olume 49, Number, 8 ACTA TECHNCA NAPOCENSS Electronc and Telecommuncaton MODELLNG AND SMULATON O PHOTOOLTAC CELLS Dorn PETREUŞ, Crtan ĂRCAŞ, onuţ COCAN Techncal Unverty of Clu-Napa, aculty of Electronc, Telecommuncaton and nformaton Technology, 6-8 G. Barţu Street, Clu-Napa, Romana, Phone +4-64-44, E-mal: Dorn.Petreuş@ael.utclu.ro Abtract: A otovoltac cell convert the olar energy nto the electrcal energy by the otovoltac effect. Solar cell are wdely ued n terretral and pace applcaton. The otovoltac cell mut be operated at ther maxmum power pont. The maxmum power pont vare wth llumnaton, temperature, radaton doe and other ageng effect. n th paper, we preent four model for a otovoltac cell. Each method wa evaluated and ther trength/weanee were dentfed. Two emprcal model wa modeled and mulated n Mathcad. The emprcal model developed are valdatng through the comparon of the obtaned charactertc wth the one gven by the manufacturer of the P panel. Key word: otovoltac (P cell, maxmum power pont (, - curve, model.. NTRODUCTON n order to create low power remote and ndependent electronc devce t neceary to collect and convert energy drectly from the envronment. Th very mportant n order to mantan a contnuou operaton. A good oluton the ue of a otovoltac devce [] A otovoltac (P cell convert the olar energy nto the electrcal energy by the otovoltac effect. The heat doe not partcpate contructvely n th pre. Heat actually lmt the performance of thee fne layer, and the preence of exce heat a gn of deteroraton n a P cell. Mot olar cell are bult from lcon, and the preence of mpurte nfluence ther performance. Solar cell effcence vary from 6% for amorou lcon-baed olar cell to 4.8% wth multple-uncton reearch lab cell. Solar cell energy converon effcence for commercally avalable multcrytallne S olar cell are around 4-9%. The maor advantage of ung P cell are: hort lead tme for degnng and ntallng a new ytem, output power matchng wth pea load demand, tatc tructure, no movng part, longer lfe, no noe, hgh power capablty per unt of weght, nexhautble and polluton free, hghly moble and portable becaue of t lght weght []. Solar array are ued n many terretral and pace applcaton. or bet utlaton, the otovoltac cell mut be operated at ther maxmum power pont (. However, the vare wth llumnaton, temperature, radaton doe and other ageng effect. The bl dagram of typcal ued for battery charger preented n fgure. The weather and load change caue the operaton of a P ytem to vary almot all the tme. A dynamc tracng method neceary to enure maxmum power extracted from the P cell. Due to the mmatch between load lne and operatng charactertc of the olar cell, the power avalable from the olar cell not alway fully extracted. Th can be demontrated by fgure. Maxmum power pont tracng (T a control technque to adut the termnal voltage of P panel o that maxmum power can be extracted. P cell N T Crcut DC-DC Converter Control crcut PWM (f cl, D OUT Over-oltage Protecton gure. Schematc dagram of a battery charger wth T. Output current [A] Curentul de eşre [A] f(u Pf(U Output Tenunea voltage de eşre [] gure. Typcal - and P- charactertc of otovoltac cell. Puterea de eşre Output power [W] Manucrpt receved ebruary 8, 8; reved May 9, 8 4
olume 49, Number, 8 ACTA TECHNCA NAPOCENSS Electronc and Telecommuncaton The open crcut voltage of the P module ( the pont of nterecton of the curve wth the horzontal ax and t vare lttle wth olar radaton change. A re n temperature produce a decreae n voltage. Short crcut current ( c, the pont of nterecton of the curve wth the vertcal ax, drectly proportonal to olar radaton and relatvely teady wth temperature varaton. Actually, the otovoltac module act le a contant current ource for mot part of t - curve [3]. or a gven olar radaton and operatng temperature, the output power depend on the value of the load. A the load ncreae, the operatng pont move along the curve toward the rght. Only one load value produce a P maxmum power. The maxmum power pont lne ha a relatvely contant output voltage at varyng olar radaton condton.. MODELNG O THE P CELLS Modelng bac tool of the real ytem mulaton. or modelng, t neceary to analyze the nfluence of dfferent factor on the otovoltac cell and to tae n conderaton the charactertc gven by the producer. The mathematcal model for otovoltac cell are baed on the theoretcal equaton that decrbe the operaton of the otovoltac cell and can be developed ung the equvalent crcut of the otovoltac cell. The emprcal model rely on dfferent value extracted from the - charactertc of the otovoltac cell and they approxmate the charactertc equaton of the olar panel ung an analytcal functon. or the otovoltac ytem modelng, we analyze the