Energy Conversion and Management 115 (2016) 288–298

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Energy Conversion and Management

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Modeling and performance analysis of a concentrated photovoltaic–thermoelectric hybrid power generation system

http://dx.doi.org/10.1016/j.enconman.2016.02.0610196-8904/� 2016 Elsevier Ltd. All rights reserved.

⇑ Corresponding authors. Tel.: +91 11 2659 6465/1253.E-mail addresses: ravitalamba.lamba247@gmail.com (R. Lamba), kaushik@ces.

iitd.ac.in (S.C. Kaushik).

Ravita Lamba ⇑, S.C. Kaushik ⇑Centre for Energy Studies, Indian Institute of Technology Delhi, India

a r t i c l e i n f o

Article history:Received 8 December 2015Accepted 21 February 2016

Keywords:Photovoltaic moduleThermoelectric moduleIrreversible CPV–TEG hybrid systemThomson effect

a b s t r a c t

In this study, a thermodynamic model for analysing the performance of a concentrated photovoltaic–thermoelectric generator (CPV–TEG) hybrid system including Thomson effect in conjunction with Seebeck,Joule and Fourier heat conduction effects has been developed and simulated in MATALB environment.The expressions for calculating the temperature of photovoltaic (PV) module, hot and cold sides of ther-moelectric (TE) module are derived analytically as well. The effect of concentration ratio, number of ther-mocouples in TE module, solar irradiance, PV module current and TE module current on power outputand efficiency of the PV, TEG and hybrid PV–TEG system have been studied. The optimum concentrationratio corresponding to maximum power output of the hybrid system has been found out. It has beenobserved that by considering Thomson effect in TEG module, the power output of the PV, TE and hybridPV–TEG systems decreases and at C = 1 and 5, it reduces the power output of hybrid system by 0.7% and4.78% respectively. The results of this study may provide basis for performance optimization of a practicalirreversible CPV–TEG hybrid system.

� 2016 Elsevier Ltd. All rights reserved.

1. Introduction

The conventional fossil fuels are the most economic power gen-eration sources. Due to escalating energy demand and oil prices,growing concerns about various emissions from fossil fuel combus-tion are compelling researchers to pay more attention towardsrenewable energy sources which are economical and viable. Solarenergy is themost abundant and clean source among the renewableenergy sources. Photovoltaic (PV) cells are used to convert solarenergy into electricity. However, the efficient conversion of solarenergy into electricity has become the primary aim for researchers.PV cells convert a part of incident absorbed solar radiation into elec-tricity and a significant part is converted into heat. Thus, the ther-malization and absorption losses which are more than 50% ofincident solar radiation in PV cells limit the application of PV cells.Therefore, the electrical conversion efficiency is only 10–15% due toheat dissipation which causes the increase in PV cell temperatureand it is known that a negative correlation exists between PV celltemperature and efficiency. Furthermore, to get higher power out-put and efficiency per unit area of PV cell, the optical concentratorsare used to concentrate solar radiation on PV cells which increases

the intensity of incident beam radiation. However, with increase inpower output per unit area, the PV cell temperature will alsoincrease significantly in concentrated PV system which results indecrease in PV cell efficiency. Therefore, to overcome this drawbackof concentrated PV systems, some means for cooling of PV systemshould be employed. Several active and passive cooling methodshave been proposed since last few decades. Royne [1] presented acomprehensive review on various cooling methods. However, inmost of these cooling methods, the dissipated heat in PV systemsis rejected to the outside ambient. The most commonly usedmethod for active cooling is photovoltaic–thermal (PV/T) whichprovide both electricity and heat simultaneously. The innovativeidea of conversion of thermal energy into electricity directly usingthermoelectric generator (TEG) has been proposed several yearsback [2]. Van Sark [3] proposed the idea of PV–TEG hybrid systemin which, the wasted thermal energy of concentrated photovoltaic(CPV) system can be utilized in TEG by connecting the TEG to theback side of PV module. Since efficiency of photovoltaic (PV) mod-ules degrades at elevated temperatures up to about 25% dependingon the module integration type in the roof. The conversion effi-ciency for roof integrated PV–TE ideal system increases up to 23%for thermoelectric materials having figure of merit of 0.004 K�1 at300 K. However, the model was developed for ideal PV–TE system.Therefore, for practical PV–TE hybrids, the efficiency reduces by10%. Chavez-Urbiola et al. [4] examined the solar hybrid system

Nomenclature

A area (m2)C concentration ratioEg band-gap energy of semiconductor (eV)G solar irradiation (W/m2)h0 convective and radiative heat transfer coefficient

