Energy Conversion and Management 123 (2016) 218–231

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Energy Conversion and Management

journal homepage: www.elsevier .com/locate /enconman

A holistic approach to thermodynamic analysis of photo-thermo-electrical processes in a photovoltaic cell

http://dx.doi.org/10.1016/j.enconman.2016.05.0900196-8904/� 2016 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail addresses: yusuf.bicer@uoit.ca (Y. Bicer), ibrahim.dincer@uoit.ca

(I. Dincer), calin.zamfirescu@uoit.ca (C. Zamfirescu).

Yusuf Bicer a,⇑, Ibrahim Dincer b, Calin Zamfirescu a

a Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, Ontario L1H 7K4, CanadabDepartment of Mechanical Engineering, KFUPM, Dhahran 31261, Saudi Arabia

a r t i c l e i n f o a b s t r a c t

Article history:Received 5 April 2016Received in revised form 27 May 2016Accepted 27 May 2016Available online 20 June 2016

Keywords:Solar energyPhotovoltaicsEnergyExergyEfficiency

In this study, a novel approach for energy and exergy analyses of a photovoltaic (PV) cell is presented, andthe exergy destructions within the relevant optical, thermal and electrical processes are quantified. Thepresent study uses a holistic approach to cover all processes and their interactions inside a PV cell; suchas photonic: photons transmission, reflection and spectral absorption, background (blackbody) radiationemission at cell temperature; electrical: electron excitation to create a photocurrent, electron-holerecombination, electrical power transmission to an external load; and thermal: internal heat generationby shunt and series resistances, and heat dissipation by conduction-convection. A physical model whichconsiders the highly complex interaction and interdependence among these processes is introducedbased on energy and exergy balances completed by writing various constitutive equations, includingcorrelations for the convective heat transfer coefficient and the photocurrent dependence of the spectraldistribution of the quantum efficiency. The irreversibilities caused by the processes are assessed in termsof their relative magnitudes of the exergy destructions. The largest exergy destruction occurs in PVgenerator-photo current generation process followed by wafer-light absorption process. The overallenergy and exergy efficiencies are then determined based on the novel model for seven different atmo-spheric and ecological conditions. The lowest and highest exergy efficiencies of the PV cell are calculatedas 9.3% and 14% for two sample locations as Oshawa in Canada and Emirdag in Turkey, respectively.Furthermore, the effects of varying ambient conditions, light spectrum, wind velocity and solar intensityon the PV cell performance are investigated for comparative evaluations.

� 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Solar energy is the most abundant source of energy on theearth. The majority of physical and chemical reactions encounteredon earth, including photosynthesis and water and air circulation inthe atmosphere, is a direct or indirect result of solar radiation. Inorder to effectively utilize solar energy, the first issue encounteredis the low density of solar radiation per unit of earth surface [1].Hypothetically, the solar spectrum is more effectively utilized ifinstead of converting the concentrated radiation in high tempera-ture heat, one produces hydrogen via high energy spectrum, oneproduces electricity with photovoltaic modules using middle spec-trum photons and one converts only the high temperature heatassociated with long wave photons to electricity using a suitablethermodynamic power cycle [2]. The spectral splitters can easily

be developed by employing an appropriate combination of opticalfilters. Various dielectric coatings can be deposited in thin films togenerate selective filters or selective reflective surfaces. There are,in this regard, various studies presented in the literature toinvestigate the PV and PV/T system performances with/withoutthose surfaces.

Rawat et al. [3] presented a study for energy and exergy perfor-mances of PV systems to define the long-term performance inactual operational conditions. The degradation rate of 3.2 kWPCdTe PV system is found to be 0.18% per year after 23 months ofoperation in composite climate which is lower than the reporteddegradation rate of earlier CdTe technology. Nagae et al. [4]demonstrated that the FOF (field output factor) of a-Si PV panelsmeaningfully depends on the change of the incident solar spec-trum. In their research, for stacked a-Si PV modules, little influenceof both APE (average photon energy) and module temperature onFOF was observed. Bicer et al. [5,6] assessed the performance of aPV cell under various spectral irradiance by conducting experimen-tal studies using different type of optic filters and measurement

Nomenclature

Ac PV cell surface area (m2)Ak spectral absorbancec photonic constant (mK)c speed of light (3 � 108 m/s)CPV concentrated photovoltaice charge of an electron (1.60217657 � 1019 C)_E energy rate (W)_Ex exergy rate (W)ex specific exergy (J/kg)h Planck’s constant (6.62606957 � 10�34 m2 kg/s)hc heat transfer coefficient (W/m2 K)I irradiance (W/m2)J current density (A/m2)k Boltzmann constant (1.3806488 � 1023 J/K)k extinction coefficientkt thermal conductivity (W/mK)n refraction indexP pressure (kPa)PV photovoltaic_Q heat transfer rate (W)R reflectanceRs internal series resistance of PV cellSF shape factorSTo total amount of normal radiation (W/m2)ST global solar radiation (W/m2)_S entropy rate (W/K)s specific entropy (J/kg K)T transmittanceT temperature (K)U overall heat transfer coefficient (W/m2 K)v wind speed (m/s)V voltage (V)_W work rate (W)

Greek symbolsgen energy efficiency

gex exergy efficiencygc ideal conversion effectiveness of solar radiationk wavelengthh incident angleU spectral quantum efficiencyp Pi number

Subscriptsabs absorbedact actualb blackbodyc cellcas casingd destructionD diodeg gapin inputm maximummax maximummin minimumoc open circuitov overallpce power conversion efficiencyPOA plane of arrayph photonrad radiationrev reversibles serials sunsc short circuitsh shuntwaf wafertot total� ambient condition

Y. Bicer et al. / Energy Conversion and Management 123 (2016) 218–231 219

devices. It was concluded that separation of spectrum could bebeneficial when whole spectrum is utilized properly. Saloux et al.[7] developed electrical and thermal models of PV/T systemoperating under different environmental conditions such as solarintensity and ambient temperature considering the irreversibili-ties. Ho et al. [8] analyzed the solar concentration limits for highconcentrated photovoltaic cells by using a two-phase coolingdesign. The results from their analysis emphasized that the limitsare close to 2000 suns for the six organic fluids investigated, butfor water and ammonia, the practical concentration limit could riseuntil about 4000 and 6000 suns, respectively.

