Spectral Irradiance Influence on Solar Cells Efficiency

energies

Article Spectral Irradiance Inﬂuence on Solar Cells Eﬃciency

David Leitão 1, João Paulo N. Torres 2,3 and João F. P. Fernandes 4,* 1 Instituto Superior Técnico, Universidade de Lisboa, 1649-004 Lisboa, Portugal; [email protected] 2 Instituto de Telecomunicações, Instituto Superior Técnico, Universidade de Lisboa, 1649-004 Lisboa, Portugal; [email protected] 3 Academia Militar, Avenida Conde Castro Guimarães, 2720-113 Amadora, Portugal 4 IDMEC, Instituto Superior Técnico, Universidade de Lisboa, 1649-004 Lisboa, Portugal * Correspondence: [email protected]

Received: 17 December 2019; Accepted: 31 August 2020; Published: 24 September 2020

Abstract: This paper investigates the influence of the spectral irradiance variation and the spectral response (SR) on the production of energy by photovoltaic cells. To determine the impact of SR and spectral irradiance on m-Si and perovskite cells, experimental tests were conducted outdoors, used optical filters to select different zones of the spectrum. For the computational simulations of the different photovoltaic modules, when subjected to a certain spectral irradiance, a model with spectral factor (SF) was implemented. The SF model accurately simulated the experiments performed for the high-pass filters. The highest relative errors for certain irradiation bands occurred due to the input variables used in the model, which did not fully describe the reality of the experiments performed. The effect of the SR and the spectral irradiance for each of them were observed through the simulations for the m-Si, a-Si, CdTe, and copper indium selenide (CIS) modules. The CIS technology presented a better overall result in the near infrared zone, producing about half of the energy produced by the CdTe technology in the visible zone. The SF, spectral incompatibility factor (MM), and spectral effective responsivity (SEF) parameters were verified to be important for studying the photovoltaic energy production.

Keywords: electromagnetic spectrum; SEF; SF; MM; spectral irradiance; SR

1. Introduction The quest to satisfy the demand for energy is one of the main causes of global warming which is increasing the amount of gases in the atmosphere [1], and therefore causing a significant environmental impact, unbalancing the ecosystems, and affecting human activity in their lifestyle and economically [2]. With this negative impact, global policies have been developed to minimize environmental impacts, and one of most immediate measures is the use of renewable energy sources [3]. The International Energy Agency (IEA) forecasts that renewable energy will account for two thirds of global investment in power plants by 2040. It is also predicted that solar energy will be the one with the greatest growth in electricity production with 74 GW by 2040. Recent studies have concluded that the variation of the spectral irradiance Figure1 as well as the spectral response (SR) Figure2 are important aspects in the performance of the photovoltaic devices [4]. Figure1 also shows a representation of the blackbody spectrum at 5800 K which is an approximation of the sun spectrum radiation. The Earth’s atmosphere behaves like a protective filter against the action of the harmful extraterrestrial radiation that arrives at our planet and like a thermal regulator of the Earth, allowing conditions necessary to life. The radiation that passes through the atmosphere interacts with the atmospheric components, making the terrestrial spectrum different from the extraterrestrial spectrum (Figure1). The intensity of these processes depends on the distance traveled by the radiation in the atmosphere. Under these conditions, ASTM, with the aim of standardizing a single reference

Energies 2020, 13, 5017; doi:10.3390/en13195017 www.mdpi.com/journal/energies Energies 2020, 13, x FOR PEER REVIEW 2 of 17

Energiesspectrum2020 , 13(Figure, 5017 1). The intensity of these processes depends on the distance traveled by2 of the 18 radiation in the atmosphere. Under these conditions, ASTM, with the aim of standardizing a single reference solar spectrum, established a standard spectrum. The currently adopted spectrum is solar spectrum, established a standard spectrum. The currently adopted spectrum is indicated in the indicated in the norm ASTM G173-03 [5,6]. norm ASTM G173-03 [5,6]. Another general conclusion is that the spectral impact depends on the location in terms of Another general conclusion is that the spectral impact depends on the location in terms of latitude, latitude, climate, rural or urban environment, among others [7] Despite the advances made in the climate, rural or urban environment, among others [7] Despite the advances made in the study of the study of the influence of irradiance on photovoltaic energy production [8], models that consider the influence of irradiance on photovoltaic energy production [8], models that consider the influence of influence of spectral effects on the field are not readily available, contrary to what happens for the spectral effects on the field are not readily available, contrary to what happens for the influence of influence of temperature and irradiance [9]. temperature and irradiance [9]. This paper focuses on the study of the impact of spectral irradiance on different photovoltaic This paper focuses on the study of the impact of spectral irradiance on different photovoltaic cells, as well as the influence of the SR on its photovoltaic energy production. The study is done for cells, as well as the influence of the SR on its photovoltaic energy production. The study is done m-Si, a-Si, CdTe, and copper indium selenide (CIS). This has been an important research topic. In for m-Si, a-Si, CdTe, and copper indium selenide (CIS). This has been an important research topic. [10], the kesterite-structured Cu2ZnSnSe4(CZTSe) material has been studied for photovoltaic In [10], the kesterite-structured Cu ZnSnSe (CZTSe) material has been studied for photovoltaic applications, considering its response2 to different4 irradiation wavelengths. In [11], the influence of applications, considering its response to different irradiation wavelengths. In [11], the influence of ultra-high irradiance levels on multi-junction solar cells were tested, under different temperatures, ultra-high irradiance levels on multi-junction solar cells were tested, under different temperatures, to study the impact on its efficiency, considering its spectral response. In [12] the performance of an to study the impact on its efficiency, considering its spectral response. In [12] the performance of Al0.3Ga0.7As/InP/Ge multijunction solar cell was analyzed under different spectral irradiance and an Al Ga As/InP/Ge multijunction solar cell was analyzed under different spectral irradiance and temperatures.0.3 0.7 These studies show the importance of the spectral irradiance impact on the operation temperatures. These studies show the importance of the spectral irradiance impact on the operation of of different photovoltaic cells. different photovoltaic cells. To accomplish with the impact study of the spectral irradiance on m-Si, a-Si, CdTe, and copper To accomplish with the impact study of the spectral irradiance on m-Si, a-Si, CdTe, and copper indium selenide (CIS), first a mathematical model is developed. It is intended to validate a indium selenide (CIS), first a mathematical model is developed. It is intended to validate a mathematical mathematical model that allows the analysis of the impact of spectral irradiance and SR for a model that allows the analysis of the impact of spectral irradiance and SR for a photovoltaic cell photovoltaic cell exposed to a given spectral irradiance. To validate the spectral factor, SF model (a exposed to a given spectral irradiance. To validate the spectral factor, SF model (a parameter that quantifyparameter the that spectral quantify gains orthe losses spectral that gains a PV moduleor losses can that experience a PV module under can the actualexperience spectrum under as comparedthe actual with spectrum the standard as compar AM 1.5-G),ed awith comparison the standard of the experimental AM 1.5-G), tests a comparison is performed of with the modelexperimental simulations tests foris performed the m-Si and with organic model with simulations perovskite for cells. the m-Si After and the validationorganic with of theperovskite model, simulationscells. After werethe validation performed of for the photovoltaic model, simulati modulesons were of m-Si, performed a-Si, CdTe, for andphotovoltaic copper indium modules selenide of m- (CIS).Si, a-Si, The CdTe, novelty and of copper this paper indium is the selenide validation (CIS). of The the theoreticalnovelty of this model paper with is experimentalthe validation results of the usingtheoretical several model spectral with filters. experimental results using several spectral filters. WeWe also also intend intend to to confirmconfirm thethe hypothesishypothesis ofof producingproducing photovoltaicphotovoltaic energyenergy withoutwithout visiblevisible light,light, makingmaking useuse of of infrared infrared light. light.

2.5 ) -1

nm 2 -2

1.5

0.5

Spectral Irradiance (W m Spectral 0 500 1000 1500 2000 2500 3000 3500 4000 Wavelength (nm)

Figure 1. Plot of the direct normal spectral irradiance, AM1.5 (___); global total spectral irradiance on a ______37Figure◦ tilted 1. sun-facingPlot of the surface,direct normal AM1.5 spectral ( ); the irradiance, extraterrestrial AM1.5 spectrum, (___); global AM0 total ( spectral); and the irradiance blackbody on irradiation spectrum at 5500 K (___)[10,11]. a 37° tilted sun-facing surface, AM1.5 (___); the extraterrestrial spectrum, AM0 (___); and the blackbody irradiation spectrum at 5500 K (___) [10,11].

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FigureFigure 2. 2. SpectralSpectral response response for for various various technologies technologies [6]. [6].