(W/m2 K)I electric current (A)k thermal conductivity (W/m K)kB Boltzmann constant (1.38 � 10�23 J/K)K thermal conductance (W/K)KI current temperature coefficient (mA/K)KV voltage temperature coefficient (V/K)l length of thermocouple elementL thickness (m)n number of p–n thermocouple elementsnid diode ideality factorns number of PV cells in seriesnp number of strings in parallelP electrical power (W)q electric charge (1.6 � 10�19 C)Q heat (W)R electrical resistance (X)RL1 output load of PV moduleRL2 output load of TEG modules seebeck coefficient (V/K)T temperature (K)UL overall heat transfer coefficient (W/m2 K)v wind velocity (m/s)V voltage (V)Z figure of merit (1/K)

Greek lettersa absorptivitybc packing factor of PV module

b0 PV cell temperature coefficient (K�1)l Thomson coefficient (V/K)r electrical conductivity (S/m)q electrical resistivity (Xm)s transmissivityg efficiency

Subscriptsa ambientb,ch bottom, cell to hot side of TEGc photovoltaic cellcontact contactsconducting metal conducting metaleff effectiveg glass coverh hot side of TEGl cold side of TEGmax maximumn n-type semiconductor materialOC open circuitp p-type semiconductor materialPV photovoltaic moduleph photo generatedTE thermoelectric moduleref reference conditionsrs reverse saturationSC short circuitSh shuntS seriesT tedlart,ca top, cell to ambient

R. Lamba, S.C. Kaushik / Energy Conversion and Management 115 (2016) 288–298 289

with TEG for four different configurations. The experiment studywas carried out for Bi2Te3 based TEGs with temperature differenceof 50–200 �C and it was found that the TEG’s efficiency, current andvoltage have linear dependency on the temperature differencebetween hot and cold junctions of TEG. Wang et al. [5] developeda novel PV–TEG hybrid system by inserting a selective absorberbetween PV and TEG. It was reported that the overall efficiency ofcombined dye-sensitized solar cell (DSSC) PV–TEG rises up to 13%due to use of solar selective absorber (SSA) and TE with 6.2 �C tem-perature gradient along the hot and cold junctions which utilizesthe low energy solar radiation transmitted through the DSSC.Although the hybrid device was not yet optimized however, it canbe used as proof-of-principle convert solar light and heat simulta-neously into electricity by a single device with high conversion effi-ciency. Vorobiev et al. [6] designed a hybrid solar system consistingof a concentrator, PC cell, heat engine and TEG. They discussed twooptions; in which one having a special PV cell construction, uses theheat energy of solar spectrumwhich was not absorbed in the semi-conductor material of the cell and the other is operating at hightemperature which uses concentrated PV cell coupled to the hightemperature stage. The analysis has been carried out for differentband-gap semiconductor materials and different thermoelectricmaterials. Zhang and Chau [7–8] proposed and implemented aPV–TEG hybrid system for automobiles inwhich TEGwas employedto utilize the waste heat of exhaust of internal combustion (IC)engine and optimized the power output with maximum powerpoint tracking (MPPT) technique. A prototype is developed andtested to validate the proposed system. He et al. [9] carried out

the energy and exergy analysis of a TE cooling and heating systemdriven by heat pipe PV/T in summer and winter operating condi-tions theoretically and experimentally. The results show that theelectrical and thermal efficiencies of the PV/T panel are 16.7% and23.5% respectively. The concluded that the energetic efficiency ofthe system is higher in summer operation mode as compared tothat of in winter operation mode. However, the exergetic efficiencyof the system is lower in summer operation mode as compared tothat of in winter operation mode. Kraemer et al. [10] and Xing Juet al. [11] developed and analyzed a spectrum splitting PV–TEGhybrid system numerically. They showed that these hybrid PV–TEG systems can maximize conversion efficiency and are moreappropriate at higher concentration. Tritt et al. [12] proposed thatfor TE power generation, the solar radiation can be utilized as heatsource. Yang and Yin [13] analyzed the novel PV–TE hybrid systemtheoretically and experimentally with water pipelines being usedas heat sink. The conversion efficiency depends on water flow tem-perature, solar irradiation and ambient temperature for givenmaterial properties of each layer. It was reported that the poweroutput of photovoltaic/thermoelectric/hot water (PV/TE/HW) sys-tem is up to 30% higher than PV/HW and conventional PV systems.Guo et al. [14] developed a two-compartment hybrid tandem cellcontaining a dye-sensitized solar cell (DSSC) at the top and a TE sys-tem at the bottom which uses the full solar spectrum in order toincrease the overall efficiency of the tandem cell. The efficiency ofhybrid tandem cell has been increased by 10% as compared to indi-vidual DSSC. Zhang et al. [15] evaluated the efficiency of concen-trated PV–TE hybrid system for different PV cells such as copper

