Simulation of a Solar Cell considering Single-Diode Equivalent Circuit Model
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1 Simulation of a Solar Cll considring Singl-Diod Equivalnt Circuit Modl E.M.G. Rodrigus, R. Mlício,, V.M.F. Mnds and J.P.S. Catalão, Univrsity of Bira Intrior R. Font do Lamiro, - Covilhã (Portugal) Phon: , Fax: mail: duardorodrigus@ntc.pt, ruimlicio@gmail.com Cntr for Innovation in Elctrical and Enrgy Enginring, Instituto Suprior Técnico Av. Rovio Pais, 9- Lisbon (Portugal) Phon: +5 7, Fax: mail: catalao@ubi.pt Instituto Suprior d Engnharia d Lisboa R. Conslhiro Emídio Navarro, 95- Lisbon (Portugal) Phon: +5 7, Fax: mail: vfmnds@isl.pt Abstract. This papr fuss on singl-diod photovoltaic cll modls. Comprhnsiv simulation studis ar carrid out in ordr to adquatly assss tmpratur dpndnc, solar radiation chang, diod idality factor and sris rsistanc influnc. A comparison btwn an idal modl singl-diod solar cll and a modl of singl-diod solar cll with a sris rsistanc is also prsntd. Finally, conclusions ar duly drawn. Ky words Photovoltaic nrgy, solar clls, modlling, simulation.. Introduction In rcnt yars, significant photovoltaic (PV) dploymnt has currd, particularly in Grmany, Spain and Japan []. Also, PV nrgy is xpctd to bcom an important playr in th coming yars in Portugal, sinc it is on of th Europan countris with th highst lvls of solar radiation. Sunshin in mainland Portugal varis btwn and hours pr yar, so th country has a hug potntial for solar nrgy xploitation. At th prsnt th tnth largst PV powr plant in th world is in Moura, Portugal, with an installd capacity of MW. Th aim is to rach 5 MW of installd capacity by, according to th Portugus National Stratgy ENE, multiplying tnfold th xisting capacity []. A PV systm dirctly convrts sunlight into lctricity. Th main dvic of a PV systm is a solar cll. Clls may b groupd to form panls or arrays. Powrlctronic convrtrs ar usually rquird to prss th lctricity from th PV dvic. Ths convrtrs may b usd to rgulat th voltag and currnt at th load, to control th powr flow in grid-connctd systms, and for th maximum powr point tracking (MPPT) of th dvic []. Th solar cll is basically a smiconductor diod xposd to light. Solar clls ar mad of svral typs of smiconductors using diffrnt manufacturing prsss []. Th lctrical nrgy producd by a solar cll at any tim instant dpnds on its intrinsic proprtis and th incoming solar radiation [5]. Th solar radiation is composd of photons of diffrnt nrgis, and som ar absorbd at th p-n junction. Photons with nrgis lowr than th bandgap of th solar cll ar uslss and gnrat no voltag or lctric currnt. Photons with nrgy suprior to th bandgap gnrat lctricity, but only th nrgy corrsponding to th bandgap is usd. Th rmaindr of nrgy is dissipatd as hat in th body of th solar cll []. A singl-diod PV cll modl is considrd in this papr, including th ffct of th sris rsistanc. Th papr uss th quivalnt circuit of a solar cll with its paramtrs as a tool to simulat in ordr to considr th irradianc and tmpratur chang, th I-V charactristics of PV cll.. Modlling A. Idal Solar Cll As mntiond prviously, th solar clls ar smiconductor with a p-n junction fabricatd in a thin wafr or layr of smiconductors. Whn xposd to light a photo currnt proportional to th solar radiation is gnratd, if th photon nrgy is gratr than th band gap. In th dark, th I-V charactristics of a solar cll hav an xponntial charactristic similar to that of a diod [7]. In ordr to maximiz th xtractd output powr from a PV powr plant with th hlp of MPPT control, th undrstanding and modlling of PV cll is ncssary []. 9 RE&PQJ, Vol., No.9, May
2 Th idal quivalnt circuit of a solar cll is a currnt sourc in paralll with a singl-diod. Th configuration of th simulatd idal solar cll with singl-diod is shown in Figur. B. Solar Cll with Sris Rsistanc Mor accuracy can b introducd to th modl by adding a sris rsistanc. Th configuration of th simulatd solar cll with singl-diod and sris rsistanc is shown in Figur. Fig.. Idal solar cll with singl-diod. In Figur, G is th solar radianc, I s is th photo gnratd currnt, I d is th diod currnt, I is th output currnt, and V is th trminal voltag. Th I-V charactristics of th idal solar cll with singldiod ar givn by: qv I = I mkt s I () whr I is th diod rvrs bias saturation currnt, q is th lctron charg, m is th diod idality factor, k is th Boltzman s constant, and T is th cll tmpratur. A solar cll can at last b charactrisd by th short circuit currnt I, th opn circuit voltag V, and th diod idality factor m. conditions, th short circuit currnt I it is th gratst valu of th currnt gnratd by th cll. Th short circuit currnt I I = I = for V = () I s conditions, th opn circuit voltag V is th gratst valu of th voltag at th cll trminals [7]. Th opn circuit voltag V V mkt I V = ln + q for I = () I = Th output powr qv mkt P = V I I () Fig.. Solar cll with singl-diod and sris rsistanc. Th I-V charactristics of th solar cll