Simulating the electrical characteristics of a photovoltaic cell based on a single-diode equivalent circuit model

Abs ac —This esea ch wo k p esen s he simula ion based s udy o a comme cial sola cell o analyzing he eal- ime beha io o a PV module. The ma hema ical modelling is based on Equi alen ci cui o he sola cell and demons a ing he p ac ical app oach o using he single diode i e pa ame e s (IM5P) mechanism. This esea ch in ol es pu ely ma hema ical o mula ion o ex ac he unknown pa ame e s o PV cell by applying he Lambe W unc ion. The I – V and P – V cha ac e is ics a e emula ed unde di e en empe a u e and adia ion le els by using he Linea Technology’s LTSpice simula o . Keywo ds— Ene gy Ha es ing, I – V & P – V Cu e, Sola Equi alen Ci cui , Lambe W unc ion. I. INTRODUCTION HE wo ld is acing huge ene gy c ises and we will un ou o uel coal and gases by 2071 as i is p edic ed by CIA (Cen al In elligence Agency) [1].This is an ala ming si ua ion which emphasizes he esea che s and scien is s a ound he globe o make al e na i e possible solu ions. Ene gy ha es ing is he only hope o o e come his issue, howe e , enewable ene gy sou ces can be u ilized o ackle mos o he ene gy hung y de ices whe he i is in o m o a la ge- scale applica ions like sola sys ems powe gene a o s o a small scale domes ic use like cell phone, Ipods, and wi eless senso ne wo ks, elabo a ed in a ecen e iew by A. S. Adila, A. Husam, J. H. Sana G. Husi [2]. The mos iable sou ce which can equip g eene ways success ully since las decade is sola ene gy. The Pho o ol aic ma ke ha e seen apid g ow h o sola powe sys ems ha en e ains he possible gap o enewable ene gy in e p e a ion o bo h mac o and mic o sys ems as epo ed in Ren21 [3]. A Pho o ol aic sys em con e s he sunligh di ec ly in o elec ici y and he main de ice is sola cell in he sys em. Sola cell a ays a e o med by g ouping hem oge he . The elec onic con e e s play a iable ole o p ocessing he elec ici y om he PV sys em as de ined by M. G. Villal a, J. R. Gazoli, E. R. Filho [4]. A sola cell is made o semiconduc o diode which is exposed o ligh and consis s o a ious ypes o semiconduc o s using di e en manu ac u ing p ocesses as e iewed by A. S. Sed a, K. C. Smi h [5]. M.A. El awil, Z. Zhao discussed ha he incoming sola adia ions and he in insic p ope ies a e esponsible o he elec ic ene gy gene a ion in a sola cell [6]. The sola adia ion is composed o pho ons o a ious ene gies, some o hem a e abso bed a p-n junc ion as shown in Fig 1., desc ibed in Union o Conce ned Scien is s [7]. I he pho ons wi h ene gies a e lowe han he bandgap o he sola cell, hey a e useless and will no gene a e elec ic cu en o ol age. Whe eas, pho ons wi h ene gy highe han he bandgap will gene a e elec ici y and he ene gy co esponding o he bandgap will be used only. The emaining ene gy is dissipa ed as hea in he body o sola cell as men ioned by J. Bikane ia, S. P. Joshi, A. R. Joshi [8]. Fig 1. Schema ic diag am demons a ing he ope a ion o p-n junc ion o a Sola Cell SIMULATING THE ELECTRICAL CHARACTERISTICS OF A PHOTOVOLTAIC CELL BASED ON A SINGLE-DIODE EQUIVALENT CIRCUIT MODEL Syeda Adila AFGHAN1, Husam ALMUSAWI2, Husi GEZA3 1Uni e si y o Deb ecen, Doc o al School o In o ma ics, [email protected] 2 Uni e si y o Deb ecen, [email protected] 3 Uni e si y o Deb ecen, [email protected] T ANNALS OF THE UNIVERSITY OF ORADEA Fascicle o Managemen and Technological Enginee ing ISSUE #1, MAY 2017, h p://www.im uo adea. o/auo. m e/ 91 Despi e o widely adop ed enewable