290 R. Lamba, S.C. Kaushik / Energy Conversion and Management 115 (2016) 288–298

indium gallium selenide, crystalline silicon, silicon thin-film andpolymer photovoltaic cell. The influence of temperature on the effi-ciency of photovoltaic cell has been taken into account based on thesemiconductor equations, which reveals different efficiency tem-perature characteristic of polymer photovoltaic cells. They foundout that the polycrystalline silicon thin-film photovoltaic cell withoptimized convective heat transfer coefficient and concentratingratio and polymer photovoltaic cells are more suitable for concen-trated and non-concentrated PV–TE hybrid system respectively. Liet al. [16] proposed a PV–TE hybrid system which uses spectrumbeam splitting technique to effectively utilize wide spectrum solarradiation range. The short wavelength solar radiation is convertedinto electricity directly by PV cells by spectrum beam splittingand the long wavelength solar radiation part is utilized to generatethermal energy of moderate to high temperature which is con-verted into electricity by TE module. A thermal energy storage unitis also coupled to the system to overcome the intermittent nature ofsolar radiation. The integrated system has been optimized to gethigher overall efficiency. Rasmus and Nielson [17] examined theperformance of PV–TEG system analytically for four different com-mercial PV cells which are crystalline silicon (c-Si), amorphous sil-icon (a-Si), copper indium gallium diselenide (CIGS) and cadmiumtelluride (CdTe) and commercial Bismuth Telluride based TEG ana-lytically. It was found out that the combined system for c-Si, CIGSand CdTe PV cells has lower power output and efficiency than thatof PV alone and for a-Si cell, the overall system performanceincreases slightly.Wu et al. [18] developed and analyzed the perfor-mance of glazed and unglazed PV–TE hybrid system theoretically.The have taken nanofluid as heat sink for TE module to decreasethe temperature of cold junction of TE module which results inenhanced the temperature difference between hot and coldjunctions of TE module. They found out that the enhanced trans-missivity of glass cover and higher concentration ration and figureof merit for glazed system results in better performance as com-pared to unglazed system. The have considered the coupling effectof wind velocity and nano fluid flow rate on overall efficiency of thesystem. However, they have not considered temperaturedependentthermoelectric properties and effect of PV and TE module currentson power output and efficiency of hybrid system. Najafi andWoodbury [19] developed a comprehensive heat transfer modelto analyze the behavior of combined photovoltaic thermal–thermo-electric (PVT–TE) power generation system. The evaluated thegenerated power by combined PVT–TE system under differentirradiance levels. The determined the performance of the hybridsystem for a typical summer day in Tuscaloosa, AL in order to eval-uate the system performance for actual meteorological data. Theoptimized the number of thermoelectric modules to get maximumoverall power output. However, they have not optimized otherparameters of the hybrid system. Lin et al. [20] established aPV–TE hybrid system with the help of thermodynamic methodand analyzed the performance and load matching of hybrid system.The effects of TEG structural parameters, figure of merit and PVcurrent on the performance of hybrid system have been discussedin their analysis. However, they have not considered the concen-trated solar radiation and the heat losses from the top surface ofPV module to ambient by convection and radiation heat transferprocesses. Liao et al. [21] developed an irreversible hybrid powergeneration system which consists of a low concentrating PVmodule and a TEG and analyzed it theoretically. They calculatedthe maximum power output of hybrid device numerically and theoptimum load resistance for CPV and TEG have been determined.They found out the optimum criteria for some important parame-ters. However, they have not considered Thomson effect in TEGmodule. Wang et al. [22] have evaluated the efficacy of an inte-grated photovoltaic (PV)–air source heat pump system (ASHP) inCentral-south China. The thermodynamic and feasibility analysis

of integrated PV–ASHP system which consider the manufacturingprocess of PV system has been carried out. In this analysis, theinstalled capacity of PV system has been decided based on the ratedpower of ASHP system for heating ventilation and air conditioning(HVAC). The direct current (DC) power of PV in inverted to alternat-ing current (AC) to run the ASHP. The exergy efficiency, exergy con-sumption cost for per unit investment for cooling and heating andCO2 emission reduction have been calculated for six different cases.

From the literature review, it is clear that there exists a few the-oretical studies on performance analysis of concentrated PV–TEGhybrid system. Furthermore, the use of glazing on PV–TE systemtraps the solar radiation in PV system and thus reduces the heatlosses to the environment and prevents the damage of PV systemdue to dust and rain. However, the influence of Thomson effectin TEG subsystem of hybrid PV–TEG system has not yet been con-sidered in the previous literature. Therefore, in the present study, atheoretical model of a concentrated PV–TEG irreversible hybridsystem including conductive, convective and radiative heat lossesin the PV module and Thomson effect in conjunction with Seebeck,Joule and Fourier heat conduction effects in the TE module hasbeen developed theoretically and simulated in MATLAB Simulinkenvironment.

