Energy Conversion and Management

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1 Energy Conversion nd Mngement 79 (2014) Contents lists vilble t ScienceDirect Energy Conversion nd Mngement journl homepge: Development of new compound method to extrct the five prmeters of PV modules Jinbo Bi,b,, Sheng Liu, Yuzhe Ho, Zhen Zhng c, Meng Jing c, Yu Zhng College of Mechnicl nd Electricl Engineering, Hohi University, 200# Jinling Beilu, Chngzhou, Jingsu, Chin b Key Lbortory of Energy Therml Conversion nd Control of Ministry of Eduction, Southest University, Nnjing, Jingsu, Chin c Stte Key Lbortory of Photovoltic Science nd Technology, Chngzhou, Jingsu, Chin rticle info bstrct Article history: Received 3 September 2013 Accepted 21 December 2013 Avilble online 8 Jnury 2014 Keywords: Photovoltic (PV) modules I V curves Five-prmeter method Prediction of PV power genertion The five-prmeter photovoltic (PV) mthemticl model hs been considered relible nd ccurte method for simulting the performnce of PV modules. This pper puts forth new compound method to extrct the five prmeters of the model with the bsic mnufcture templte dt. As the two differentil vlues t the short nd open circuit points of the I V curve t stndrd testing conditions (STC) re fundmentl dt to obtin the five prmeters nd not normlly vilble from the templte dt, we use piecewise I V curve-fitting method combined with the four-prmeter PV model to clculte them with which n explicit extrction method is then presented to extrct the five prmeters t STC conditions by using five individul lgebric equtions. Furthermore, the five prmeters re revised ccording to certin operting conditions. In order to evlute the effectiveness of the proposed method, the simulted I V chrcteristic curves for three types of PV modules over rnge of operting conditions re compred with the mesured dt. The experimentl results demonstrte tht the method hs high ccurcy. This method is lso used to predict the genertion power of n ctul PV power sttion; the simultion results show good greement with the field dt. This proposed method is esy to crry out nd especilly useful for simulting the ctul performnces of PV modules or rrys t vrious operting conditions nd predicting the output power of rel PV power sttions. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction PV is method of generting electricl power by converting solr irrdince into direct current electricity using semiconductors. With the rpid development of the globl PV industry, especilly in Chin, the cost of PV modules hs decresed drmticlly. Thus, distributed or centrlized PV power sttions re redily vilble for instlltion. Currently, solr PV is the third most importnt renewble energy source in the world fter the hydro nd wind power in terms of instlled cpcity [1]. Now importnt res of reserch in PV technologies re focusing not only on lower costs nd higher efficiency but lso on improving the efficiency nd relibility of PV systems [2 5]. Accurte prediction of the power genertion performnce cn result in improved opertionl efficiency of PV systems becuse the designers cn optimize the PV systems performnce [5 7]. To chieve this gol, the mnufcturer templte dt together with environmentl Corresponding uthor t: College of Mechnicl nd Electricl Engineering, Hohi University, 200# Jinling Beilu, Chngzhou, Jingsu, Chin. Tel.: ; fx: E-mil ddress: bi_jinbo@hotmil.com (J. Bi). prmeters hve been utilized to simulte the I V chrcteristic curves of PV modules under vrious environmentl conditions [8,9]. At present, most mthemticl models for simulting PV modules re bsed on the one-diode theory [10,11]. Considering the presence or bsence of the shunt resistnce R sh, these models cn be divided into two types: four-prmeter models nd five-prmeter models [12]. In ddition to the shunt resistnce R sh, the other four prmeters re the photocurrent I ph, the reverse sturtion current I o, the seril resistnce R s nd the modified idel fctor. The five-prmeter model hs been confirmed to be more ccurte thn the four-prmeter model [13,14]. Furthermore, s the shunt resistnce R sh is the key prmeter to nlyze more complex situtions of PV modules or rrys, such s mismtch nd hot-spot phenomen, the five-prmeter model is more logicl nd comprehensive thn the four-prmeter model. Consequently, the five-prmeter model hs been widely pplied to simulte the I V performnce of PV modules or to predict the genertion output of rel PV power sttions. In recent yers, the esy nd ccurte extrction of these prmeters hs been hot reserch topic in the solr PV field [15 21]. De Soto [16] hs used the mnufcturer dt in combintion with severl nonliner equtions to extrct the five prmeters nd predict the solr cell I V curves t ny operting conditions /$ - see front mtter Ó 2014 Elsevier Ltd. All rights reserved.