Current efficiency values of PV systems continue to improve asreported by many researchers. Peumans and Forrest [9] evaluatedpower conversion efficiency of an organic thin-film double-heterostructure photovoltaic cells using vacuum-deposited copperphthalocyanine/C60. In 2001, they found the efficiency as 3.6% andresulted that the efficiency of organic solar cells employing an EBLcan be significantly higher than conventional cells, depending onmaterials and processing parameters. As reported by Green et al.[10] on regular basis, currently Si (multi-crystalline) PV cell con-firmed efficiencies can rise up to 21.2% while thin film (GaAs) typescan be more efficient reaching up to 28.8% for terrestrial cells.Furthermore, for a concentration of 508 suns, GaInAsP/GaInAsbased multi-junction cell efficiency was measured as 46% for areally small cell with an area of 0.0520 cm2.

There have been a couple of studies related to exergy analysis ofPV or PV/T systems. Zamfirescu and Dincer [11] proposed thermo-dynamic model to study the exergetic content of incident solarradiation reaching on the Earth’s surface which can be used toproduce work through a dually cascaded thermodynamic cycle.The model shows that the whole Earth functions as a heat enginecoupled to a brake such that the insolation and also the climateare predictable as a constructal design of the global flow system.Agrawal and Tiwari [12] compared the performances of varioustypes of PVT collectors operated throughout the year. The unglazedPVT air collector in their study had the highest exergetic efficiency.They also emphasized the inverse relation between the cell tem-perature and electrical efficiency of the PVT by suggesting furtherlife cycle cost assessment studies. Sudhakar and Srivastava [13]performed energy and exergy analysis of a PV array to determineexergy losses during the PV conversion process considering theoperating and electrical parameters, PV module temperature, over-all heat loss coefficient, open-circuit voltage, short-circuit currentand fill factor as experimentally. They concluded that the exergylosses increased with increasing module temperature and theexergy efficiency can be improved if the heat can be removed fromthe PV module surface. Energy and exergy efficiencies for PV mod-ule were found to be 6.4% and 8.5%, respectively. Joshi and Tiwari[14] evaluated exergy analyses of a hybrid photovoltaic–thermal(PV/T) parallel plate air collector for cold climate circumstance of

220 Y. Bicer et al. / Energy Conversion and Management 123 (2016) 218–231

India (Srinagar). The efficiency of a hybrid PV/T parallel plate aircollector was calculated for four climatic circumstances. It wasfound that there is a rise of about 2–3% exergy because of thermalenergy in addition to its 12% electrical output from PV/T system,which makes an overall electrical efficiency of about 14–15% ofPV/T system. Joshi et al. [15] assessed the exergy efficiency forPV and PV/T systems by studying the PV and PV/T performanceand possible improvements. The exergy efficiency of PV/T changesfrom a minimum of 11.3% to a maximum of 16% and exergyefficiency of PV alters from a minimum of 7.8% to a maximum of13.8%, respectively. Sahin et al. [16] studied thermodynamiccharacteristics of solar photovoltaic (PV) cells in terms of exergy.They applied exergy analysis to a PV system and its components,and exergy flows, losses and efficiencies were evaluated. Energyefficiency was found to be between 7% and 12% while exergyefficiency changes from 2% to 8%. Shan et al. [17] analyzed theperformances of PV/T systems by changing the configurations ofthe pipes over or below the PV cell. In their research, they investi-gated the overall heat transfer and thermodynamic aspects tocalculate the thermal power, electrical power, thermal efficiencyand hence overall efficiency of the PV/T system. The thermal powergain was maximum at noon time for all type of configurationsreaching to 360 W for the case where there are pipes both underand over the PV cell.

A set of different approaches to exergy efficiency definitions ofPV and PV/T systems have been raised. Akyuz et al. [18] defined thePV exergy efficiency in terms of the location of the sun and timewhere the incidence angle and the day of the year were taken asparameters for the calculation of PV exergy efficiency. The devia-tions of exergy efficiency were examined for two cases using realexperimental data acquired from an installed PV system in Turkey.Shahsavar et al. [19] presented a study to analyze the energy andthe exergy performance of a naturally ventilated photovoltaic-thermal (PV/T) air collector using experimentally validated mode.They also studied the effect of the solar radiation, channel depth,collector length, and PV cell efficiency on total energy and exergyefficiency of system concluding that setting glass cover on photo-voltaic panels leads to an increase of the outlet air and PV paneltemperature and decrease of the operating voltage and current ofthe PV panels. Sarhaddi et al. [20] studied energy and exergy anal-ysis for the thermal and electrical parameters, exergy componentsand exergy efficiency of a typical PV/T air collector. Proposing anew exergy efficiency definition, they found thermal efficiency,electrical efficiency, overall energy efficiency and exergy efficiencyof PV/T air collector as about 17.18%, 10.01%, 45% and 10.75%respectively. Ceylan and Gürel [21] conducted experiments forPV efficiency and obtained overall exergy efficiency as about 17%for 45 �C set temperature and 21% for 55 �C set temperature. Theyconcluded that increasing outlet water temperature of the modulewill reduce the electrical efficiency of the module. Singh et al. [22]proposed two channels over and below the solar cell in order toextract the heat by modelling the system thermally. They evalu-ated varying weather conditions, such as cloudy and hazy daysfor performance evaluations. The thermal gain was maximum inMay for the city of Srinagar, India. They compared the singlechannel and dual channel to investigate the impact on the celltemperature and found that dual channel decreases the celltemperature nearly half compared to single channel.

A few reviews based on solar energy systems have beenprepared. Wu et al. [23] presented a comprehensive review andsystematic summarization of methodology for calculating heatand exergy losses of conventional PV/T systems. They emphasizedimportance of identifying the causes and locations of the thermo-dynamic limitation, determinations of exergy loss within compo-nents and distributions in PV/T system. They concluded thatthere is still further works needed with respect to the calculations

of heat and exergy losses. Tiwari et al. [24] reviewed descriptionand thermal model of PV and hybrid photovoltaic thermal (HPVT)systems, using water and air as the working fluid resulting that theuse of BIPVT systems is always advantageous from the economicpoint of view than similar BIPV system. The manufacturing costis least (1.5 $/kWp) for amorphous silicon (a-Si) and is most(2.5 $/kWp) for mono-crystalline silicon. Royne et al. [25]overviewed various methods that can be used for cooling of photo-voltaic cells especially under concentrated light. They implied thatcooling system needs a design to keep the cell temperature lowand uniform, be simple and reliable, keep dependent powerconsumption to a minimum and allows the utilization of extractedthermal heat.

