e olume V needed o i iga e oma oes,
• he si e cha ac e is ics, including he sola adia ion G and he ambien empe a u e
a
T
,
• he ba e y’ dep h o discha ge dod,
• he PV module cha ac e is ics, such as he PV powe , cu en and ol age.
Fig. 2 P inciple o he p oposed sizing algo i hm
The p oposed sizing app oach aims o p o ide he op imum PV modules’ su ace (
op
S
), he numbe o
ba e ies (
op
ba
n
) and he ese oi olume V ha gua an ees he ins alla ion au onomy. In ac , he idea
consis s in sea ching he op imal componen s sizes ha ensu e he ene ge ic balance be ween he ene gy
(
c
E
) cha ged in he ba e y bank, and he ene gies
AM
E
and
PM
E
ex ac ed om i du ing he AM and PM
imes, espec i ely, as i is shown in Fig. 3. Indeed, he ba e y bank supplies he pump when he PV modules
do no gene a e he su icien elec ical powe o he pump powe supply, and i is cha ged wi h he PV
ene gy gene a ed in excess. The ene gy balance can be exp essed as ollows (Fig. 3):
PM
AMcEE
E+≈
(10)
Fig.3 Diag am o he ene gy balance p inciple
The p oposed sizing app oach is composed o wo main algo i hms. In ac , in Algo i hm 1, he op imum
sizes o he PV sys em componen s a e e alua ed o each mon h M o he Toma oes ege a i e cycle ( om
Ma ch o July) as i is desc ibed in Fig. 4. These esul s a e used in Algo i hm 2 which e alua es he inal
alue o he sys em componen s sizes, as i is desc ibed in Fig. 5. These wo algo i hms a e de ailed in he
ollowing subsec ions.
3.1 Algo i hm 1: E alua ion o he mon hly PV modules’ su ace and he ba e ies’ numbe
Algo i hm 1 inds
he PV module su ace
(
M
S
) and he numbe o ba e ies ( M
ba
n
) o each mon h M
du ing he c ops’ ege a i e cycle. The algo i hm has he ollowing p ocess:
S ep 1 Es ima ion o he di used adia ion (
( )
d, Hd
) and di ec adia ion (
( )
d, Hb
) using he mean
alue o mon hly global sola adia ion (H) on a ho izon al PV module as ollows [1, 24, 35]:
( )
( )
HK.K
.K..
wcoswwsin
wcoswcos
d
, H
sss
s
d32 1372189
45633911
24 −+
−
−
−
=
π
(11)
( ) ( )
Hwcosba
wcoswwsin
wcoswcos
d, H s
ss
s+
−
−
=24
π
(12)
( ) () ()
d,
Hd
, H
d, H db −=
(13)
whe e:





−+= 3
50104090
π
s
wsin
..a
(14)





−+= 3
476706609
0
π
s
wcos..b
(15)
w: he angle o he sun a a speci ic hou ,
s
w
: he angle o he sun a sunse ,
K
: he clea ness index.
which is close o he a ge alue o 1.7. Table 4 also shows ha July is he mos c i ical mon h o i iga ion
because i equi es mo e wa e olume o i iga ion. The e o e, he sys em componen s sizing o July a e
selec ed as he sizing o he sys em. The achie ed componen s’ size allows he load o be supplied du ing he
eques ed pumping du a ion, he ba e y bank o be ope a ed sa ely, and he wa e olume equi ed o i iga e
oma oes o be pumped. The equi ed daily wa e needed and ac ual pumped wa e olumes a e illus a ed in
Fig. 8 o he c op ege a i e cycle. Table 5 shows ha he leaked wa e olumes in May and July a e 1314.6
3
m
and 963
3
m
, espec i ely. I is clea ha he mon h o May has he maximum leaked wa e . The e o e,
he wa e olume co esponds o May is chosen o o he ese oi . Hence, using equa ions (27)- (30), and
conside ing
%
ese oi
80=
η
, he inal alue o he ese oi olume ha ensu es he sys em au onomy o
his a m is 1800
3
m
. This olume ensu es an au onomy o 10.22 consecu i e days in May and 5.62 in July
wi h no need o pump wa e o he ese oi . These alues a e su icien o p o ide wa e e en when he sky
is cloudy (9 days in May and 4 days in July) and he PV modules a e no p oducing elec ici y and he
ba e ies a e ully discha ged. This is an excellen esul which p o es ha he sys em is o ally au onomous
o bo h elec ic ene gy and wa e conside a ions.