2. Modeling of an irreversible CPV–TEG hybrid system

The schematic and electrical equivalent circuit of proposedCPV–TEG hybrid system is shown in Figs. 1 and 2 respectively. Itconsists of, from top to bottom, a concentrator, a PV module, aTEG module and a heat sink. The PV module consists of series con-nected crystalline Silicon PV cells. The TEGmodule consists of ther-moelectric elements which are connected electrically in series andthermally in parallel. The bottom of the PV module is attached tothe hot side of TEG and the cold side of TEG is attached to the heatsink. In this hybrid CPV–TEG system, the thermal energy, producedin the CPV subsystem acts as a high temperature heat reservoir forTEG module and thus can be utilized efficiently in TEG to generatemore power. Therefore, the performance of overall system can beimproved. In this combined CPV–TEG system, the CPV and TEGmodules are thermally connected and electrically isolated.

In order to study the overall performance of combined system,the two subsystems are analyzed one by one. To develop the the-oretical model of combined system, the following simplifyingassumptions have been taken:

1. For simplifying the analysis, steady state conditions have beenconsidered.

2. The temperature gradient along the thickness of glass cover hasbeen considered negligible due to very less thickness of glasscover.

3. The system is insulated from two sides and therefore, onedimensional heat transfer has been considered for the analysis.

4. There is no other mode of heat transfer present other thanFourier’s heat conduction phenomena from the hot junction tothe cold junction of TEG which is due to the inherent thermalconductivity of thermoelectric materials.

5. Convective and radiative heat transfer from the sides of thermo-electric couples are neglected.

3. CPV subsystem

The concentrated solar radiation impinges on the PV modulesurface. After absorption, a part of it is converted into electricityby PV module through photovoltaic effect, some part is lost tothe environment from the top of PV module by convection, radia-tion and conduction through glass cover and remaining part is

Concentrator

Hot side

- - - - -

Cold side

Tedlar

Fig. 1. Schematic of CSP–TEG hybrid system.

Fig. 2. Electrical equivalent circuit of a PV–TE hybrid system.

R. Lamba, S.C. Kaushik / Energy Conversion and Management 115 (2016) 288–298 291

delivered to the hot side of TE module in the form of thermalenergy. Therefore, the energy balance equation for PV modulecan be given as [19]:

CGAPVsg ½acbc þaTð1�bcÞ� ¼Ut;caAPV ðTPV �TaÞþUb;chAPV ðTPV �ThÞþgcbcsgCGAPV ð1Þ

Here, Ut,ca is the overall heat transfer coefficient from the PV moduleto environment including conduction, convection and radiationwhich is given as [19]:

Ut;ca ¼ Lgkg

þ 1h0

� ��1

ð2Þ

The expression for h0 which includes convective and radiation heattransfer from the top surface of PV module to environment is givenas [23]:

h0 ¼ 5:7þ 3:8v ð3Þ

The heat generated in PV module is delivered from back side of PVmodule to hot side of TEG module through conduction and thus, theoverall heat transfer coefficient from PV module to the TE modulecan be given as [19]:

Ub;ch ¼ LPVkPV

þ LTkT

� ��1

ð4Þ

The temperature dependent PV cell efficiency is given by followingexpression [24]:

gc ¼ gref ½1� b0ðTPV � Tref Þ� ð5Þ

By rearranging Eq. (1), the simplified expression for PV moduletemperature is given as:

TPV ¼ CGðasÞeff þ Ut;caTa þ Ub;chTh

U00L

ð6Þ

Here,

ðasÞeff ¼ sg ½bc½ac � gref ð1þ b0Tref Þ� þ aTð1� bcÞ� ð7ÞAnd,

U00L ¼ ðUt;ca þ Ub;chÞ � CGsgbcb0gref ¼ UL � CGsgbcb0gref ð8Þ

Here, UL is the overall heat transfer coefficient from PV module tooutside environment at the top surface and from PV module to TEmodule at the bottom surface. U00

L includes the overall heat transfercoefficient and the temperature coefficient for the efficiency of con-centrated PV module.

To calculate the power generated by PV module, an electricalmodel is developed in which the PV cell is represented by a solarradiation dependent current source in parallel with diode. Theelectrical equivalent circuit of PV cell is shown in Fig. 3. The I–Vcharacteristics of a PV module can be expressed as [25–27]:

IPV ¼ npIph � npIrs expqðVPV þ IPVRSÞkBTPVnidns

� �� 1

� �� VPV þ IPVRS

RShð9Þ

Since shunt resistance of PV cell is much higher than the load resis-tance, so the I–V characteristics equation can be simplified as:

IPV ¼ npIph � npIrs expqðVPV þ IPVRSÞkBTPVnidns

� �� 1

� �ð10Þ

Fig. 3. Electrical equivalent circuit of a PV cell.