sola solu ion, he e’s s ill lack o unde s anding he pe o mance e iciency and powe ex ac ion, when i comes o he selec ion o sola panels o a ays by he end use s. Many ma hema ical models a e highligh ed o demons a ing he non-linea esponse o a PV sys em as highligh by E. M. G. Rod igues, R. Melicio, V. M. F. Mendes and J. P. S. Ca alao [9]. The common echnique is o model he sola equi alen ci cui and amongs all possible pa ame ic models, he single diode model is he popula one, which is also known as 1M5P (Single Mechanism, Fi e Pa ame e s). I is used o p edic he eal- ime beha io o a sola cell men ioned by Ye ayew and Jyo hsna [10]. Fo I – V and P – V cha ac e is ics, he complica ed p ocedu e is equi ed which in ol es ce ain equa ions and calcula ions. The sola cell in ol es non- linea and exponen ial exp essions ha esul s he equa ions as implici , which is complica ed, i e a i e, and ime consuming. J. Cubas, S. Pindado, C. D. Manuel [11] demons a ed in hei esea ch ha he explici echnique is equi ed which consis s o analy ical o mula ion wi h use o Lambe W unc ion o making he pa ame ic model simple . In his pape , he single diode equi alen ci cui is being modelled o a comme cial sola cell o ob aining he unknown pa ame e s om he manu ac u e ’s da ashee . Ma lab is used o he o mula ion o he explici exp essions whe eas, he LTSpice ci cui simula o is used o model and simula e he pe o mance o sola cell by demons a ing he I – V and P – V cu es a empe a u e and i adia ions a ia ions o sola equi alen ci cui . II. MODELLING OF SOLAR CELL A. Ideal Single Diode Model o Pho o ol aic Cell The pho o ol aic echnology is based on he p inciple o elec on hole c ea ion in each cell ha consis s o wo di e en laye s; p ype and n ype. Howe e , The I - V cu e cha ac e is ics o a sola cell a e like he exponen ial cha ac e is ics o he ideal diode as desc ibed by Walke [12]. To unde s and he phenomenon o any sola cell, panel o an a ay, i is needed o de i e he elec ical pa ame e s o PV cell in o he equi alen ci cui as a necessa y equi emen . As shown in he Fig. 2, he ideal sola cell consis s o cu en sou ce IL, which is pa allel o he diode ID. The model con aining 3 pa ame e s also known as 1M3P (Single mechanism h ee pa ame e s) sugges ed by M. Azzouzi, D. Popescu and M. Bouchahdane [13]. Fig. 2. Ideal Single Diode Model (1M3P) The e o e, he equa ion can be de i ed by using he Ki chho ’s law: Whe e ID equals o, The ou pu cu en is ep esen ed by he ollowing non-linea I – V equa ion: Howe e , his model does no be able o p oduce accu a e esul s o modelling I – V and P – V cu es o a sola cell. Fig. 3 Single Diode Equi alen Ci cui (1M5P) B. Single Diode Model wi h Se ies and Shun Resis o s To speci y he mos popula and p ac ical unc ioning o a sola cell, M. Wol and H. Rauschenbach [14] deno ed he ep esen a ion o losses by he esis o s as shown in he Fig. 3, ha ing a cu en sou ce connec ed in pa allel wi h a diode and wo esis o s, one in se ies and o he in pa allel. Azzouzi, Popescu and Bouchahdane [13] also men ioned ha his model composed o i e pa ame e s o which i known as 1M5P (Single mechanism, i e pa ame e s), as cu en , ol age, and powe cu es can be easily deduced by his model by calcula ing he i e unknown pa ame e s. Mos ly he sho ci cui , open ci cui and maximum powe poin s a e included in he da ashee o sola cells as illus a ed in Fig. 4. ANNALS OF THE UNIVERSITY OF ORADEA Fascicle o Managemen and Technological Enginee ing ISSUE #1, MAY 2017, h p://www.im uo adea. o/auo. m