Sensitivity analysis for photovoltaic water pumping systems: Energetic and economic studies

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. 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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