Effects of solar irradiation conditions on the outdoor performance of photovoltaic modules

15 July 1998

Ž .Optics Communications 153 1998 153–163

Full length article

Effects of solar irradiation conditions on the outdoor performanceof photovoltaic modules

Antonio Parretta a,), Angelo Sarno a, Luciano R.M. Vicari b,1

a ( )ENEA Centro Ricerche, Localita Granatello, C.P. 32, I-80055 Portici Na , Italy`b Istituto Nazionale per la Fisica della Materia, UniÕersita di Napoli ‘Federico II’, Dipartimento Scienze Fisiche,`

Facolta d’Ingegneria, p. le Tecchio 80, I-80125 Naples, Italy`

Received 28 October 1997; revised 6 April 1998; accepted 7 April 1998

Abstract

Energetic losses, relative to the standard conditions of testing, in photovoltaic modules in outdoor operation, wereŽ .analyzed and the role of the optical effects is discussed. The following four loss effects were estimated: a reflection of

Ž . Ž . Ž .unpolarized light, b spectrum, c intensity of the light and d temperature of the module. Four independent models wereused to describe these four losses. The models were validated by the experimental data of an outdoor measurement campaignperformed on 08 tilted modules at 418N latitude in South Italy. Disagreement reaching 5% under clear sky conditions wasfound between theoretical predictions and experimental data for the instantaneous total loss. As a result of a critical analysisof the literature data on this subject, it could be explained by invoking the presence of a fifth loss mechanism: thepolarization of the incident light. Final relative losses, due to the particular state of the incident sunlight, amount to about7–8% of a total of 14–15%. Of these, 3% is due to the low irradiation level, 1–2% to the polarization of the skylight and

Ž .3% to the reflection of the incident light on the front cover of the module. The spectral effects are negligible less than 1% .The remaining 7% loss is due to temperature effects on the module. All the loss data are reported as a function of the air

Ž .mass AM . The maximum operating efficiency is reached at AMf1.5. q 1998 Elsevier Science B.V. All rights reserved.

PACS: 42.79.Ek; 84.60.Bk; 84.60.JtKeywords: PV modules; Energetic losses; Performance characteristics

1. Introduction

The operating efficiency of an installed PV module,w xh 1 , is not well predicted by its datasheet, related toRRC

Ž . w xstandard test conditions STC 2 : normal and unpolarizedlight, 1000 Wrm2 of irradiance, AM1.5G spectrum and258C of cell temperature. These reference conditions, infact, are hardly attainable in the field as they combine theirradiance of a clear summer day, with the module temper-ature of a clear winter day and the spectrum of a clear

) E-mail: [email protected] E-mail: [email protected]

w xspring day 3 . Thus, the experimental efficiency of theŽ .module h , and the energy supplied by the module inRRC

the field, can be 20% or more lower than that expectedŽ . w xh in PV systems installed in central Europe 4 . TheSTC

true rating of the module is better described by thew xkWhrkWp figure 4 , i.e. the total energy produced per

unit peak power. To improve upon this, it is necessary tooptimize the yield of the module’s electrical output with

w xrespect to the specific conditions of the site 5 , and thisrequires a better understanding of the energetic loss mech-anisms.

w xBucher 1 reported an extensive analysis of the well-known four loss mechanisms: module reflectivity, spectraleffects, low light level and temperature dependence, with

0030-4018r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.Ž .PII S0030-4018 98 00192-8

( )A. Parretta et al.rOptics Communications 153 1998 153–163154

respect to a wide range of operating conditions, such as tiltangle, latitude, etc. for different module’s technologies.For each loss mechanism a quantity, called the perfor-

Ž .mance ratio PR , is introduced. It is the factor by whichthe efficiency is reduced when that mechanism is operat-ing.

Our previous investigation of the energetic losses in PVsystems was focused on reflection losses and temperature

w xeffects 6,7 . In the present work, we derive a simplemethod of calculating the outdoor performances of crys-talline-Si PV modules, making use of a limited number ofparameters, calculated or derived from the moduledatasheet, or taken from the literature. We analyze the four

w xlosses described by Bucher 1 . To simplify the descriptionof spectral effects, we have limited the present study to 08

tilted modules, which are affected only by the direct anddiffuse light of the sky hemisphere. By comparing thecalculated and experimental data, we have found that afifth loss mechanism should be invoked. It is the polariza-tion of the incident light, which was not directly measuredby us, but whose literature data account well for thedifferences found between calculated and experimentalinstantaneous loss data.

2. Experimental

2.1. Outdoor measurements

The outdoor measurements were performed in the siteŽ .of Manfredonia, South of Italy 418N latitude . The tested

module, a commercial BP Solar BP585 of recent technol-ogy, consists of 36 monocrystalline silicon cells. Itsdatasheet is reported in Table 1. We had to measure theelectrical parameters of the specific module used in thiswork ourselves because the parameters on the datasheetare just averages of the BP585 class of modules. The I–Vmeasurements were carried out by the solar simulatorSPIRE, model SPI-SUN 240. The results are shown inTable 2. These measurements gave the maximum power,P , and the nominal efficiency values 2% smaller thanm

those reported on the datasheet. Even though small, thisdifference is important in the evaluation of the polarizationloss, as will be discussed later.