e/ 92 Fig. 4. I – V and P – V cha ac e is ics o a ypical sola cell III. MATHMATICAL MODELING OF SINGLE DIODE EQUIVALENT CIRCUIT A. Wa aa, A. M. Ash a , A. Fouad, S. Saad [15] desc ibed ha i is impo an o de i e he cha ac e is ics equa ions o sola cell o calcula ing he i e- pa ame e s o an equi alen sola ci cui . Conside ing he Fig. 3, he equa ion is gi en as: To ully de ine he ela ionship be ween he ou pu cu en o pho o ol aic cell and he e minal ol age o he single diode model is gi en by he ollowing equa ion: Along wi h The mal Vol age; [V] Whe e IL deno es he cu en gene a ed by he incidence o ligh , ID deno es he diode cu en , RS ep esen s he se ies esis ance, o leakage cu en Rsh is deno ed as Shun esis o , a is he ideali y ac o , V is he he mal ol age, q as an elec on cha ge, he Bol zman cons an K; he n as numbe o cells in se ies and T as he empe a u e. Sola cell is equi ed o be cha ac e ized by he sho ci cui cu en Isc, he open ci cui ol age Voc, and ideali y ac o a. Equa ion (4) can be ew i en as: Sho Ci cui cu en : I = Isc, o V=0 Open ci cui Vol age: I = 0 o V = Voc Maximum powe poin equa ion: I = Imp, o V = Vmp A. Requi ed Equa ions o Calcula ing Unknown Pa ame e s In o de o ob ain he alue o se ies esis o , i is need o calcula e he implici exp ession, which is uns able and ime consuming a he same ime, o he sake o making exp ession decoupled, analy ical o mula ion is equi ed o make i explici . The e o e, he implici cu en - ol age exp ession is con e ed as an explici one by applying he echnique o sol e he ol age as a unc ion o cu en and ice e sa, i is in ended o make use o popula s a egy as sugges ed by J. Ami , S. Sandeep, K. A inashi [16], Villegas [17], K. Robe s, S. R. Vallu i [18] ha is known as Lambe W unc ion. Fo calcula ing Rs: Whe e, (9) Fo calcula ing Rsh: Fo calcula ing I0: Fo calcula ing IL: ANNALS OF THE UNIVERSITY OF ORADEA Fascicle o Managemen and Technological Enginee ing ISSUE #1, MAY 2017, h p://www.im uo adea. o/auo. m e/ 93 IV. METHODOLOGY A. Pa ame e Iden i ica ion and Calcula ion om Manu ac u e ’s Da ashee In o de o e alua e he unknown pa ame e s (IL, IO, Rs, Rsh) and o simpli y he calcula ions o speci ic model, P. M. Cuce, E. Cuce [19] elabo a ed ha he ideali y ac o should be conside ed as gene ic alue which is sugges ed o monoc ys alline cell ype as a = 1.2 and is independen o any empe a u e and i adia ion. The ollowing p ocedu e is ollowed o calcula ing he pa ame e s om manu ac u e ’s da ashee . 1) App oxima ing he ideali y ac o a as 1.2 o Monoc ys alline Cell 2) Calcula ing he Se ies Resis ance Rs wi h Equa ion (8) Calcula ing he Shun Resis ance Rsh wi h Equa ion (10) 3) Calcula ing he Sa u a ion Cu en IO wi h Equa ion (11) 4) Calcula ing he Pho odiode Cu en IL wi h Equa ion (12) The elec ical cha ac e is ics a e gi en in he TABLE I, which demons a es he pe quisi e da a o inse ion in o he exp essions. The inpu pa ame e s om he da ashee a (STC) S anda d Tes Condi ions a e 1000 W/m2 inciden no mal adiance, Cell empe a u e is 25 0C and Ai Mass AM1.5g. TABLE I ELECTRICAL SPECIFICATIONS OF IXOLAR SOLARMD SLMD481H08L I – V Cu e Cha ac e is ics Speci ica ions Uni s Open Ci cui Vol age (Voc) 5.04 V Sho Ci cui Cu en (Isc) 0.2 A Vol age a maximum powe poin (Vmpp) 4.0 V Cu en a maximum powe poin (Impp) 0.178 A Maximum Peak Powe (Pmpp) 0.714 W Tempe a u e Coe icien s o Isc (alpha) 0.12 mA/(cm2) K Tempe a u e Coe icien o Voc (be a) -2.1 mV/K The ob ained pa ame e s a e demons a ed in TABLE II, whe e he unknown pa ame e s