2.2. Solar Solar and and Photovoltaic Photovoltaic Energy Energy TheThe sun sun is is mainly mainly responsible responsible for for the the available available ener energygy on on Earth, Earth, giving giving rise rise to to multiple multiple resources resources availableavailable in in the the Earth Earth such such as as hydropower, hydropower, wind wind energy, energy, photovoltaic photovoltaic energy, energy, and even even the the energy energy present in fossil fuels from organic life previously nourished by thethe sun.sun. TheThe solar solar spectrum spectrum consists consists of of radiation radiation with with diff differenterent levels levels of of energy, energy, th thisis spectrum spectrum is is divided divided intointo several several regions regions as as follows: follows: 𝛾γ rays,rays, X X rays, rays, ultraviolet ultraviolet (UV), (UV), visible; visible; infrared infrared (IR), (IR), microwave; microwave; radioradio waves, waves, and and long long waves [13]. [13]. AA photovoltaic cell cell is is a a device device capable capable of of conver convertt light light energy energy that that comes comes from from any any light light source source directlydirectly intointo electricity,electricity, throughout throughout a process a process denominated denominated photovoltaic photovoltaic effect. effect. In other In words,other words, a current a currentis generated is generated due to the due incidence to the ofincidence photons, of which photons, are light which beams are and light packages beams ofand electromagnetic packages of electromagneticradiation or energy radiation that can or energy be absorbed that can by be a solarabsorbed cell [by14 ].a solar When cell the [14]. incoming When the light incoming has a proper light haswavelength, a proper thewavelength, energy of the the energy photons of isthe transferred photons is to transferred the electrons to the which electrons jump which to a higher jump levelto a higherof energy, level known of energy, as conduction known as band,conduction and a holeband, is and originated a hole andis originated dropped and on the dropped valence on band, the valencecreating band, two charge creating carriers, two charge i.e., an ca electron-holerriers, i.e., an pair. electron-hole In this excited pair. state, In this electrons excited arestate, free electrons to move areon thefree material. to move on Since the amaterial. photovoltaic Since cella photovolta is composedic cell of is semiconductor composed of semiconductor materials of N materials and P types of Nthat and form P types a P-N that junction, form a anP-N electrical junction, field an iselectrical originated field which is originated causes electronswhich causes and holeselectrons move and in holesopposite move directions, in opposite which directions, is the process which that is the creates process an electrical that creates current an electrical in the cell current [15]. in the cell [15]. A PV cell can be modeled by a current source in parallel with a diode both in parallel with a resistanceA PV andcell acan series be resistance,modeled by which a current leads tosource its current, in parallel I, voltage, with V,a givendiode byboth Equation in parallel (5), wherewith aI, resistanceIS, and Iph andare a the series current resistance, at the outputwhich leads of the to cell, its current,IS is the I, saturation voltage, V, current given by of Equation the diode, (5),R whereSH is a

Ishunt, IS, and resistance, Iph are theR Scurrentis a leekedge at the output resistance, of theIph cell,, the IS photogenerated is the saturation current, current theof theV and diode,VT RareSH is the a shuntvoltage resistance, to the cell R terminalsS is a leekedge and the resistance thermal, voltage, Iph, the respectively,photogeneratedn is thecurrent, diode’s the ideality V and factor.VT are the voltage to the cell terminals and the thermal voltage, V+IR respectively, n is the diode’s ideality factor. s V + IRs = nVT I Iph Is e 1 𝑉+𝐼𝑅 (1) − − − RSH 𝐼=𝐼 −𝐼 𝑒 −1− (1) 𝑅 In an ideal solar cell RSH and RS 0. In an ideal solar cell RSH →→ ∞ ∞and RS → 0.→ 3. Inﬂuence of External Parameters 3. Influence of External Parameters The irradiance inﬂuences the value of the short-circuit current, since it is directly proportional to this,The Equation irradiance (2), influences where Isc theand valueG are of thethe short-circuitshort-circuit currentcurrent, and since the it irradiance,is directly proportional respectively, sc toI∗ this,and EquationG* are the (2), short-circuit where I and current G are and the the short-circuit irradiance, bothcurrent under and standard the irradiance, test condition respectively, (STC), ∗SC 𝐼respectivelyand G* are [ 16the]. short-circuit current and the irradiance, both under standard test condition (STC), respectively [16]. G ISC = ISC∗ (2) G𝐺∗ 𝐼 =𝐼∗ (2) 𝐺∗

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The temperature influences the open circuit voltage, since it decreases with the increasing of the temperature. This occurs because the gap energy is affected by the increase of the temperature, which affects the saturation current of the diode [15]. The SR is the ratio between the generated current of the photovoltaic cell and the irradiance on the solar cell plane for a given wavelength. Indicating how the photons of different wavelengths contribute to the generated current [17]. In this work the SR of four photovoltaics technologies are considered, m-Si, a-Si, CdTe, and CIS, which are represented in Figure2. The spectral factor (SF) of a non-concentrating PV device is defined as, [6]: R R ( ) ( ) ( ) EG λ SR λ dλ EG∗ λ dλ SF = R R (3) ( ) ( ) ( ) EG∗ λ SR λ dλ EG λ dλ where the SR(λ) is the SR of the device when it is at the reference temperature as a function of the wavelength respectively, E and E are the spectral irradiance that effectively reaches the cell and G G∗ under STC as a function of the wavelength. From Equation (3), when SF assumes values higher than one, it has spectral power gains, whereas when this is less than one, it has losses, this in relation to the STC. The short-circuit current of a photovoltaic module is proportional to the product of the spectral irradiance and the integrated SR along the wavelength [6]: Z Icc E (λ)SR(λ)dλ (4) ∝ G

Therefore, SF can still be rewritten as [6]:

I G SF = SC (5) ISC∗ G∗

The spectral effective responsivity (SEF) is defined as [18]: R EG(λ) SR(λ)dλ SEF = R (6) EG(λ) dλ λ<λ0 where λ0 is the wavelength corresponding to the band gap energy of the material. The index expresses in units of A/W the ratio between the short-circuit current only accounting for irradiance and spectral effects and the spectrum power available for the photovoltaic conversion [16]. The spectral mismatch factor (MM) is defined in the IEC 60904-7 standard [19] as a way of quantifying the relative spectral impact between a sample PV device and a reference PV device by means of: R R ( ) ( ) ( ) EG λ SRsample λ dλ EG∗ λ SRre f dλ MM = R R (7) sample/re f ( ) ( ) ( ) EG∗ λ SRsample λ dλ EG λ SRre f dλ where SRsample(λ) represents the spectral response of the sample PV device and SRref(λ) the spectral response of the reference PV device, both at the reference cell temperature. From this definition, MMsample/ref accounts for spectral gains if greater than one or spectral losses if lower than one, for the sample PV device with respect to the reference PV device [20].

4. Methods and Procedures The objective of this experiment is to determine the I-V and P-V characteristics of solar cells, with and without wavelength selective ﬁlters, for diﬀerent conditions of irradiance. The current and voltage were measured outside laboratory conditions. The experimental tests were carried out with the main objective of obtaining the characteristic curves of m-Si and organic perovskite solar cells, under real solar radiation, in order to observe the Energies 2020, 13, x FOR PEER REVIEW 5 of 17

To measure the irradiation that reached the solar cell, an irradiation detector was placed behind the filter and was subsequently removed before the experimental procedure started. The detector that was used to measure the irradiance was a Sciencetech SOL-METER (TES-1333), a digital meter with a solar calibrated detector with an accuracy angle, cosine corrected <5% for angles <60°. The meter converts detector measurements to a Sun value. It has a handheld meter that is compact, has a sturdy design, andEnergies is 2020appropriate, 13, 5017 for indoor or outdoor applications. 5 of 18 The Sciencetech reference detector, which is an integral part of solar simulator calibration and Energies 2020, 13, x FOR PEER REVIEW 5 of 17 solar cellimpact I-V characterization, of the spectral irradiance consists and of the aSR calibrof theated cell insolar the productiondetector made of electric of silicon. energy and The also reference detectorTo measure tocomes validate with the the calibrationirradiationSF model. For datathat this, reachedtaken several by optical the Sciencetech, solar filters cell, were ancalibrating used irradiation to select it to the detector a specific NIST-certified was zones placed of the solar behind cell, onthe an filter accompanying spectrum.and was Withsubsequently certificate. this, a structure removed It reads was constructed solar before simulator the that experimental maintained irradiance the procedure cells in directed“sun” units;started. toward one the The sunsun detector and is equal that to supported2 the optical filters used Figure3. 1000was usedW/m to, at measure 25 degrees the Celsiusirradiance and was air massa Sciencetech 1.5 global. SOL-METER (TES-1333), a digital meter with a solar calibrated detector with an accuracy angle, cosine corrected <5% for angles <60°. The meter converts detector measurements to a Sun value. It has a handheld meter that is compact, has a sturdy design, and is appropriate for indoor or outdoor applications. The Sciencetech reference detector, which is an integral part of solar simulator calibration and solar cell I-V characterization, consists of a calibrated solar detector made of silicon. The reference detector comes with calibration data taken by Sciencetech, calibrating it to a NIST-certified solar cell, on an accompanying certificate. It reads solar simulator irradiance in “sun” units; one sun is equal to 1000 W/m2, at 25 degrees Celsius and air mass 1.5 global.