Table 1Parameters of Siemens SP75 PV cell [28].

Parameter Symbol Value

Area of PV module APV 0.6324 m2

Band-gap energy of PV semiconductor Eg 1.12 eVReference solar radiation Gref 1000 W/m2

Short circuit current ISC,ref 4.8 AOpen circuit voltage VOC 21.7 VMaximum current Imax 4.4 AMaximum voltage Vmax 17.0 VReverse saturation current at reference

temperatureIrs,ref 0.118 lA

Short circuit current temperature coefficient KI 2.06 mA K�1

Open circuit voltage temperature coefficient KV �0.077 V K�1

Diode ideality factor nid 1.5Number of PV strings connected in parallel np 1Number of PV cells connected in parallel ns 36Maximum power output of PV module Pmax 75 WSeries resistance RS 0.0018 OReference temperature Tref 300 K

292 R. Lamba, S.C. Kaushik / Energy Conversion and Management 115 (2016) 288–298

The reverse saturation current of diode in PV cell depends on celltemperature and it is given by following equation [26,27]:

Irs ¼ CIrs;refTPV

Tref

� �3

expqEg

kBnid

1Tref

� 1TPV

� �� �ð11Þ

The photocurrent, Iph of PV cell varies with PV cell temperature andsolar irradiance. It is given by following equation [26–27]:

Iph ¼ ½CISC;ref þ KIðTPV � Tref Þ� GGref

ð12Þ

Therefore, the power output and efficiency of PV module can be cal-culated from Eqs. (10)–(12) which are given as:

PPV ¼ npGGref

ðISC;ref þKIðTPV �Tref ÞÞ�npIrs;refTPV

Tref

� �3"

� expqðVPV þ IPVRSÞkBTPVnidns

� ��1

� �exp

qEg

kBnid

1Tref

� 1TPV

� �� �� ��2�RL1 ð13Þ

gPV ¼npGGref

ðISC;ref þKIðTPV �Tref ÞÞ�npIrs;refTPV

Tref

� �3"

� expq VPV þ IPVRSð ÞkBTPVnidns

� ��1

� �exp

qEg

kBnid

1Tref

� 1TPV

� �� �� ��2� RL1

CGAPVð14Þ

In the present study, Siemens SP75 crystalline Silicon PV modulehas been used and the various parameters of this module are shownin Table 1.

4. TEG subsystem

The heat delivered from back side of PV module to the hot sideof TEG module can be utilized in TEG module to generate electric-ity directly. The multicouple TEG system is a semiconductor basedthermoelectric device and two heat reservoirs at the hot and coldsides. The basic TEG unit consists of a p-type and n-type semicon-ductor elements which are connected electrically in series andthermally in parallel. The conversion of heat into electricity isbased on Seebeck and Peltier effects. Along with these effects, thereexists Fourier’s heat conduction due to temperature gradientbetween hot and cold junctions, Joule’s heat due to electricalcurrent flowing through TEG module and Thomson’s heat due totemperature gradient and electrical current both.

Based on the above effects, the rate of net heat flow from backside of PV module to hot side of TEG module and rate of net heatrejection from cold side of TEG module to the cold reservoir canbe written respectively as follows [29–36]:

Qh ¼ n shITETh � I2TERTE

2þ KTEðTh � TlÞ � lITEðTh � TlÞ

2

!ð15Þ

Ql ¼ n slITETl þ I2TERTE

2þ KTEðTh � TlÞ þ lITEðTh � TlÞ

2

!ð16Þ

Here, the electrical resistance RTE and thermal conductance KTE ofthe thermocouples for the TEG module are defined as follows:

RTE ¼qplpAp

þ qnlnAn

� �þ Rcontact þ Rconducting metal ð17Þ

KTE ¼ kpAp

lpþ knAn

ln

� �þ Kcontact þ Kconducting metal ð18Þ

In this analysis, the electrical resistance of the contacts between thejunctions is assumed to be 10% of total electrical resistance ofthermocouples and it is assumed that perfect thermal contact existsbetween the junctions. Therefore, the thermal conductancebetween the junction contacts has been considered to be negligible.The electrical resistance and thermal conductance of the conductingmetal are negligible.