ha e been calcula ed by he de ined equa ions and pushing he ideali y ac o as cons an and independen . TABLE II CALCULATED PARAMETERS OF IXOLAR SOLARMD SLMD481H08L B. Simula ing he Sola Equi alen Ci cui In his pape , he comme cial sola cell iXola Sola MD SLMD481H08L [20] is being selec ed o analyzing I – V and P – V cu es based on ma hema ical o mula ion and using he Linea Technology’s LTSpice (Linea Technology Simula ion P og am wi h In eg a ed Ci cui Emphasis) so wa e. Howe e , he ob ained alues will be modelled on he sola equi alen ci cui o e ol ing he beha io o sola module on simula o . As de ined in sec ion IV. A, he inpu pa ame e s ha e been calcula ed o modelling and simula ion pu pose o sola equi alen ci cui as shown in Fig. 5. Fig. 5 Single diode Equi alen ci cui o iXola Sola MD SLMD481H08L V. RESULTS AND DISCUSSIONS A. I – V and P – V cu e simula ion The gene a ed I – V and P – V cu e o comme cial sola cell has been plo ed as demons a ed in Fig. 6 and Fig. 7. The simula ions a e ma hema ically o mula ed based on he da ashee in o ma ion. These plo s a e being u he simula ed based on wo a ia ions o sola equi alen ci cui . The en i onmen dependence has been modelled o analyze he PV cell esponse and he cha ac e is ics poin s o adequa e he ou pu pe o mance o he cell. Fo his pu pose, he empe a u e and i adia ions le els a e adop ed o con igu e he sys em esponse in he eal- ime en i onmen . Pa ame e s Calcula ed Values I0 9.0837e-10 IL 0.2009 Rs 1.7795 Rsh 398.4280 a 1.2 ANNALS OF THE UNIVERSITY OF ORADEA Fascicle o Managemen and Technological Enginee ing ISSUE #1, MAY 2017, h p://www.im uo adea. o/auo. m e/ 94 Fig. 6. I – V cu e o Sola Equi alen Ci cui o iXola Sola MD SLMD481H08L Fig. 7. P – V cu e o Sola Equi alen Ci cui o iXola Sola MD SLMD481H08L B. E ec o sola i adia ion on I – V cu e The simula ion is being pe o med on he same sola ci cui o di e en le els o sola i adia ion, which a ies om 200 W/m2 o 1000 W/m2 by main aining he empe a u e cons an a 25 oC. I can be seen in Fig. 8, ha he gene a ed cu en depends on he inciden ligh , as long as he i adia ion is inc easing he cu en also inc eases. As he e is sligh change o ol age wi h espec o he inc emen o he cu en . Fig. 8. Sola I adia ion le els om 200 W/m2 o 1000 W/m2 a 25 0C C. E ec o empe a u e on I – V and P – V cu e. In his simula ion, he empe a u e is being a ied om 15 0C o 85 0C and keeping he i adia ion le el cons an a 1000 W/m2. Fig. 9 and Fig. 10, shows he I – V and P – V cu e gene a ed on di e en empe a u e anges. As i is clea ly indica ed ha by a ying he empe a u e om low o high, he ol age is being a ec ed. Inc easing he empe a u e causing he dec eased ol age and maximum powe poin a he same ime. While he cu en gene a ed by inciden ligh emained cons an . Fig. 9. I – V Cha ac e is ics o Tempe a u e a ia ion be ween 15 0C o 85 0C a 1000 W/m2 VI. CONCLUSION In his esea ch wo k, he comme cial sola cell is being examined o p edic he sola cell esponse on he simula o based on he I – V and P – V cha ac e is ics. Fo such s udy, he sola cell is being modelled as a single diode equi alen ci cui (1M5P), he only sou ce a ailable is he manu ac u e ’s da ashee ha is being conside ed o ex ac he unknown pa ame e s. Ce ain calcula ion and explici exp essions ha e been pe o med o ge mos o he op imal alues o he module. This way he calcula ion is being done on he Ma lab so wa e and he ob ained pa ame e s we e simula ed on LTSpice simula o on he equi alen ci cui . The esul s ha e been analyzed on he