The effects of materials used in PV and PV/T systems onefficiency values were also investigated. Chow et al. [26] impliedthat in PV/T, the use of glass cover on the flat-plate hybrid solarcollector is preferable to the photothermic process but not to thephotovoltaic process. Based on experimental data and validatednumerical models, a study of the suitability of glass cover on athermosyphon-based water-heating PV/T system were carriedout. From the exergy analysis point of view, the increase of PV cellefficiency, packing factor, water mass to collector area ratio, andwind velocity are considered preferable to go for an unglazed sys-tem, whereas the increase of on-site solar radiation and ambienttemperature are favorable for a glazed system. Xu et al. [27] pre-sented a theoretic outline for the thermodynamic analyses of thesolar power tower system using molten salt as the heat transferfluid. Both the energy and exergy losses in each section and inthe overall system are assessed to detect the reasons and positionsof the thermodynamic imperfection. The results showed that themaximum exergy loss occurs in the receiver system, followed bythe heliostat field system, although main energy loss occurs inthe power cycle system. Al-Nimr and Al-Shohani [28] studied threelocations in Iraq in terms of the solar radiation data and environ-ment temperature in order to make a comparison with the PVenergy outputs. They also assessed the amount of greenhousegases prevented by using a single PV module. They concluded thatoverall solar radiation is the primary decision making parameter.Different electrical models of PV cells and modules have beenproposed and studied so far e.g., Farret et al. [29]. However,considering electrical, optical and thermal processes, there hasnot been any study based on our knowledge.

In this paper, a novel approach to the processes inside a PV cellis addressed. In the previous studies, although there are exergyanalysis for PV cells, they did not focus on exergy losses anddestructions caused by internal processes. In this new approach,absorption, radiation, reflection, heat dissipation, heat penetrationand electrical power transmission processes are exegeticallyanalyzed and irreversibility caused by these processes arecomparatively assessed. The specific objectives of the presentstudy are then listed as follows:

� to design and identify the state points throughout the system,� to analyze the presently proposed system using energy andexergy analysis methodologies, including energy, entropy andexergy balance equations on each of the processes of thesystem,

� to determine the irreversibilities with their magnitudes insidethe PV cell, and

� to investigate overall energy and exergy efficiencies of the PVcell and its sub processes.

2. Description of processes

The steps of exergy analysis of a PV cell under imposed operat-ing conditions are illustrated in this section. The purpose of the

RLo

ad

Rs

RshDiode

Idea

l PV

gen

erat

or JshJdark

Jload

Jph

V

Fig. 2. Equivalent electric circuit diagram of PV cell.

Y. Bicer et al. / Energy Conversion and Management 123 (2016) 218–231 221

exergy analysis is to assess the system (PV cell) with respect to atotally reversible power cycle operating under the same energysource (photonic radiation) and the environment. The exergyanalysis and assessment study determines the exergy efficiencyand exergy destruction of the overall system and of the sub-processes, namely; photonic, thermal and electrical as illustratedin Fig. 1 where the equivalent electrical circuit diagram of a PV cellis shown in Fig. 2.

In the second analysis step, the streams and the state points aredescribed in detail. The state points in Fig. 1 are described as givenin Table 1 below. Only a part (4) of the incident photons (1) areabsorbed by the wafer (photovoltaic generator). Much of theenergy of the absorbed photons is dissipated as heat (5) due tovibronic interaction. The generated photovoltaic power istransferred to the shunt resistance (6), to the p-n junction for itspolarization (8), to the load (14) and to the internal seriesresistance (11).

The solar spectra and air mass can be predicted according to themethodology adopted by NREL (National Renewable EnergyLaboratory) which are based on the paper of Gueymard [30] andcan be calculated with the help of software SMARTS described inGueymard [31]. Beside the air mass, the solar spectrum dependson the water content and ozone in the atmosphere, also on turbid-ity, aerosol types and concentration, cloudiness and haziness andoptical thickness of the atmosphere. The most important parame-ter that influences both the intensity of solar radiation at earthsurface and the spectrum is the air mass. The air mass is definedas the ratio between the path length of sunrays through the

Wafer

3

4

1

2

6

11

Ideal PV generator

Light fluxElectric powerHeat flux

State Description1 Light radiation input2 Light radiation reflected3 Light transmitted by the4 Light radiation absorbed5 Heat dissipation due to v6 Electric power transferr7 Dissipated heat by the s8 Electrical power transfe9 Dissipated heat by the p10 Blackbody radiation at c11 Electric power transferr12 Dissipated heat by the s13 Heat flux dissipated by 14 Useful power output del

Fig. 1. Schematic diagram of P

atmosphere and the effective atmosphere thickness at local zenith.Air mass depends on the zenith angle, the day of the year and thegeographical latitude. At sea level when sun is at zenith then airmass is AM = 1, while if sun is at horizon then AM = 38.2 whereasAM1.5 is the most widely adopted case (zenith angle = 48.2�).

Monocrystalline wafer is made of silicon with a single, constantcrystal assembly grown from a minor seed crystal which is gradu-ally pulled out of a polysilicon melt into a cylindrical formed ingot.The ingot is cut into wafers by means of a diamond saw. Siliconwaste from the sawing method may be recycled into polysilicon.Polycrystalline wafer is made of polycrystalline silicon comprises

Shunt resistance

Ideal p-n junction

Serial resistance

Cell Casingat Tc

8

5

12

13

14

9

10

7

by the wafer wafer according by the waferibronic interaction of the photons

ed to the shunt resistancehunt resistancerred to the p-n junction-n junctionell temperature c

ed to the internal series resistanceeries resistancethe casing into the environment at 0

ivered to the load

V cell as a new approach.

Table 1Descriptions and definitions of state points within the system.