Xuan et al. [37] specified the temperature dependent materialproperties of Bi2Te3 which are given as:

s ¼ ½sp � ð�snÞ�¼ 2� ð22224:0þ 930:6Tm � 0:9905T2

mÞ � 10�9 ð19Þ

qn ¼ qp ¼ ð5112:0þ 163:4Tm þ 0:6279T2mÞ � 10�10 ð20Þ

kn ¼ kp ¼ ð62605:0� 277:7Tm þ 0:4131T2mÞ � 10�4 ð21Þ

R. Lamba, S.C. Kaushik / Energy Conversion and Management 115 (2016) 288–298 293

l ¼ ½lp � ð�lnÞ� ¼ 2� ð930:6Tm � 1:981T2mÞ � 10�9 ð22Þ

The power output of TEG system can be written as follows:

PTE¼Qh�Ql¼n ðshTh�slTlÞITE� I2TERTE�lITEðTh�TlÞh i

¼ I2TERL2 ð23Þ

Using Eq. (23), the electric current flowing through TEG system canbe written as:

ITE ¼ n½ðshTh � slTlÞ � lðTh � TlÞ�nRTE þ RL2

ð24Þ

Tl ¼n2 I

2TERTE½nshITEþUb;chAPV ð1�hpÞ�þ nKTEþ n

2lITE �

APVhpCGðasÞeff þn2KTERTEI2TEþTa UlAl nshITEþnKTE� n

2lITEþUb;chAPV ð1�hpÞ �þUt;caAPVhp nKTEþ n

2lITE ��

nshITEþnKTE� n2lITEþUb;chAPV ð1�hpÞ

�nKTE�nslITEþ n

2lITEþUlAl �� �� nKTEþ n

2lITE �

nKTE� n2lITE

�� �� ð32Þ

By substituting Eq. (24) into Eq. (23), the power output can be givenas:

PTE ¼ n2½ðshTh � slTlÞ � lðTh � TlÞ�2RL2

ðnRTE þ RL2Þ2ð25Þ

The efficiency of the TEG system can be calculate from Eqs. (15) and(16) which is given as:

gTE ¼PTE

Qh¼ Qh � Ql

Qh

¼ðshTh � slTlÞITE � I2TERTE � lITEðTh � TlÞh ishITETh � I2TERTE

2 þ KTEðTh � TlÞ � lITEðTh�TlÞ2

� ð26Þ

5. Combined CPV–TEG system

The input heat flow from hot reservoir of TEG module which isthe back side of PV module, to the hot side of TEG module is con-sidered to be conductive which can be expressed as:

Qh ¼ Ub;chAPV ðTPV � ThÞ ð27Þwhere the expression for Ub,ch is given is Eq. (4). The thermal con-ductance between the CPV and TEG depends on the thickness andthermal conductivity of tedlar and PV cell. Therefore, the effect ofthermal conductance between CPV and TEG can be considered byvarying the thickness of tedlar. The heat rejection from cold sideof TEG module to cold heat reservoir is considered to obey Newton’slaw which can be expressed as:

Ql ¼ UlAlðTl � TaÞ ð28ÞThe value of UlAl = 20W/K has been considered to get maximumtemperature difference between hot and cold side junctions of theTE module which causes maximum difference between (Qh–Ql)which results in higher power output of thermoelectric module.

By equating Eqs. (15) and (27) and then solving for Th, theexpression for Th is given as:

Th ¼ Ub;chAPVTPV þ nKTE � n2lITE

�Tl þ n

2 I2TERTE

nshITE þ nKTE � n2lITE þ Ub;chAPV

ð29Þ

Substituting the expression for TPV from Eq. (6) into Eq. (29) andthen solving for Th, the expression for Th is given as:

Th ¼APVhpðCGðasÞeff þ Ut;caTaÞ þ nKTE � n

2lITE �

Tl þ n2 I

2TERTE

nshITE þ nKTE � n2lITE þ Ub;chAPV ð1� hpÞ ð30Þ

Here, hp ¼ Ub;ch

U00L.

By equating Eqs. (16) and (28) and then solving for Tl, theexpression for Tl is given as:

Tl ¼n2 I

2TERTE þ nKTE þ n

2lITE �

Th þ UlAlTa

nKTE � nslITE þ n2lITE þ UlAl

ð31Þ

Substituting the expression for Th from Eq. (30) into Eq. (31) andthen solving for Tl, the expression for Tl is given as:

The temperature of PV module, hot and cold sides of the TEG can becalculated from Eqs. (6), (30), and (32) respectively at different solarradiation and TEG electric current values provided the other param-eters of the PV–TEG hybrid system are given. After calculating TPV,Th and Tl, the power output and efficiency of the combined PV–TEG hybrid system can be expressed as:

P ¼ PPV þ PTE ð33Þ

P ¼ I2PVRL1 þ n2 shTh � slTlð Þ � l Th � Tlð Þ½ �2RL2

nRTE þ RL2ð Þ2ð34Þ

g ¼ PCGAPV

¼ PPV þ PTE

CGAPVð35Þ

g ¼ I2PVRL1

CGAPVþ n2 shTh � slTlð Þ � l Th � Tlð Þ½ �2RL2

CGAPV nRTE þ RL2ð Þ2ð36Þ

As it is known that with increase in PV module temperature, themodule efficiency decreases. However, by attaching a TEG to theback side of PV module, the module temperature decreases thanthat of PV system alone due to heat conducted away to the TEGmodule. Therefore, the efficiency of PV system improves and thusthe overall efficiency of hybrid system also improves.