2 J. Bi et l. / Energy Conversion nd Mngement 79 (2014) Nomenclture modified idel fctor 4 modified idel fctor of the four-prmeter model ref modified idel fctor t STC conditions E g energy bnd gp (ev) E g,ref energy bnd gp t STC conditions (ev) G solr irrdince (W/m 2 ) G ref solr irrdince t STC conditions (1000 W/m 2 ) I current generted by the PV modules (A) I mp current t MPP (A) I o diode reverse sturtion current (A) I o, 4 diode reverse sturtion current of the four-prmeter model (A) I o,ref diode reverse sturtion current t STC conditions (A) I ph photocurrent prmeter (A) I ph,4 photocurrent of the four-prmeter model (A) I ph,ref photocurrent t STC conditions (A) I sc short circuit current of the PV modules (A) k Boltzmnn constnt ( J/K) n diode idel fctor P power generted by the PV modules (W) P mp power t MPP (W) q electron chrge ( C) R s series resistnce (X) R s,4 series resistnce (X) of the four-prmeter model R s, ref series resistnce t STC conditions (X) R sh shunt resistnce (X) R sh, ref shunt resistnce t STC conditions(x) T cell temperture (K) T mbient temperture (K) T NOCT cell temperture t NOCT (K) T ref cell temperture t STC conditions (K) U L loss coefficient V voltge generted by the PV modules (V) V oc open circuit voltge of the PV modules (V) V mp voltge t MPP(V) bsorption rtio of the PV modules s trnsmission rtio on the PV module surfce g energy conversion efficiency of the PV modules temperture coefficient of the short circuit current (V/K) l I,sc After compring the simulted dt with the experimentl dt, the results demonstrte tht his method is effective in predicting the performnce of four types of solr cells. However, some difficulties my be encountered when powerful mthemticl tools re used to solve these nonliner equtions [17]. Without solving complex nonliner equtions, Lo Brno [17] hs presented n improved five-prmeter extrction method which uses n itertive rithmetic. This method cn lso describe the I V chrcteristic curves of PV module t ny operting conditions. However, side from the bsic mnufcturer templte dt such s the short circuit current, the open circuit voltge, nd the mximum power t the mximl power point (MPP), the method requires two differentil vlues t the short nd open circuit points t STC conditions. As the two vlues re not normlly vilble from the mnufcturer dt, dditionl experiments must be conducted to obtin them. To extrct the five prmeters more conveniently, De Bls [18] hs used grphic method to clculte the two differentil vlues from the stndrd I V curves normlly provided by the mnufcturer. But this method llows for humn error in estimtion, nd deling with lrge number of curves from different mnufcturers is cumbersome. Moreover, when the PV modules re upgrded, the curves will lso chnge, thus requiring reclcultion of the vlues. To further simplify the process of computing the two vlues, Celik [19] hs suggested tht the two vlues could be set s constnt, which he sets to pproximtely 0.33 nd 135 X for tested PV modules, nd he lso proposes simple method to extrct the five prmeters. Experiments demonstrte the effectiveness of this method. However, different types of PV modules do hve different vlues. Thus, this method is not quite ccurte nd not pproprite for ll types of solr PV modules. Previous reserch results hve verified tht there re two kinds of extrction methods to extrct the five prmeters. One method requires the use of nonliner eqution solvers, which my bring some clcultion problems, such s difficulty in ttining convergence, more computtion tsks or unpredictble errors. The other is to use the reltively simple explicit methods, but this needs two differentil vlues t the short nd open circuit points, which re not vilble from the mnufcture dt. Severl methods hve been proposed to obtin these differentil vlues, but these methods re not esily relized nd thus involve some inconvenience. To simplify the clcultion procedures for obtining the five prmeters, while still mintining simultion ccurcy, the pper proposes compound method to extrct the five prmeters without nonliner eqution solvers. Furthermore, by using piecewise curve-fitting method nd four-prmeter PV model, the two required differentil vlues t the short nd open circuit points cn be esily clculted with the bsic mnufcturer templte dt. Subsequently, the five prmeters of the five-prmeter model cn be directly obtined by severl explicit equtions. Experimentl results demonstrte tht this method hs high ccurcy in simulting the I V chrcteristic curves of PV modules nd rrys t ny opertion conditions, nd it cn lso predict the genertion output of rel PV power sttions. 2. A compound method to extrct the prmeters of the fiveprmeter model 2.1. One-diode mthemticl model for PV module or rry A PV module consists of number of solr cells in series. Ech cell is typiclly p n junction, which cn directly convert solr energy into electricl energy. The common technique of modeling PV module is to estblish the equivlent circuit, which cn be described by one-diode nd two-diode models [11]. The former hs been widely ccepted to simulte the I V chrcteristics of PV modules [16]. The one-diode PV mthemticl model cn be represented by Eq. (1), nd its equivlent circuit is shown in I ph I o I sh Fig. 1. One-diode equivlent circuit for PV module or rry. I R sh R S R L I