Table 1Datasheet of the BP585 mono-Si module showing the STC electri-cal parameters of the BP585 class

P s85 W P s80.0 Wm min

V s22.1 V h s13.5%oc STC2I s5.00 A S s142.5 cmsc cell2V s18 V S s6307 cmm mod

I s4.72 A 36 cells in seriesm

Table 2STC electrical parameters of the BP585 module measured by oursolar simulator

P s83.0 W FFs0.76m

V s21.7 V V s18.2 Voc m

I s5.06 A I s4.56 Asc m

h s13.16%STC

The nominal power P , and efficiency, h , differ about 2%m STC

with respect to the corresponding values of the datasheet.

The outdoor measurements were carried out with themodule placed on a two-axes solar tracker, south orientedand tilted at 08 angle. The radiometric data were acquiredby a nearby station equipped with an Eppley PSP pyra-

Žnometer for horizontal global radiation measurements hp.refers to horizontal plane , an Eppley PSP pyranometer

with added sun-shading band for horizontal diffuse radia-tion measurements and an Eppley NIP pyrheliometermounted on a solar tracker for direct radiation measure-ments. Another Eppley PSP pyranometer, mounted on themodule solar tracker, was used for in-plane global radia-

Ž .tion measurements mp refers to module plane . The radio-metric data, temperature and the electrical parameters ofthe modules were collected by a central data acquisition

Ž .and control unit see Fig. 1 . Data were recorded everythree minutes for a maximum of 8 hours a day and for a

Ž .total of about five days 800 points in total . Fig. 2 showsŽ .the direct at normal incidence and diffuse solar radiations

measured by the radiometric station. The data of Fig. 2refer to ‘generic sky’ conditions. The sky conditions are

w xclassified as a function of the clearness, ´ 8 . Fig. 3shows the clearness, ´ , of our data set. It varies in theinterval 1–9.5, corresponding in practice to a sky ofvariable conditions from overcast, to intermediate and to

Ž .clear. The high values of clearness ´f2–9.5 correspondw xto a clear-turbidrclear sky 8 , which will be hereafter

referred to as ‘clear sky’. The ‘clear sky’ data wereselected for separate analysis. They correspond to 195 for240 measurements of the 411–650 interval shown in Figs.2 and 3.

Inaccuracies of the radiometric instruments are notŽ .negligible about 2.5% and their influence on the results

of the models is complex. Our approach was to comparethe four radiometric detectors to extract the most reliablevalues for the diffuse and direct components of sunlight. Inparticular, we compared the global radiation measured by

Ž .the pyranometer on the radiation station hp with thatmeasured by the pyranometer placed on the module planeŽ .mp . It was found that the ‘hp’ pyranometer measured, onaverage, 20 Wrm2 more than the ‘mp’ pyranometer. Wethen compared the two global radiations with that obtainedby summing up the diffuse and direct radiations measuredby the other two detectors. It was found that the measure-ments of the three detectors of the radiometric station are

( )A. Parretta et al.rOptics Communications 153 1998 153–163 155

Fig. 1. Schematic diagram of the data acquisition and control unit.

congruent within about 10 Wrm2. Finally, we used theradiation data from the radiometric station for elaboratingour loss models. We followed two methods for extractingthe radiation data:

Method A: the diffuse and direct radiations were mea-sured and the global radiation was obtained by theirsum;Method B: the global and direct radiations were mea-sured and the diffuse radiation was obtained by theirdifference.It is evident that, when we refer to the solar radiation

Ž .on the horizontal plane hp , the direct component isobtained by multiplying the pyrheliometer reading by thecosine of the zenith angle of the sun’s disc light on thesame plane. The data of loss calculated by applying the

Ž .Fig. 2. Direct normal incidence and diffuse solar irradiationsŽ .measured by the radiometric station Method A in the course of

the outdoor campaign. A selected number of points refer to ‘clearsky’ conditions.

two methods are very close. Only a little difference wasŽ .found on the final polarization loss see Table 4 . In

Section 4 we report the results obtained by applyingmethod A. Some of the data obtained by applying methodB are shown in parentheses.

Further errors were derived under generic sky condi-tions, due to a different shadowing, by clouds, of theradiometric station and the module solar tracker. Thesefew errors, when of particular relevance, were manuallycorrected on the data file.