6. Results and discussion

It is clear from Eqs. (32) and (34) that the overall performance ofPV–TEG hybrid system depends on various PV and TE moduleparameters. These parameters are concentration ratio, number ofthermocouples in TE module, Figure of merit of TE module, ther-moelectric properties of TE module material, temperature of PVmodule, hot and cold sides of TE module. For simulations study,a Siemen SP 75 PV module has been considered. The parametersof the PV module are listed in Table 1.

The various parameters used in modelling of PV–TEG hybridsystem are given in Table 2. The values of other parametersassumed are following: Ta = 298 K, UlAl = 20 W/K and RL2/R = 1.The solar radiation has been varied from 100 to 1000 W/m2 to con-sider both the summer and winter solar radiation range. Based onthese input parameters, the various performance parameters arecalculated. The operating temperatures TPV, Th and Tl have been cal-culated by using the above parameters and then power output of

Table 2Values of parameters used in modelling of PV–TEG hybrid system.

Parameter Symbol Value

Thermal conductivity of silicon PV cell kPV 148W/m KThermal conductivity of glass cover kg 1.1 W/m KThermal conductivity of tedlar kT 0.2 W/m KAbsorptivity of PV module ac 0.9Absorptivity of tedlar aT 0.5Packing factor of PV module bc 0.85Temperature coefficient of PV module b0 0.005 K�1

Thickness of PV cell LPV 0.0003 mThickness of glass cover Lg 0.003 mThickness of tedlar LT 0.000175 mWind velocity over PV module v 2.5 m/sPV module efficiency at standard test conditions

(STC)gref 13%

Transmissivity of glass cover sg 0.95

Fig. 4. Variation of power output of PV system with solar radiation at differentconcentration ratio for n = 127, UlAl = 20 W/K and RL2/R = 1.

Fig. 5. Variation of power output of TEG system with solar radiation at differentconcentration ratio for n = 127, UlAl = 20 W/K and RL2/R = 1.

Fig. 6. Variation of power output of hybrid PV–TEG system with solar radiation atdifferent concentration ratio for n = 127, UlAl = 20 W/K and RL2/R = 1.

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PV, TEG and hybrid PV–TEG system varying with solar radiationhas been plotted in Figs. 4, 5 and 6 respectively at different valuesof concentration ratio for n = 127, UlAl = 20 W/K and RL2/R = 1. Insummer and winter, the maximum solar radiation is 1000W/m2

and 600 W/m2 for clear sky conditions. It is clear from Figs. 4 and5 that the variation in power output of hybrid system follows the

behaviour of PV system alone. In both the plots, the power outputfirst increases with solar radiation and gets an optimum value andthen power output decreases with increase in solar radiation. Athigher solar radiation, more part of incident solar radiation is con-verted into heat which increases the module temperature andresults in decreases in PV power output and thus overall poweroutput of hybrid system. Also the maximum for power output isat lower value of solar radiation for higher concentration ratio.The power output of TEG module increases with increase in solarradiation due to increase in module temperature which results inincrease in heat input to the TEG module as shown in Fig. 5. Thepower output of TEG module increases with increase in concentra-tion ratio due to higher heat input supplied to the TEG module.

The variation of power output with concentration for PV, TEGand hybrid PV–TEG system has been plotted in Fig. 7 forG = 1000 W/m2, n = 127, UlAl = 20 W/K and RL2/R = 1. However, thepower output of TEG system always increases with concentrationratio but for PV and hybrid PV–TEG system, the power output firstincreases and then decreases with increase in concentration ratio.

The variation of efficiency of PV, TEG and hybrid PV–TEG systemwith concentration ration has been plotted in Fig. 8 for G = 1000W/m2, n = 127, UlAl = 20 W/K and RL2/R = 1. The efficiency of PVand hybrid PV–TEG system decreases with increase in concentra-tion ratio due to increase in module temperature and the efficiencycurves of both systems follow the same pattern. The efficiency ofTEG system increases with increase in concentration ratio due tohigher heat supplied to TEG module.