Fig. 8 Daily needed (V) and pumped (
pumped
V
) wa e olumes du ing oma oes ege a i e cycle o he case
s udy
Table 3 Pa ame e s used in execu ing Algo i hm I including ini ial alues o PV module su ace and ba e ies
numbe
Table 4 Algo i hm 1 esul s summa y
Table 5 F equency o cloudy days and wa e olume needed o i iga ion
5. Resul s compa ison wi h HOMER ool
In o de o check he accu acy o he p oposed sizing app oach, i s esul s a e compa ed wi h hose
ob ained using HOMER comme cial so wa e. In ac , using Home , he needed modules su ace ob ained is

142 m², and he ba e y numbe is 14 ba e ies (210 A.h/ 12V). While,
op
S
was 101.5 m² and
op
ba
n
was 8
ba e ies o 210 A.h/ 12 V as ob ained using p oposed app oach. The simula ion esul s using HOMER
so wa e a e p esen ed in Fig. 9 and Fig. 10. The PV modules’ size sugges ed by HOMER is highe han he
su ace ob ained by he p oposed algo i hm. This can be explained because HOMER gi es huge impo ance o
he day au onomy and includes when calcula ing he ba e y bank capaci y.
Fig. 9 The hou ly in e e ou pu powe in kW in each mon h o ege a i e cycle a e aged o e mon hs’ days
using HOMER
Fig. 10 Ba e ies bank s a e o cha ge o each mon h o he ege a i e cycle a each hou in a day a e aged
o e mon hs’ days using HOMER
6. Economic iabili y o PV/ ba e ies/pump and diesel only/pump op ions
In his sec ion, he o al wa e pumping sys em cos including ini ial in es men s and ope a ional cos s a e
compa ed o h ee di e en sys em implemen a ions. The i s sys em is composed o a diesel engine only
which supplies elec ici y o he wa e pump. In he second sys em, he pump is supplied by bo h PV modules
and a diesel engine. Finally, he hi d sys em is a ully enewable op ion in which he elec ici y is supplied o
he pump by PV modules and ba e ies bank. The op ion composed o PV/ Ba e ies/ DG is no s udied he e
since i is assumed ha he wa e pumping will be only pe o med du ing he day.
6.1 Cos s analysis o wa e pumping plan s
The o al cos o wa e pumping ins alla ion plan is calcula ed o he di e en op ions assuming i has N
pa s. The o al cos includes ini ial in es men , main enance and pa s eplacemen s cos s [38].
6.1.1 Cos o diesel wa e pumping sys em
This sys em is composed o a diesel gene a o which supplies elec ici y o he wa e pump. Hence, i s
cos
1s
cos
can be e alua ed using equa ion (31):
( )( )
dieselydiesel_ dieselsMnCn cos 1
1−+=
(31)
whe e:
diesel
n
: numbe o diesel engines used.
diesel_
C
: in es men p ice o he diesel engine (€/ o
y
n
yea s o ope a ing).
y
n
: numbe o yea s o sys em ope a ion.
diesel
M
: diesel gene a o main enance cos (€/ module pe yea ).
The e alua ion o he diesel cos
diesel_
C
includes uel and engine oil cos s. I is e alua ed as ollows:
yoiloiloil ueldiesel ueldieseldiesel_
n
*V
*
C*
nV
*
*
CCC ++=
∆
(32)
whe e:
diesel
C
: diesel gene a o p ice (€/ module o
y
n
).
uel
C
: cos o he uel (€/ l).
diesel
∆
: ime du a ion o ope a ion (h/ day).
uel
V
: olume o uel consump ion (l/ h).
oil
C
: cos o engine oil (€/ l).
oil
n
: numbe o oil changing imes by yea .