2.2. The program code

A program code was developed to calculate the fourŽ . Ž .losses relative to STC: a reflection of light, b spectral

Ž . Ž .effects, c low irradiance level and d temperature. Each

w xFig. 3. Clearness ´ of the sky, calculated following Ref. 8 ,during the outdoor campaign. A selected number of points refer to‘clear sky’ conditions.


of these four loss models is described in Section 3. Theprogram code requires four relevant parameters: the equiv-alent refractive index of the module, n , the relativeeq

Ž X . Ž X .spectral coefficients for the direct k and diffuse kdir diff

sunlight components, and the temperature coefficient atŽ y1.maximum power, g 8C . No parameters are required in

the low irradiance level loss model. The four parameterscan be fixed, if known from the literature or calculated ormeasured. They can also be varied in a reasonable intervalif optimized values are required which minimize the scat-ter between calculated and experimental data. The inputdata to the program code are the time, the radiometricvalues for the direct, diffuse and global radiations on thehorizontal plane, the global radiation on the module plane,the module temperature and its relevant electrical parame-

Ž .ters V , I , V , I . Finally, the four parameters used inoc sc m m

three of the four models of loss were also included in theinput data of the program code. Output data were theinstant and cumulative loss for each loss mechanism, theinstant power and efficiency.

The procedure used to calculate the four losses isbriefly outlined here. The starting nominal efficiency, hSTC

sh , is progressively modified by the computer program0w xaccording to each model of loss in the following order 3 :

h sh PR is the efficiency after calculation of the1 0 R

reflection losses;h sh PR is the efficiency after calculation of the2 1 S

spectral effects;h sh PR is the efficiency after calculation of the3 2 G

low irradiance level effects;Ž .h sh PR sh PR PR PR PR is the efficiency4 3 T 0 R S G T

after calculation of the temperature effects.If G is the total measured irradiance incident on theinc

module plane, we have:nominal power: P sh G ;STC STC inc

experimental power: P sh G ;exp RRC inc

final calculated power: P sh G .4 4 inc

3. The loss models

3.1. Reflection and absorption at the front coÕer of themodule

The loss of light at normal incidence, due to reflectionand absorption at the front cover of the module, is alreadypresent in the nominal efficiency, h . In fact, this effi-STC

ciency is derived after exposing the module, in a solarsimulator, to a non-polarized, parallel beam of light withAM1.5G spectrum, incident perpendicularly on the surfaceof the module. A further loss is observed when the moduleis installed because of the angular distribution of theincident light. To calculate the losses for reflectionrab-sorption of light at the front cover of the module, it isnecessary to have an optical model of the module and amodel for the integration of all light contributions from the

w xsky hemisphere. Other authors 9 have pointed out the factthat the simple airrglass interface model is adequate todescribe the reflection losses relative to STC for crys-talline-Si modules. We followed a similar approach, withthe difference that we modeled the module as a homoge-neous dielectric with equivalent refractive index n . Theeq

Ž . Ž .relative reflection loss is then described by the T u rT 08

factor which is obtained by applying the Fresnel equationw x10 :

T u s1yR u s0.5n cos u rcos u t 2 qt 2 ,Ž . Ž . Ž . Ž .eq t i p s

1Ž .

Ž . w Ž . Ž .xwhere: t s 2 sinu cosu r sin u qu cos u yu , tp t i i t i t sŽ . Ž .s 2 sinu cosu rsin u qu ; u is the angle of the inci-t i i t i

Ž .dent beam, u the angle of the transmitted beam, T u thetŽ .transmittance of the airrdielectric interface, R u the re-

flectance of the airrdielectric interface.Ž .T u is the transmittance of a collimated light beam

incident on the surface of the module at the angle u . Thetotal transmitted irradiance from the sky hemisphere, withrespect to that transmitted at normal incidence, was calcu-

w xlated by a numerical method 6 . An isotropic model wasadopted for the calculation of the transmission of thediffuse light.

3.2. Spectral effects

w xThe reference spectrum at STC is AM1.5G 11 . Thespectrum of natural sunlight incident on the module isgenerally different, as it depends on a great variety offactors, like time of year, sun elevation, meteorologicalconditions and tilt of the module. The spectrum of the lightaffects the photocurrent in accordance with the spectralresponse of the module. We can express the photocurrentI and, at first approximation, the short circuit current I ,ph sc

as linear with the irradiation level:

I f I sk G , 2Ž .sc ph s abs Žs.

Ž .where the quantity k ArW depends, for a given mod-sŽ .ule, on the spectrum of light the s suffix and Gabs

Ž 2. Ž .Wrm is the absorbed irradiance. In Eq. 2 the irradi-ance G is defined in the spectral range above 305 nm. Inthis range, the irradiance of the reference AM1.5G spec-trum amounts to 1000 Wrm2. The tabulated data give998.8 Wrm2 in the 305–4045 nm interval and f988Wrm2 in the 305–2800 nm interval. The measured spec-tra are generally normalized to 1000 Wrm2 after integra-tion from 305 nm to infinity. This is a common practicewhen measuring the irradiances by pyranometers, whichhave a flat response up to about 2800 nm and can collect99% of the reference spectrum. At 08 tilt angle only thedirect and diffuse components of sunlight are incident onthe module and the current per unit area can be written as

I sk G qk G . 3Ž .sc dir abs Ždir . diff abs Ždiff .