State Description

1 Light radiation input at temperature T1 ¼ Trad and with spectralirradiance Ik;1

2 Light radiation reflected by the wafer according to spectral reflectanceRk

3 Light transmitted by the wafer according to spectral transmittance Tk

4 Light radiation absorbed through the wafer according to spectralabsorbance Ak and eventually contributing to photocurrent generation

5 Heat dissipation due to vibronic interaction of the absorbed photonswith the wafer

6 Electric power transferred to the shunt resistance, _W 006 ¼ JshVD

7 Dissipated heat by the shunt resistance, transferred to the casing at Tc,_Q 006 ¼ _W 00

5

8 Electrical power transferred to the p-n junction, _W 008 ¼ JdarkVD

9 Dissipated heat by the p-n junction transferred to the cell casing at Tc

10 Blackbody radiation at cell temperature Tc absorbed by the p-n junction,

I10 ¼ _Q 009

11 Electric power transferred to the internal series resistance, _W 0011 ¼ JLoadVs

12 Dissipated heat by the series resistance, transferred to the casing at Tc,_Q 0012 ¼ _W 00

11

13 Heat flux dissipated by the casing into the environment at T0

14 Useful power output delivered to the load, _W 0014 ¼ JLoadVLoad

222 Y. Bicer et al. / Energy Conversion and Management 123 (2016) 218–231

minor grains of monocrystalline silicon. Cube shaped ingots can beprepared directly by casting molten polysilicon, which are then cutinto wafers parallel to monocrystalline wafers. Solar cells made ofc-Si are made from wafers between 160 to 240 lm thickness.Surface texturing, either in combination with an anti-reflectioncoating or by itself, can also be used to diminish reflection. Anyroughening of the surface decreases reflection by growing theprobabilities of reflected light bouncing back onto the surface,rather than out to the immediate air.

In the current study, an optical model so called OPAL 2 isutilized where it is an optical simulator for the front surface of aphotovoltaic solar cell [32]. In the mentioned model, the structureof a solar cell is selected and OPAL 2 computes the reflection fromits front surface, the absorption in its thin-film coatings, and thetransmission into its substrate over a series of wavelengths. OPAL2 at the same time estimates the photocurrent that is generatedwithin the cell for a given incident spectrum. The generation pat-tern is estimated. The assumptions in the model are as follows:(i) all transmitted light moves perpendicularly to the plane of thesubstrate, and (ii) secondary-pass light is absorbed evenly in thesubstrate. Thus, the net generation should be accurate for a givenset of inputs, but the distribution of that generation withinsubstrate is approximate. Substrate width of wafer is assumed tobe 180 mm in the current study. It is made of crystalline at 300 K[32]. In the current study, a monocrystalline silicon (m-Si) typePV cell with an area of 100 cm2 is utilized for the analyses. Theanalyzed spectra include the wavelengths between 280 nm and4000 nm.

The spectral distribution of solar light is obtained using SMARTSsoftware developed by NREL [31]. Seven different conditions areselected for a comparative assessment. In this regard, two locationsare identified for the analyses as case studies, which are Oshawa inCanada and Afyon in Turkey. These geographical areas havedifferent climatic conditions. The details of the selected conditionsare listed in Table 2. The solar wavelength range is assumedto be between 280 nm and 4000 nm, and the solar constant is1367W/m2. The solar constant is defined as the quantity of solarenergy (W/m2) at normal incidence outside the atmosphere(extraterrestrial) at the mean sun-earth distance. However, the

standard spectrum at the Earth’s surface is called AM1.5. The airmass values and irradiances for specific locations are calculatedbased on the coordinates and date of the year via SMARTS soft-ware. It is assumed that PV cell has two axis tracking unit, hencesolar position and cell position are equal in terms of azimuth andzenith angle. The time of the day is taken to be as 1.00 pm localstandard time for all cases. The direct, diffuse and global tilted irra-diance values for selected cases are shown in Table 3. The gaseousabsorption and pollution are varied for cases 6 and 7. Ecologicalconditions such as vegetation, soil type and geographic irregularityaffect the PV performance because of Albedo effect. The Albedo isthe percentage of incoming radiation reflected off a surface whichcontribute to total irradiance on the PV surface. The referenceatmosphere is also changed for the cases based on the season.The U.S. Standard Atmosphere is an atmospheric model in whichpressure, temperature, density, and viscosity of the Earth’satmosphere alternate over an extensive collection of altitudes orelevations. The model which is constructed over an existinginternational standard, was first distributed in 1958 by the U.S.Committee on Extension to the Standard Atmosphere. It was thenupdated in 1962, 1966, and 1976. It is essentially reliable in proce-dure with the International Standard Atmosphere, opposing mostlyin the assumed temperature distribution at higher altitudes. MLSand MLW represent the middle latitude summer and middlelatitude winter, respectively. The middle latitudes are between23�2602200 North and 66�3303900 North, and between 23�2602200

South and 66�3303900 South latitude, or, the Earth’s temperate zonesbetween the tropics and the Arctic and Antarctic polar regions. Theaerosol type is set to S&F RURAL or S&F URBANwhere it is based onShettle and Fenn [33] and SRA CONTL or SRA URBAN where it isbased on IAMAP preliminary standard atmosphere [34]. Equivalentcircuit parameters of PV cell such as saturation current, seriesresistance etc. are utilized from Refs. [35,36] as shown in Table 4.

3. Analysis and modeling

In the analyses section, steady-state energy balance equations(EBE) are written for each process which is each functional unitfrom the above Fig. 1. A code to solve the system is constructedin Engineering Equation Solver (EES). The energy and exergy bal-ance equations of the processes are given in Table 5.

In order to determine the maximum amount of work from solarradiation incident on the Earth, ideal conversion effectiveness ofsolar radiation (gc) may be expressed:

gc ¼ 1� To

Ts

and the maximum work utilized from solar radiation (exergy) canbe obtained through the following equation:

_Exmax ¼ gcSTowith STo ¼ ST

cosh

where STo is the total amount of normal radiation, ST is the amountof measured radiation, Ts is the temperature of sun and h representsthe incidence angle.

Alternatively, the relative potential of maximum energyavailable from radiation can be calculated based on Petela’sequation as follows [37]:

gp ¼ 1� 43To

Tsþ 13

To

Ts

� �4

In general, the overall heat loss from a PV cell can be written asfollows:

Table 2Conditions of selected seven cases.

