PEAK-POWER AND INTERNAL SERIES RESISTANCE MEASUREMENT UNDER NATURAL AMBIENT CONDITIONS

Transcription

1 K-OW N NNL SS SSNC MSUMN UN NUL MBN CONONS NS WGN Univerity of pplied Science ortmund,.o.box 5 8, ortmund, Germany, Fax , wagner@fh-dortmund.de btract Quality inpection of -module include meaurement of peak-power pk and internal erie reitance. eakpower i defined a maximum power under tandard tet condition (SC). the peak-power can decreae due to degradation ect, a continuou quality inpection ha to be realized on-ite under natural ambient condition. Loe in the -module can be deribed by an internal erie reitance. n increaing how internal loe a well a degrading contact. meauring method i preented, which can meaure under natural ambient condition and directly diplay the reult peak-power pk and internal erie reitance. --characteritic meaured under ambient condition can be corrected concerning temperature and irradiation according to C 689. he deription of the characteritic by the ective olar cell characteritic make it poible to explicitely carry out the calculation for pk. C 689 alo deribe a method for the evaluation of the internal erie reitance. graic method i ued in order to determin certain point in the --characteritic, which erve a input-value for the calculation of the erie reitance. he accuracy of thi graic method i limited by the accuracy of the graically determined point. Uing the method of the ective olar cell characteritic it i poible to explicitely calculate the demanded point of the --characteritic, thu beeing capable of explicit calculation of the erie reitance. he method of the ective olar cell characteritic i preented a well a ome ignificant reult concerning pk and meaurement under natural ambient condition.. NOUCON Quality inpection of -Module under natural ambient condition i a neceery ervice for uer of otovoltaic equipment, conidering a guarantee period of up to year or even more. he operating behaviour of a olar cell i deribed by it current-voltage-characteritic (-characteritic). By meaurement of preent -characteritic under natural ambient condition, the correct functioning of a olar generator, coniting of one or everal module, can be hown (Schulte K.M. et al 993). eviation of the -characteritic from the theoretically expected characteritic permit to draw conluion concerning internal interruption, partial hading, mimatching etc. n addition to the preent operating behaviour, information about poible degradation pree hould be obtained. Meaurement of tationary characteritic feature uch a peak power and internal erie reitance are neceary. Meaurement of peak-power pk need tandard tet condition (SC, C 694 3), which demand a very high ort for the tet equipment, which lead in addition to high cot per meaurement. lo the experimental ort for the meaurement of the internal erie reitance in a laboratory i rather high. Meaurement of pk and under natural ambient condition need mathematical correction of the meaured --characteritic, conidering irradiance and cell temperature. For the deription of the --characteritic of olar cell there exit everal equivalent circuit diagram with their affilated --characteritic equation, of which a uitable one for the mathematical correction of the -characteritic to SC hall be elected.. FFC SOL CLL CHCSC.. emand on olar cell equivalent circuit diagram. he purpoe of --characteritic approximation by mean of equivalent circuit diagram lie in the explicit calculability of matching problem between olar generator and everal load. calculation method for matching problem in otovoltaik engineering therefore demand the following option: xplicit calculation of current-voltage-characteritic equation () xplicit calculation of the parameter of the characteritic equation from the meaured parameter,,,. egree of accuracy of approximation within the range of degree of accuracy of meauring method (tate-ofthe-art: %) Fig.. Current voltage characteritic max d M=d/d