3 296 J. Bi et l. / Energy Conversion nd Mngement 79 (2014) Fig. 1 [12]. The circuit consists of seril resistnce nd diode in prllel with shunt resistnce. The circuit cn be used not only for PV module including severl cells, but lso n individul PV cell or PV rry including severl PV modules. I ¼ I ph I o I sh ¼ I ph I o exp V þ IR s where ¼ nkt q 1 V þ IR s R sh I ph is the photocurrent (A), I o is the diode reverse sturtion current (A), q is the electron chrge ( C), k is the Boltzmnn constnt ( J/K), n is the diode idel fctor, R s is the series resistnce (X), R sh is the shunt resistnce (X), T is the cell temperture (K), nd is the modified idel fctor. In Eqs. (1) nd (2), the five prmeters of the five-prmeter model re R s, R sh, I ph, I o, nd Method to extrct the five prmeters The typicl I V nd P V curves of PV module re shown in Fig. 2. One cn see tht the P V curve hs only one pek point, clled the MPP. The I V chrcteristic curve of PV module cn be simulted with the five prmeters [12]. To obtin the vlue of the five prmeters, we estblish five lgebric equtions, including I ph,, I o, R s, nd R sh prmeters, together with the bsic mnufcturer dt, including the short circuit current I sc, the open circuit voltge V oc, the MPP voltge V mp nd the current I mp, which re ll t STC conditions for rting PV module. The STC minly refers to 1000 W/m 2 solr irrdince nd 25 C PV module temperture. ð1þ ð2þ Substitute the vlues t the short circuit (0, I sc ) nd open circuit (V oc, 0) points into Eq. (5), thus, At the short circuit point: R sh ¼ R s ð6þ þ I 0 R sh exp IscRs At the open circuit point: R sh ¼ R s ð7þ I¼0 þ I 0 R sh exp Voc Becuse of the single pek chrcteristics of PV module output t STC conditions, the vlue of the output power differentil eqution t the MPP is equl to zero. Therefore, dp ¼ I m þ V m ¼ 0 ð8þ P¼Pm P¼Pm tht is V m I m P¼Pm ¼ V m I m Combine Eqs. (9) nd (5) then, R sh ¼ R s þ ð10þ ðv mþimrsþ þ I 0 R sh exp with Eqs. (3), (4), (6), (7), nd (10), five lgebric equtions re built, from which the five prmeters cn then be clculted. After series of simplifictions, the explicit solutions for the five prmeters cn be obtined s follows: ð9þ h i V mp I¼0 ði sc I mp ÞþV mp R s ¼ h i I mp ð I¼0 Þ ði sc I mp ÞþV mp þ I¼0 ð I mp þ V mp I sc þ V oc I mp þ V mp ð11þ I sc þ V oc As shown in Fig. 2, there re three importnt points in the I V nd P V curves: the short circuit point, the open circuit point nd the MPP point. As the voltge (V) nd current (I) vlues of the three points re the bsic templte dt nd lwys known, they re hence used to crete relevnt equtions s below: At the short circuit point: V =0,I = I sc. Eq. (1) cn thus be represented s follows: I sc ¼ I ph I o exp qi scr s 1 I scr s ð3þ R sh At the open circuit point: I =0, V = V oc. Substituting the vlues into Eq. (1) yields: R sh ¼ R s I ph ¼ I sc ð1 þ R s =R sh Þ ¼ þ R s I¼0 I sc þ V oc I¼0 ð12þ ð13þ ð14þ I ph ¼ I o exp V oc 1 þ V oc R sh ð4þ Besides the two equtions bove, three other equtions should be set up to obtin the vlues of the five prmeters. We consider the differentil eqution of Eq. (1), then ¼ R R sh s ð5þ þ I o R sh exp VþIRs Fig. 2. Typicl I V nd P V curves of PV module.

4 J. Bi et l. / Energy Conversion nd Mngement 79 (2014) I o ¼ðI ph V oc =R sh Þ=ðexpðV oc =Þ 1Þ ð15þ As shown in Eqs. (11) (15), the five prmeters cn be obtined if the vlues of I sc, V oc, V mp, I mp, / (V = 0), nd / (I = 0) re given. The first four vlues re the bsic mnufcturer dt, but the ltter two vlues re not. Hence, the min issue of this method is to obtin the two differentil vlues t the short circuit nd open circuit points, tht is / (V =0orI = 0) t STC conditions. The method for clculting the two vlues is presented in the next section Method for clculting / (V = 0 or I = 0) t STC conditions A piecewise curve-fitting method depending on the I V chrcteristic curve is used to obtin the two differentil vlues. In order to depict the required I V curve t STC conditions beforehnd, the four-prmeter PV model is used becuse the four prmeters of the model re reltively esy to obtin with the mnufcture templte dt. Hence, we lso present simple extrction method for the four-prmeter model below Method for extrcting the four prmeters of the four-prmeter PV model As the shunt resistnce R sh prmeter is not considered in the four-prmeter PV model, extrcting the four prmeters is esier thn tht in the five-prmeter model. Nevertheless, the fourprmeter model still hs high ccurcy t STC conditions [22]. The simplified I V eqution of the four-prmeter model cn be obtined from Eq. (1). R sh is ssumed to be infinite in the fourprmeter model, so the lst item in Eq. (1) cn then be neglected; thus I ¼ I ph;4 I o;4 exp V þ IR s;4 1 ð16þ 4 In contrst to the five-prmeter model, in Eq. (16) the subscript 4 represent the four prmeters of the four-prmeter model. The corresponding four prmeters re the seril resistnce R s,4 (X), the photocurrent I ph,4 (A), the reverse sturtion current I o,4 (A), nd the modified idel fctor 4. Anlyticl, itertive, nd non-liner eqution solver methods hve ll been used in extrcting the four