Input 1 2 3 4 5 6 7

Location Oshawa, Canada Oshawa, Canada Oshawa, Canada Emirdag, Afyon,Turkey

Emirdag, Afyon,Turkey

Emirdag, Afyon,Turkey

Emirdag, Afyon,Turkey

Coordinates N 43.9 N 43.9 N 43.9 N 39.047234 N 39.047234 N 39.047234 N 39.047234W 78.85 W 78.85 W 78.85 E 31.375753 E 31.375754 E 31.375755 E 31.375756

Date 15-Aug-16 15-Jun-16 15-Jan-16 15-Jun-16 15-Jan-16 15-Jan-16 15-July-16Atmosphere U.S standard

atmosphere 1976MLS MLW MLS MLW MLW MLS

Aerosol type S&F_RURAL SRA Urban SRA Urban S&F_RURAL S&F_RURAL S&F_RURAL SRA_CONTLTemperature (ground

level, K)287.6 293.7 271.9 289.7 268.7 268.7 289.7

Cell temperature (K) 314.9 319.6 294.8 318.5 296.2 297.4 317.5Wind speed (m/s) 2.88 3.28 4.16 2.4 2.2 2.2 2.5Altitude (m) 100 100 100 1000 1000 1000 1000Albedo and ground

reflectanceGrass and deciduoustrees

Concrete Concrete Dry grass Soil Mountain Wheat crop

Zenith angle(apparent)

31.357 22.448 65.493 20.898 61.626 61.626 21.75

Azimuth (from North) 199.04 207.28 189.05 226.01 194.93 194.93 220.14Turbidity 0.084 0.084 0.084 0.084 0.084 0.094 0.094Gaseous absorption

and pollutionBased on referenceatmosphere

Based on referenceatmosphere

Based on referenceatmosphere

Based on referenceatmosphere

Based on referenceatmosphere

Moderatepollution

Moderatepollution

Table 3Direct, diffuse and global tilted irradiance values for selected cases.

Irradiance 1 2 3 4 5 6 7

Direct beam (W/m2) 935.18 912.94 825.56 949.2 898.55 879.09 933.19Sky diffuse (W/m2) 89.78 87.3 53.85 106.28 74.45 98.53 96.44Ground reflected (W/m2) 16.29 11.83 59.88 12.92 32.87 72.56 8.98Global (W/m2) 1041.25 1012.07 939.29 1068.4 1005.87 1050.18 1038.61

Table 4Parameters for PV equivalent circuit analyses (data from Refs. [35,36]).

Parameter Value

Vload (V) 0.437Jload (A/m2) 69.1Acell (m2) 0.01Rs (X) 0.0364Rsh (X) 60.2409Jdark (A/m2) 6.45E�10J0 (A/m2) 3.27E�06Voc (V) 0.558Jsc (A/m2) 76

Y. Bicer et al. / Energy Conversion and Management 123 (2016) 218–231 223

_Qloss ¼ UPVAcðTc � ToÞ ð1Þ

with UPV ¼ 24:1þ 2:9v [38,39].Here, UPV is the heat exchange coefficient corresponding to thetotal surface area of the cell because the heat is lost by the twofaces of the PV cell where lateral surfaces are neglected, (v) isthe wind speed assumed, Tc is cell temperature, To is ambient tem-perature and Ac is the PV surface area. Each internal process is

Table 5Energy and exergy balance equations of the processes inside the PV cell.

Process Energy balance equa

Wafer - light absorption _E1 ¼ _E2 þ _E3 þ _E4

PV generator - photocurrent generation _E4 ¼ _E5 þ _E6 þ _E8 þShunt resistance - dissipation _E6 ¼ _E7Ideal p-n junction - dissipation _E8 þ _E10 ¼ _E9

Series resistance - dissipation _E11 ¼ _E12

Cell casing - heat transfer _E5 þ _E7 þ _E9 þ _E12 ¼Overall _E1 ¼ _E2 þ _E3 þ _E13 þ

defined separately, and energy and exergy balance equations arewritten.

The cell temperature Tc is calculated based on the followingcorrelation [40]:

Tc ¼ To þ IPOAeð�3:473�0:0594�vÞ ð2Þ

3.1. Wafer – light absorption process

The solar light is received by the wafer and a portion of thespectra are transmitted and reflected. Here, the absorbed spectrumis considered as useful.

The input energy rate to the system is defined as follows:

_E1 ¼ Ac

Z 1

0Ikdk ð3Þ

where Ac is the cell surface areaA part of incoming energy is reflected by wafer as _E2:

_E2 ¼ Ac

Z 1

0RkIkdk ð4Þ

tion Exergy balance equation

_Ex1 ¼ _Ex2 þ _Ex3 þ _Ex4 þ _Exd;waf

_E11 þ _E14_Ex4 ¼ _Ex5 þ _Ex6 þ _Ex8 þ _Ex11 þ _Ex14 þ _Exd;ph_Ex6 ¼ _Ex7 þ _Exd;sh_Ex8 þ _Ex10 ¼ _Ex9 þ _Exd;dark_Ex11 ¼ _Ex12 þ _Exd;s

_E10 þ _E13_Ex5 þ _Ex7 þ _Ex9 þ _Ex12 ¼ _Ex10 þ _Ex13 þ _Exd;cas

_E14_Ex1 ¼ _Ex2 þ _Ex3 þ _Ex13 þ _Ex14 þ _Exd;cell

224 Y. Bicer et al. / Energy Conversion and Management 123 (2016) 218–231

where Rk is the spectral reflectance of wafer.The spectral reflectance is calculated based on the extinction

coefficient of the material (k) and the refraction index n accordingto Ref. [41].

Rk ¼ðnðkÞ � 1Þ2 þ kðkÞ2

ðnðkÞ þ 1Þ2 þ kðkÞ2

The refractive index (n) and extinction coefficient (k) are relatedto the interaction between a material and incident light, and areassociated with refraction and absorption, respectively. Bothrefractive index (n) and extinction coefficient (k) depend essen-tially on the wavelength.