FigureFigure 3. Open 3. Open structure, structure, withwith m-Si m-Si cell. cell.

To measure the irradiation that reached the solar cell, an irradiation detector was placed behind In addition to the structure, high-pass (HP) (Table 1) and band-pass (BP) (Table 2) optic filters, the filter and was subsequently removed before the experimental procedure started. The detector that a variablewas resistance, used to measure a voltmeter, the irradiance and an was ammeter a Sciencetech are SOL-METERused, as can (TES-1333), be seen in a digital the scheme meter with of Figure 4 and in thea solarexperimental calibrated detectorset up Figure with an 5. accuracy The value angle, of cosine the irradiance corrected < outside5% for angles the structure<60◦. The was meter obtained by usingconverts an irradiation detector measurementsmeter. to a Sun value. It has a handheld meter that is compact, has a sturdy design, and is appropriate for indoor or outdoor applications. The Sciencetech reference detector, which is an integral part of solar simulator calibration and solar cell I-V characterization, consists of a calibrated solar detector made of silicon. The reference detector comes with calibrationFigure data 3. taken Open by structure, Sciencetech, with calibrating m-Si cell. it to a NIST-certified solar cell, on an accompanying certificate. It reads solar simulator irradiance in “sun” units; one sun is equal to 2 In addition1000 W/m to, at the 25 degreesstructure, Celsius high-pass and air mass (HP) 1.5 (Table global. 1) and band-pass (BP) (Table 2) optic filters, In addition to the structure, high-pass (HP) (Table1) and band-pass (BP) (Table2) optic filters, a variablea variableresistance, resistance, a voltmeter, a voltmeter, and and an an ammeter ammeter are used,used, as as can can be seenbe seen in the in scheme the scheme of Figure of4 Figure 4 and in theand experimental in the experimental set up set Figure up Figure 5. 5The. The value value of thethe irradiance irradiance outside outside the structure the structure was obtained was obtained by usingby an using irradiation an irradiation meter. meter.

Figure 4. Scheme of the assemblies of the experiments.

FigureFigure 4. Scheme 4. Scheme of ofthe the assemblies assemblies of of the the experiments. experiments.

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(1) (4) (3)

(3)

(2)

Figure 5. Experimental assembly. ( 1)) Structure; Structure; ( (2) variable variable resistance; resistance; ( 3) ammeter and and ( (4)) voltmeter. voltmeter.

Table 1. High-pasHigh-passs ﬁlterfilter characteristics.

ReferenceReference Transmission Transmission (%) (%) Cutting Cutting Wavelength Wavelength FSQ-OG550FSQ-OG550 90 90 550 550 nm nm FSQ-OG515FSQ-OG515 90 90 515 515 nm nm

Table 2. Characteristics of bandpass filters. Table 2. Characteristics of bandpass ﬁlters. Reference Center Wavelength Bandwidth Transmission (%) Reference Center Wavelength Bandwidth Transmission (%) 87-811 1000 nm 25 nm 99 87-81184-775 1000 700 nm nm 50 25 nm nm 99 99 84-77584-774 700 650 nm nm 50 50 nm nm 99 99 84-77484-773 650 600 nm nm 50 50 nm nm 99 99 84-773 600 nm 50 nm 99 84-772 550 nm 50 nm 99 84-772 550 nm 50 nm 99 84-771 500 nm 50 nm 99 84-771 500 nm 50 nm 99 84-77084-770 450 450 nm nm 50 50 nm nm 99 99 84-76984-769 400 400 nm nm 50 50 nm nm 99 99

The experiments performed for the m-Si cell have as an objective to analyze the impact of the spectralThe irradiance experiments and performed the SR of for the the cell m-Si in cellthe haveproduction as an objectiveof electric to energy analyze by the comparing impact of the spectralexperimental irradiance data obtained and the with SR ofthose the generated cell in the by production the SF model of for electric this cell. energy The byperovskite comparing organic the experimentalcell is used because data obtained it is a little with studied those generated technology by which the SF aims model to for analyze this cell. the Theimpact perovskite of the spectral organic cellirradiance is used in because the production it is a little of studiedelectric energy technology and to which have aimsan idea to analyzeof its possible the impact SR. of the spectral irradianceThe tests in the without production HP filters of electric (Figure energy 6a) for and the to m- haveSi cell an ideawere of performed its possible in SR.order to obtain the meanThe value tests of without the short-circuit HP filters (Figurecurrent6 a)when for thethe m-Sim-Si cell cell were is exposed performed to inthe order standard to obtain spectral the meanirradiance. value This of the value short-circuit was used current in the whenvalidation the m-Si of the cell SF is exposedmodel for to HP the filters. standard spectral irradiance. This valueThe tests was for used the in HP the filters validation (Figure of 6b) the were SF model designed for HP to filters.observe the impact on the variation of the incidentThe tests spectrum for the HP filtered filters (Figureby these6b) werefilters designed in obtaining to observe the characteristic the impact on curves the variation of m-Si of and the incidentperovskite spectrum organic filteredcells. by these filters in obtaining the characteristic curves of m-Si and perovskite organic cells. (a) (b) The tests without the BP filters (Figure7a) were performed in order to obtain the mean value of the short-circuit current, when the m-Si cell was exposed to the standard spectral irradiance, since this value was used in validation of the SF model.

(a) (b)

Energies 2020, 13, 5017 7 of 18 Energies 2020, 13, x FOR PEER REVIEW 7 of 17 Energies 2020, 13, x FOR PEER REVIEW 7 of 17 (a) (b) Figure 6. Structure. (a) No high-pass (HP) filters; (b) with HP filters.

The tests without the BP filters (Figure 7a) were performed in order to obtain the mean value of the short-circuit current, when the m-Si cell was exposed to the standard spectral irradiance, since this value was used in validation of the SF model. The BP filters allow selection of a specific zone of the spectrum and the tests carried out with these (Figure 7b) had the objective of observing the impact of the spectral irradiance and the SR on Figure 6. Structure. (a) No high-pass (HP) ﬁlters; (b) with HP ﬁlters. the photovoltaic energyFigure production 6. Structure. in ( ath) Noe m-Si high-pass and perovskite (HP) filters; organic (b) with cells HP filters. used.

The tests without the BP filters(a) (Figure 7a) were performed(b) in order to obtain the mean value of the short-circuit current, when the m-Si cell was exposed to the standard spectral irradiance, since this value was used in validation of the SF model. The BP filters allow selection of a specific(1) zone of the spectrum and the tests carried out with these (Figure 7b) had the objective of observing the impact of the spectral irradiance and the SR on the photovoltaic energy production in the m-Si and perovskite organic cells used.

(a) (b) Figure 7. FigureStructure. 7. Structure. (a) No (a )band-pass No band-pass (BP) (BP) filters;filters; (b )( withb) with BP filters. BP filters. (1) BP filter. (1) BP filter.