6.1.2 Cos o PV/ diesel wa e pumping sys em
This sys em is composed o PV modules and diesel gene a o o supply wa e pump wi h elec ici y. In
his case, he diesel gene a o is used when he powe gene a ed by he PV modules is insu icien o ope a e
he wa e pump. The cos
2s
cos
o his sys em can be e alua ed as [38]:
( ) ( ) ( )
( )
( ) ( )( )
dieselydiesel_ dieselin yin in in
chopychopchopchopchopp yp p s
MnCnynMyC
ynMyCnMnCn cos
111
11
2
−++−−+++
−−++++=
(33)
whe e:
p
n
: numbe o PV modules,
p
C
: PV module cos (€/ module o
y
n
).
p
M
: PV module main enance cos (€/ module pe yea ).
chop
n
: numbe o choppe s.
chop
C
: choppe cos (€/choppe o
y
n
).
chop
y
: numbe o imes he choppe is eplaced du ing
y
n
yea s.
chop
M
: main enance cos o one choppe (€/ choppe pe yea ).
in
C
: cos o in e e (€/ in e e o
y
n
).
in
y
: numbe o in e e s eplaced du ing
y
n
yea s.
in
M
: main enance cos o one in e e (€/ in e e pe yea ).
6.1.3 Cos o PV/ba e ies bank wa e pumping sys em
This sys em is composed o PV modules and a ba e ies bank which supply he wa e pump wi h
elec ici y. In his case, he ba e ies bank supplies he wa e pump when he PV powe gene a ed is
insu icien o ope a e i . The cos
3s
cos
o his sys em can be e alua ed by [38]:
( ) ( )( ) ( )
( )
( )
11
11
3
−−+++
++−−++++=
in yin in in
chopchopchopbbybbbba p yp p s
ynMyC
yCnMynCyCnMnCn cos
(34)
whe e:
ba
n
: numbe o ba e ies.
b
C
: ba e y cos (€/ ba e y o
y
n
).
ba
y
: numbe o imes he ba e ies a e eplaced du ing
y
n
yea s.
ba
M
: main enance cos o one ba e y (€/ ba e y pe yea ).
6.2 Cos compa ison o di e en wa e Pumping Sys ems
The pa ame e s used in he cos analysis o he di e en op ions calcula ed o he case s udied a m in
Tunisia a e desc ibed in Table 6.
Table 6 Pa ame e s used o cos s analysis o di e en wa e pumping op ions [39]
The cos o op ions used diesel gene a o s includes engine oil and uel consump ion cos s, which a e
summa ized in Table 7 o wo op ions.
Table 7 Diesel gene a o pa ame e s used o he cos analysis
The cos s analysis o he di e en op ions a e e alua ed based on clima ic and economic da a in Tunisia
using esul s ob ained o he case s udied a m which a e
op
S
= 101.5 m² and op
ba
n
=8 ba e ies o 210 A.h/
12 V). The o al cos o hese h ee sys ems a e summa ized in Table 8.
Table 8 Cos s summa y o he h ee wa e -pumping op ions o a m in Tunisia
I is no iced ha sys em 2, which consis s o PV/ DG / Pump, is he mos expensi e sys em. I is subjec
o ela i ely high p ice o diesel uel in Tunisia (i is assumed ha uel p ice is cons an du ing 20 yea s o
ope a ion). Howe e , sys em 1, which uses DE, only ha e ela i ely close o al cos o sys em 2. Finally, he
cos o Sys em 3 is he cheapes among he h ee sys ems o wa e pumping plan supply in Tunisia. I is
necessa y o men ion ha sys ems wi h DG equi es con inuous main enance and need ope a o p esence on
egula bases o uel and change oil o he engine which make hem no p ac ical solu ions o supplying
elec ici y o emo e wa e pump sys ems.