prmeters of the fourprmeter PV model [11]. Among them, the nlyticl methods re simpler thn others nd lso hve high ccurcy. Therefore, in this section n nlyticl method is proposed to extrct the four prmeters. First, we substitute the bsic mnufcturer dt, including the short circuit point (0, I sc ), the open circuit point (V oc, 0), nd the MPP (V mp, I mp ) into Eq. (16); then At the short circuit point: I = I sc, V =0 I sc ¼ I ph;4 I o;4 exp I scr s;4 1 4 ð17þ In Eq. (17), becuse of the existence of the seril resistnce, smll prt of the photocurrent flows into the equivlent dioxide. Thus, the current tht flows through the dioxide cn be neglected. Therefore, Eq. (17) cn be simplified s below. I ph;4 I sc ð18þ the clculted vlue of 4 is nerly to As the open circuit voltge V oc in solr cell is pproximtely 0.5 to 0.6 V, the vlue of V oc,4 / 4 will be bout 9.7 to 23.3, the exponentil vlue of which is much greter thn one. Therefore, Eq. (19) cn be expressed s I o;4 I ph;4 expð V oc = 4 Þ At the MPP: I=I mp, V = V mp I mp ¼ I ph;4 I o;4 exp V mp þ I mp R s;4 1 4 ð20þ ð21þ In Eq. (21), becuse the vlue of 4 is pproximtely to nd the vlue of V mp is lwys greter thn 1, the exponentil prt exp((v mp + I mp R s,4 )/ 4 ) will then be much greter thn 1; thus, the term -1 cn be neglected. Substituting Eq. (21) into Eq. (19) will yield the following eqution: 4 ln R s;4 ¼ 1 Imp I ph;4 V mp þ V oc I mp ð22þ Shown bove re three effective lgebric equtions. To extrct the four prmeters, fourth eqution should be estblished. As power P cn be clculted s the product of I nd V, the differentil of P with respect to V cn be described s follows: I ð23þ Bsed on Eq. (16), the prtil derivtive of I with respect to V cn be described ¼ I sc expððv V oc þ IR s Þ= 4 Þ= 4 1 þ R s I sc expððv V oc þ IR s Þ= 4 Þ= 4 ð24þ At the MPP (I=I mp nd V=V mp ), dp/ is equl to zero. By substituting these vlues into Eqs. (23) nd (24) nd combining them with Eq. (21), 4 cn then be given by: 4 ¼ð2V mp V 1 Þ= I sc I sc I mp þ ln 1 I mp I sc ð25þ Consequently, by using Eqs. (18), (20), (22), nd (25), the vlues of the four prmeters 4, R s,4, I ph,4, nd I o,4 of the four-prmeter model cn be clculted, nd the I V curve of the PV modules t STC conditions cn then be simulted with high ccurcy[22] A piecewise curve-fitting method In this section, piecewise curve-fitting method is developed to clculte the two differentil vlues t the short nd open circuit points, / (V = 0) nd / (I = 0) t STC conditions. Fig. 3 shows typicl I V chrcteristic curve of PV module. The curve cn At the open circuit point: I =0,V = V oc 0 ¼ I ph;4 I o;4 exp V oc;4 1 4 ð19þ To simplify Eq. (19), the vlue of V oc,4 / 4 should be further nlyzed. By substituting the vlues of the idel diode fctor n (from 1 to 2), T (298 K), q ( ), nd k ( ) into Eq. (2), Fig. 3. Chrcteristic I V curve of PV module.

5 298 J. Bi et l. / Energy Conversion nd Mngement 79 (2014) clerly be divided into three prts: low-voltge, mid-voltge, nd high-voltge zones. According to the ctul mesurement for the I V curve of PV module [23], ner the short circuit point the voltge my chnge by pproximtely 94% when the current chnges by 0.5%, nd therefore this re cn be considered to be the high-voltge zone. However, ner the open circuit point the voltge chnges only bout 1% when the current chnges by pproximtely 50%; thus, the re is considered to be the low-voltge zone. The mid-voltge zone is between the two zones. As shown in Fig. 3, the I V curve in the low-voltge nd high-voltge zones is smooth nd cn be ppropritely represented by stright lines. The slope of the stright lines cn therefore be considered s the differentil vlues of the I V curve in the two zones. Then, the following eqution cn be obtined: DV DI ð26þ We cn select two points in the ech zone to clculte the slope. As shown in Fig. 3, points (0, I sc ) nd (V(0.5 (I sc + I mp )), 0.5 (I sc + I mp )) re within the low-voltge zone nd points (V(0.5 I mp ), 0.5 I mp ) nd (V oc, 0) re within the high-voltge zone. We will thus hve DI 1 = 0.5 (I sc I mp ) in the low-voltge zone nd DI 2 = 0.5 I mp in the high-voltge. We substitute the current vlues 0.5 (I sc + I mp ) nd 0.5 I mp into Eq. (16) to clculte the corresponding voltge vlues, then ¼ DV 4 ln 0:5 ði sc I mpþ 1 I o;4 þ 1 0:5 ði sc þ I mp ÞR s;4 ¼ DI 1 0:5 ð27þ ði sc I mp Þ ¼ DV 4 ln 2 ¼ I¼0 DI 2 I o;4 þ 1 0:5 I mp R s;4 V oc 0:5 ð28þ I mp Isc 0:5 I mp In the bove two equtions, / (V = 0) is the differentil vlue t the short circuit point, nd / (I = 0) is tht t the open circuit point. These two vlues re only relevnt to the four prmeters of the four-prmeter PV model nd the bsic mnufcturer dt, including I sc, I mp nd V mp. As the four prmeters cn lso be clculted with the bsic mnufcturer dt by using Eqs. (18), (20), (22), nd (25), we cn thus esily obtin the two differentil vlues with only simple lgebric equtions, but without relly depicting the I V curve. Finlly, by substituting the two clculted vlues into Eqs. (11) (15), the five prmeters of the five-prmeter PV model t STC conditions cn be obtined I V chrcteristics of PV module t vrious operting conditions The output chrcteristics of PV module re complex nd re minly ffected by the solr irrdince, the