The BP filters allow selection of a specific(1) zone of the spectrum and the tests carried out with The SFthese model (Figure was7b) haddeveloped the objective in of observingMatlab thewith impact the of objective the spectral irradianceof simulating and the SRand on thestudying the performancephotovoltaic of several energy solar production technologies in the m-Si when and perovskite exposed organic to a cells given used. local spectral irradiance. To accomplish thisThe it was SF model necessary was developed to validate in Matlab the model, with the comparing objective of simulating the experimental and studying results the obtained performance of several solar technologies when exposed to a given local spectral irradiance. for the m-Si cell with the data generated by the model. To accomplish this it was necessary to validate the model, comparing the experimental results The modelobtained makes for the use m-Si of cell Equations with the data (7) generated and (9) by to the determine model. SF of the cell and the short-circuit current when FigureitThe is modelexposed 7. Structure. makes to usea (givena of) EquationsNo band-passspectral (7) and irradiance. (BP) (9) tofilters; determine (Theb) with SF simulation of BP the filters. cell and model (1 the) BP short-circuit filter.was performed in Simulink. Withcurrent this when model it is exposed it was to possible a given spectral to simulate irradiance. a certain The simulation solar modelcell technology was performed when in exposed The SFSimulink. model Withwas this developed model it was possiblein Matlab to simulate with a certainthe objective solar cell technology of simulating when exposed and tostudying a the to a given irradiationgiven irradiation and and solar solar spectrum. spectrum. performance of several solar technologies when exposed to a given local spectral irradiance. To The Icc is calculatedThe Icc is calculated taking taking into intoaccount account the the spectral spectral irradiance irradiance that ethatffectively effectively reaches the reaches solar the solar accomplish this it was necessary to validate the model, comparing the experimental results obtained cell and the cellSR andof the SRcell of thetechnology cell technology under under study. study. for the m-Si cellThe with SF the model data was generated used to simulate by the diff model.erent solar modules, i.e., Si-m, Si-a, CeTd, and CIS. The SF model was used to simulate different solar modules, i.e., Si-m, Si-a, CeTd, and CIS. To The modelTo analyze makes how use these of technologies Equations responded (7) and to (9) diff erentto determine zones of the solarSF of spectrum the cell (namely and the to the short-circuit analyze howUV, these visible, technologies and near-IR) SF,resp SEF,onded and MM to aredifferent calculated zones for each of technology the solarusing spectrum Equations (namely (3), (6) to the UV, current when it is exposed to a given spectral irradiance. The simulation model was performed in visible, and andnear-IR) (7). SF, SEF, and MM are calculated for each technology using Equations (3), (6) and Simulink. WithThe this SR model values used it was for the possible different technologiesto simulate are showna certain in Figure solar2. The cell module technology specifications when exposed (7). to a given irradiationwere taken from and the solar datasheets spectrum. of each module, as shown in Table3. The SR values used for the different technologies are shown in Figure 2. The module The Icc is calculatedTable 3.taking into account the spectral irradiance that effectively reaches the solar specifications were taken fromSpecifications the datasheets of m-Si, a-Si, CdTe,of each and copper module, indium as selenide shown (CIS) in modules. Table 3. cell and the SR of the cell technology under study. 2 Technology Module Isc (A) Voc (V) Module Area (m ) The SFTable model 3. Specificationswasm-Si used to PV-MLU255HC ofsimulate m-Si, a-Si, different [ 21CdTe,] and solar 8.89 copper modules, indium 37.8 i.e., selenide Si-m, (CIS) Si-a, 1.656 modules. CeTd, and CIS. To analyze how these technologiesa-Si SCHOTT responded ASI® 100 [to22] differ3.85ent zones of 40.9 the solar spectrum 1.450 (namely to the CdTe First Solar Series 6™ [23] 2.54 218.5 2.475 Technology Module Isc (A) Voc (V) Module Area (m2) UV, visible, and near-IR)CIS SF, SEF, and SF170-S MM [24] are calculated 2.2 for each 112 technology using 1.228 Equations (3), (6) and (7). m-Si PV-MLU255HC [21] 8.89 37.8 1.656 a-Si SCHOTT ASI® 100 [22] 3.85 40.9 1.450 The SR values used for the different technologies are shown in Figure 2. The module CdTe First Solar Series 6™ [23] 2.54 218.5 2.475 specifications were taken from the datasheets of each module, as shown in Table 3. CIS SF170-S [24] 2.2 112 1.228

Table 3. Specifications of m-Si, a-Si, CdTe, and copper indium selenide (CIS) modules. 5. Experimental Results Technology Module Isc (A) Voc (V) Module Area (m2) 5.1. Experimental Testm-Sis with High-PassPV-MLU255HC Filters [21] 8.89 37.8 1.656 a-Si SCHOTT ASI ® 100 [22] 3.85 40.9 1.450 This section present sand compares the experimental data obtained for the experiments CdTe First Solar Series 6 ™ [23] 2.54 218.5 2.475 performed withoutCIS the HP filters andSF170-S the experiments[24] ca2.2rried out112 with the HP1.228 filters, Table 1, in order to analyze the impact of the variation of the incident spectrum caused by these filters, and the obtained characteristic curves of m-Si and organic perovskite cells.

5.1.1. M-Si Cell

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5. Experimental Results

5.1. Experimental Tests with High-Pass Filters This section present sand compares the experimental data obtained for the experiments performed without the HP filters and the experiments carried out with the HP filters, Table1, in order to analyze the impact of the variation of the incident spectrum caused by these filters, and the obtained characteristic curves of m-Si and organic perovskite cells.

5.1.1. M-Si Cell Energies 2020, 13, x FOR PEER REVIEW 8 of 17 Several tests without HP filters were performed on unfiltered m-Si cells from 14 to 21 May 2018, betweenSeveral 11:00 tests a.m. without and 4:00 HP p.m. filters The were HP filterperformed tests were on unfiltered performed m-Si between cells from 15 and 14 to 19 21 June May 15 2018, and onbetween 21 May 11:00 21 2018, a.m. betweenand 4:00 11:00p.m. The a.m. HP and filter 4:00 te p.m.,sts were and performed a total of sixbetween assays 15 were and performed19 June 15 and for eachon 21 filter. May 21 2018, between 11:00 a.m. and 4:00 p.m., and a total of six assays were performed for eachBecause filter. the filters do not allow the passage of a part of the solar spectrum, the irradiance that reachesBecause the solar the cellfilters is do smaller. not allow Therefore, the passage the experimental of a part of the results solar withoutspectrum, filters the irradiance obtain higher that short-circuitreaches the currentsolar cell and is maximumsmaller. Therefore, power values, the experimental as expected, andresults for thewithout open circuitfilters voltageobtain higher there areshort-circuit no large variations, current and Table maximum4. power values, as expected, and for the open circuit voltage there are no large variations, Table 4. Table 4. Values of open circuit voltage, maximum power, and respective variations for different tests withTable and 4. withoutValues of HP open filters circuit for m-Sivoltage, cell maximum for an irradiance power, of and 910 respective W/m2. variations for different tests with and without HP filters for m-Si cell for an irradiance of 910 W/m2. Filters Voc (V) ∆Voc (%) PM (mW) ∆PM (%) No filtersFilters 0.563 Voc (V) Δ V ——oc (%) PM (mW) 95.35 Δ PM (%) —— OG 515No filters 0.553 0.563 ------1.78 95.35 72.86 ------23.59 OG 550OG 515 0.557 0.553 1.781.07 72.86 68.73 23.59 27.92 OG 550 0.557 1.07 68.73 27.92

AnalyzingAnalyzing Figure Figure8 and8 and the the remaining remaining data, data, it is it observed is observed that that the short-circuitthe short-circuit current current for the for OG the 515OG filter 515 filter is higher is higher than thatthan of that the of OG the 550 OG filter, 550 onfilter, average on average 13.33mA 13.33 above mA (correspondingabove (corresponding to 7.00% to deviation).7.00% deviation). This is This due tois thedue radiance to the radiance difference differ transmittedence transmitted by the filters, by the and filters, also and by the also spectral by the responsespectral response of the m-Si of cell.the m-Si cell.

300 120 250 100 200 80

Current (mA) Current 150 60 100 40 Power (mW) 50 20 0 0 0 0.2 0.4 0.6 0 0.2 0.4 0.6 Voltage (V) Voltage (V)

(a) (b)

FigureFigure 8. 8.Experiments Experiments performed performed on on 21 21 May May 2018: 2018: without without filters filters (— ),(— with), with filter filter OG 515OG ( —515), and(—), filter and OGfilter 550 OG (— 550) for (— m-Si) for cell. m-Si (a cell.) Voltage-current (a) Voltage-current curves curves and (b )and voltage-power (b) voltage-power curves. curves. Both curves Both curves were 2. acquiredwere acquired for G = for910 G W= 910/m W/m2. 5.1.2. Perovskite Organic Cell 5.1.2. Perovskite Organic Cell Tests were carried out on perovskite organic cells on 7 August 2018 at 3:45 p.m. and 4:30 p.m., Tests were carried out on perovskite organic cells on 7 August 2018 at 3:45 p.m. and 4:30 p.m., with one test being performed without a filter and one for each HP filter. with one test being performed without a filter and one for each HP filter. Analyzing the results obtained in Figure 9, it is observed that the voltage-current characteristic curves for this technology have an approximately linear shape. The value of the open circuit voltages varies greatly depending on the filter that is used, Table 5, in contrast to the m-Si cell.

Energies 2020, 13, 5017 9 of 18

Analyzing the results obtained in Figure9, it is observed that the voltage-current characteristic curves for this technology have an approximately linear shape. The value of the open circuit voltages Energies 2020, 13, x FOR PEER REVIEW 9 of 17 varies greatly depending on the ﬁlter that is used, Table5, in contrast to the m-Si cell.

