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Design and E alua ion o a Renewable Wa e Pumping Sys em
Imene Yahyaoui
Dep . Sys ems Eng and
Au oma ic
Indus ial Eng School
Uni . Valladolid, Spain
imene@au om.u a.es
Giuseppe Tina
Dep . Elec ic,
Elec onic and Compu e
Uni . Ca ania, I aly
Giuseppe. [email protected]
c .i
Mahe Chaabene
Dep . Elec ic Eng
Na ional Eng School
Uni . S ax, Tunisia
mahe chaabane@yahoo.
com
Fe nando Tadeo
Dep . Sys ems Eng and
Au oma ic
Indus ial Eng School
Uni . Valladolid, Spain
e nando@au om.u a.es
Abs ac : The design and e alua ion o a s and-alone pho o ol aic sys em o well pumping in ag icul u al
applica ion is p esen ed. Gi en en i onmen al (i adiance and ambien empe a u e), sys em (PV and ba e y
echnology, a ay geome y) and load (mon hly daily demand) da a, he op imal size o main componen s o
PV sys ems a e ob ained by a sizing algo i hm; speci ically he ou pu a e: he su ace o PV a ay and he
ba e y pack capaci y. The decision is made based on he es ima ed powe gene a ion, he equi ed powe o
he load, he wa e needed by he c ops and he ba e y equi emen s. The p oposed design is hen e alua ed
using yea ly simula ions, on hou ly base, pe o med by a specialized comme cial so wa e, named PVSys ,
o show ha he p oposed op imal size ensu es also a high eliabili y e alua ed by wo indices: numbe o
au onomous days (NAD) and Loss o Load P obabili y (LOLP).
Keywo ds: pho o ol aic panels; algo i hm; sizing; pumping; PVSys .
INTRODUCTION
The main componen s o a s and-alone pho o ol aic (PV)
sys em, ha supplies a gi en load a e: a PV a ay, a ba e y
pack, an MPPT/ cha ge egula o . The MPPT/cha ge egula o
mus be used o ope a e co ec ly wi h bo h PV modules and
ba e ies. This appliance pe o ms no only he cha ge and
discha ge o he ba e ies in o de o a oid damage o poo
ene gy pe o mance bu also he maximum powe poin
acking (MPPT) in such a way o ha e an e icien PV
con e sion.
Sizing he componen s o hese PV ins alla ions a ec hei
au onomy and cos [1, 2]. Hence, i is necessa y o ix du ing
he design adequa e alues o he componen s sizes, such as
he pho o ol aic panel su ace and he ba e y capaci y [3, 4].
In ac , o ag icul u al applica ions, du ing he c ops
ege a i e cycle, he pho o ol aic ins alla ion size selec ed
mus gua an ee he wa e olume needed o he c ops
i iga ion, he sys em au onomy and he ba e y bank sa e
ope a ing [3]. Indeed, knowing he wa e olume needed o
i iga ing he c ops, he si e cha ac e is ics, he sola adia ion
and he pho o ol aic panel ype, sizing aims o p o ide he
adequa e alues o he panel su ace, ba e y capaci y and (in
some ins ances) he ese oi olume. In his sense,
esea che s ha e es ablished a ious me hods o op imize
pho o ol aic ins alla ions componen s [5]. Fo ins ance, some
wo ks ha e ocused on de eloping analy ic me hods based on
a simple calcula ion o he panels su ace and ba e y bank
capaci y using he ene ge ic balance [6-8]. O he wo ks ha e
concen a ed on he cos e sus eliabili y ques ion [9].
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 [10-14]. This LLP app oach
has also been combined wi h a i icial neu onal ne wo ks and
gene ic algo i hms [9, 10].
Howe e , hese me hods may esul in an o e sized sys em
o one loca ion and an unde sized one o ano he loca ion
[15]. The o e sized case esul s in high ins alla ion cos s.
Whe eas, an unde sized case, he ins alla ion is unable o
supply he load wi h he ene gy needed [16, 17]. Mo eo e ,
he ins alla ion li e ime is sho e , due o he excessi e use o
he ba e ies. Fo hese easons, he sizes mus be ca e ully
selec ed o each speci ic applica ion and loca ion [15].