We now introduce the ‘relative’ kX coefficients, asfollows:

I sk k rk G q k rk GŽ . Ž .sc STC dir STC abs Ždir . diff STC abs Ždiff .

sk kX G qkX G , 4Ž .Ž .STC dir abs Ždir . diff abs Ždiff .

where the coefficient k can be easily obtained from theSTC

datasheet of the module:

k s I rG s I r G T 08Ž .Ž .STC scŽSTC . abs ŽSTC . sc ŽSTC . ŽSTC .

s I r 1000T 08 , 5Ž . Ž .Ž .scŽSTC .

Ž .where T 08 is the transmittance of the front cover of theŽ . X Xmodule and can be derived from Eq. 1 . The k and kdir diff

coefficients can be calculated if the direct and diffuseŽ . Ž .spectral irradiances, E l and E l , are known,dir diff

Ž .together with the external spectral response SR l of theext

module:`

SR l E l dlŽ . Ž .H ext incŽdir .kdir 305Xk s sdir `kSTC E l dlŽ .H incŽdir .305

=

`

E l dlŽ .H incŽSTC .305 , 6Ž .

`

SR l E l dlŽ . Ž .H ext incŽSTC .305

`

SR l E l dlŽ . Ž .H ext incŽdiff .kdiff 305Xk s sdiff `kSTC E l dlŽ .H incŽdiff .305

=

`

E l dlŽ .H incŽSTC .305 . 7Ž .

`


Ž . Ž .If E l and E l are normalized to 1000incŽdir. incŽdiff.2 Ž . Ž .Wrm , Eqs. 6 and 7 become:

`

SR l E l dlŽ . Ž .H ext incŽdir .305Xk sdir `


lgSR l E l dlŽ . Ž .H ext incŽdir .

305s , 6aŽ .lg


`

SR l E l dlŽ . Ž .H ext incŽdiff .305Xk sdiff `


lgSR l E l dlŽ . Ž .H ext incŽdiff .

305s . 7aŽ .lg


Table 3Coefficients kX calculated for different module technologies anddifferent spectra

Module AM1.5G AM1.5Dir AM1.5DiffX X XŽ . Ž . Ž .k k kSTC dir diff

BP585 1.0 0.98 1.07w xmono-Si 12 1.0 0.99 1.04

w xpoly-Si 13 1.0 0.98 1.05w xpoly-Si 14 1.0 0.99 1.02

The reported references are for the spectral response data.

Ž . Ž .In Eqs. 6a and 7a the integrals extend effectively up toŽl , the gap wavelength of the semiconductor l s1200g g

. Ž . Xnm for c-Si , as the SR l is zero for l)l . The kext g

coefficient describes the spectral effect associated with theparticular normalized spectrum, direct or diffuse. It con-tains not only the information about the spectral mismatchbetween the spectrum of light and module spectral re-

Ž .sponse that is the ‘real’ spectral effect but also theŽ .information about the irradiance in the 305–l 1200 nmg

interval, with respect to the reference. Table 3 gives thekX , kX coefficients, calculated with 50 nm resolution,dir diff

for modules of different technology at the reference AM1.5spectrum. The AM1.5Diff spectrum is obtained by sub-tracting the tabulated AM1.5Dir spectrum from the tabu-lated AM1.5G spectrum. The AM1.5 reference spectrum isa good approximation of our average experimental spec-trum. We have, indeed, found an energetically averaged airmass value of 1.57, which is quite close to the 1.5 refer-ence.

3.3. Low irradiance leÕel effects

The reduction of the irradiance level below 1000 Wrm2

generally results in a decrease of the efficiency dependingw xon the module technology 1 . To calculate the low irradi-

ance level loss, we need an equation for the I–V curve ofthe module. For this purpose, we have used a simple,single exponential equation containing only two empiricalparameters, I and A :0 0

I V s I y I exp Vr A V y1 . 8Ž . Ž .Ž .Ž .ph 0 0 T

Ž .A direct consequence of Eq. 8 is that I s I . The Isc ph 0Ž .and A parameters can be derived by writing Eq. 8 for0

the Is0 and Is I conditions:m

0s I y I exp V r A V y1 , 8aŽ .Ž .Ž .sc 0 oc 0 T

I s I y I exp V r A V y1 , 8bŽ .Ž .Ž .m sc 0 m 0 T

where the I , V , I and V quantities at Gs1000sc oc m m

Wrm2 of irradiance can be obtained from the moduleŽ .datasheet see Table 1 or from solar simulator measure-


Fig. 4. Performance ratio, PR , relative to the irradiance level,G

calculated by using the datasheet of the mono-Si module.