A part of the incoming energy is lost because of transmittanceas _E3:

_E3 ¼ Ac

Z 1

0TkIkdk ð5Þ

where Tk is the spectral transmittance of wafer.Combining above expressions, energy captured by PV generator

is defined as follows:

_E4 ¼ Ac

Z 1

0ð1�Rk � TkÞIkdk ð6Þ

The exergy rate of state points from 1 to 4 can be calculated asfollows:

_Exi ¼ _E1ð1� T0=T iÞ; i ¼ f1;4g

The exergy destruction rate occurred in wafer – light absorptionprocess is defined as follows:

_Exd;tot;waf ¼ _Ex1 � _Ex4 ð7Þ

Here, temperatures of state points can be calculated from followingformulas [42]:

T1 ¼ hcSk

R10 IkdkR10 kIkdk

; T2 ¼ hcSk

R10 RkIkdkR10 kRkIkdk

;

T3 ¼ hcSk

R10 T kIkdkR10 kT kIkdk

; T4 ¼ hcSk

R10 ð1�Rk � T kÞIkdkR1

0 kð1�Rk � T kÞIkdk

As discussed in Chen et al. [42], the series of constants such as con-stant speed and wavelength can be extended with the temperatureconstant of a photon Tk and the entropy constant of a photon Sk.Therefore, when the photon interacts with a reference environmentof temperature To the energy conversion into work corresponds to aCarnot factor in accordance to Tk and To. This quantifies an exergydestruction by an individual photon. Thus, when a multi-chromatic photon radiation interrelates with matter at a referencetemperature To, the exergy destruction can be projected providedthat the spectral distribution of the radiation is identified.

3.2. PV generator – photocurrent generation process

It can be named as ideal because there is no ohmic dissipations,etc., but there is only vibronic dissipation due to quantum effi-ciency Ui;k < 1.

The dissipated heat by the photocurrent generator is defined asfollows:

_E5 ¼ _Qph ¼ SF kðTph � TcÞ ð8Þ

where SF is the shape factor for a conduction through plane wallwhere it is a 100 cm2 PV cell here, k is the thermal conductivityof silicon and Tph is the final temperature of the surface.

The energy rate in the shunt resistance is defined as total volt-age over the resistance divided by shunt resistance based on Ohm’slaw:

_E6 ¼ _Wsh ¼ ðVLoad þ JLoadAcRsÞ2=Rsh ð9Þ

The energy rate in ideal p-n junction is expressed as follows:_E8 ¼ _Wdark ¼ ðVLoad þ JLoadAcRsÞAcJdark ð10Þ

where Jdark is the current density over diode.The energy rate on series resistance is calculated based on

Ohm’s law:

_E11 ¼ _Ws ¼ RsðJLoadAcÞ2 ð11Þ

Finally, the energy utilized by the load is determined as follows:

_E14 ¼ _WLoad ¼ JLoadVLoad ¼ _Wmax ¼ FFJscVoc ð12Þ

since the cell generates maximum power.The exergy of heat dissipation at state point 5 is determined as

follows:

_Ex5 ¼ _Qphð1� T0=TcÞ ð13Þ

The exergy rate definitions of state points at 6, 8, 11 and 14 isequal to electrical work:

_Ex6 ¼ _Wsh; _Ex8 ¼ _Wdark; _Ex11 ¼ _Ws; _Ex14 ¼ _WLoad:

The exergy balance for the PV generator can be written as fol-lows and be solved to determine the exergy destruction by thephotocurrent generation process ( _Exd;tot;ph):

_Exd;tot;ph ¼ _Ex4 � _Ex6 þ _Ex8 þ _Ex11 þ _Ex14 ð14Þ

3.3. Shunt resistance – dissipation process

The shunt resistance behaves as heat source due to shunting ofthe generated photocurrent and can be expressed as follows:

_E7 ¼ _Q sh ¼ V sh

R2sh

ð15Þ

The exergy rate at state point 7 is determined:

_Ex7 ¼ _Q shð1� T0=TcÞ ð16Þ

The exergy destruction in shunt resistance – dissipation processis expressed:

_Exd;tot;sh ¼ _Ex6

3.4. Ideal p-n junction – dissipation process

Ideal p-n junction also dissipates heat because of dark currentover the diode which can be calculated as per following formula:

_E9 ¼ _Qdark where _Qdark is equal to AcJdarkVD

The blackbody radiation emitted from the p-n junction at statepoint 10 can be determined for the wavelengths between 280 nmand 4000 nm as

_E10 ¼ AcrT4c ð17Þ

The exergy rates at state points 9 and 10 are determined:

_Ex9 ¼ _Qdarkð1� T0=TcÞ ð18Þ

_Ex10 ¼ _E10ð1� T0=T10Þ ð19Þ

where T10 ¼ hcSk

R1

kgIk;bðTcÞdkR1

kgkIk;bðTcÞdk

[42] and kg ¼ hcEg.

The overall exergy destruction rate in ideal p-n junction –dissipation process is calculated as follows:

_Exd;tot;dark ¼ _Ex8 þ _Ex10 ð20Þ

Table 6Comparison of maximum solar energy conversion efficiencies for the selected cases.

Case Carnot efficiency Petela efficiency Difference

1 0.9502 0.9336 0.01662 0.9492 0.9322 0.0173 0.953 0.9373 0.01574 0.9499 0.9332 0.01675 0.9535 0.938 0.01556 0.9535 0.938 0.01557 0.9499 0.9332 0.0167

Y. Bicer et al. / Energy Conversion and Management 123 (2016) 218–231 225

3.5. Series resistance – dissipation process

Due to voltage drop over the series resistance, heat isgenerated:

_E12 ¼ _Q s ¼ IsVs ð21Þ

The exergy rate at state point 12 is expressed:

_Ex12 ¼ _Q sð1� T0=TcÞ ð22Þ

The exergy destruction rate in series resistance – dissipationprocess is defined: _Exd;tot;s ¼ _Ex11.

3.6. Cell casing – heat transfer process

There is a temperature difference between cell surface Tc andambient T0. Therefore a heat loss or heat penetration can occurdepending on the temperature values. It can be defined:

_E13 ¼ _Q cell ¼ hcAcðTc � ToÞ ð23Þ

0 400 800 1200 1600 20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Wavele

Irrad

ianc

e(W

m-2

nm-1

)

Fig. 3. (a) Reflection, absorption and transmission of selected wafer and (b) Global, ab

The exergy rate at state point 13 is written as follows based onTc and T0.