2 . xiting equivalent circuit diagram. From the following equivalent circuit diagram in tationary condition that one hall be elected, which meet all three mentioned option:, Fig. 5. wo-diode-model ery good approximation accuracy. Fig.. deal model. Low approximation accuracy. = ( e ) () + = ) () Fig. 3. Simple model, Good approximation accuracy. + = ( e ) (3) + = ) (4) alue for can become negative. = + + ( e ) ( e =? explicit olution unknown. + ) None of the 4 preented equivalent circuit diagram (Fig. to Fig.5) meet all three demanded option. he intereting thing about the imple model of Fig.3 i the very good approximation accuracy which reache the approximation accuracy of the two-diode-model, if a negative anwer for the erie reitance i accepted. (Wagner. 999). negative reitor do not exit in reality, the component in the equivalent circuit diagram cannot be an ohmic reitance. he equivalent circuit diagram ha to be modified by a fictitiou otoelectric component which preent either a poitive or a negative reitance. he new component i to be preented by (otovoltaik reitance). mportant: the true internal erie reitance mut not be confued with the otovoltaik reitance, p (6) Fig. 6. quivalent circuit diagram for the, ective olar cell characteritic Fig. 4. Standard model Good approximation accuracy. = ( e + + ) =? explicit olution unknown. p (5) Follow the ective olar cell chracteritic: + = ( e ) (7) xplicit verion + = ) (8) With the introduction of the otovoltaik reitance the explicit calculability of matching problem between olar generator and everal load i poible with an accuracy of %, related to the maximum power of the olar generator.

3 .3 arameter of the characteritic equation. For the determination of the 4 independent equation parameter,,, there are alo 4 independent meaured parameter neceary. n the preent cae thee meaured parameter are,,,. f in addition the lope M at open-circuit voltage i to be conidered (Fig. ) d M = ( =) (9) d then for the 4 equation parameter 5 equation are available: ( = ) = () ( ) = () = = = () ( ) p max d ( ) ( = d p max ) = (3) d ( = ) = M (4) d Uing thi nonlinear ytem of imultanuou equation the equation parameter can approximately be determined a follow (Wagner. 999): = M + ( ) (5) ( M + ) = (6) Normally the 4 parameter,,, can be obtained with a meauring error <%. he meaurement of the lope M however i more difficult and o contain a higher ytematic meauring error. with the imultaneou equation (), (), (), (3) and the 4 meaured parameter,,, the equation parameter,,, can be calculated traight-forward, and a conequently the lope M can be calculated traight-forward with (8) there mut exit a traight-forward function M = f,,, ) (9) ( p max he following in general valid approximate function for the lope M could be derived, which a a reult allow the application of the ective olar cell equation with an accuracy of % (Wagner. 999). M = + k 3 ( k p max + k with the equation-contant k = p max ) + k + () () he following example how the working point of a reitor L at direct connection to the olar module. What a reitor ha to be connected in order to caue a current of L =? = 3.65 =.7 = 3.5 = M =. =.64 Ω = 3.9 = 3.53 m = 3.65 () = e (7) = (8) Current () 4 3 Condition for the calculation of the 4 equation parameter i the exitence of the 5 meaured parameter,,,, M with ufficient accuracy oltage () Fig. 7. eitor a load of a olar module ( = ) =.5 with eq. (8) follow L =.5 Ω L (3)

4 3. SS SSNC 3.Meauring method he international tandard C 6 89 preribe the following predure for temperature and irradiance correction to meaured --characteritic of crytalline ilicon otovoltaik device. For the determination of the erie reitance under imulated unlight the following condition have to be kept: t ambient temperature characteritic are meaured at different irradiance (of which the extent doe not need to be known) but of the ame pectral ditribution. n the coure of the meaurement the temperature of the cell mut be kept contant (permiible tolerance ± C) From the two characteritic two working point and have to be obtained of which the erie reitance can be calculated. he international tandard C 6 89 preribe the following predure for the determination of the two working point: efinition of current interval between hort-circuit current and the current in the elected working point of the characteritic (where index indicate the characteritic with the lower hort-circuit current) = (4).5 etermination of the working point and with equation (8) =( -,,,, ) (5) =( -,,,, ) (6) Calculation of the erie reitance = (7) the actual pectrum during the meaurement i not relevant for the calculation of, the meaurement can alo take place under open air condition with natural unlight. he condition of unchanged pectral ditribution can be kept by a hort meaurement interval for the two characteritic ( < min) he change of irradiance without change of pectral ditribution can be obtained by decreae of tranmiion by an extenive filter, which i put above the -module immediately after the firt meaurement without filter. a filter a cloe-mehed reen i applied with a mehditance of about.5 mm. hu the pectrum keep unchanged. 3. xemplary meauring reult he determination of the internal erie reitance i to be demontrated with the example of the following meaurement. Current () oltage () Fig. 8. Meaurement for -determination Meaurement =.998 =.35 =.8 = Meaurement =.795 =.958 =.73 = M =. 65 M =. 55 =.98 Ω =.488 = 6.44 =.998 =.7 Ω =.455 = 4.4 = (8) (9) Fig.8 how the meaured point of the characteritic a well a the calculated ective olar cell characteritic, calculated with eq. (8). efinition of current interval with eq. (4) =.5 =. 398 (3) etermination of the working point with eq. (8) =( -,,,, )=8.38 (3) etermination of the working point with eq. (8) =( -,,,, )=9.663 (3) nternal erie reitance = (33) =. 67 Ω (34)