Ž .ments see Table 2 . We finally have the following expres-sions for the I and A parameters:0 0

A s 1rV V yV rln 1y I rI , 9Ž .Ž .Ž . Ž .0 T m oc m sc

Ž .V r V yVoc m ocI s I r 1y I rI y1 . 10Ž .Ž .0 sc m sc

For our mono-Si module we obtain: I s8.94=10y7;0

A s55.35. The performance ratio, PR , relative to the0 Gw xlow irradiance level loss, is defined as in Ref. 3 :

PR sh G rh STCŽ . Ž .G

s P G rP STC =1000rGw xŽ . Ž .m m

s I G V G FF Gw x� Ž . Ž . Ž .sc oc

r I STC V STC FF STC =1000rG.w x 4Ž . Ž . Ž .sc oc

11Ž .

Assuming a linear dependence between the short circuitŽ . Ž .current I and irradiance G :sc

I G sS kG , 12Ž . Ž .sc mod

Ž .Eq. 11 finally becomes:

PR s V G FF G r V STC FF STC . 11aw x w xŽ . Ž . Ž . Ž . Ž .G oc oc

Fig. 4 shows the performance ratio, PR , calculated forGŽ .the tested mono-Si module. By using Eq. 8 , the I and0

A parameters can be simply derived from the datasheet of0

the module and no complicated programs for the fitting ofthe experimental I–V curve are required. Even simple, Eq.Ž .8 is suitable for deriving the low irradiance level loss at a

Ž .good approximation f1% . This is shown in AppendixA.

3.4. Temperature effects

Deviations of the module temperature from the refer-ence 258C value determine the linear variation of thesupplied power, and then of the efficiency, by the factor:

P T rP 25 s 1ygDT , 13Ž . Ž . Ž . Ž .Ž . Ž . y3 Ž y1. w xwhere DTsT 8C y25; gs 4–6 =10 8C 1,15 .

w xFrom Ref. 3 we derive an average value of g for c-Simodules: gs5.3=10y3

8Cy1. The performance ratio fortemperature, is given by

PR s1ygDT . 13aŽ .T

3.5. Polarization effects

The polarization of the sky radiance was studied byw xFrisch 16 , who reported polarization values for a specific

w xclear sky condition. From these values, Krauter 17 de-rived an extra reflection loss of about 5% with respect toirradiation conditions of unpolarized light. Unfortunatelythe polarization of light in the field is not known and no

w xsimple model is available to determine it 9 .

4. Results and discussion

If the n , kX , kX and g parameters are automati-eq dir diff

cally optimized by the computer program in order to givethe minimum scatter between the calculated and the exper-imental loss data, we obtain values for g which are too

Ž y3 y1.high )7=10 8C with respect to the literature dataw x15 . This could be explained if we had neglected a lossmechanism which is more effective under conditions whichdetermine higher module temperatures. To investigate thiseffect, we have assigned realistic values to the four param-eters and then analyzed the resulting scatter of the data.The starting values for the parameters were: n s1.5,eq

typical refractive index of glass; kX s0.98, calculated bydirŽ . X Žus see Table 3 ; k s1.07, calculated by us see Tablediff

. y3 y1 w x3 ; gs4.8=10 8C , taken from the literature 15 andŽconfirmed by measurements at our solar simulator gs4.7

Ž . y3 y1."0.3 =10 8C .By using these parameters in the computer program, we

obtained a final calculated, cumulative, energy loss aboutŽ .2% 1% lower than that obtained experimentally. To

verify if this difference could be attributed to a polariza-tion effect, we analyzed the instantaneous loss difference,

Ž . Žcalled D in % , under clear sky conditions those consid-w x w x.ered by Frisch 16 and Krauter 17 , as a function of the

w xsky clearness. Perez 8,18 defines the sky clearness ´ , asthe quantity which describes the transition from a totallyovercast sky to a low turbidity clear sky. The sky clearness´ is given by

3 3´s D q I rD qk z r 1qk z , 14w x Ž .Ž .h h

where D is the horizontal diffuse irradiance; I the normalh

incidence direct irradiance; ks1.041; z the solar zenithŽ .angle in radians .

Fig. 5 shows D as a function of ´ . The experimentalvalues of ´ range between 2 and 9.5. We can see that thepoints are roughly linearly correlated and the values of loss

w xrange between 0 and 5%, as foreseen by Krauter 17,19when the incident radiation is polarized. Sjerps-Koomen


Ž .Fig. 5. The difference D % between experimental and calculatedinstantaneous loss is shown as a function of the clearness ´ . Fourlosses have been considered in the calculation: reflection, spectral,low irradiance level and temperature.

w x9 hypothesized a model of polarization loss in PV mod-ules, where the loss is approximated as an increasing linearfunction of the clearness index K , defined as:t

K sG rG , 15Ž .t h 0

where G is the global horizontal irradiance and G is theh 0Ž 2.extra-terrestrial irradiance (1350 Wrm . The loss

Ž .should vary between 0% for overcast skies K F0.35tŽ . Ž .and 5% for clear skies K G0.75 . Our data of D % aret

shown in Fig. 6 as a function of K and correspond, as int

Fig. 5, to clear sky conditions. As can be seen, the quantityŽ .D % precisely follows the Sjerps-Koomen model: it is

zero on average at K F0.35, increases linearly at highert

K values and reaches exactly 5% at the maximum valuest

of K .tThese results show that, for low clearness skies, that is

under conditions of negligible polarization of light, thequantity D is very low, whereas it reaches the same valueŽ .5% of polarization loss obtained by Krauter when the sky