6.3 Wa e pumping sys em cos analysis sensi i i y o geog aphic condi ions
I has been shown ha he PV/ Ba e ies/ Pump sys em is he mos economic sys em o wa e pumping
plan s in Tunisia. The cos analysis was done based on clima ic, geog aphic and economic pa ame e s in he
coun y. In his sec ion, he economic s udy is epea ed o wo mo e coun ies; Spain (la i ude: 40.25°) and
Jo dan (la i ude: 31°) o in es iga e he e ec o geog aphic pa ame e s a ia ions on he inal esul s. Hence,
he cos o p e iously p oposed op ions is ecalcula ed o Spain and Jo dan. These coun ies a e chosen due
o simila i ies in clima ic condi ion (all a e on he Medi e anean see). In addi ion, hese coun ies we e
chosen because hey ha e almos simila sola ene gy amoun s compa ed o hose o Tunisia. Fo ins ance, in
July, he sola adia ion e alua ed on a il ed PV module in Tunisia, Spain and Jo dan a e espec i ely:
9136.7 Wh/m², 9100 Wh/m² and 9121 Wh/m².
Simila calcula ions we e done o sizing he PV/ba e ies bank o Spain and Jo dan using he p ocess
men ioned in he p oposed sizing algo i hms o Sec ion 3. Conside ing also ha he c ops wa e need is he
same and using clima ic da a o hese wo coun ies, he inal PV modules’ su ace a ea and he numbe o
ba e ies a e summa ized in Table 9.
Table 9 Sizing o PV/ ba e ies/ pump sys em using clima ic da a o Tunisia, Spain and Jo dan
Table 9 shows ha he e is a e y la ge simila i y in he sys em sizing o all h ee coun ies as expec ed.
They ha e almos simila sola adia ion amoun and clima ic pa ame e s (Medi e anean clima e). The o al
cos o wa e pumping sys em in he di e en coun ies a e e alua ed using upda ed uel p ices summa ized
in Table 10. I is shown in Table 10 ha he uel p ice in Spain is he mos expensi e compa ed o Tunisia
and Jo dan. Indeed, i is almos doubled. Hence, he o al cos s o he h ee op ions o implemen ing wa e
pumping sys ems (DG/ Pump, PV/ DG/ Pump and PV/ Ba e ies/ Pump) a e e alua ed and p esen ed in Table
11.
Table 10 Fuel p ices in Tunisia, Spain and Jo dan [40]
Table 11 Cos s e alua ion o he h ee sys ems op ions using da a o Tunisia, Spain and Jo dan
I is clea ha he DG only/Pump sys em is he mos expensi e op ion o wa e pumping specially in
Spain. This jus i ies he ac ha Spanish go e nmen s a egy is o encou age using enewable ene gy ins ead
o ossil uel. The cos analysis esul s showed ha he PV/ba e ies/ pump sys em is he cheapes solu ion o
wa e pumping sys ems in all h ee coun ies wi h simila clima ic condi ions.

The esul s shown in Table 8 also show ha he cos o sys em 3, which is e alua ed o 20 yea s, can be
ecupe a ed in abou 15.5 yea s in Spain. Thus, he sys em will ope a e ee o cha ge du ing 4.5 yea s.
Howe e , in Tunisia and Jo dan, he numbe o yea s o ecupe a e he PV/ba e ies/pump cos is highe han
he sys em li e ime. Thus, sys em 3 is s ill he op imum solu ion in Tunisia and Jo dan bu i s p ice canno be
ecupe a ed as .
I is known ha each li e o diesel has 720 g o CO2 and equi es 1920 g o O2 o combus . As a esul , a
20 kW DG would p oduce a pollu an o abou 65117 Kg o CO2 du ing 20 yea s [41]. Thus, he
PV/ba e ies/Pump op ion is also p e e able o lowing he pollu ion.
7. Conclusion
An algo i hm o sizing he componen s o a wa e pumping ins alla ion is p oposed and alida ed using
measu ed clima ic da a o a 10 ha a m in No he n Tunisia. The sizing algo i hm ensu es he sys em
au onomy, he sa e ope a ion o he sys em componen s and pumping he wa e olume needed o i iga e
Toma oes du ing i s ege a i e cycle (Ma ch o July). Mo eo e , a compa ison o he componen s sizes wi h
hose ob ained using HOMER p o es he sizing algo i hm eliabili y in op imizing he componen s size,
while ul illing he objec i es ela ed o sa ing ene gy and wa e .