5 4. K OW 4.Meauring method eak power i the maximum power under tandard tet condition (SC) =, ) (35) pk max( j Standard et Condition (SC): rradiance = (36) m W Solar pectrum M.5 (37) Solar cell temperature j = 5 C (= 98 K) (38) he actual maximum power point (M) varie with irradiance and temperature. Meaurement of peak power under natural ambient condition mean correction of the actual M to SC. Not only the irradiance, but alo the pectral ditribution of the irradiance ha an important influence on the iciency of the olar cell.he pectral repone of the olar cell i expreed by it hort-circuit current. ropoition: For a linear deription of the pectral repone a pectrally aeed ective irradiance i to be introduced. efinition: he ective irradiance for a olar cell only conit of that part of the olar pectrum which take part in energy-converion in thi olar cell. By analogy with the unit Lux (lx) of lighting technology, where brightne i pectrally aeed by the pectral enibility of the human eye, it i propoed here to deribe the pectral enibility of the otovoltaic olar cell by an ective irradiance with the new unit hotovoltaik Lux (ox). he hort-circuit current of the olar cell i a linear meaure for the ective irradiance. t M.5 applie ox = = W m Beyond M.5 applie ox (39) = K (4) he olar module to be meaured erve a it own ox-meter when it ox-contant K ox i known.he ox-contant can be meaured at M.5-condition at a clear day under natural ambient condition. M.5 applie, when for the radiation angle applie co( Θ Z ) = (4) M follow for M=.5 co( Θ Z ) = (4).5 he time, at which thi radiation angle applie, can be determined with known date of the year and geografic poition. (uffie J.., Beckman W.. 98). xample: ortmund (λ = 7 eat. longitude, ϕ = 5 north. latitude) ugut 7. (Wagner. 999) eult in Central uropean Summer ime M =.5( am) M =.5( pm) h9 min 6 h4 min (43) For the determination of the ox-contant, at M.5- condition the irradiance ha to be meaured with a pyranometer a well e the actual hort-circuit current of the olar module. M.5 K ox = (44) M.5 With the known ox-contant for the module to be meaured an additional meaurement of the irradiance i not neceary. ll further calculation will refer to the ective irradiance, meaured in ox. For the determination of the peak-power of a -module firt it ox-contant mut be known. With the known ox-contant, an actual characteritic of the module can be meaured any time. Now the actual ective characteritic parameter can be evaluated. With the cell-temperature j and the temperature coicient c of power, the expected peak-power now can be calculated (Wagner. 999). Correction to SC: = (45) p max p max = + c ( + j j j follow the peak-power pk p max j ) ) ( ) (46) = (47) For a complete preentation of the --characteritic under SC the following relation can be ued. = p max = (48)