cell temperture nd the electricl lod. Furthermore, the cell temperture of PV module highly depends on the solr irrdince nd the mbient temperture. The output chrcteristics of PV module consequently hve obvious non-linerity reltive to the environmentl conditions. And the I V curves t different environmentl conditions will lso be different. Thus, the five prmeters t non STC conditions re different from those t STC conditions. Therefore, in order to simulte the I V curve t other environmentl conditions, we revise the five prmeters bsed on those extrcted t STC conditions. First, the photocurrent I ph prmeter is pproximtely liner with the solr irrdince, nd its vlue lso highly depends on the solr irrdince, the cell temperture nd the temperture coefficient of the short-circuit current l I,sc. Townsend hs proposed method to clculte I ph t specific conditions s follows [22]: I ph ¼ G G ref ði ph;ref þ l I;sc ðt T ref ÞÞ ð29þ where subscript ref represents the prmeters t STC conditions. G ref, I ph, ref, nd T ref re the solr irrdince, the photocurrent, nd the cell temperture t STC conditions. G, I, nd T re the corresponding prmeters t the new specific condition. Wolf [24] indictes tht the diode idel fctor n chnges slightly with the vrition of the solr irrdince nd the cell temperture. Thus, we cn ssume tht n hs constnt vlue t different solr irrdince nd cell temperture. According to the definition of the modified idel fctor prmeter, its vlue cn then be described s being proportionl to the cell temperture s follows: ¼ T ref T ref ð30þ where ref nd T ref re the modified idel fctor nd the cell temperture t STC conditions; nd T re the corresponding vlues t the new specific condition. With regrd to the diode reverse sturtion current I o prmeter, its vlue chnges with the cell temperture nd cn be obtined from the following eqution bsed on the diode theory [25]: I o I o;ref ¼ T 3 exp 1 k T ref E g T Tref E!! g T T ð31þ where I o,ref nd T ref re the reverse sturtion current nd the cell temperture t STC conditions, respectively. I o nd T re the corresponding vlues t the new specific condition. E g is the mteril s energy bnd gp. The vlue of E g for the silicon solr cells t STC conditions is equl to ev. Its vlue t other opertion conditions is slightly dependent on the cell temperture T s follows [26]: E g E g;tref ¼ 1 0: ðT T ref Þ ð32þ The seril resistnce R s prmeter determines the shpe of the chrcteristic I V curve ner the MPP. As most PV systems hve Mximum Power Point Trcking (MPPT) functions, the influence of R s on the I V chrcteristic curves of PV modules cnnot be neglected. Virtuni [27] indictes tht R s increses with the cell temperture nd decreses with the solr irrdince. The reltionships mong them cn thus be described s follows: R s ¼ T R s;ref T ref 1 b ln G G ref ð33þ where R s,ref, T ref, nd G ref re the seril resistnce, the cell temperture, nd the solr irrdince t STC conditions, respectively. R s, T, nd G re the corresponding vlues t the new specific condition. The vlue of ß pproches The shunt resistnce R sh prmeter determines the slope of the I V curve t the short circuit point. The lrger R sh is, the fltter the slope of the short circuit point will be. According to the NIST (Ntionl Institute of Stndrds nd Technology) experimentl investigtion on the slope vlue t the short circuit point, R sh increses when the solr irrdince incident on PV module decreses [23]. As it is pproximtely inversely proportionl to the bsorbed solr irrdince by PV module, the eqution cn hence be described s follows: R sh ¼ G ref R sh;ref G ð34þ where R sh,ref nd G ref re the shunt resistnce nd the solr irrdince t STC conditions. R sh nd G re the corresponding vlues t the new operting condition.

6 J. Bi et l. / Energy Conversion nd Mngement 79 (2014) From Eqs. (29) (33), it cn be found tht the cell temperture T is the importnt nd essentil fctor in clculting the revised five prmeters t the new specific condition. However, during the ctul opertion of PV system, directly monitoring the cell temperture is inconvenient. In this section, the cell temperture is evluted bsed on the solr irrdince nd the mbient temperture.according to the energy conservtion lw, prt of the bsorbed solr energy on the surfce of PV module is converted to electric power energy, nd the rest is converted to therml energy. The cell temperture T should thus increse nd be higher thn the mbient temperture, nd the reltionship between them cn be described s follows [12]: sg ¼ gg þ U L ðt T Þ ð35þ where T is the mbient temperture, s is the trnsmission rtio on PV module surfce, is the bsorption rtio of PV cells, g is the electricl energy conversion efficiency of the PV module, nd U L is the loss coefficient tht includes ll losses during the het trnsfer process. To predict the cell temperture T, we use the norml opertion cell temperture (T NOCT ) method [28]. T NOCT refers to the cell temperture t solr irrdince of 800 W/m 2, mbient temperture of 20 C, wind speed of 1 m/s, nd g = 0 (open loop). As T NOCT cn be directly cquired from the bsic mnufcturer dt, Eq. (35) cn thus be represented s below: s ¼ T NOCT 293:15 U L 800 ð36þ Assuming s/u L is invrint, the cell temperture T cn then be described s follows: T ¼ T þ G s U L 1 g s ¼ T þ G T NOCT 293: g s ð37þ where s is pproximtely 0.9 nd g/s is much smller thn 1 [22]. Hence, the clcultion of the cell temperture T cn be simplified by only using the solr irrdince G, T NOCT, nd the mbient temperture T s below T ¼ T þ G s U L 1 g s ¼ T þ G T NOCT 293: ð38þ Finlly, ccording to Eqs. (29) (34), we cn obtin the vlues of the revised five prmeters t the new operting condition. Then the I V chrcteristic curves of PV module or rry t ny opertion conditions cn be simulted. 