The componen s sizing op imiza ion is con i med wi h he cos analysis o di e en wa e pumping
op ions, including he Diesel Gene a o / Pump, PV/ DG/ Pump and he PV/ ba e ies/Pump sys ems. The cos
sensi i i y o hese op ions o clima ic, geog aphic and economic pa ame e s is analyzed o h ee di e en
coun ies which a e Tunisia, Spain and Jo dan. The ob ained esul s shows ha he PV/ ba e ies/ pump
sys em is he cheapes op ion o he h ee coun ies. Mo eo e , he cos o his sys em can be ecupe a ed in
15.5 yea s in Spain due o he expensi e uel p ices. Finally, CO2 emission is elimina ed when using PV/
ba e ies/ pump sys em, which makes i an en i onmen iendly and cheap solu ion.
Acknowledgmen s
The au ho hank M . Lamine Yahyaoui and he ag icul u e adminis a ion o Medjez El Beb, Tunisian
Minis y o Ag icul u e, o p o iding us wi h da a, and he Elec ic Depa men a he Fede al Uni e si y o
Espi i u San o o B azil o hei suppo .
D . Yahyaoui is unded by he p ojec (FAPES 0838/2015) gi en by he Fundação de Ampa o à Pesquisa
e Ino ação do Espi i o San o (FAPES), B azil.
8. Re e ences
[1] Yahyaoui I. Speci ica ions o Pho o ol aic Pumping Sys ems in Ag icul u e: Sizing, Fuzzy Ene gy
Managemen and Economic Sensi i i y Analysis. 2016; Book, ISBN: 9780128120392, Al e na i e Ene gy,
Else ie .
[2] Jakh ani A Q, O hman A K, Rigi A, Ragai H, Samo S R, & Kamboh S A. A no el analy ical model o
op imal sizing o s andalone PV sys ems. Ene gy, 2012; 46, 675-682.
[3] Kha ib T, Mohamed Z A, & Sopian K. A e iew o PV sys ems size op imiza ion echniques. Renewable
and Sus ainable Ene gy Re iews, 2013; 22, 454-465.
[4] Capizzi G, Bonanno F, & Tina G M. Expe iences on he Design o S and-Alone PV Sys em by
De e minis ic and P obabilis ic Me hods. P oceedings o he In e na ional Con e ence on Clean Elec ical
Powe (ICCEP), 328–335.
[5] Acakpo i A, Xa ie F F & Awuah-Ba ou R. Analy ical me hod o sizing PV wa e pumping sys em.
P oceedings o he 4 h IEEE In e na ional Con e ence on Adap i e Science & Technology, 2012; 65-69.
[6] Kha ib T, Mohamed A, Sopian K, & Mahmoud M. A new app oach o op imal sizing o s andalone PV
sys ems. In e na ional Jou nal o Pho o Ene gy, 2012.
[7] Sh es ha G B, & Goel L. A s udy on op imal sizing o s and-alone PV s a ions. IEEE T ansac ions on
Ene gy Con e sion, 13, 1998; 373-378.
[8] Ba a L, Ca alano i S, Fon ana F, & La o an e F. An analy ical me hod o de e mine he op imal size o a
PV plan . Sola Ene gy, 1984; 33, 509-514.
[9] G oumpos P P, & Papageo giou G. An op imal sizing me hod o s and-alone PV powe sys ems. Sola
Ene gy, 1987; 38, 341-351.
[10] Melli A, Benghanem M, Hadj A ab A, & Guessoum A. Modelling o sizing he PV sys em pa ame e s
using a i icial neu al ne wo k. P oceedings o he IEEE Con e ence on Con ol Applica ions, 2003; 353-
357.
[11] Yang H, Zhou W, Lu L, & Fang Z. Op imal sizing me hod o s and-alone hyb id sola –wind sys em wi h
LPSP echnology by using gene ic algo i hm. Sola Ene gy, 2008; 82, 354-367.
[12] Klein S A, & Beckman W A. Loss-o -load p obabili ies o s and-alone PV sys ems. Sola Ene gy, 1987;
39, 499-512.
[13] Abouzah I, & Ramakuma R. Loss o powe supply p obabili y o s and-alone PV sys ems: a closed o m
solu ion app oach. IEEE T ansac ions on Ene gy Con e sion, 1991; 6, 1-11.