wo cases; one on he empe a u e a ia ion and keeping i adia ion cons an and second on he i adia ion le els keeping empe a u e cons an . The plo s o I -V cu es indica e ha as a as empe a u e inc eases he cell cu en sligh ly inc eases and he Fig. 10. P – V Cha ac e is ics o Tempe a u e a ia ion be ween 15 0C o 85 0C a 1000 W/m2 ANNALS OF THE UNIVERSITY OF ORADEA Fascicle o Managemen and Technological Enginee ing ISSUE #1, MAY 2017, h p://www.im uo adea. o/auo. m e/ 95 ol age is being dec eased. I is obse ed ha P – V cha ac e is ics o sola cell deno es he dec ease in ol age as he empe a u e is being dec eased which p opo ionally a ec s he powe ou pu o he cell. Howe e , he inc emen in he i adia ion le els also inc eases he ou pu powe . Finally, his simula ion based s udy p o ides he end use s o es ablish he ealis ic ma hema ical modelling o sola cell, panel o an a ay o es ima e he elec ical beha io o PV sys ems o planning hei own sys ems. REFERENCES [1] Fuels, The End o Fossil. Eco ci y B i ain's G eenes Ene gy, h ps://www.eco ici y.co.uk/ou -g een-ene gy/ene gy- independence/ he-end-o - ossil- uels, (Da e o Access: No embe 2016). [2] A. S. Adila, A. Husam, J. H. Sana G. Husi. “Es ima ion o minimum ou pu powe h eshold o ene gy ha es ing module: An inspec ion o ba e y and cha ging pa ame e s o cell phones.” P oceedings o 4 h In e na ional Mecha onic S uden Mic o- Con e ence Budapes , 56-71, 2017. [3] REN21. Renewables Global S a us Repo 2016. Pa is: REN21 Sec e ai : REN21 Publica ions, 2016. [4] M. G. Vilal a, J. R. Gazoli, E. R. Filho, "Comp ehensi e app oach o modeling and simula ion o pho o ol aic a ays",IEEE T ansac ions on Powe Elec onics, Vol. 24, No. 5, 1198-1208, May 2009. [5] A. S. Sed a, K. C. Smi h, Mic oelec onic Ci cui s, Ox o d Uni e si y P ess, London, U.K. 2006. [6] M. A. El awil, Z. Zhao, "G id-connec ed pho o ol aic powe sys ems: Technical and po en ial p oblems- A e iew", Renewable and Sus ainiable Ene gy Re iews, Vol. 14, No. 1, 112-129, Jan 2010. [7] Union o Conce ned Scien is s- Science o a heal hy plane and sa e wo ld. "How sola panels wo k", h p://ucsusa.o g/, (Da e o Access: Ap il 2016). [8] J. Bikane ia, S. P. Joshi,A. R. Joshi, "Modeling and simula ion o a p cellusing one-diode model", In e na ional Jou nal o Scien i c Resea ch Publica ions, Vol. 3, No. 10, 1-4, Oc 2013. [9] E. M. G. Rod igues, R. Melicio, V. M. F. Mendes, J. P. S. 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Ash a , A. Fouad, S. Saad,. “Ma hema ical Model o Pho o ol aic Cells.” Leona do Jou nal o Sciences Vol.12, No. 23, 13-28, 2013. [16] J. Ami , S. Sandeep, K. A inashi,. “Sola cell a ay pa ame e s using Lambe W- unc ion.” Sola Ene gy Ma e ial & Sola Cells 90, 25-31, 2006. [17] D. Villegas, “Analysis o sola cell using he Lambe W unc ion wi h Maple.” P oceedings o SPIE - Ene gy Ha es ing and S o age: Ma e ials, De ices, and Applica ions V. Bal imo e, Vol. 9115, 2014. [18] K. Robe s, S. R. Vallu i. “Sola Cells and he Lambe W Func ion.” Celeb a ing 20 yea s o he Lambe W unc ion. London, Canada, 2016. [19] P. M. Cuce, E. Cuce,. “A no el model o pho o ol aic modules o pa ame e es ima ion and he modynamic assesmen .” In e na ional Jou nal o Low-Ca bon Technology Vol. 7, 159- 165, 2011. [20] iXola Sola MD SLMD481H08L,A ailable online h p://ixapps.ixys.com/Da aShee /ixys_sola .pd (Da e o Access: Janua y 2017). ANNALS OF THE UNIVERSITY OF ORADEA Fascicle o Managemen and Technological Enginee ing ISSUE #1, MAY 2017, h p://www.im uo adea. o/auo. m e/ 96