1400 350 1200 300

1000 250 800 200 600 150 Power (μW) Current (μA) Current 400 100 200 50

0 0 0 0.4 0.8 1.2 1.6 0 0.4 0.8 1.2 1.6 Voltage (V) Voltage (V)

(a) (b)

FigureFigure 9. 9. TestsTests carried carried out out on on 7 7August August 2018: 2018: without without filters filters (— (—), ),with with filter filter OG OG 515 515 (— (—),), and and those those withwith filter filter OG OG 550 550 (— (—)) for for perovskite perovskite organic organic cell. cell. (a (a) )Voltage-current Voltage-current curves curves and and (b (b) )voltage-power voltage-power 2. curves.curves. Both Both curves curves were were acquired acquired for for G G = =10001000 W/m W/m2. Table 5. Values of open circuit voltage, maximum power, and respective variations for different tests Table 5. Values of open circuit voltage, maximum power, and respective variations for different tests with and without HP filters for perovskite organic cell for an irradiance of 1000 W/m2. with and without HP filters for perovskite organic cell for an irradiance of 1000 W/m2.

Filters Voc (V) ∆Voc (%) PM (µW) ∆PM (%) Filters Voc (V) Δ Voc (%) PM (μW) Δ PM (%) No ﬁltersNo filters 0.180 0.180 ------—— 292 292 ------—— OG 515OG 515 0.105 0.105 41.7 41.7 97.7 97.7 66.50 66.50 OG 550OG 550 0.049 0.049 72.9 72.9 66.8 66.8 77.09 77.09

5.2.5.2. Experimental Experimental Test Testss with with Band-Pass Band-Pass Filters Filters InIn this this section, section, we we compare compare the the results results of of the the assa assaysys performed performed with with BP BP filters, filters, Table Table 2,2, for for m-Si m-Si andand perovskite perovskite organic organic cells. cells. As As previously previously mentio mentioned,ned, these these filters filters have have a avery very narrow narrow bandwidth bandwidth whichwhich allows allows passage passage to very specificspecific zoneszones ofof the the solar solar spectrum. spectrum. This This leads leads to to the the cells cells receiving receiving low lowlevels levels of irradiance, of irradiance, which which in turn in turn induces induces short-circuit short-circuit currents currents lower lower than than those those observed observed in the in teststhe testswithout without the filters.the filters. TheseThese experimental experimental results results provide provide the the data data for for the the analyses analyses of of the the influence influence of of the the SR SR of of each each of of thethe technologies technologies and and the the spectral spectral irradiance irradiance on on the the energy energy production. production.

5.2.1.5.2.1. M-Si M-Si Cell Cell ByBy analyzing analyzing Figure Figure 10 10 which which showing showing the the evolution evolution of of the the characteristic characteristic curves curves of of the the cells cells with with thethe BP BP filters, filters, together together withwith TableTable6 ,6, we we can can conclude conclude that that the the response response to the to 500the nm500 andnm 700and nm 700 filters nm filtersis that is there that there is a higher is a higher maximum maximum power. power. However,However, it it is is worth worth remembering remembering that the 1000 nm filterfilter containscontains aa bandwidthbandwidth of of 25 25 nm, nm, leading leading to tolower lower power power values values (0.465 (0.465 mW). mW). Thus, Thus, the the maximum maximum power power for for a a 1000 1000 nm nm filter filter with with a a bandwidth bandwidth of of50 50 nm nm is is expected expected to to bebe approximatelyapproximately doubledouble which is approximately 0.93 0.93 mW, mW, and and is is the the highest highest valuevalue of of the the BP BP filters. filters.

Energies 2020, 13, 5017 10 of 18 Energies 2020, 13, x FOR PEER REVIEW 10 of 17

FigureFigure 10.10. Tests performedperformed with BP filtersfilters onon AugustAugust 2121 20182018 forfor thethe m-Sim-Si cell.cell. (a)) Voltage-currentVoltage-current curvescurves andand ((bb)) voltage-powervoltage-power curves.curves. Table 6. Values of open circuit voltage, short-circuit current, maximum power, and respective variations 5.2.2.for Perovskite the tests with Organic and without Cell BP filters of m-Si cell for an irradiance of 1000 W/m2. Similar to the results discussed in Section 5.2.1, the results obtained for perovskite organic cell, Filters Voc (V) ∆Voc (%) Isc (mA) ∆Isc (%) PM (mW) PM (%) Figure 11, reinforce the hypothesis that the characteristic curve of this technology can be described No filters 0.500 —- 23.0 —- 6.647 100 by a linear equation. 1000 25 nm —- —- —- —- 0.93 14.05 ± 1000The nm results, shown 0.410 in Figure 11 18.0 and in Table 2.63 7, show that the 88.51 500 nm and 0.467 550 nm filters 7.02are those with700 the nm highest peak 0.433 power values. 13.4 Since the 1000 3.30 nm filter has 85.59 half the bandwidth 0.708 of the 10.66 rest it is expected650 nm that a BP 0.411 filter of 1000 17.8 nm with 502.62 nm bandwidth 88.56 will have 0.461a maximum power 6.93 of approximately600 nm 5.36 0.426 µW, exceeding 14.8 the values reached 3.34 in the remaining 85.42 filters. 0.665 10.00 550 nm 0.428 14.4 3.25 85.81 0.674 10.13 500 nm 0.432 13.6 3.30 85.59 0.704 10.59 450 nm 0.423 15.4 2.89 87.38 0.560 8.42 400 nm 0.413 17.4 2.46 89.26 0.444 6.68

5.2.2. Perovskite Organic Cell Similar to the results discussed in Section 5.2.1, the results obtained for perovskite organic cell, Figure 11, reinforce the hypothesis that the characteristic curve of this technology can be described by a linear equation. The results, shown in Figure 11 and in Table7, show that the 500 nm and 550 nm filters are those with the highest peak power values. Since the 1000 nm filter has half the bandwidth of the rest it is expected that a BP filter of 1000 nm with 50 nm bandwidth will have a maximum power of approximately 5.36 µW, exceeding the values reached in the remaining filters. Figure 12 shows the values of the spectral irradiance and the maximum power normalized to their respective maximum values. From an analysis of this information, it is possible to hypothesize that theFigure perovskite 11. Tests organicperformed cell with used BP in filters this on work 7 Augu willst have 2018 afor better the perovskita SR in the organic visible cell. zone (a) up Voltage- to 550 nm and increasecurrent curvesa again nearand ( 1000b) voltage-power nm. Therefore, curves. we conclude that this cell has good use of the irradiance in this zone of the near-IR. Since no information is available between 750 nm and 950 nm, nothing can be completedTable 6. Values in this range.of open circuit voltage, short-circuit current, maximum power, and respective variations for the tests with and without BP filters of m-Si cell for an irradiance of 1000 W/m2.

Filters Voc (V) Δ Voc (%) Isc (mA) Δ Isc (%) PM (mW) PM (%) No filters 0.500 ---- 23.0 ---- 6.647 100 1000 ± 25 nm ------0.93 14.05 1000 nm 0.410 18.0 2.63 88.51 0.467 7.02 700 nm 0.433 13.4 3.30 85.59 0.708 10.66 650 nm 0.411 17.8 2.62 88.56 0.461 6.93 600 nm 0.426 14.8 3.34 85.42 0.665 10.00 550 nm 0.428 14.4 3.25 85.81 0.674 10.13 500 nm 0.432 13.6 3.30 85.59 0.704 10.59 450 nm 0.423 15.4 2.89 87.38 0.560 8.42

Energies 2020, 13, x FOR PEER REVIEW 10 of 17

Figure 10. Tests performed with BP filters on August 21 2018 for the m-Si cell. (a) Voltage-current curves and (b) voltage-power curves.

Energies 2020, 13, x FOR PEER REVIEW 11 of 17

400 nm 0.413 17.4 2.46 89.26 0.444 6.68

Table 7. Values of open circuit voltage, short-circuit current, maximum power, and respective variations for the tests with and without BP filters of perovskite organic cell.

Filters Voc (V) Δ Voc (%) Isc (μA) Δ Isc (%) PM (μW) PM (%) Figure 11. 11. TestsTests performed performed with with BP BPfilters ﬁlters on 7 onAugu 7 Augustst 2018 for 2018 the for perovskita the perovskita organic organiccell. (a) Voltage- cell. (a) No filters 0.561 ---- 11.22 ---- 15.70 100 currentVoltage-current curvesa curvesaand (b) voltage-power and (b) voltage-power curves. curves. 1000 ± 25 nm ------5.36 34.11 1000 nm 0.234 58.29 45.60 59.358 2.678 17.06 Table 6. Values of open circuit voltage, short-circuit current, maximum power, and respective Table 7. Values of700 open nm circuit voltage, 0.232 short-circuit 58.68 current, 44.80 maximum 60.071 power, 2.586 and respective 16.47 variations 2 variationsfor the tests for with the650 andtests nm without with and BP0.237 without ﬁlters of BP 57.72 perovskite filt ers of 46.00 m-Si organic cell cell. 59.002for an irradiance 2.705 of 1000 17.23 W/m .