Ž .Fig. 6. The difference D % between experimental and calculatedinstantaneous loss is shown as a function of the clearness indexK . The same four losses as in Fig. 5 have been considered.t

Fig. 7. Cumulative loss, at the end of the test campaign, for eachŽ . Ž . Ž .of the five mechanisms: 1 spectral, 2 polarization, 3 low

Ž . Ž .irradiance level, 4 reflection and 5 temperature.

light is polarized under a particular clear sky condition.Further, our quantity D exactly corresponds to the polariza-

w xtion loss modeled by Sjerps-Koomen 9 . We deduce thatthe quantity D describes the loss due to polarization of thesky light. At the same time, our results validate the modelproposed by Sjerps-Koomen. By including polarization asthe fifth loss mechanism, we obtained the final cumulativelosses, at the end of the measurement campaign, as re-ported in the diagram of Fig. 7. On a total relative loss of

Ž .about 15% 14% , we observe a 3% loss by reflection,w xwhich is in agreement with the literature data 1,9 . The

w xrelative spectral effect remains very low, as expected 1 .The low irradiance level loss is about 3%, quite low,because the module has been exposed to an average irradi-

2 Ž .ation of 550 Wrm see Fig. 4 . The temperature loss, ofŽ .about 7%, is the most important one ;50% of the total

and corresponds to an energetically averaged module tem-perature of about 408C. The polarization loss results to

Ž .about 2% 1% . This loss, however, cannot be quantifiedvery precisely because it depends on the precision of thefour loss models and of the radiation measurements. Moreprecise loss models than those used by us, in particular thatof the low light level effect, and more precise measure-ments of solar radiation, besides the investigation of agreater set of experimental data, could improve the accu-racy of our model and the polarization loss evaluation.This could be the subject for future work.

We have investigated the effect of n on the reflectioneq

loss. This loss is fairly insensitive to n in the 1.5–2.0eqŽ .interval see Fig. 8 . This means that the optical behaviour

of the module, in terms of reflection relative to the normalincidence, can be modeled in an approximately equivalentway with n values in the 1.5–2.0 interval, when theeq

simple airrdielectric model is adopted. This is a conse-Ž . Ž .quence of the fact that the T u rT 08 curve, which

determines the relative reflection loss, see Section 3.1,remains constant for n values between 1.5 and 2.0 ateq

Ž .different incident angles u see Fig. 9 . A similar be-w xhaviour was recognized by Sjerps-Koomen 9 who found,


Fig. 8. Final reflection loss, calculated for both generic and clearsky conditions, as a function of the equivalent refractive index neq

of the module. The loss remains quite constant near the maximumof the curve.

by calculation, the same relative reflection loss for theŽ .airrglass model glass refractive index of 1.5 and for a

three-slab model. The three-slab system, which approxi-mates well to the module’s cover, is an optical model,

Ž .comprising a glass sheet, an encapsulation layer EVAŽ . w xand an anti-reflection AR coating 9 . That behaviour can

be explained by the equivalence, as far as conditionsrelative to STC are considered, of the three-slab model toan airrdielectric interface, with the dielectric taking neq

values in the 1.5–2.0 interval. However, only equivalentrefractive indices near 2.0 can justify reflections at normal

w xincidence of unpolarized light as high as 12% 19 . Using,in the computer program, the following input parameters:

n s2.0; kX s0.98;eq dir

kX s1.07; gs4.8=10y38Cy1

diff

we obtained results of loss as reported in Table 4. TheŽ .results obtained by applying method B see Section 2 are

shown in Table 4 in parentheses. We see that the spectralloss is very small and this confirms the fact that the

Fig. 9. Relative transmittance curves of an airrdielectric interface,relative to the normal incidence, as function of the incidenceangle, at different refractive indices of the dielectric.

Table 4Ž .Final results of loss method A

Loss Generic sky Clear sky

Ž . Ž . Ž . Ž .Abs % Rel % Abs % Rel %

Ž . Ž .Spectral y0.3 y0.2 y2 0.7 0.8 5Ž . Ž .Polarization 2.1 0.6 14 2.1 0.6 14Ž . Ž .Low irradiance 3.0 3.1 20 2.7 2.8 18Ž . Ž .Reflection 3.4 3.4 22 3.3 3.2 23Ž . Ž .Temperature 7.0 7.0 46 5.8 5.8 40

Ž . Ž .Total 15.2 13.9 100 14.6 13.2 100

In parentheses are the results relative to the method B used forradiation measurements.

energetically averaged AM value is close to the reference1.5. The spectral loss increases moving from ‘generic sky’to ‘clear sky’ conditions. This is clear considering that thedirect component of the sunlight increases with respect tothe diffuse component moving in the same way and thatthe spectral coefficient kX is lower than kX . In Sectiondir diff