3. Vlidtion of the proposed method nd nlysis of the results To evlute the effectiveness nd ccurcy of the proposed compound five-prmeter extrction method, severl experiments were conducted, nd relevnt comprisons were nlyzed Reliztion procedures for the proposed method Assuming the bsic mnufcturer templte dt for PV module is known in dvnce, nd these dt include the open circuit voltge (V oc ), the short circuit current (I sc ), the current (I mp ) nd voltge (V mp ) t the MPP, the nominl operting cell temperture (T NOCT ) nd the temperture coefficient of short-circuit current l I,s, then the reliztion procedures to simulte the chrcteristic output of PV module or rry t vrious opertion conditions cn be described s follows: (1) According to Eqs. (18), (20), (22), nd (25), clculte the four prmeter of the four-prmeter model t STC conditions. (2) According to Eqs. (27) nd (28), obtin / (V = 0) nd / (I = 0) t STC conditions. Tble 1 Templte dt of the three types of PV modules t STC conditions (G = 1000 W/m 2, T = 298 K). Types of PV modules I sc (A) V oc (V) I mp (A) V mp (V) Monocrystlline Multicrystlline Thin-film (3) According to Eqs. (11) (15), obtin the five prmeters of the five-prmeter model t STC conditions. (4) Get the solr irrdince nd the mbient temperture t the new specific condition, nd then clculte the cell temperture T ccording to Eq. (38). (5) According to Eqs. (29), (30), (31), (33), nd (34), clculte the revised five prmeters t the new specific condition. (6) According to Eq. (1), simulte nd depict the I V nd P V chrcteristic curves for PV module or rry t the new specific condition Accurcy evlution of the two differentil vlues nd comprison of the simulted I V curve t STC conditions The clcultion ccurcy of the two differentil vlues t the open nd short circuit points (/ (V = 0) nd / (I = 0)) plys n importnt role in the proposed method. Three types of PV modules presented by NIST re used to compre the experimentl nd clculted vlues [23]. The bsic templte dt of the three types of PV modules re listed in Tble 1. To clculte the two differentil vlues, first we substitute the bsic templte dt in Tble 1 into Eqs. (18), (20), (22), nd (25). The four prmeters of the four-prmeter PV model cn then be obtined. Moreover, by using Eqs. (27) nd (28), the two differentil vlues cn be clculted. Tble 2 shows the comprison between the experimentl nd clculted vlues for the three types of PV modules nd their reltive errors. As shown in Tble 2, the reltive error of / (V = 0) for the three types of PV modules is below 7%. In ddition, the reltive error of / (I = 0) for the monocrystlline nd multicrystlline PV modules is below 1%, nd tht of the thin-film silicon PV modules is below 5%. To evlute the influence of the reltive error on the I V chrcteristic curve, the clculted nd experimentl vlues of / (V = 0) nd / (I = 0) re used to obtin the five prmeters of the five-prmeter model t STC conditions. The I V nd P V chrcteristic curves t STC conditions re simulted bsed on the extrcted prmeters. Fig. 4 shows the simulted I V nd P V curves of the three types of PV modules using the clculted nd experimentl differentil vlues. Fig. 5 lso shows the reltive error of the genertion power for the three types of PV modules within the vilble rnge. As shown in Fig. 4, the simulted I V nd P V curves with the clculted nd experimentl differentil vlues for the three types of PV modules hve high consistency. Fig. 5 shows tht the genertion power error is very smll within the vilble rnge of power genertion t STC conditions. Especilly for the monocrystlline nd multicrystlline silicon, the reltive error is below 1%, nd tht of the thin-film silicon is less thn 1.6%. Thus, the method is sufficiently ccurte to simulte the I V nd P V curves t STC conditions I V nd P V chrcteristics of PV rrys t specific operting conditions To verify the ccurcy of the proposed method in simulting the I V nd P V chrcteristic curves t new operting conditions,