Filters 600 nmV oc (V) 0.257Δ Voc (%) 54.19 Isc (mA) 49.90 Δ 55.526 Isc (%) P 3.185M (mW) 20.29PM (%) Filters Voc (V) ∆Voc (%) Isc (µA) ∆Isc (%) PM (µW) PM (%) No filters550 nm 0.500 0.268 ---- 52.23 23.0 51.90 53.743 ---- 3.429 6.647 21.84 100 No ﬁlters1000 ± 25 0.561nm500 nm ---- 0.268 —- ---- 52.23 11.22 ---- 51.60 54.011 ---- —- 3.482 0.93 15.70 22.18 14.05 100 1000 25 nm 450—- nm 0.248 —- 55.79 —- 48.30 56.952 —- 2.975 5.36 18.95 34.11 ± 1000 nm 0.410 18.0 2.63 88.51 0.467 7.02 1000 nm 0.234 58.29 45.60 59.358 2.678 17.06 700 nm400 nm 0.433 0.230 13.4 59.00 3.30 44.40 60.428 85.59 2.540 0.708 16.18 10.66 700 nm 0.232 58.68 44.80 60.071 2.586 16.47 650 nm 0.411 17.8 2.62 88.56 0.461 6.93 650 nm 0.237 57.72 46.00 59.002 2.705 17.23 Figure 60012 showsnm the 0.426values of the 14.8 spectral ir 3.34radiance and 85.42 the maximum 0.665 power 10.00 normalized to 600 nm 0.257 54.19 49.90 55.526 3.185 20.29 their550 respective nm550 nm maximum 0.268 0.428 values. 52.23 From 14.4 an analysis 51.90 3.25 of this information, 85.81 53.743 0.674 it is 3.429 possible 10.13 to hypothesize 21.84 that500 the nm perovskite500 nm 0.268 organic 0.432 cell used 52.23 13.6in this work 51.60 3.30 will have 85.59 54.011a better SR 0.704in the 3.482 visible 10.59 zone 22.18 up to 550 nm450 and nm increase450 nm 0.248again near 0.423 1000 55.79 nm. 15.4 Therefore, 48.30 2.89 we conclude 87.38 56.952 that this 0.560 2.975cell has 8.42 good 18.95use of the irradiance400 nm in this zone 0.230 of the near-IR. 59.00 Since no 44.40information is 60.428 available between 2.540 750 nm and 16.18 950 nm, nothing can be completed in this range.

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

Nomalized Spectral Irradiance Nomalized 0 400 450 500 550 600 650 700 750 800 850 900 950 1000 Wavelength (nm)

FigureFigure 12. 12. NormalizedNormalized maximum maximum power power for forBP BPfilters filters for perovskite for perovskite organic organic cell, in cell, blue. in Spectral blue. Spectralirradiance irradiance normalized, normalized, in orange. in orange. 6. Simulation Results 6. Simulation Results In this section, we validate the SF model, by comparing the results obtained from the simulation In this section, we validate the SF model, by comparing the results obtained from the simulation with the experimental ones for the m-Si cell and for the different optical filters used. After the validation with the experimental ones for the m-Si cell and for the different optical filters used. After the validation of the model, we apply it to four different technologies, i.e., m-Si, a-Si, CdTe, and CIS, to analyze the behavior of these technologies when irradiated for different zones of the solar spectrum. Table 8 shows the mean values of the short-circuit currents adapted for an irradiance of 1000 W/m2, for the tests with the aperture for HP filters and BP filters, since these apertures have different dimensions.

Table 8. Average values of the short-circuit current under STC for the experiments performed with the aperture for filters used.

∗ Experience 𝑰𝒄𝒄 (A) Aperture for HP filter 0.271968 Aperture for BP filter 0.030144

Energies 2020, 13, 5017 12 of 18 of the model, we apply it to four different technologies, i.e., m-Si, a-Si, CdTe, and CIS, to analyze the behavior of these technologies when irradiated for different zones of the solar spectrum. Table8 shows the mean values of the short-circuit currents adapted for an irradiance of 1000 W /m2, for the tests with the aperture for HP filters and BP filters, since these apertures have different dimensions.

Table 8. Average values of the short-circuit current under STC for the experiments performed with the aperture for ﬁlters used.

* Experience Icc (A) Aperture for HP ﬁlter 0.271968 Aperture for BP ﬁlter 0.030144 Energies 2020,, 13,, xx FORFOR PEERPEER REVIEWREVIEW 12 of 17

6.1.6.1. Simulation for HP High-Pass Filters Filters ThisThis sectionsection presents some of thethe resultsresults ofof thethe simulationssimulations performed to to validate validate the the model, model, comparingcomparing thesethese withwith thethe experimentalexperimental resultsresults obtainedobtained withwith HighHP filters Pass for filters the for m-Si the cell. m-Si cell. 2 ForFor 2121 MayMay 2018,2018, thethe resultsresults forfor thethe OGOG 515515 filterfilter withwith anan irradianceirradiance ofof 915915 WW/m/m 22 areare shownshown inin 2 FigureFigure 1313,, andand FigureFigure 1414 showsshows thethe OGOG 550550 filterfilter withwith aa 910910 WW/m/m 22... The The curvescurves thatthat areare closestclosest toto thethethe experimentalexperimental datadata areare shownshown in in red, red, and and the the simulated simulatedted characteristic characteristiccharacteristic curves curvescurves are areare shown shownshown in inin yellow. yellow.yellow. It isItIt possibleisis possiblepossible to to observeto observeobserve that thatthat the thethe characteristic characteristiccharacteristic curves curvescurves are areare close closeclose to eachtoto eacheach other. other.other.

FigureFigure 13.13. Experimental data acquired ( x),), characteristic characteristic curve curve that that approaches approaches thethe experimentalexperimental datadata (((—------),),), andandand simulatedsimulatedsimulated characteristiccharacteristiccharacteristic curvecurvecurve (((—------),),), forforfor thethethe OGOGOG 515515515 ﬁlter.filter.filter.

FigureFigure 14.14. Experimental data acquired ( x),), characteristic characteristic curve curve that that approaches approaches thethe experimentalexperimental datadata (((—------),),), andandand simulatedsimulatedsimulated characteristiccharacteristiccharacteristic curvecurvecurve (((—------),),), forforfor thethethe OGOGOG 550550550 ﬁlter.filter.filter.

Table 9 presents the values of thethe short-circuitshort-circuit currents,currents, thethe curvescurves thatthat approximateapproximate thethe experimental data, the curves obtained by simulationtion usingusing thethe SFSF modelmodel andand calculatedcalculated byby thethe method without SF using Equation (6) for the irradiance incident on the solar cell, as well as the values of the relative errors for both models. These filters have low relative error values which propitiate a good approximation of the SF model. However, the variation of the relative error for the different simulations could possibly be related to the variation of the spectral irradiance throughoutthroughout thethe days.days. AnotherAnother possiblepossible explanationexplanation isis thethe variationvariation ofof thethe SRSR ofof thethe cellcell withwith thethe temperaturetemperature changingchanging thethe amountamount ofof solarsolar energyenergy converted into electric energy.

6.2. Simulation for BP Filters This section presents some of the results of thethe simulationssimulations performedperformed toto validatevalidate thethe model,model, comparing these with the experimental results obtained with HP filters for the m-Si cell.

Energies 2020, 13, 5017 13 of 18

Table9 presents the values of the short-circuit currents, the curves that approximate the experimental data, the curves obtained by simulation using the SF model and calculated by the method without SF using Equation (6) for the irradiance incident on the solar cell, as well as the values of the relative errors for both models.

Table 9. Values of short-circuit current and their respective relative errors for HP ﬁlters.

I I Model Relative Relative Error sc I SF sc Day Hour Filter Experimental sc without Error SF Model without Model (A) (A) SF (A) Model (%) SF (%) OG 515 0.189 0.192 0.183 1.53 3.33 21/5/2018 15h–15:50h OG 550 0.176 0.179 0.170 1.59 3.35 OG 515 0.208 0.203 0.193 2.21 7.45 12:30h–13:30h 15/6/2018 OG 550 0.193 0.191 0.181 1.30 6.05 OG 515 0.203 0.209 0.199 3.10 1.83 15:21h–16h OG 550 0.188 0.193 0.185 2.39 1.56 OG 515 0.179 0.189 0.180 5.42 0.40 18/6/2018 12:42h–14:16h OG 550 0.166 0.179 0.170 5.30 2.48 OG 515 0.180 0.185 0.176 2.56 2.38 12:23h–12:45h 19/6/2018 OG 550 0.169 0.179 0.166 3.43 1.56 OG 515 0.182 0.189 0.180 3.68 1.26 13h–13:27h OG 550 0.170 0.179 0.168 5.18 1.04

These ﬁlters have low relative error values which propitiate a good approximation of the SF model. However, the variation of the relative error for the diﬀerent simulations could possibly be related to the variation of the spectral irradiance throughout the days. Another possible explanation is the variation of the SR of the cell with the temperature changing the amount of solar energy converted into electric energy.