3.2 it is shown that the kX coefficient of a particular lightcomponent defines the spectral gain associated with thatcomponent. The temperature loss is higher under genericsky than under clear sky conditions. This is an effect of thedifferent solar irradiation and ambient temperature be-tween the two situations. The polarization loss, of about2%, accounts for only 14% of the total energetic loss. Thissmall effect is due to the fact that, according to Krauterw x20 , both direct radiation and radiation reflected by cloudsare unpolarized. The polarization effect, thus, is producedonly by the diffuse component of the solar radiation,which, see Fig. 2, shows irradiance values around 100Wrm2, that is only 20% with respect to an average totalradiation of 550 Wrm2. The precision of the polarizationloss evaluation directly depends on the precision of theSTC electrical parameters of the module. In fact, the use ofthe datasheet STC values, which refer just to the class ofBP585 modules, instead of the values obtained directly onthe specific tested module, should enhance the polarizationloss to about 4%, introducing a relative error of about50%. Therefore, the precise evaluation of the energeticlosses in PV modules requires the knowledge of the pre-cise STC electrical parameters of the tested module. Thesecan be obtained by the datasheet of the module if theyrefer to the specific module itself and not just to the classto which it belongs.

The losses obtained by applying method B are practi-Ž .cally the same as those of method A see Table 4 with the

exception of the polarization loss, which now results toabout 1% instead of 2%. Also in this case, as for the STCparameters, the errors on the radiometric measurementsdirectly transfer to the polarization loss. This is a conse-quence of the fact that, in our model procedure, thepolarization loss is not modeled independently, like the


Žother four reflection, spectrum, low irradiance level and.temperature , but just evaluated as the difference between

that predicted by the model, applied to four losses, and theexperiment. In the future, using a procedure for indepen-dently modelling the five losses will certainly give moreprecise values for them, because an optimization of theresults by the computer will be possible in that case.

The dependence of the four modeled losses with re-spect to the air mass, under clear sky conditions, is shownin Fig. 10. Each loss shows a peculiar behaviour withrespect to AM. The reflection loss increases monotonicallywith increasing AM because the direct light, which bringsmost part of the irradiance under clear sky conditions, hasan increased incidence angle on the module’s cover at

Ž Ž ..higher AM values and thus is more reflected see Eq. 1 .The spectral loss decreases a little with AM and at AM)

Ž .2.5 becomes negative spectral gain because the diffuselight component, which produces a higher current with

Ž X .respect to the direct one has a higher k coefficient ,becomes increasingly more significant at higher AM val-ues. The low irradiance level loss increases with AM,because a higher AM value corresponds to a lower irradia-tion on the module, due to higher atmospheric absorption,

Žand consequently a lower performance ratio PR see Fig.G.4 . Finally, the temperature loss sharply decreases with

increasing AM values because at lower irradiations themodule temperature decreases. At high AM values, atemperature gain is observed which corresponds to a mod-ule temperature lower than 258C. The scatter of data oftemperature loss is due to different conditions of ambient

Ž .temperature. The highest losses are observed at low 1–1.5AM values due to high temperatures reached under these

Ž .conditions, and at high 2.5–3.0 AM values, due to highreflection and low irradiance level under these conditions.Finally, the dependence of the polarization loss on the airmass is shown in Fig. 11. This loss decreases with increas-ing AM values in a similar way as it decreases with

Ž .decreasing K values see Fig. 6 .t

Ž .Fig. 10. Calculated loss % , for the four modeled loss mecha-nisms, as function of the air mass.

Ž .Fig. 11. Polarization loss % , corresponding to the quantity D, asa function of the air mass.

The operating efficiency, h , under generic sky con-RRC

ditions, is shown in Fig. 12 as a function of AM. It isgenerally lower than the nominal efficiency, h s13.2%,STC

and reaches a maximum of 11.5% at AMf1.5. A fewpoints with h )h can be found at low AM valuesRRC STCŽ .1–1.5 , but these are due to discrepancies between mea-sured radiation and effective radiation incident on the

Ž .module, and at high AM values )5 due to real condi-tions with module temperatures lower than 258C. Thetemperature mechanism is, in fact, the one which can givea gain in efficiency, relative to STC, when the moduletemperature is lower than 258C. The other mechanismwhich can give relative gain is the spectral one, but, as wehave seen, it produces little effects. Among the opticallosses, the reflection loss is the only one which, in prac-tice, can be reduced. These results show that, under theactual solar irradiation conditions, only a maximum of3–4% of energy is lost by reflection, relative to normalincidence. Calculated yearly reflection losses by other

w xauthors 9 , for similar latitudes and for horizontal mod-

Fig. 12. Experimental, or operating, efficiency, h , of theRRC

module as a function of the air mass. The maximum efficiency isreached at AMf1.5. The nominal efficiency, h , is indicatedSTC

for comparison.


ules, are only just 4–5%. This, then, is the total energypotentially savable by a technological improvement in themodule manufacturing process aimed at a better collectionof non-perpendicular light. This situation could changesignificantly, if different irradiation conditions were expe-rienced, particularly at higher contents of diffuse lightŽ . w x w xnorthern Europe 5 or with vertically tilted modules 9 .Finally, we observe that the losses which depend directlyon the ‘state’ of the incident light, i.e. its angular distribu-tion, intensity, spectrum and polarization, amount to about

Ž . Ž .8% 7% absolute 50% relative .