_Ex13 ¼ _Q cellð1� T0=TcÞ ð24Þ

The total exergy destruction rate in cell casing – heat transferprocess is determined as follows:

_Exd;tot;cas ¼ _Ex5 þ _Ex7 þ _Ex9 þ _Ex12 � _Ex10 ð25Þ

3.7. Overall system

The overall energy balance can be calculated:

_E1 ¼ _E2 þ _E3 þ _E13 þ _E14 ð26Þ

The overall exergy balance can be expressed:

_Exd;tot;cell ¼ _Ex1 � _Ex14 ð27Þ

The energy efficiency of overall system is determined asfollows:

gen ¼ _E14= _E1 ð28Þ

The exergy efficiency of the overall system is determined asfollows:

gex ¼_Ex14_Ex1

¼_Wact

_W tot;rev

ð29Þ

where _Wact ¼ _Wmax ¼ _Ex14 is the power generated by the actual celland _W tot;rev is the power produced by a totally reversible generatorconnected to the source of radiation 1 with radiation temperatureT1 and to the reference environment at T0.

000 2400 2800 3200 3600 4000ngth (nm)

GlobalGlobalReflectedTransmittedTransmitted

AbsorbedAbsorbed

(b)

(a)

sorbed, reflected and transmitted irradiance through the wafer inside the PV cell.

Fig. 4. Effects of ambient temperature on cell exergy efficiency and exergy destruction rates for case 1.

Fig. 5. Effects of average wind speed on cell efficiency and cell temperature for case 2.

Fig. 6. Effects of cell surface temperature on cell efficiency and exergy destruction rates for case 3.

226 Y. Bicer et al. / Energy Conversion and Management 123 (2016) 218–231

4. Results and discussion

The analyses are conducted using Engineering Equation Solver(EES) in order to determine the temperature, entropy and exergyof each state point.

The maximum conversion efficiencies from solar energy arecomparatively calculated and presented in Table 6 for the specificselected cases. The Petela equation yields lower conversionefficiencies compared to Carnot equation however, the maximum

difference is 1.7% for case 2. The results obtained using bothefficiency equations give similar values.

The reflection and transmission characteristics of silicon waferare shown in Fig. 3a for the entire wavelength from 280 nm to4000 nm. The UV portion of the spectrum is partially absorbedand reflected. The average absorption value of the wafer is about93% where this part contributes to power generation. As seen inFig. 3b, the global tilted irradiance on the PV cell surface is closeto transmitted beam. The maximum transmitted irradiance value

Fig. 7. Effects of global tilted irradiance at state point 1 on cell efficiency and exergy destruction rates for case 4.

Fig. 8. Effects of average wind speed on cell temperature and cell casing-heat transfer process for case 5.

Fig. 9. Effects of ambient temperature on cell temperature and exergy destruction rates for case 6.

Y. Bicer et al. / Energy Conversion and Management 123 (2016) 218–231 227

is seen at about 500 nm with a value of 1.703W/m2/nm. Between400 nm and 500 nm, a portion of the solar light correspondingto a maximum of 0.2526W/m2/nm is reflected and a lowerportion of solar light is absorbed with a maximum value of0.05126W/m2/nm. After 2600 nm, the solar irradiance is quite low.

Various parametric studies are conducted for the selected cases.In Fig. 4, the effect of varying ambient temperature on PV cell

efficiency and exergy destruction rates are illustrated. The ambienttemperature affects the cell performance and causes a slightdecrease in exergy efficiency of PV cell. The exergy destructionrate of photo current generation process decreases from 8.386Wto 8.354 W when the ambient temperature increases from 285 Kto 305 K. The overall exergy destruction in the cell decreases to8.805W at 305 K for case 1.

Fig. 10. Effects of ambient temperature on cell exergy efficiency and exergy destruction rates for case 7.

7.8

8

8.2

8.4

8.6

8.8

9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1 2 3 4 5 6 7Ce

ll to

am

bien

t hea

t tra

nsfe

r rat

e (W

)

Inte

rnal

hea

t tra

nsfe

r rat

e (W

)

CASEIdeal p-n junc�on PV generator Serial resistance Shunt resistance Cell casing

Fig. 11. Heat transfer rates for the internal and external processes inside the PV cell.

8.834

8.701

8.186

8.946

8.306

8.691

8.712

8.381

8.244

7.851

8.46

7.928

8.292

8.248

7 7.2 7.4 7.6 7.8 8 8.2 8.4 8.6 8.8 9

1

2

3

4

5

6

7

Exergy destruc�on rate (W)

Case

PV generator – photocurrent genera�on process Overall cell

Fig. 12. Exergy destruction rates of the PV generator and overall cell for all cases.

228 Y. Bicer et al. / Energy Conversion and Management 123 (2016) 218–231

The speed of the local wind is important for PV cell perfor-mance. An increase in the wind velocity rises the heat transfer ratefrom the cell. The useful energy increases henceforth overallenergy and exergy efficiencies slightly rise to about 10.5% and

11%, respectively for a wind speed of 7 m/s as shown in Fig. 5.Besides, the exergy destruction rates for the dissipation processof ideal p-n junction and heat transfer process of cell casing heattransfer process decrease for case 2 since the cell temperature

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

1 2 3 4 5 6 7

Exer

gy d

estr

uc�o

n ra

te (W

)

Case

Cell casing – heat transfer process

Wafer – light absorp�on process

Shunt resistance – dissipa�on process

Serial resistance – dissipa�on process

Ideal p-n junc�on – dissipa�on process

Fig. 13. Exergy destruction rates of various processes inside the PV cell for all cases.