6 For the application of formula (46) two additional information are neceary. emperature coicient c of power Cell temperature j he temperature coicient c of power ha to be adopted from the data-heet of the -module. f no information are available, the following value can be ued a default value for crytalline ilicon cell: typical c =,44 K (49) Cell temperature change depending on irradiance and ambient temperature. Often the nominal operating cell temperature i given in the data-heet. NOC= j ( N, ambn ) (5) et condition for the evaluation of NOC Nominal Operating Cell emperature rradiance W N = 8 (5) m mbient temperature ambn = C (5) he nominal operating cell temperature ha to be adopted from the data-heet of the -module. f no information are available, the following value can be ued a default value for crytalline ilicon cell: typical NOC = 48 C (53) With the meaured ambient temperature amb and NOC the cell-temperature j then can approximately be calculated. (Wagner. 999). Follow the cell temperature, depending on irradiance and ambient temperature. (, ) ) j amb = amb + ( NOC (54) ambn N 4.. xemplary meauring reult he meaurement of the firt characteritic of Fig. 8 for -determination ha been made at the following ective irradiance: = 777 ox (55) n order to reduce irradiance without changing the pectrum, a cloe-mehed reen i applied over the module. So the ective irradiance i reduced by the factor k = =.398 (56) Follow = 39 ox (57) he following temperature ha been determined: j = 94 K (58) emark: a both meaurement have been carried out within a hort time interval, and in addition, the celltemperature doe not change in a harp rie due to the cloe-mehed reen, the cell temperature i approximately the ame in both cae. For the calculation of the peak power with the formula (45), (46) and (47) the following value have been ued: Meaurement j =.8 = =.488 =.98 Ω = 94 K = 777 ox Meaurement j =.73 = =.455 =.7 Ω = 94 K = 39 ox (45) (46 ) m (47 ) (45) (46 ) m (47 ) pk m m pk =.35 = 6.59 = 39W =.36 = 7.6 = 4 W (59) (6) n the preent cae the meaurement concern a polycrytalline module, year of production 99. Quality inpection: February. ata-heet information: eak-power pk = 5 W (6) olerance ± % (6) Loe due to degradation in year <% (63) With the guaranteed leat power at delivery date of 45W and degradation-loe <5W after year follow the acceptable leat peak-power of 4 W. n the preent cae the -year-guarantee i atified.

7 5. CONCLUSONS he deription of the operating behaviour of olar cell by the ective olar cell characteritic allow explicit calculation of the parameter of the ective olar cell characteritic from the meaured parameter,,,.with an accuracy of %, related to the maximum power of the olar generator. he explicit calculation of the internal erie reitance now become poible and replace the grahic method potulated in C 689. For meaurement we need two --characteritic of ame temperature but different irradiance.he change of irradiance without change of pectral ditribution can be obtained by decreae of tranmiion by an extenive filter (cloe-mehed reen). he filter i put above the -module after the firt meaurement without filter. For the determination of the peak-power a new deription of the irradiance i propoed. By analogy with the unit Lux (lx) of lighting technology it i propoed here to deribe the pectral enibility of the otovoltaik olar cell by an ective irradiance with the new unit hotovoltaik Lux (ox). K ox M M NOC pk L p hox-contant of -module lope at open circuit point(/) Maximum ower oint Nominal Operating Cell emperature( C) peak power (W) maximum power at SC eitance (Ω) Load reitance (W) arallel reitance (Ω) hotovoltaik-reitance (/) Serie reitance (Ω) SC Standard et Condition (, j at M.5) emperature ( C or K) ambn j j L C (ambient temperature for NOC) Junction-temperature (K) 5 C (cell temperature at SC) oltage () iode-voltage () ctual voltage at working point () Open circuit voltage () oltage at M () emperature-voltage (K) NOMNCLU M ir Ma c emperature coicient of power rradiance (W/m ) W/m (rradiance at SC) N L ffective irradiance (ox) 8 W/m (rradiance for NOC) Current () evere current () iode-current () Current at actual working point () hoto-current () Current at M () Short-circuit current () FNCS uffie J.., Beckman W.. (98) Solar ngineering of hermal ree. John Wiley and Son, New York, Bribane. C 89. (99) redure for temperature and irradiance correction to meaured - characteritic of crytalline ilicon otovoltaic device. N N 689. (994) erfahren zur Umrechnung von gemeenen Strom-Spannung-Kennlinien von otovoltaihen Bauelementen au kritallinem Silizium auf andere emperaturen und intrahlungen. Schulte K.M., Sommerfeld., Wagner. (993) Mobile Me-Sytem für -Stromverorgunganlagen Final report, reearch project G-Solar NW, Jülich Wagner. (999) hotovoltaik ngineering. ie Methode der ffektiven Solarzellen-Kennlinie. Springerverlag, Berlin, Heidelberg, New York.