[14] F henakis V, Mason J E, & Zweibel K. The echnical, geog aphical, and economic easibili y o sola
ene gy o supply he ene gy needs o he US.Ene gy Policy, 2009; 37, 387-399.
[15] Sugan hi L, Iniyan S, & Samuel A A. Applica ions o uzzy logic in enewable ene gy sys ems–a e iew.
Renewable and Sus ainable Ene gy Re iews, 2015; 48, 585-607.
[16] Melli A, Benghanem M, & Kalogi ou S A. Modeling and simula ion o a s and-alone PV sys em using an
adap i e a i icial neu al ne wo k: P oposi ion o a new sizing p ocedu e. Renewable Ene gy, 2007; 32,
285-313.
[17] Yahyaoui I, Chaabene M, & Tadeo F. An algo i hm o sizing PV pumping sys ems o oma oes i iga ion.
P oceedings o he IEEE In e na ional Con e ence on Renewable Ene gy Resea ch and Applica ions
(ICRERA), 2013; 1089-1095.
[18] Yahyaoui I, Ammous M, & Tadeo F. Algo i hm o op imum sizing o a PV wa e pumping sys em.
In e na ional Jou nal o Compu e Applica ions (IJCA), 2015; 11, 21-28.
[19] Me z A, Adle D, Bagus S, Blanke H, Bo ha M, B ouwe E, & Fiedle M. Indus ial high pe o mance
c ys alline silicon sola cells and modules based on ea su ace passi a ion echnology. Sola Ene gy
Ma e ials and Sola Cells, 2014; 120, 417-425.
[20] Jo dehi A R. Time a ying accele a ion coe icien s pa icle swa m op imisa ion (TVACPSO): A new
op imisa ion algo i hm o es ima ing pa ame e s o PV cells and modules. Ene gy Con e sion and
Managemen , 129, 2016; 262-274.
[21] Kenny R P, F iesen G, Chianese D, Be nasconi A, & Dunlop E D. Ene gy a ing o PV modules:
compa ison o me hods and app oach. P oceedings o he 3 d IEEE Wo ld Con e ence on PV Ene gy
Con e sion, 2003; 2015-2018.
[22] Xiao W, Dun o d W G; & Capel A. A no el modeling me hod o PV cells. P oceedings o he 35 h IEEE
Annual Con e ence on Powe Elec onics Specialis s, 2004; 1950-1956.
[23] Adamo F, A i issimo F, Di Nisio A, & Spada ecchia M. Cha ac e iza ion and es ing o a ool o PV
module modeling. IEEE T ansac ions on Ins umen a ion and Measu emen , 2011; 60, 1613-1622.
[24] Yahyaoui I, Sallem S, Kamoun M B A, & Tadeo F. A p oposal o o -g id pho o ol aic sys ems wi h non-
con ollable loads using uzzy logic. Ene gy Con e sion and Managemen , 2014; 78, 835-842.
[25] Ba dhi M, G andi G, & Tina G M. Compa ison o PV cell empe a u e es ima ion by di e en he mal
powe exchange calcula ion me hods. Renew Ene gy Powe , Qual J 2012; (ICREPQ’ 12), 10.
[26] Se na A, & Tadeo A. O sho e hyd ogen p oduc ion om wa e ene gy. In e na ional Jou nal o Hyd ogen
Ene gy, 2014 , 39, 1549- 1557.
[27] Pe ei a L S, Allen R G, Smi h M, & Raes D. C op e apo anspi a ion es ima ion wi h FAO56: Pas and
u u e. Ag icul u al Wa e Managemen , 2015; 147, 4-20.
[28] Saleh M Ismail, Kiyoshi O, & Nu A K. E ec o i iga ion equency and iming on oma o yield, soil
wa e dynamics and wa e use e iciency unde d ip i iga ion. P oceedings o he Ele en h In e na ional
Wa e Technology Con e ence, 2007; 15-18.
[29] Olcan C. Mul i-objec i e analy ical model o op imal sizing o s and-alone PV wa e pumping sys ems.
Ene gy Con e sion and Managemen , 2015; 100, 358-369.