In [18], he de e minis ic me hod and he p obabilis ic
app oach a e used o analyze he impac on design he PV
sys em and he ba e y s o age o h ee geog aphic si es in
I aly, cha ac e ized by di e en alues o sun adia ion and
ambien empe a u e. To ind he bes comp ise be ween wo
con lic ing obiecje i es ( eliabili y and cos s) a uzzy logic
based mul i-objec i e op imiza ion app oach was used in [19].
This pape p esen s a con inua ion o p e ious published
wo ks by some he au ho s [16, 17], whe e an a sizing
algo i hm has been p esen ed. He e, he algo i hm is de ailed
and alida ed by means o hou ly p obabilis ic simula ions,
ha spans one yea , using a widely used gene al so wa e o
he s udy o PV sys ems (G id-connec ed, s and-alone o
hyb id), named PVSys [20] (Figu e 1).
I.SIZING ALGORITHM PRINCIPLE
A good sizing mus ul ill he elec ical demand o he load
[15]. Hence, he main objec i e is o ensu e he load supply
h oughou he day, while cha ging he ba e y wi h he excees
o he ene gy and gua an eeing he wa e olume needed o
he i iga ion. The scheme o he p oposed app oach is
p esen ed in Figu e 1 [16, 17]. The algo i hm depends on:
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• he wa e olume needed,
• he si e cha ac e is ics,
• he panel cha ac e is ics.
The algo i hm aims o ind he panels su ace
op
S
and
he ba e y capaci y op
ba
C
ha gua an ee he ins alla ion
au onomy when supplying he pump. Hence, he idea consis s
in sea ching he op imal componen s sizes ha ensu e he
balance be ween he cha ged and he ex ac ed ene gies
c
E
and
e
E
, espec i ely. In ac , he ba e y bank supply he load
by
ba
E
when he panel does no gene a e he su icien
ene gy
load
E
, and is cha ged wi h a pa o he PV ene gy
p oduced
p
E
(Figu e 2). The balance be ween he
accumula ed and he ex ac ed ene gies does no gua an ee he
au onomy, due o he luc ua ion in he sola adia ion and he
ene gy losses. Thus, o ensu e he au onomy and p o ide he
ene gy demanded by he load, he algo i hm is pe o med by
adop ing an e iciency coe icien
η
(sligh ly g ea e han 1).
Hence, he ene gy balance can be exp essed as ollows:
ce
EE
η
≈
(1)
The sizing algo i hm is pe o med using wo sub
algo i hms du ing he ege a i e cycle: he Algo i hm 1
de e mines he sizes o he panel su ace
M
S
and he ba e y
capaci y
M
ba
C
o each mon h M. Then, Algo i hm 2 is
pe o med o deduce he inal sizes based on he sizes
de e mined o each mon h and he a ailable componen s,
p o iding he numbe s o panels and ba e ies needed.
Algo i hm 1 is de ailed now ollowing Figu e 4.
a) Algo i hm 1: De e mina ion a each mon h o he
minimum panel su ace and ba e y bank capaci y
S ep 1 Es ima ion o he di used and di ec adia ion.
S ep 2 Deduc ion o he hou ly daily sola adia ion
dis ibu ion
( )
dhH ,
in a il ed panel [17].
S ep 3 Es ima ion o he hou ly cell empe a u e
( )
h
T
c
[16].
S ep 4 Deduc ion o he hou ly panel e iciency
( )
h
p
η
[17].
Panel cha ac e is ics
Inpu s
Ou pu s
Cons ain s
Objec i e
Panels su ace
Wa e needed SIZING
ALGORITHM
Ba e y bank capaci y
P o ec he ba e ies agains
deep discha ge
Ensu e he
ene gy balance Gua an ee he
wa e needed
( )
AM PM
Ec E E
η
+

max 0.78dod∆≤
ese oi
VV=
op
S
op
ba
n
Si e cha ac e is ics
Fig. 1 Planning o he p oposed sizing algo i hm
S ep 5 Calcula ion o he wa e needed V [16, 17]:
( ) ( )
( )
11
11
iR
c To m
iR
L
V kE L

−−
= −+


−

(2)
whe e:
c
k
: c op g ow h coe icien o mon h M,
To
E
: e e ence e apo anspi a ion a e age o mon h M,
m
: a e age ain olume o mon h M,
i
: leaching e iciency,
R
L
: leaching ac ion gi en in he soil.