Y. Bicer et al. / Energy Conversion and Management 123 (2016) 218–231 229

declines by rising wind velocity. Fig. 6 shows the changes in effi-ciencies and exergy destruction rates for case 3 based on the celltemperature. If the cell temperature increases from 290 K to295 K, the efficiencies decrease from about 26% to about 9%,whereas the exergy destruction rates increase for the photo cur-rent generation process and overall PV cell. Ideal p-n junction,shunt resistance and casing heat transfer processes have minorexergy destruction rates as shown in Fig. 7. When the global tiltedirradiance on the PV cell surface increases from 900W/m2 to1100W/m2, the energy and exergy efficiencies enhances to12.04% and 12.59%, respectively although exergy destruction ratefor casing heat transfer process increases for case 4. The useful out-put at state point 14 increases when the incoming irradiationboosts. Based on the correlations utilized in the study, the effectof wind speed on cell temperature is illustrated in Fig. 8 for case5. The wind speed has a positive impact on cell temperature byincreasing the overall heat transfer coefficient. However, thechange is not so high where it decreases to 293.4 K for 4 m/s windspeed. In addition, the ambient temperature is directly propor-tional to cell temperature as seen in Fig. 9. The overall exergydestruction rate for the PV cell slightly decreases with increasingambient temperature. The exergy efficiency of the PV cell increasesvery minor when the ambient temperature is changed from 280 Kto 300 K for case 7. The exergy destruction rate of photocurrent

1 2 3Energy Efficiency (%) 10.82 9.695 8.881Exergy Efficiency (%) 11.34 10.16 9.308

-1

1

3

5

7

9

11

13

15

Effici

ency

(%)

Fig. 14. Overall energy and exergy efficien

generation process and overall cell goes down to 8.231 W and8.695 W, respectively at 300 K as shown in Fig. 10.

The generation of heat internally plays an important role in PVcell performance as comparatively illustrated in Fig. 11. The cellcasing heat dissipation process is the major contributor whereasthe other processes are lower than 1W. The second highest heatdissipation occurs in PV generator where it corresponds to0.665W for case 3. The serial and shunt resistance have heat dissi-pation rates of 0.017W and 0.004 W for case 5. Noteworthy powerlosses triggered by the existence of a shunt resistance are charac-teristically because of manufacturing defects, instead of poor solarcell scheme. Little shunt resistance sources power losses in the PVcells by giving an alternative current route for the light producedcurrent. Such a change decreases the quantity of current travellingover the solar cell junction and diminishes the voltage of the PVcell. The influence of a shunt resistance is mainly serious at lowintensity levels. Because, there will be fewer current which is pro-duced by light. The loss of the current to the shunt consequentlytakes a greater effect. Furthermore, at minor voltages in whichthe actual resistance of the PV cell is great, the effect of a resistancein parallel is huge.

The total exergy destruction rates for all cases are shown inFig. 12. Since the highest contributor is PV generator, it is compar-atively shown in the figure. The highest exergy destruction occurs

4 5 6 711.92 13.33 13.28 11.72

12.48 13.96 13.89 12.29

cy values of the PV cell for all cases.

230 Y. Bicer et al. / Energy Conversion and Management 123 (2016) 218–231

in case 4 with a value of 8.946 W. This is the case in Emirdag,Afyon, Turkey for June 2016, the ambient temperature is 289.7 Kand the wind velocity is 2.4 m/s, however, case 3 yields lowestexergy destruction rate which is January 2016 in Oshawa, Canada,the ambient temperature is 271.9 K and the wind speed is4.16 m/s. This can be interpreted as the effect of ambient temper-ature and cell temperature on non-useful heat dissipation. Fig. 13illustrates the exergy destruction rates of the internal processesfor all cases. Wafer light absorption process is the highest contrib-utor for all the cases where it corresponds to 0.4652 W for case 4.Cell casing heat transfer process is the second highest contributoramong the other internal processes followed by series resistancedissipation process. In overall, the energy and exergy efficienciesare calculated based on the given conditions and presented inFig. 14. The lowest and highest exergy efficiencies of the PV cellare calculated for case 3 and case 5 corresponding to 9.3% and13.96%, respectively. Case 5 represents Emirdag, Afyon, Turkey inJanuary 2016 where the cell temperature is 296.2 K, the windspeed is 2.2 m/s, the altitude is 1000 m and soil ground reflectanceconditions are present. The efficiencies for case 6 is slightly lower(0.1%) than case 5 where the differences are in turbidity,atmospheric pollution and mountainous ground reflectance condi-tions. The winter conditions yield better efficiencies for Emirdag,Afyon, Turkey, on the contrary, summer conditions yield higherefficiencies for Oshawa, Ontario, Canada.

5. Conclusions

In this study, holistic exergy analyses of a PV cell under variousclimatic conditions are comparatively conducted. The parameters,such as ambient temperature, wind velocity, gaseous absorptionand pollution, turbidity, albedo reflectance and seasons are variedin order to investigate the effects on PV cell performance. Twodifferent climatic locations are selected in Turkey and Canada.The internal processes of a PV cell include: transmission, reflectionand absorption of photons through wafer, background (blackbody)radiation emission at cell temperature, electron excitation togenerate a photocurrent, electron-hole recombination, internalheat generation by shunt and series resistances, heat dissipationby conduction-convection, and electrical power transmission to aload. The purpose of the exergy analysis is to assess the PV cellwith respect to a totally reversible power cycle operating underthe same photonic radiation and the environment. The exergydestruction rates for each internal process are determined, andthe overall energy and exergy efficiencies of the PV cell are calcu-lated. The following concluding remarks can be extracted from thepresent study:

� The highest PV cell exergy efficiency (13.96%) is obtained forcase 5 in Emirdag, Afyon, Turkey in winter, contrariwise, thelowest exergy efficiency (9.3%) is obtained for case 3 in Oshawa,Ontario, Canada in winter.

� The velocity of wind and the cell temperature have significantinfluences on the overall PV performance.

� The heat transfer rate from cell casing to environment is quitehigh corresponding to about 90% of the overall input. Hence,this heat can be utilized using photovoltaic/thermal systems.

� The atmospheric conditions such as aerosol type, turbidity andgaseous absorption/pollution vaguely affect the performance.

� The Albedo and ground reflectance conditions contribute toirradiance levels received by the PV cell and eventually affectthe efficiency.

� The PV generator-photo current generation process has thehighest exergy destruction rate among the sub-processes.

� The wafer-light absorption and transmission process has secondlargest exergy destruction in the PV cell.

Acknowledgement

The authors acknowledge the support provided by the NaturalSciences and Engineering Research Council of Canada.

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