[30] Linquis B, Snyde R, Ande son F, Espino L, Inglese G, Ma as S, & Russo A. Wa e balances and
e apo anspi a ion in wa e -and d y-seeded ice sys ems. I iga ion Science, 2015; 33, 375-385.
[31] Fleische E, Böl e J, & Klemm O. Summe e apo anspi a ion in wes e n Sibe ia: a compa ison be ween
eddy co a iance and Penman me hod o mula ions. Hyd ological P ocesses, 2015; 29, 4498-4513.
[32] Obid Ka eem R, Khaleel Basim, & Ni e, Kadhim. The Compa ison be ween di e en me hods o
es ima ing consump i e use o wa e in I aq. Jou nal o Babylon Uni e si y/ Enginee ing Sciences, 2013;
21, 27-36.
[33] Wichelns D, & Qadi M. Achie ing sus ainable i iga ion equi es e ec i e managemen o sal s, soil
salini y, and shallow g oundwa e . Ag icul u al Wa e Managemen , 2015; 157, 31- 38.
[34] W ixon G T, & McCa hy S. Op imiza ion and analysis o PV sys ems using a compu e model.
P oceedings o he IEEE Con e ence on PV Specialis s, 1988; 1293-1297.
[35] Zekai S. Sola ene gy undamen als and modeling echniques: a mosphe e, en i onmen , clima e change
and enewable ene gy, 2008; 276, Sp inge , ISBN 978-1-84800-133-6.
[36] Chaabene M. Ges ion éne gé ique des sys èmes pho o ol aïques, mas e cou se a he Na ional School o
Enginee ing o S ax, Tunisia, 2009.
Pa ame e s Values
ba
η
90 %
in
η
92 %
l
η
95 %
ma ching
η
80 %
op
η
90 %
eg
η
90 %
η
10.58 %
max
dod
∆
78 %
pump
P
4500 W
Table 2 Clima ic pa ame e s, panel e iciency and i iga ion pa ame e s used in he case s udy
Ma ch Ap il May June July
a
T
(°C)
14
17.25
20
22
30
H
(Wh)(16)
4023.6 5512.3 5815.2 7392.2 7163.2
k
(%)
54 51 54 61 64
p
W
(Wh) (3)
5908.6 7562.1 8030.9 9479.0 9136.7
p
η
(%) (1)
10.16 10.06 9.91 9.75 9.37
Wa e olume
ha/m 10
3
(8)
60.70 100.37 179.82 241.10 321.03
Pumping du a ion
∆
(h) (20)
2.5 4.13 7.41 9.93 13.25
Mon hs
Pa ame e s

Table 3 Pa ame e s used in execu ing Algo i hm 1 including ini ial alues o PV module su ace and ba e ies
numbe
Table 4 Algo i hm 1 esul s summa y
Ma ch
Ap il
May
10
days
10
days
11
days
10
days
10
days
10
days
i
p c
W
(Wh)
5760
7180
8120
Maximum
numbe o cloudy
days pe mon h
i
c
n
(27)
9
7
9
Clouds a e pe
day
i
c
A
(%) (28)
30.15
23.23
28.38
I iga ion
equency
i
[1]
3
3
2
2
2
1
1
au
d
1
1
1
1
1
1
1
ech
d
3
3
2
2
2
1
1
Ini ial panel
su ace
i
S
(m²)
(21), (22)
61
61
68
89
89
107
203
Ini ial numbe s o
ba e ies
i
ba
n
(23)
4
4
4
5
5
5
10
June
July
10 days
10 days
11 days
i
p c
W
(Wh)
8500
8340
Maximum numbe o
cloudy days pe
mon h
i
c
n
(27)
3
4
Clouds a e pe day
i
c
A
(%) (28)
13.03
14.11
I iga ion equency
i
[1]
1
1
2
2
au
d
1
1
1
1
ech
d
1
1
2
2
Ini ial panel su ace
i
S
(m²) (21), (22)
234.5
337
168.5
168.5
Ini ial numbe s o
ba e ies
i
ba
n
(23)
14
18
18
18
Mon hs