6.2. Simulation for Band Pass Filters This section presents some of the results of the simulations performed to validate the model, Energies 2020, 13, x FOR PEER REVIEW 13 of 17 comparing these with the experimental results obtained with Band Pass filters for the m-Si cell. Simulations were performed for the the filters filters indicated indicated in in Table Table 22.. However, inin this paper, wewe onlyonly present the simulations for the 650 nm filter, filter, Fi Figuregure 15,15, where the SF model generates a good approximation and for the 400 nm filter, filter, Figure 1616,, whichwhich obtainsobtains thethe highesthighest relativerelative errorerror values.values.

Figure 15. ExperimentalExperimental data data acquired acquired ( (xx),), characteristic characteristic curve curve that that approaches approaches the the experimental experimental data data (---—), and simulated characteristic curve (—---), for the 650 nm ﬁlter.filter.

Figure 16. Experimental data acquired (x), characteristic curve that approaches the experimental data (---), and simulated characteristic curve (---), for the 400 nm filter.

Although the SF model has high values of relative errors for certain irradiation bands, Table 10, these errors can be justified by the input variables used by the SF model, which do not fully describe the reality of the experiments performed. For the spectral irradiance variation in these spectrum ranges, the m-Si cell has a SR different from that used to describe it, or a variation of the bandwidth of the BP filters. A small variation of these variables causes a considerable variation in the irradiance value that effectively reaches the solar cell, causing a large variation of the values of the short-circuit current within the order of magnitude of this one. It should be noted that the SF model obtained an average relative error of 33.07%, which could decrease with the use of the appropriate variables as compared with 38.39% obtained for the model without SF.

Table 9. Values of short-circuit current and their respective relative errors for HP filters.

Isc Relative Error Model Model Day Hour Filter Isc Experimental (A) Isc SF Model (A) Relative Error SF Model (%) without without SF SF (A) (%) 15h– OG 515 0.189 0.192 0.183 1.53 3.33 21/5/2018 15:50h OG 550 0.176 0.179 0.170 1.59 3.35 12:30h– OG 515 0.208 0.203 0.193 2.21 7.45 13:30h OG 550 0.193 0.191 0.181 1.30 6.05 15/6/2018 15:21h– OG 515 0.203 0.209 0.199 3.10 1.83 16h OG 550 0.188 0.193 0.185 2.39 1.56 12:42h– OG 515 0.179 0.189 0.180 5.42 0.40 18/6/2018 14:16h OG 550 0.166 0.179 0.170 5.30 2.48 12:23h– OG 515 0.180 0.185 0.176 2.56 2.38 19/6/2018 12:45h OG 550 0.169 0.179 0.166 3.43 1.56 OG 515 0.182 0.189 0.180 3.68 1.26

Energies 2020, 13, x FOR PEER REVIEW 13 of 17

Simulations were performed for the filters indicated in Table 2. However, in this paper, we only present the simulations for the 650 nm filter, Figure 15, where the SF model generates a good approximation and for the 400 nm filter, Figure 16, which obtains the highest relative error values.

EnergiesFigure2020, 1315., 5017Experimental data acquired (x), characteristic curve that approaches the experimental data14 of 18 (---), and simulated characteristic curve (---), for the 650 nm filter.

Figure 16. Experimental data acquired (x), characteristic curve that approaches the experimental datadata ((—---),), andand simulatedsimulated characteristiccharacteristic curvecurve ((—---),), forfor thethe 400400 nmnm ﬁlter.filter.

Although the SF model has high values of relative errors for certain irradiation bands, bands, Table Table 10,10, thesethese errorserrors cancan bebe justifiedjustified byby thethe inputinput variablesvariables usedused byby thethe SFSF model,model, whichwhich do not fully describe thethe realityreality of of the the experiments experiments performed. performed. For For the spectralthe spectral irradiance irradiance variation variation in these in spectrum these spectrum ranges, theranges, m-Si the cell m-Si has cell a SR has di ffaerent SR different from that from used that to us describeed to describe it, or a variationit, or a variation of the bandwidthof the bandwidth of the BPof the filters. BP filters. A small A variationsmall variation of these of variablesthese variables causes causes a considerable a considerable variation variation in the irradiancein the irradiance value thatvalue eff thatectively effectively reaches reaches the solar the cell, solar causing cell, causing a large a variation large variation of the values of the ofvalues the short-circuit of the short-circuit current withincurrent the within order the of order magnitude of magnitude of this one. of this one. It should be noted that the SF model obtained an average relative error of 33.07%, which could decrease withTable the 10. useValues of the of short-circuitappropriate current variables and theiras compared respective with relative 38.39% errors obtained for BP filters. for the model without SF. I I Model Relative Error sc I SF Model sc Relative Error Filters Experimental sc without SF Model without (mA) SF Model (%) Table 9. Values(mA) of short-circuit current and their(mA) respective relative errors for HP filters.SF (%)

1000 nm 2.63 2.44 2.53Isc 7.22 3.8Relative Error Model Model Day700 nmHour Filter 3.3 Isc Experimental 3.0 (A) Isc SF Model (A) 3.1 Relative 9.09 Error SF Model (%) 6.06 650 nm 2.62 2.412 2.53without 7.94 3.44without SF SF (A) (%) 600 nm 3.34 2.99 3.12 10.48 6.59 15h– OG 515 0.189 0.192 0.183 1.53 3.33 21/5/2018 550 nm15:50h OG 3.25 550 0.176 3.14 0.179 3.23 0.170 3.38 1.59 0.62 3.35 500 nm12:30h– OG 3.3 515 0.208 3.12 0.203 3.25 0.193 5.45 2.21 1.52 7.45 450 nm13:30h OG 2.89 550 0.193 2.68 0.191 2.82 0.181 7.27 1.30 2.42 6.05 15/6/2018 400 nm15:21h– OG 2.46 515 0.203 2.38 0.209 2.41 0.199 3.25 3.10 2.03 1.83 16h OG 550 0.188 0.193 0.185 2.39 1.56 12:42h– OG 515 0.179 0.189 0.180 5.42 0.40 18/6/2018 It should14:16h be notedOG 550 that the SF 0.166 model obtained 0.179 an average 0.170 relative error 5.30 of 33.07%, which 2.48 could 12:23h– OG 515 0.180 0.185 0.176 2.56 2.38 decrease19/6/2018 with12:45h the useOG of550 the appropriate 0.169 variables 0.179 as compared 0.166 with 38.39% 3.43 obtained for the 1.56 model without SF. OG 515 0.182 0.189 0.180 3.68 1.26

6.3. Simulation for Band Pass Filters for Different Technologies In this section, we use the model developed to simulate four solar modules of the m-Si, a-Si, CIS, and CdTe technologies, and the SR for each technology is shown in Figure2. Figure 17 shows the spectral irradiance converted by the different modules. It is possible to observe the impact of SF of each technology and the spectral irradiance that is effectively converted into electric energy by each technology. The simulations are carried out considering that the incident spectral irradiance is equal to the reference spectral irradiance, for three different zones of the spectrum, namely UV, visible, and IR, in order to analyze the influence of each of these zones on the production of photovoltaic energy. Energies 2020, 13, x FOR PEER REVIEW 14 of 17

13h– OG 550 0.170 0.179 0.168 5.18 1.04 13:27h

Table 10. Values of short-circuit current and their respective relative errors for BP filters.

Isc Experimental Isc SF Model Isc Model without Relative Error SF Relative Error Model Filters (mA) (mA) SF (mA) Model (%) without SF (%) 1000 nm 2.63 2.44 2.53 7.22 3.8 700 nm 3.3 3.0 3.1 9.09 6.06 650 nm 2.62 2.412 2.53 7.94 3.44 600 nm 3.34 2.99 3.12 10.48 6.59 550 nm 3.25 3.14 3.23 3.38 0.62 500 nm 3.3 3.12 3.25 5.45 1.52 450 nm 2.89 2.68 2.82 7.27 2.42 400 nm 2.46 2.38 2.41 3.25 2.03

6.3. Simulation for BP Filters In this section, we use the model developed to simulate four solar modules of the m-Si, a-Si, CIS, and CdTe technologies, and the SR for each technology is shown in Figure 2. Figure 17 shows the spectral irradiance converted by the different modules. It is possible to Energiesobserve2020 the, 13 impact, 5017 of SF of each technology and the spectral irradiance that is effectively converted15 of 18 into electric energy by each technology.