S ep 6 Calcula ion o he pumping du a ion [17]:
V
Q
∆=
(3)
whe e
Q
is he wa e low (m²/h).
S ep 7 Calcula ion o he minimum panel su ace
i
S
and
he ini ial ba e y capaci y
i
ba
C
using equa ions (4) and
(5) espec i ely:
21
pump au
i ech
p ba l p eg in op he ma ching
P d
Sd
W
η ηη η η η η
∆
= +


(4)
max
dodV
dE
C
ba
au d
ba i∆
=
(5)
wi h:
pump
P
: pump powe (W),
au
d
: eques ed days o au onomy,
ech
d
: days needed o echa ge he ba e y,
p
W
: a e age daily adia ion (Wh/
2
m
/ day),
ba
η
: elec ical e iciency o he ba e y bank,
l
η
: elec ical e iciency o he es o he ins alla ion
(includes ohmic wi ing and misma ching wi ing losses),
p
η
: e iciency o each pho o ol aic panel,
eg
η
: egula o pe o mance,
in
η
: in e e pe o mance,
op he
η
: panel pe o mance - op ical and he mal e ec s (%),
ma ching
η
: panel ma ching pe o mance (%),
d
E
: daily ene gy consump ion (Wh),
ba
V
: ba e y ol age (V),
max
dod
∆
: maximum pe mi ed a ia ion o he dep h o
discha ge
dod
.
S ep 8 Calcula ion o
p i
P
co esponding o he
minimum panel su ace
i
S
, using (6) [17]:
p i p i
P SH
η
=
(6)
ce
EE
η
≈
ba
C
Cha ge he ene gy
demanded by he load
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Pho o ol aic
panels
Load
p
E
load
E
load
E
Ba e y
Fig. 2 Ene gy balance p inciple
S ep 9 Calcula ion o he ene gies expec ed o be daily
s o ed and ex ac ed om he ba e y
c
E
and
e
E
.
S ep 10 I he ex ac ed ene gy is highe han he s o ed
ene gy, he algo i hm inc eases he panel su ace by he
minimum inc emen o he PVP size comme cially
a ailable: he algo i hm looks o he bes con igu a ion o
gua an ee he balance be ween he demanded and he
p oduced ene gies, by equalizing he ene gies s o ed
c
E
and ex ac ed ene gies
e
E
in he ba e y bank (1).
S ep 11 Ba e y capaci y
M
ba
C
deduc ion o mon h M
[17]:
ba
c
ba
V
E
C
M
=
(7)
b) Algo i hm 2: Calcula ion o he minimum panel su ace and
ba e y bank capaci y o he whole ege a i e cycle
Using Algo i hm 2 (Figu e 3), he inal alues o he panel
su ace
op
S
and he ba e y bank capaci y
op
ba
C
, a e
deduced.
op
S
co esponds o he maximum alue o he panel
su ace ob ained du ing he mon hs. The inal ba e y capaci y
is he co esponding alue o
op
S
, since i is he mos c i ical.
II.APPLICATION TO A CASE STUDY
The p oposed algo i hm is applied now o e alua e he
componen s sizes o a case s udy: he p oposed algo i hm is
es ed du ing he mon hs ha co espond o he ege a i e
cycle o oma oes (Ma ch o July), using da a o he a ge
a ea (No he n o Tunisia: la i ude: 36.39°, longi ude: 9.6°).
Following Algo i hm 2, he Algo i hm 1 was i s
e alua ed o all he mon hs in he ege a i e cycle: he sola
adia ion accumula ed on a il ed panel is e alua ed; hen, he
panel yield is calcula ed o each mon h; in pa allel, he wa e
needed V is e alua ed depending on he ege a i e cycle and
he si e [17]. Then, i he s o ed ene gy is highe han he
ex ac ed ene gy, he su ace is inc eased by he minimum
su ace in he ma ke (in ou case, he inc emen is 0.5
2
m
).