Mon hs
Pa ame e s
Pa ame e s
Table 5 F equency o cloudy days and wa e olume needed o i iga ion
Ma ch
Ap il
May
June
July
Wa e
olume
ha/m 10
3
(8) 60.70 100.37 179.82 241.10 321.03
Daily pumped
wa e (m³)
274
281.6
291
321
321
Maximum
numbe o
cloudy days pe
mon h
i
c
n
(27)
9
7
9
3
4
I iga ion
equency
i
[1]
3
3
2
2
2
1
1
1
1
2
2
Leak wa e (m³)
(29)
7
129
119.5
420
1314.6
417
963
321
Rese oi
olume (m³)
(30)
1793
1541
Ma ch
Ap il
May
June
July
e o
η
1.30 1.23 1.28 1.13 1.14
PMAM
EE +
(Wh/
day)
10991 14481 10239 12511 24046
c
E
(Wh/ day)
18725 23035 16807 18033 35314
pump
E
(Wh/ day)
11258 18615 33350 44716 59541
PV
E
(Wh)
20371 29296 43378 55035 82802
M
S
(m²)
37.5 41.5 54.5 61.5 101.5
M
ba
n
(26)
4 5 4 5 8
η
(25)
1.66 1.57 1.64 1.44 1.46
PMAM
cEE
E
+
=
1
η
(25
)
1.7 1.59 1.64 1.44 1.47
Pa ame e s
Mon hs
Mon hs
Pa ame e s
Table 6 Pa ame e s used o cos s analysis o di e en wa e pumping op ions [39]
Pa ame e s
Name
Value
y
n
(yea s)
he ins alla ion li e ime
20
p
C
(€/ module o
y
n
)
he PV module cos
265.81
p
M
(€/ module pe yea )
he PV module main enance cos
2.66
b
C
(€/ ba e y o
y
n
)
he ba e y cos
264
ba
y
he numbe o imes he ba e ies
a e eplaced du ing
y
n
yea s 4
ba
M
(€/ ba e y pe yea )
he main enance cos o one
ba e y 2.64
chop
n
he numbe o choppe s
1
chop
C
(€/choppe o
y
n
)
he choppe cos
200
chop
y
he numbe o imes he choppe
is eplaced du ing
y
n
yea s 0
chop
M
(€/ choppe pe yea )
he main enance cos o one
choppe 2
in
C
(€/ in e e o
y
n
)
he cos o he in e e
1942
in
y
he numbe o he in e e
eplaced du ing
y
n
yea s 0
in
M
(€/ in e e pe yea )
he main enance cos o one
in e e 19.42
diesel
C
he diesel gene a o cos
4475
diesel
M
(€/ in e e pe
yea )
he main enance cos o he
diesel
44.75
Table 7 Diesel gene a o pa ame e s used o he cos analysis
Numbe o hou s he diesel
gene a o ope a es (h)
13.25 (DG only)
5 (DG/ PV)
Fuel consump ion
4.7
l/h
Fuel p ice
0.48
€
Oil olume
8
l/ 3 mon hs
Oil cos pe li e
5.91
€
Table 8 Cos s summa y o he h ee wa e -pumping op ions o a m in Tunisia
Sys em
Sys em 1: DG/
Pump
Sys em 2: PV/DG/
Pump
Sys em 3: PV/Ba e ies/
Pump
Cos s (€)
67044
69772
51263
Table 9 Sizing o PV/ ba e ies/ pump sys em using clima ic da a o Tunisia, Spain and Jo dan
PV su ace (m²)
Ba e y bank numbe
Tunisia
101.5
8
Spain
102.5
8
Jo dan
102
8
Table 10 Fuel p ices in Tunisia, Spain and Jo dan [40]
Coun y
Tunisia
Spain
Jo dan
Cos s (€/l)
0.57
1.03
0.53
Coun y
Resul s
Table 11 Cos s e alua ion o he h ee sys ems op ions using da a o Tunisia, Spain and Jo dan
DG/Pump
PV/DG/Pump
PV/Ba e ies/Pump
Numbe o yea s
o ecupe a e
sys em cos
Tunisia
67044
69772
51263
65
Spain
115330
75605
50306
15.5
Jo dan
62845
81879
50147
79
Coun y
Sys em