5. Conclusions

We have outlined here a procedure for the calculationof the energetic losses, relative to the standard conditionsof testing, STC, for crystalline-Si modules operating underoutdoor conditions. We have applied four loss models to aset of measurements taken on a mono-Si module of recenttechnology, in June at 418N latitude and 08 tilt angle. Wehave recognized the presence of a further loss mechanism:the polarization of the incident light. Our data of loss, infact, are in agreement with the predictions of a model of

w xpolarization loss hypothesized by other authors 9 . Analy-sis of the relative reflection losses have shown that themodule can be modeled as a dielectric with refractiveindex between 1.5 and 2.0. A final reduction of powerŽ .efficiency of about 15% was found due to the contribu-tion of all the losses. The ‘optical’ losses, that are thosestrictly related to the ‘state’ of the incident light, likereflection, spectral effects, low irradiance level and polar-

Ž .ization losses, amount to about 8% absolute 50% relative .Of these, 3% is due to the low level of the irradiation, 2%to the polarization of the incident light and 3% to thereflectionrabsorption of the incident light on the frontcover of the module. The spectral effects are negligibleŽ .less than 1% . A 7% loss is due to the heating of themodule, as an indirect effect of the solar irradiation.

Regarding the accuracy of our individual loss models,we can draw the following conclusions.

Ž .i The reflection loss model, based on the use of theFresnel equations, applied to a simple airrdielectric inter-face, is simple but very accurate, as recognized also by

w xother authors 9,21 . It does not require any improvement.Ž .ii The spectral loss model used in the present work is

very simple and based on the use of the standard AM1.5spectra. It requires to be improved to make it suitable todescribe all the variations in the spectrum of the skyradiance, resulting from the different weather conditionsexperienced by the module in the field.

Ž .iii The model of the low irradiance level loss adoptedin the present work is very simple and has shown anaccuracy of about 1% or less. It requires, to be applied,only the knowledge of the STC electrical parameters of themodule, reported on its datasheet. An improvement of this

model is necessary, and requires the application of DEMmodels for the description of the I–V curve.

Ž .iv The model of temperature loss simply requires theknowledge of the temperature coefficient at the maximumpower. As the temperature loss in c-Si modules is relevantw x15 , however, it must be measured very accurately, if notgiven by the module manufacturer.

Ž .v A simple model for the light polarization loss is notyet available. However, our results, based on the compari-son between calculated and experimental data, seem toconfirm, and then validate, the model proposed by Sjerps-

w xKoomen 9 for the description of this loss. We suggesthere to apply and test, in future works on energetic lossesin PV modules, the Sjerps-Koomen model for polarizationloss.

Finally, the accuracy of the whole proposed model ofenergetic loss depends on the accuracy of the STC electri-cal parameters used and on the accuracy of the solarirradiance measurements.

Acknowledgements

The authors gratefully acknowledge Riccardo SchioppoŽ .and Michele Zingarelli ENEA, Manfredonia for the valu-

able support given in performing both the outdoor mea-surements and the data collection and transfer to thePortici laboratory. They also acknowledge Haruna Yakubufor the revision of the English text. One of the authors isparticularly indebted to Gaspare Noviello for all the infor-mation received about the outdoor testing of PV modulesduring his work at the ENEA Delphos site of ManfredoniaŽ .FG .

Appendix A. Accuracy of the proposed model for thecalculation of the low irradiance level loss

To know the accuracy of the proposed model for thecalculation of the low irradiance level losses, we have

Ž .Fig. 13. Comparison between our model SEM and the DEMmodel for the calculation of the performance ratio PR as func-G

tion of the irradiance level.


Ž .compared our model here named SEM , containing onlyŽ Ž ..two parameters see Eq. 8 , with the double exponential

Ž . w xmodel DEM containing five parameters 22 . The data forw x Ž .the comparison were taken from Ref. 22 cell A_C3 .

The performance ratio PR was calculated by both modelsG

at different irradiance levels from 100 to 1000 Wrm2. Theresults are shown in Fig. 13. The two PR curves show aG

similar behaviour with differences within about 1.5%.Considering that the solar radiation is distributed on all therange of irradiance values, the average error on PR isG

below 1%. We can conclude that our simplified model offitting of the I–V curve is sufficiently accurate to limit theerrors in the calculation of the low irradiance level lossesto less than 1%.

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Effects of solar irradiation conditions on the outdoor performance of photovoltaic modules

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