Algo i hm 1 esul s a e summa ized in Table 1, which
shows ha he p oposed s a egy always ensu es he wa e
needs, espec s he limi s on he ba e y-bank’ dep h o
discha ge and he ene gy balance (1). This has been es ed
du ing he mon hs o oma oes ege a i e cycle: he
e iciency coe icien
η
is a ound he ixed alues h oughou
all he conside ed mon hs. Fo his alue,
max
dod∆
is
gua an eed o be equal o 0.78.
Fo ins ance, in July, he minimum
η
is 1.46, and he
alue ob ained wi h Algo i hm 1
1
η
is equal o 1.47. On he
o he hand, in Ma ch, he gene a ed pho o ol aic powe
du ing he mo ning supplies he pump oge he wi h he
ba e y bank du ing he pumping du a ion. A e ha , he
pho o ol aic powe gene a ed cha ges he ba e y bank. The
quo ien be ween he cumula ed and ex ac ed ene gies is
1.66, which is nea o a ge alue 1.7. We mus poin ou ha
o he ene gy balance, an e o coe icien is used o conside
he clouds. Hence, in ou s udy, we ake in o accoun he
possibili y o ha ing cloudy days. Fo example, in Ap il he
loss o ene gy each day is 23.23 %. The ob ained esul s
(Table 1) p o e ha he panels su ace and ba e y bank
capaci y ob ained using he p oposed Algo i hm 1 sa is y he
ene gy balance. This is possible hanks o he calcula ion o
he ba e y capaci y, which is done by conside ing he same
max
dod∆
alue ha can be eached. Since July is he mos
c i ical mon h o i iga ion, he sys em componen s sizing o
July is selec ed. The ob ained size allows he load o be
supplied du ing he eques ed pumping du a ion
∆
, and also
p o ides he ene gy
c
E
needed o cha ge he ba e y bank.
III.VALIDATION USING PVSYST
The ins alla ion size has been also es ed using PVSys ,
since he sola adia ion, he ambien empe a u e and he load
equi emen s o he a ge ci e can be manually choosed. This
ool allows de e mine and alida e ins alla ions componen s
sizes. In addi ion, i akes in o accoun a ios losses ela ed
wi h componen s o clima ic pa ame e s. Hence, PVSys
e alua e he size e icicency using he sola ac ion (SF),
which de e mines whe he he panel su ace is able o supply
he load wi h he needed ene gy. Mo eo e , i pe o ms a
mo e de ailed e alua ion o he ins alla ion size: he sys em
losses (Ls), he unused ene gy (Lu) and he ene gy supplied
o he use (Y ). The PVSys simula ion shows ha he
adop ed size (S= 101.5
2
m
and
ba
C
=1680 A.h) gi es good
esul s. In ac , Figu es 5 and 6 show ha du ing he c ops
ege a i e cycle, he sola ac ion (SF), which de e mine
whe he he sola ins alla ion p o ides he load wi h he
su icien ene gy, is p a ically equal o one, excep in June
and July, in which i is equal o 0.962 and 0.934, espec i ely
(Table 2). This leak o ene gy can be co e ed by conside ing
an addi ional wa e olume in he ese oi .
Fig. 3 Sizing Algo i hm 2
Fo M=1:
max
M
, e alua e
M
S
and
M
ba
C
using Algo i hm 1
.
{ }
Mop ba ba
op
SSwhenCC
SSSS
Mop ==
=max21 ,..,,max
M
ba M
CS ,
ba
E
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Mo eo e , he ob ained size is es ed du ing he yea
(Figu e 7), by aking in o accoun all he possible losses
ela ed o he componen s o clima ic pa ame e s.
The esul s show ha he choosen size allows supplying
he load and ha ing no mo e han 3.4 % o load losses, which
ep esen s a good esul .
Fig. 4 Sizing Algo i hm 1 o each mon h M
Fig. 5 No malized p oduc ion using PVSys
Fig. 6 Pe o mance Ra ion and sola ac ion using PVSys
PR: Pe o mance Ra io (Y /Y ):0.211
1.2
1.0
Pe o mance Ra io PR
Jan
Feb
Ma
Ap
May
Jun
Jul
Aug
Sep
Oc
No
Dec
0.8
0.6
0.4
0.2
0
SF: Sola F ac ion (ESol/ELoad):0.966
Jan
Feb
Ma
Ap
May
Jun
Jul
Aug
Sep
Oc
No
Dec
Lu: Unused ene gy ( ull ba e y)
Lc: Collec ion loss (PV-a ay losses)
Ls: sys em losses and ba e y cha ging
Y : Ene gy supplied o he use
1.91 kWh/kWp/day
1.07 kWh/kWp/day
1.34 kWh/kWp/day
1.15 kWh/kWp/day
10
8
6
4
2
0
No m
alized ene gy [kWh/kWp/day]
Si e cha ac e is ics
S ep 1: Es ima ion o he di used and he
di ec adia ions
d
H
and
b
H
[17].