nfluence of dfferent factor on the olar panel and to conder the charactertc gven by the producer. The mathematcal model for P array are baed on the theoretcal equaton that decrbe the functonng of the P cell and can be developed ung the equvalent crcut of the P cell. The emprcal model rely on dfferent value extracted from the - curve of the P array and they approxmate the charactertc equaton of the olar panel ung an analytcal functon. There are many model for a otovoltac cell. Th paragra preent an overvew of the dfferent equvalent crcut of the olar cell. a The One-Dode-Model for P cell The One-Dode -Model the mot mple and the mot ued model for P cell (fgure 3. The mplfed equvalent crcut of a olar cell cont of a dode and a current ource whch are connected n parallel. The current ource generate the oto current Ph, whch drectly proportonal to the olar rradance [W/m ], ambent temperature T a [ºC], and two output parameter: current [A] and voltage []. The p-n tranton area of the olar cell equvalent to a dode. The charactertc equaton of the one dode model could be derved from Krchhoff' current law: ( d h d h R Sh R S R load gure 3. The equvalent crcut for the one dode model. Wth: oto current; d dode current; h dode revere aturaton current; S load current. The oturrent gven by the equaton: [ + P ( + P ( T T ] P ( Where W/m, T 98.5K, P [Am /W], P [m /W] and P 3 [/K] are contant, uually gven by the producer, and T the uncton temperature. The current d can be calculated ung: d at at P 4 exp a T 3 f exp e N ( E T g + R T 3-9 where: e,67733 [C] the charge of the electron; a 5 the dode deally factor, uualy f ; N repreent the number of cell n ere; -3,38658 [ J/K] Boltzmann contant; R [Ω] model the ere retance, E g [e] the band gap, and P 4 [A/K 3 ] a correcton factor. The parameter (P 4 [A/K 3 ], R [Ω], R h [Ω] can be obtaned from the olar panel dataheet. The dode revere aturaton current h gven by: + R (3 h (4 Rh b The Two-Dode-Model for P cell An even more exact modelng could be acheved by the Two-Dode-Model (fgure 4. Here two dfferent dode wth dfferent dode deally factor a f are connected n parallel. Th model ha the modellng advantage of a better accuracy but t ha the dadvantage of relyng more parameter to mplement. 43
olume 49, Number, 8 ACTA TECHNCA NAPOCENSS Electronc and Telecommuncaton R S d d R h h R load n tandard tet condton (T 5 C and W/m, the rato c / at can be approxmated wth 9. Replacng A and mang the notaton B ln c at the value of, the expreon of become: gure 4. The equvalent crcut for the two dode model. c + ln R (9 B c The equaton that decrbe the equvalent crcut can alo be derved from the node-law of Krchhoff: at, ( P + P T P, d T 3 d exp h ( E T where at, the aturaton current. The et of parameter P [Am /W], P [Am /WK], P [A/K 3 ], and P [A/K 5/ ] can be obtaned n th cae alo from the olar panel dataheet. c The frt emprcal model for P cell The One-Dode-Model and the Two-Dode-Model ue a large number of parameter. t dffcult to determne many of thee parameter. So, the expermental model wa developed. The frt emprcal model propoed rele on a mall number of parameter:, c and maxmum power P of the olar panel. Wth another et of three parameter, T, E, T, the effect of the ( c uncton temperature and lght ntenty can be taen nto conderaton. The equaton that decrbe the - charactertc gven by: d g (5 (6 Ung the approxmaton c and ubttutng the contant e /a f T wth A, the expreon of the - curve become: at c exp[ A( + R ] (7 c f then and the factor A can be calculated by: c c ln A ln (8 A at at At maxmum power pont ( the value of the current S and P /. The value of R and can be obtaned by reolvng the ytem: P P B + c B ln c c + R R ( d The econd emprcal model for P cell The econd emprcal model propoed begn wth the equaton: where: ( v ( ( v ( c ln ln ( c and the value (, are meaured cloe to the regon of. The emprcal value of parameter, wa obtaned by optmzng the model n uch a way that the expermental and theoretcal - curve would concde at the. A ueful outcome of th method the ablty to predct the ung the equaton: c ( + + (3 A the lght ntenty ncreae, the current ncreae lnear, and the output voltage ncreae logarthmc. A re of 5ºC n temperature produce a re of % n current, and a decreae of m/ C per cell n voltage. Thee relaton can be modeled by relaton: 44