with singl-diod and sris rsistanc ar givn by: q ( V + RsI ) I = I mkt s I (5) conditions, th inclusion of a sris rsistanc in th modl implis th us of a rcurrnt quation to dtrmin th output currnt in function of th trminal voltag. A simpl itrativ tchniqu initially trid only convrgd for positiv currnts. Th Nwton Raphson mthod convrgs mor rapidly and for both positiv and ngativ currnts [7]. Th short circuit currnt I q ( RsI ) I = = mkt I Is I for V = () Normally th sris rsistanc is small and ngligibl in computing (). Hnc, it is usd () as a good approximation of (). Th opn circuit voltag V is givn by: V mkt I V = ln + q for I = (7) I = Th output powr q ( V + RsI ) mkt P = V I I () Th diod saturation currnt at th oprating-cll tmpratur 7 RE&PQJ, Vol., No.9, May
3 I Tc T εq ( ) m k T T = I c (9) whr I is th diod saturation currnt at rfrnc condition, T c is th p-n junction cll tmpratur, T is th cll p-n junction tmpratur at rfrnc condition, and ε is th bandgap. ºC 5ºC. Simulation Rsults 5ºC Th mathmatical modls for th idal solar cll and th solar cll with sris rsistanc wr implmntd in Matlab/Simulink. Th I-V charactristics for various conditions of solar radiation and m =., considring th idal solar cll, ar shown in Figur Fig. 5. I-V charactristics for th tmpratur variation btwn and. Th P-V charactristics for th tmpratur variation btwn and and m =., considring th idal solar cll, ar shown in Figur. W/m 5 ºC 5ºC 75W/m 5W/m 5W/m Fig.. I-V charactristics for various conditions of solar radiation. Th I-V charactristics for a diod idality factor variation btwn and, considring th idal solar cll, ar shown in Figur. 5ºC Fig.. P-V charactristics for th tmpratur variation btwn and. Th I-V charactristics for various conditions of solar radiation and m =., considring th solar cll with sris rsistanc, ar shown in Figur 7. W/m m= m=.75 m=. 75W/m m=.5 5W/m m=.5 m= 5W/m Fig.. I-V charactristics for a diod idality variation btwn and. Th I-V charactristics for a tmpratur variation btwn and and m =., considring th idal solar cll, ar shown in Figur Fig. 7. I-V charactristics for various conditions of solar radiation (considring sris rsistanc). Th I-V charactristics for a diod idality factor variation btwn and, considring th solar cll with sris rsistanc of R s = mω, ar shown in Figur. 7 RE&PQJ, Vol., No.9, May
4 m=.5 m= m=.75 m=. ºC 5ºC m=.5 m= 5ºC U (V) Fig.. I-V charactristics for a diod idality variation btwn and (considring sris rsistanc). Th I-V charactristic for a tmpratur variation btwn and and m =., considring th solar cll with sris rsistanc of R s = mω, ar shown in Figur Fig.. P-V charactristics for R s = mω. Th P-V charactristics for th R s variation btwn and mω ar shown in Figur. ºC mω 5mΩ mω 5ºC 5mΩ mω 5ºC Fig. 9. I-V charactristics for th tmpratur variation btwn and (considring sris rsistanc). Th P-V charactristics for th tmpratur variation btwn and and m =., considring th solar cll with sris rsistanc of R s = mω, ar shown in Figur. Th P-V charactristics for R s = mω ar shown in Figur. 5 ºC 5ºC Fig.. P-V charactristics for th R s variation. With th chang of th tmpratur, th solar radiation, and th diod idality factor, th I-V and P-V will chang accordingly.. Conclusion Th bhaviour of idal solar cll modl and th bhaviour of th solar cll with sris rsistanc modl ar studid in this papr. Includd ffcts ar: tmpratur dpndnc, solar radiation chang, diod idality factor and sris rsistanc influnc. Th solar cll with sris rsistanc modl offrs a mor ralistic bhaviour for th photovoltaic systms. Particularly, this modl is to b considrd in panls with sris clls, bcaus th sris rsistanc is proportional to th numbr of solar clls in th panl. 5ºC Rfrncs Fig.. P-V charactristics for th tmpratur variation btwn and (considring sris rsistanc). [] F. Sprtino and J. S. Akilimali, Ar manufacturing I V mismatch and rvrs currnts ky factors in larg photovoltaic arrays?, IEEE Transactions on Industrial Elctronics, Vol. 5, No., pp. 5-5, Nov RE&PQJ, Vol., No.9, May
5 [] M. Laranja, Portugus National Stratgy ENE. Availabl: [] M. G. Villalva, J. R. Gazoli, and E. R. Filho, Comprhnsiv approach to modling and simulation of photovoltaic arrays, IEEE Transactions on Powr Elctronics, Vol., No. 5, pp. 9-, May 9. [] A. S. Sdra and K. C. Smith, Microlctronic Circuits. London, U.K.: Oxford Univ. Prss,. [5] M.A. Eltawil, Z. Zhao, Grid-connctd photovoltaic powr systms: Tchnical and potntial problms A rviw, Rnwabl and Sustainabl Enrgy Rviws, Vol., No., pp. 9, Jan.. [] Photovoltaic systms tchnology, Univrsitat Kassl, Kassl, Grmany,. [7] G.R. Walkr, Evaluating MPPT topologis using a Matlab PV modl, Journal of Elctrical & Elctronics Enginring, Vol., No., pp. 9-5,. [] J. Yuncong, J.A.A. Qahouq, and I. Batarsh, Improvd solar PV cll Matlab simulation modl and comparison, in: Pr. IEEE Intrnational Symposium on Circuits and Systms ISCAS, Tualosa, Alabama, USA,. 7 RE&PQJ, Vol., No.9, May
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