7 300 J. Bi et l. / Energy Conversion nd Mngement 79 (2014) Tble 2 Comprison between the clculted nd experimentl differentil vlues. Types of PV modules /(V = 0) /(I = 0) Clculted Experimentl Reltive Error (%) Clculted Experimentl Reltive Error (%) Monocrystlline Multicrystlline Thin-film Fig. 5. Reltive error of the genertion power for the three types of PV modules. () Monocrystlline (b) Multicrystlline experiments were conducted using multicrystlline nd monocrystlline PV modules provided by Trin Solr Limited. Eight multicrystlline PV modules (TSM-230PC05) nd nine monocrystlline PV modules (TSM-180DC01) re seprtely connected in series. The bsic mnufcture templte dt of the modules re listed in Tble 3. The two types of PV rrys re mounted in the open brcket s shown in Fig. 6. The solr irrdince, the mbient temperture, nd the I V curve re ll mesured by MP-170 (Fig. 7), which is photovoltic module & rry tester. The MP- 170 is then connected to personl computer, nd the output dt cn be collected by dt logger. The voltge nd current mesurement ccurcy re within ±1.0%FS (Full Scle). The pyrnometer mesurement ccurcy is within ±1.5% FS nd the temperture mesurement ccurcy is within ±1.5 C@25 C. First, by using Eqs. (11) (15) with the mnufcture templte dt, the five prmeters t STC conditions cn be clculted. Then, ccording to the rel-time mesurement vlues of the solr irrdince nd the mbient temperture, the five prmeters re revised bsed on Eqs. (29) (34). After tht, the I V chrcteristics of the PV rrys t ny ctul operting conditions cn be simulted. Fig. 7 highlights the simultion nd experimentl I V curves t certin solr irrdince nd mbient temperture. As shown in Fig. 8, the simulted nd experimentl I V nd P V curves for the two types of PV rrys hve high uniformity. The experimentl dt re somewht smller thn the simulted becuse of the slight ttenution of the PV modules nd mismtch inside the PV rrys in the ctul opertion. The reltive error of the genertion power of the multicrystlline PV rry t the MPP is pproximtely 1.2%, nd tht of the monocrystlline PV rry is only 0.79%. Consequently, the proposed method hs high ccurcy to simulte the I V nd P V chrcteristics for PV module or rry t ny operting conditions. (c) Thin-film Fig. 4. Comprison of Simulted I V nd P V curves t STC conditions with the clculted nd experimentl differentil vlues for the three types of PV modules Comprison of prediction nd experimentl genertion output of rel PV power sttion In order to verify the ccurcy of the proposed method in predicting the genertion output of rel PV power sttion,

8 J. Bi et l. / Energy Conversion nd Mngement 79 (2014) Tble 3 Templte dt of experimentl PV modules. Types of PV modules Product model P mp (W) I sc (A) I mp (A) V oc (V) V mp (V) T NOCT ( C) l I,sc (%/ C) Multicrystlline TSM-230PC Monocrystlline TSM-180DC () Multicrystlline (TSM-230PC05) (b) Monocrystlline (TSM-180DC01) Fig. 6. Experimentl PV rrys. () Ambient temperture mesurements with thermocouple (b) Solr irrdince mesurements with pyrnometer (c) I-V curve mesurements Fig. 7. MP-170 mesuring pprtus. eight multicrystlline PV modules (TSM-230PC05) re connected in series nd connected to n inverter which hs MPPT functions. First, ccording to the monitored solr irrdince nd mbient temperture, the rel-time output power of the PV power sttion cn be clculted by the proposed method. The clculted output power is then compred with the ctul dt gthered from the direct current (DC) prt of the inverter. Fig. 9 demonstrtes the trends of the simulted power genertion, the rel-time mesured power genertion nd the solr irrdince on typicl dy. After further clcultion, the mesured nd simulted power genertion per pek power nd the reltive errors between them re lso shown in Fig. 10. Fig. 9 highlights tht the vrition trends of the simulted nd mesured generted power re consistent with the solr irrdince; the curves of the simulted nd mesured genertion power lso hve high consistency. As lso shown in Fig. 9, most of the time the rel-time reltive error is within 5% nd t few points the vlue is within 10%. The possible resons for the reltive errors re described s follows: (1) Certin mount of generted power difference exists when the inverter my not precisely trck the MPP. (2) Becuse of the time dely in the sensors nd the dt cquisition pprtus, time difference my hve occurred between the rel-time dt gthered from the inverter nd the simulted dt. (3) Line losses exist within the PV rry nd the inverter. (4) Smll ttenution of the PV modules nd mismtch within the PV rry exist.

9 302 J. Bi et l. / Energy Conversion nd Mngement 79 (2014) () Multicrystlline PV rry (b) Monocrystlline PV rry Fig. 8. Comprsiosn of I V nd P V curves with simulted nd experimentl dt t specific operting conditions. t ny opertion conditions nd predict the rel-time genertion output of ctul PV power sttions well. 4. Conclusions Fig. 9. Comprison between simulted nd mesured genertion power nd solr irrdince of PV power sttion. Fig. 10. Comprison between simulted nd mesured genertion output per pek power nd their reltive errors. Fig. 10 lso demonstrtes tht fter 2:00 PM the reltive errors between the mesured nd simulted genertion power is positive nd show n incresing trend. This could be becuse the het ccumultion process during the fternoon. The PV modules would therefore hve lesser het dissiption nd higher cell temperture thn predicted. Then it could hve led to the higher simulted power genertion thn the rel-time mesurement. We cn conclude tht the proposed method cn ccurtely simulte the I V nd P V chrcteristic curves of PV module or rry This study proposes new compound method to extrct the five prmeters of the five-prmeter PV model. With the bsic mnufcture templte dt, the I V nd P V chrcteristics of PV module or rry t ny opertion conditions cn be simulted. As the two differentil vlues t the short nd open circuit points t STC conditions re the fundmentl dt to