olume 49, Number, 8 ACTA TECHNCA NAPOCENSS Electronc and Telecommuncaton (,T + (,T nt q ln β nα ( T T ( T T (4 where: T 5 C the tandard temperature of the P cell; W/m the tandard lght ntenty; T [ C] the operatng temperature; the operatng lght ntety; n the number of olar cell connected n ere; the voltage of the cell at T and ; the current delvered by the cell at T and ; β the temperature coeffcent of the current, uually condered.4; α the temperature coeffcent of the voltage, uually condered... SMULATON O THE P CELLS Both emprcal model propoed were mplemented n order to mulate them. or the P cell mulatng, one choe the olar panel ASE 3-DG-UT (3W manufactured by ASE Amerca, nc. Th panel ha the followng pecfcaton: Maxmum Output power: P 3W; Short crcut current: c.6a; Open crcut voltage: 95; oltage at maxmum power: 68; Current at maxmum power:.47a. The - charactertc gven by the producer for th olar panel hown n fgure 5. B (6 c c (,B,R + ln R or comparon, a et of value (v, for current and voltage wa extracted from - charactertc gven by the producer, and then both, model and expermental - curve were repreented n fgure 6. Model fuct. Expermental gure 6. The - curve before optmzaton, for the frt emprcal model. Ung a clacal method for mnmzng error, a functon ε r, havng varable B and R wa defned: (,B,R (,B,R v ε r( B,R (7 v + The - charactertc ung the optmum value determned for B and R preented n fgure 7. gure 5. The - curve for ASE 3-DG-UT (3W. or the frt emprcal model, nowng the value of, and, from equaton ( reult: B P R c B + c ln c c (5 The load voltage expreon a dependent on load current, load retance R and parameter B wll be: Model funct. Expermental gure 7. The - curve after optmzaton, for the frt emprcal model. or the econd emprcal model, conderng the value.3a and 6 the emprcal value of the parameter.58 wll be obtaned wth (. f the value (, are cloer to, then the - curve cloer to the one gven by the producer. 45
olume 49, Number, 8 ACTA TECHNCA NAPOCENSS Electronc and Telecommuncaton The comparatve repreentaton of the - curve obtaned from the expermental value and the propoed functon for model are preented n fgure 8. ( v ( v ( nterectng the functon (v wth the - curve obtaned for the olar panel, the can be ndcated. The output power veru output voltage preented n fgure. Model funct. Expermental gure 8. The - curve before optmzaton, for the econd emprcal model. Power [W] Power Defnng an error functon ε r : ( v, ( v, l ε r ( (8 + l and mnmzng the error, the optmum value of the parameter determned, ac 4.647. The - curve after the optmzaton hown n fgure 9. gure. Output power veru output voltage. or determnng the nfluence of the lght ntenty on the P cell, three lght ntente were condered: W/m, 3W/m and 7W/m. The correpondng voltage value for ntente ş are gven by the producer ( 98; 9. The expreon for paramater correpondng to the mnmal error ( and are ubttuted wth and become: ln ln ( c The expreon decrbng the - charactertc for dfferent lght ntente become: Model funct. Expermental gure 9. The - curve after optmzaton, for the econd emprcal model. f the optmum value of the parameter ac, from the equaton, the expreon of the power delvered by the olar panel become: p ( ac v ( v ( v v ( v (9 c Ung the Mathcad functon maxmze the value of the wa determned and a lnear functon (v wa defned to etablh the : v ( ( ( v, c ( c c, ln. where: ( + ln, ( and ( ( The expreon of the output power wll be: p ( v, ( v, v (3 The correpondng - curve and the output power varaton are preented n fgure and. 46
olume 49, Number, 8 ACTA TECHNCA NAPOCENSS Electronc and Telecommuncaton Lnear functon (v gure. The lght nfluence on the - curve. gure. The temperature nfluence on the - curve. Power [W] gure. The lght nfluence on the output power.. CONCLUSONS n th paper, we preent four otovoltac cell model. Two emprcal model propoed were mplemented and mulate n Mathcad oftware pacage. or the P cell mulatng, one choe the olar panel ASE 3-DG-UT (3W manufactured by ASE Amerca, nc. The - curve, before and after optmzaton, are preented for both emprcal model. After optmzaton, model and expermental - curve are very cloed. Alo, t preented the envronmental parameter (lght and temperature nfluence on the - curve and on the output power. or determnng the nfluence of the temperature, n P cell are condered beng connected n ere. The expreon decrbng the - charactertc for dfferent operatng temperature : v ( ( l ( v,t c T (4 T ( [ ( ] c T : c β T T where:. ( T : n α( T T The pont of maxmum power are found at the nterecton between functon (v and the - charactertc a n fgure 3. ACKNOWLEDGEMENTS Th wor wa upported by the CNCSS, n the frame of natonal grant D_9/7. REERENCES [] S. Roundy, P. Wrght, and J. Rabaey, Energy Scavengng for Wrele Senor Networ, Kluwer Academc Publher, 4. [] D. E. Carlon, Recent Advance n Photovoltac, Preedng of the nterety Engneerng Conference on Energy Converon, pp. 6-66, 995. [3] A. El-M. Metwally, Modellng and Smulaton of a Photovoltac uel Cell Hybrd Sytem, PhD the, aculty of Electrcal Engneerng Unverty of Kael, Germany, pp. 4, Aprl 5. 47