S ep 2: Deduc ion o he sola adia ion in a
il ed panel
H
[16, 17].
S ep 3: Es ima ion o he empe a u e
c
T
[17].
S ep 4: Deduc ion o he panel’ e icieny
p
η
S ep 5: Calcula ion o he needed wa e olume V
[16, 17].
S ep 6: Calcula ion o he pumping du a ion
∆
[16, 17].
p
η
H
S ep 7: Calcula ion o he ini ial panel’ su ace and he ini ial ba e y bank capaci y
i
ba
C
and ini ialize .
S ep 8: Calcula ion o he pho o ol aic powe
p i
P
co esponding o he ini ial su ace [17].
i
S
i
SS=
V
∆
p i
P
S ep 9: Calcula ion o he ene gies cha ged and ex ac ed om he ba e y bank and
e
E
.
c
E
c
E
e
E
S ep 10:
Yes
M
SS=
S ep 11 : Deduc ion o
M
ba
C
(7)
No
Dec emen S
Yes
Inc emen S
No
and
e
cEE
η
≈
ec E
E
η
>
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Fig. 7 Loss diag am o e he whole yea
IV.CONCLUSION
A sizing algo i hm o decide on he sizing o he
ins alla ion elemen s was p esen ed and alida ed using
PVSys ool. The algo i hm is es ed o a 10 ha land su ace
in he no he n o Tunisia. The sizing esul s ensu es
supplying he pump du ing he pumping pe iod, he ene gy
needed by he load and he needed wa e olume o c ops
i iga ion.
ACKNOWLEDGEMENTS
This wo k was unded by Minis e io de Ciencia e
Inno ación (Spain) unde g an DPI2014-54530-R and
FEDER unds.Miss Yahyaoui is unded by a g an MICInn
BES-2011-047807.
V. REFRENCES
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o pho o ol aic-ene gy s o age sys ems o au onomous small islands”.
In e na ional Jou nal o Elec ical Powe & Ene gy Sys ems, 32(1),
24-36.
[2] Sid ach-de-Ca dona, M; & Mo a López, Llanos. (1998). “A simple
model o sizing s and-alone pho o ol aic sys ems”.Sola Ene gy
Ma e ials and Sola Cells,55(3), 199-214.
[3] Kha ib, Tame ; Mohamed, Zah.A; & Sopian, K. (2013). “A e iew o
pho o ol aic sys ems size op imiza ion echniques”. Renewable and
Sus ainable Ene gy Re iews, 22, 454-465.
[4] Jakh ani, Abdul Qayoom; O hman, Al-Khalid; Rigi , And ew; Ragai.
Hen y; Samo, Saleem. Raza; & Kamboh, Shakeel. Ahmed. (2012). “A
no el analy ical model o op imal sizing o s andalone pho o ol aic
sys ems”. Ene gy, 46(1), 675-682.
[5] Acakpo i, Ame i; Xa ie , Fi a in. F ancois; & Awuah-Ba ou ,
Robe . (2012). “Analy ical me hod o sizing pho o ol aic wa e
pumping sys em”. In he p oceedings o he 4 h IEEE In e na ional
Con e ence on Adap i e Science & Technology, 65-69.
[6] Sh es ha, G. B; & Goel, L. (1998). “A s udy on op imal sizing o
s and-alone pho o ol aic s a ions”. IEEE T ansac ions on Ene gy
Con e sion, 13(4), 373-378.
[7] Ba a, Luciano; Ca alano i, Se gio; Fon ana, F; & La o an e, F.
(1984). “An analy ical me hod o de e mine he op imal size o a
pho o ol aic plan ”. Sola Ene gy, 33(6), 509-514.