obtin the five prmeters nd not normlly vilble from the templte dt, the pper lso put forwrd piecewise fitting method combined with the fourprmeter model to clculte the two vlues. An explicit method is then presented to extrct the five prmeters t STC conditions with five lgebric equtions. Furthermore, we put forwrd the method to revise the five prmeters t ny operting conditions. In order to evlute the effectiveness of the proposed method, the simulted nd experimentl I V nd P V curves re compred t STC conditions nd specific operting conditions. Tests show tht the simulted curves hve high consistency with the mesured. The method is lso used to predict the rel-time genertion power of PV power sttion. The experimentl results show tht the method hs high ccurcy. To summrize, the proposed method is good method to simulte the I V nd P V chrcteristics of PV module or rry nd good tool to predict the rel-time genertion output of PV power sttion. Furthermore, it provides n esy nd fesible mens to study the comprehensive performnce for PV module or rry under more complex situtions, such s hot-spot nd mismtch, to which the four-prmeter model is not pplicble becuse the shunt resistnce R sh is not considered. Acknowledgments This work ws supported by the Nturl Science Foundtion of Jingsu Province, Chin, No. BK The uthor would lso like to thnk the Progrm for Outstnding Innovtive Tlents in Hohi University. References [1] Hepbsli A. A key review on exergetic nlysis nd ssessment of renewble energy resources for sustinble future. Renew Sust Energy Rev 2008;12(3): [2] Joshi AS, Dincer I, Reddy BV. Performnce nlysis of photovoltic systems: review. Renew Sust Energy Rev 2009;13(8):

10 J. Bi et l. / Energy Conversion nd Mngement 79 (2014) [3] Chow TT. A review on photovoltic/therml hybrid solr technology. Appl Energy 2010;87: [4] M T, Yng H, Lu L. Performnce evlution of stnd-lone photovoltic system on n isolted islnd in Hong Kong. Appl Energy 2013;112: [5] Ghoneim AA. Design optimiztion of photovoltic powered wter pumping systems. Energy Convers Mnge 2006;47(11 12): [6] Hmd AA, Alsd MA. A softwre ppliction for energy flow simultion of grid connected photovoltic system. Energy Convers Mnge 2010;51(8): [7] Hernndez J, Gordillo G, Vllejo W. Predicting the behvior of grid-connected photovoltic system from mesurements of solr rdition nd mbient temperture. Appl Energy 2013;104: [8] Zhou W, Yng H, Fng Z. A novel model for photovoltic rry performnce prediction. Appl Energy 2007;84: [9] Pnchul AF, Hyes WW, Kimber AA. First-yer performnce of 20-MW PV power plnt. IEEE J Photovolt 2012;2(3): [10] Ishque K, Slm Z, Syfruddin. A comprehensive MATLAB Simulink PV system simultor with prtil shding cpbility bsed on two-diode model. Sol Energy 2011;85(9): [11] Chn DSH, Phng JCH. Anlyticl methods for the extrction of solr-cell single-nd double-diode model prmeters from IV chrcteristics. IEEE Trns Electron Dev 1987;34(2): [12] Duffie JA, Beckmn WA. Solr of therml processes. Hoboken: Wiley & Sons; [13] Lo Brno V, Orioli A, Ciull G. On the experimentl vlidtion of n improved five-prmeter model for silicon photovoltic modules.. Sol Energy Mt Sol C 2012;105: [14] Chegr M, Nehou N, Bouhemdou A. Orgnic nd inorgnic solr cells prmeters evlution from single I V plot. Energy Convers Mnge 2008;49(6): [15] Orioli A, Di Gngi A. A procedure to clculte the five-prmeter model of crystlline silicon photovoltic modules on the bsis of the tbulr performnce dt. Appl Energy 2013;102: [16] De Soto W, Klein SA, Beckmn WA. Improvement nd vlidtion of model for photovoltic rry performnce. Sol Energy 2006;80(1): [17] Lo Brno V, Orioli A, Ciull G, Di Gngi A. An improved five-prmeter model for photovoltic modules. Sol Energy Mt Sol C 2010;94(8): [18] De Bls MA, Torres JL, Prieto E, Grcı A. Selecting suitble model for chrcterizing photovoltic devices. Renew Energy 2002;25(3): [19] Celik AN, Acikgoz N. Modelling nd experimentl verifiction of the operting current of mono-crystlline photovoltic modules using four- nd fiveprmeter models. Appl Energy 2007;84:1 15. [20] Ismil MS, Moghvvemi M, Mhli TMI. Chrcteriztion of PV pnel nd globl optimiztion of its model prmeters using genetic lgorithm. Energy Convers Mnge 2013;73: [21] Khn F, Bek S-H, Prk Y, Kim JH. Extrction of diode prmeters of silicon solr cells under high illumintion conditions. Energy Convers Mnge 2013;76: [22] Townsend TU. A method for estimting the long-term performnce of directcoupled photovoltic systems. MS Thesis, Solr Energy Lbortory, University of Wisconsin, Mdison; [23] King DL, Krtochvil JA, Boyson WE. Photovoltic rry performnce model. Sndi Ntionl Lbortories, SAND ; [24] Wolf M, Ruschenbch H. Series resistnce effects on solr cell mesurements. Adv Energy Convers 1963;3(2): [25] Messenger RA, Ventre J. Photovoltic systems engineering. Boc Rton: CRC; [26] Vn Zeghbroeck B. Principles of semiconductor devices nd heterojunctions. 1st ed. Englewood Cliffs, New Jersey: Prentice Hll; [27] Virtuni A, Lotter E, Powll M. Performnce of Cu (In, G) Se solr cells under low irrdince. Thin Solid Films 2003;431: [28] Dvis MW, Fnney AH, Dougherty BP. Prediction of building integrted photovoltic cell tempertures. J Sol Energ-T ASME 2001;123(3):