FigureFigure 17.17. Spectral irradiance that is eeffectivelyﬀectively convertedconverted into electrical energy by m-Si, a-Si, CdTe, andand CISCIS technologies.technologies.

ObservingThe simulations Figure are 18 ,carried with the out data considering in the Table that 11 th, ite isincident possible spectral to conclude irradiance that in is theequal UV to zone the thereference maximum spectral power irradiance, values obtained for three are different reduced, zone thes a-Siof the technology spectrum, has namely the best UV, SF visible, and a betterand IR, use in oforder irradiation. to analyze For the the influence visible zone, of each although of these the zones a-Si on module the production obtains the of highestphotovoltaic SF value, energy. the CdTe moduleObserving presents Figure the best 18, maximumwith the data power in the values Table per 11, module it is possible area. to Finally, conclude for thethat IV in zonethe UV the zone CIS technologythe maximum presents power better values use obtained of the spectral are reduced, irradiance the and a-Si performance, technology has generating the best about SF and half a ofbetter the energy produced by the CdTe technology in the visible zone. Energiesuse of 2020irradiation., 13, x FOR ForPEER the REVIEW visible zone, although the a-Si module obtains the highest SF value,15 of the 17 CdTe module presents the best maximum power values per module area. Finally, for the IV zone the CIS technology presents better use of the spectral irradiance and performance, generating about half of the energy produced by the CdTe technology in the visible zone. (c) (a) (b)

Figure 18. SimulatedSimulated voltage-power voltage-power curves curves for for the the m-Si, a-Si, CdTe, and CIS modules. ( a)) ultraviolet (UV) zone, 250–380 nm; ( b) visible zone, 380–750 nm; and (c) infrared (IR)(IR) zone,zone, >>750750 nm.

Table 11. Values of spectral factor (SF), spectral incompatibility factor (MM), spectral eﬀective 7. Conclusions and Recommended Works responsivity (SEF), and maximum power per area of each module of m-Si, a-Si, CdTe, and CIS for the TheUV, visible,main objectives and IR zones. of this work are the study of the impact of spectral irradiance and spectral response (SR) on the photovoltaic energy production of the solar technologies used throughout2 this SF MM SEF PM/A (W/m ) work.Technology UV V IR UV V IR UV V IR UV V IR We found that the m-Si cell and the perovskite organic cell respond differently to the various filters m-Siused, when 0.134 exposed 1.098 to 1.221 the same 1.00 spectral 1.00 irradiance. 1.00 0.074 It was 0.607 also 0.821 observed 0.218 that 69.855 the perovskite58.998 a-Si 0.691 2.010 0.007 5.14 1.83 0.01 0.253 0.731 0.014 0.303 59.546 0.018 organicCdTe cell has 0.226 a good 1.590 SR in 0.579the visible 1.68 zone 1.45 up to 0.47 550 nm, 0.100 and 0.704 then near 0.793 1000 0.429 nm. 114.914Additionally,28.751 it was foundCIS that 0.084this cell 0.964 generates 1.396 voltage-current 0.63 0.88 characteristic 1.14 0.049 0.557curves 0.824with an 0.060 approximately 52.437 59.638 linear shape. Although the spector factor (SF) model has high relative error values for certain irradiation bands, these errors were justified based on the input variables used in the model, which did not fully describe the reality of the simulated experiments performed. More detailed development of this model is necessary, considering the possible deviations of the observed conditions. The simulations performed with the SF model for the m-Si, a-Si, CdTe, and CIS modules allowed us to observe the effect of SR and the spectral irradiance for each of them, since they have performances and exploitations for different areas of the spectrum. Finally, it was concluded that the SF, the spectral mismatch factor (MM), and the spectral effective responsivity (SEF) are important and necessary factors for the study of photovoltaic energy production. However, they are not enough, and the knowledge of the internal characteristics of the solar modules is also necessary. The existing potential in the IV zone should also be noted, with a significant impact on the production of photovoltaic energy, not only in the experimental tests performed, but also in the simulations performed for the SF model. Thus, the hypothesis of producing electric energy without the presence of visible light was validated.

Table 11. Values of spectral factor (SF), spectral incompatibility factor (MM), spectral effective responsivity (SEF), and maximum power per area of each module of m-Si, a-Si, CdTe, and CIS for the UV, visible, and IR zones.

SF MM SEF PM/A (W/m2) Technology UV V IR UV V IR UV V IR UV V IR m-Si 0.134 1.098 1.221 1.00 1.00 1.00 0.074 0.607 0.821 0.218 69.855 58.998 a-Si 0.691 2.010 0.007 5.14 1.83 0.01 0.253 0.731 0.014 0.303 59.546 0.018 CdTe 0.226 1.590 0.579 1.68 1.45 0.47 0.100 0.704 0.793 0.429 114.914 28.751 CIS 0.084 0.964 1.396 0.63 0.88 1.14 0.049 0.557 0.824 0.060 52.437 59.638

Energies 2020, 13, 5017 16 of 18

7. Conclusions and Recommended Works The main objectives of this work are the study of the impact of spectral irradiance and spectral response (SR) on the photovoltaic energy production of the solar technologies used throughout this work. We found that the m-Si cell and the perovskite organic cell respond differently to the various filters used, when exposed to the same spectral irradiance. It was also observed that the perovskite organic cell has a good SR in the visible zone up to 550 nm, and then near 1000 nm. Additionally, it was found that this cell generates voltage-current characteristic curves with an approximately linear shape. Although the spector factor (SF) model has high relative error values for certain irradiation bands, these errors were justified based on the input variables used in the model, which did not fully describe the reality of the simulated experiments performed. More detailed development of this model is necessary, considering the possible deviations of the observed conditions. The simulations performed with the SF model for the m-Si, a-Si, CdTe, and CIS modules allowed us to observe the effect of SR and the spectral irradiance for each of them, since they have performances and exploitations for different areas of the spectrum. Finally, it was concluded that the SF, the spectral mismatch factor (MM), and the spectral effective responsivity (SEF) are important and necessary factors for the study of photovoltaic energy production. However, they are not enough, and the knowledge of the internal characteristics of the solar modules is also necessary. The existing potential in the IV zone should also be noted, with a significant impact on the production of photovoltaic energy, not only in the experimental tests performed, but also in the simulations performed for the SF model. Thus, the hypothesis of producing electric energy without the presence of visible light was validated. In relation to the study of the impact of spectral irradiance and SR on photoelectric energy production we suggest that the following works should be carried out:

Study the spectral response, efficiency, and energy efficiency of the transparent luminescent solar • concentrator technology for a building for one year; Study in more depth the various independent spectral indices and dependent PV devices; • Perform experimental tests with concentrator panels and compare the results with simulations for • the model using SF for HCPV; Perform experimental tests with multiple junction solar cells and compare the results with • simulations for the model using the spectral matching ratio; Perform experimental tests in a dark environment and on cloudy days with PV devices directed • to a body that emitted infrared radiation, for CIS, CISG and m-Si technologies. To study the effect of temperature on the production of photovoltaic energy as a function of the • incident wavelength in a solar cell, the following are proposed: Study the SR variation with the temperature variation for a fixed spectral irradiance, • preferably constant along the wavelength; Study the SR variation with the temperature variation with the parameters already used in the • prediction of the temperature impact in a solar cell. To be able to analyze the efficiency of any solar cell using the simulation for any operating • condition, the following is suggested: Develop a model capable of simulating any type of solar technology, for any operating condition, • making use of the various spectral indices.

Author Contributions: Conceptualization, D.L., J.P.N.T. and J.F.P.F.; methodology, D.L., J.P.N.T. and J.F.P.F.; software, D.L.; validation, J.P.N.T. and J.F.P.F.; formal analysis, D.L., J.P.N.T. and J.F.P.F.; investigation, D.L.; data curation, D.L.; writing—original draft preparation, D.L.; writing—review and editing, J.P.N.T. and J.F.P.F.; supervision, J.P.N.T. and J.F.P.F.; funding acquisition, J.P.N.T. All authors have read and agreed to the published version of the manuscript. Energies 2020, 13, 5017 17 of 18

Funding: This work is financed by national funds through FCT - Foundation for Science and Technology, I.P., through IDMEC, under LAETA, project UIDB/50022/2020 and under IT, project UIDB50008/2020. Conflicts of Interest: The authors declare no conflict of interest.

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