[8] G oumpos, P. P; & Papageo giou, G. (1987). “An op imal sizing
me hod o s and-alone pho o ol aic powe sys ems”. Sola Ene gy,
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[9] Melli , A; Benghanem, M; Hadj A ab, A; & Guessoum, A. (2003).
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on Con ol Applica ions, 353-357.
[10] Yang, Hongxing; Zhou, Wei; Lu, Lin; & Fang, Zhaohong. (2008).
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[11] Kha ib, Tame ; Mohamed, Azah; Sopian, K; & Mahmoud, M. (2012).
“A new app oach o op imal sizing o s andalone pho o ol aic
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s and-alone pho o ol aic sys ems”. Sola Ene gy, 39(6), 499-512.
Ho izon al global i adia ion
Global inciden in coll. plane
IAM ac o on global
E ec i e i adiancy on cells
PV con e sion
A ay nominal ene gy (a STC e ic)
PV loss due o i adiance le el
PV loss due o empe a u e
Module quali y loss
Module a ay misma ch loss
Ohmic wi ing loss
Loss by espec o he MPP
unning
Unused ene gy a he ou pu
o he a ay
E ec i e ene gy a he ou pu o he a ay
Con e e loss du ing ope a ion (e iciency)
Con e e loss due o powe h eshold
Con e e loss o e nominal con . ol age
Con e e loss due o ol age h eshold
Ba e y s o ed ene gy balance
Ba e y e iciency loss
Ba e y e iciency loss
Ba e y sel -discha ge cu en
Ene gy need o he use
Ene gy supplied o he use
1808 kWh/m²
1939 kWh/m² * 81 m² Cells
-2.9 %
+10.5 %
E iciency a STC= 15.80 %
-3.5 %
-10.9 %
-1.2 %
-1.1 %
-0.6 %
0.0 %
-42.7 %
11.52 MWh
-5.5 %
0.0 %
0.0 %
0.0 %
+0.2 %
-35.7 %
-23.8 %
0.0 %
5.51 MWh
10.89 MWh
S o ed
70.6%
Di ec use 29.4%
Missing ene gy
3.4 %
0.2 MWh
24.68 MWh
5.33 MWh
Loss diag am o e he whole yea

PREPRINT
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Table 1 Panel su ace and ba e y capaci y o each mon h M
Table 2 Ene gy balance and main PVSys esul s
Resul s
Mon hs
GlobHo
(kWh/
2
m
)
GlobE
(kWh/
2
m
)
E A ail
(MWh) E Unused
(MWh) E Miss
(MWh) E Use
(MWh) E Load
(MWh) Sol F ac
Janua y 78.0 117.8 1.221 0.630 0.000 0.000 0.000 1.000
Feb ua y 89.1 116.0 1.185 0.608 0.000 0.000 0.000 1.000
Ma ch 140.0 161.3 1.587 0.959 0.000 0.419 0.419 1.000
Ap il 164.1 161.8 1.708 1.089 0.000 0.540 0.540 1.000
May 208.1 183.6 2.055 0.855 0.000 1.116 1.116 1.000
June 225.0 187.0 1.966 0.466 0.056 1.429 1.485 0.962
July 237.0 201.8 1.973 0.099 0.129 1.824 1.953 0.934
Augus 208.0 196.7 1.891 0.968 0.000 0.000 0.000 1.000
Sep embe 166.0 184.2 1.767 0.905 0.000 0.000 0.000 1.000
Oc obe 128.0 166.7 1.661 0.851 0.000 0.000 0.000 1.000
No embe 89.9 138.6 1.412 0.724 0.000 0.000 0.000 1.000
Decembe 75.1 123.8 1.266 0.649 0.000 0.000 0.000 1.000
Yea 1808.3 1939.5 19.692 8.801 0.185 5.328 5.513 0.966
Ma ch Ap il May June July
Cloud co e age
c
A
(%) 30.15 23.23 28.38 13.03 14.11
e o
η
1.30 1.23 1.28 1.13 1.14
( )
2
M
Sm
37.5 41.5 54.5 61.5 101.5
M
ba
C
(Ah) 840 1050 840 1050 1680
1c
e AM ePM
E
EE
η
=+
1.66 1.57 1.64 1.44 1.46
Resul s
Mon hs