The three dimensional variation of power of hybrid PV–TEG sys-tem with PV module current and TE module current has beenshown in Fig. 9 for C = 1, n = 127, UlAl = 20W/K and RL2/R = 1. Thedifferent current values of PV and TE module are calculated atmaximum power point for solar radiation varying from 100 to1000W/m2. The power of hybrid system increases with increasein PV module and TE module currents. The effect of concentrationratio on the variation in efficiency of PV, TEG and hybrid PV–TEGsystem with solar radiation has been shown in Figs. 10–12respectively for n = 127, UlAl = 20W/K and RL2/R = 1. The efficiencypattern for hybrid PV–TEG system follows that of PV system. Theefficiency of PV and hybrid PV–TEG system decreases with increasein solar radiation due to negative relationship between PV moduleefficiency and temperature. The efficiency of PV and hybrid

Fig. 7. Variation of power output of PV, TEG and hybrid PV–TEG system withconcentration ratio for G = 1000 W/m2, n = 127, UlAl = 20 W/K and RL2/R = 1.

Fig. 8. Variation of efficiency of PV, TEG and hybrid PV–TEG system withconcentration ratio for G = 1000 W/m2, n = 127, UlAl = 20W/K and RL2/R = 1.

Fig. 9. Three dimensional variation of power of hybrid PV–TEG system with PV module current and TE module current for C = 1, n = 127, UlAl = 20W/K and RL2/R = 1.

Fig. 10. Variation of efficiency of PV system with solar radiation at differentconcentration ratio for n = 127, UlAl = 20W/K and RL2/R = 1.

Fig. 11. Variation of efficiency of TEG system with solar radiation at differentconcentration ratio for n = 127, UlAl = 20W/K and RL2/R = 1.

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Fig. 12. Variation of efficiency of hybrid PV–TEG system with solar radiation atdifferent concentration ratio for n = 127, UlAl = 20 W/K and RL2/R = 1.

Fig. 13. Variation of power output of PV and TE system with solar radiation atdifferent number of thermocouples for C = 1, UlAl = 20 W/K and RL2/R = 1.

Fig. 14. Variation of power output of hybrid PV–TEG system with solar radiation atdifferent number of thermocouples values for C = 1, UlAl = 20W/K and RL2/R = 1.

Fig. 15. Variation of power output of hybrid PV–TEG and TEG system with andwithout Thomson effect for C = 1 and 5, n = 127, UlAl = 20 W/K and RL2/R = 1.

Fig. 16. Variation of temperature of PV system with solar radiation at differentconcentration ratio for n = 127, UlAl = 20W/K and RL2/R = 1.

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PV–TEG system is less at higher concentration ratio. Also, thedecrement in efficiency with solar radiation is lesser at smallerconcentration ratio. The efficiency of TEG system increases withincrease in solar radiation and concentration ratio which is obviousdue to higher heat input.

The effect of number of thermocouple elements on the variationof power output of PV and TEG simultaneously and hybrid PV–TEGwith solar radiation has been shown in Figs. 13 and 14 respectivelyC = 1, UlAl = 20W/K and RL2/R = 1. The contribution of power outputof TEG to the overall power output of hybrid PV–TEG system is veryless as compared to that of PV system by considering Thomsoneffect and therefore, the pattern for power output variation withsolar radiation is same for both PV and hybrid PV–TEG system.The power output of TEG system increases with increase in bothsolar radiation and number of thermocouple elements due tohigher heat input.

The influence of Thomson effect on power output of hybrid PV–TEG and TEG system has been shown in Fig. 15 for C = 1 and 5,n = 127, UlAl = 20 W/K and RL2/R = 1. When Thomson effect is con-sidered in the TEG analysis, then the power output of hybrid PV–TEG and TEG system decreases due to Thomson heating. The poweroutput of TEG system is affected more as compared to hybrid PV–TEG system by Thomson effect. The reduction in power output ofhybrid PV–TEG system due to Thomson effect is more at higherconcentration ratio values due to very high temperature of PVmodule. The variation of temperature of PV module and cold sideof TEGmodule with solar radiation for different concentration ratio

Fig. 17. Variation of temperature of cold side of TEG system with solar radiation atdifferent concentration ratio for n = 127, UlAl = 20 W/K and RL2/R = 1.

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values has been plotted in Figs. 16 and 17 respectively for n = 127,UlAl = 20 W/K and RL2/R = 1. It is obvious that the temperature of PVmodule increases with increase in both solar radiation and concen-tration ratio due to more amount of incident solar energy con-verted into heat. The heat generated in PV module is conductedto hot side of TEG module through tedar. Therefore, the hot sidetemperature of TEG module is little lesser than that of PV moduleand follows the behaviour of PV module temperature. The temper-ature of cold side of TEG module also increases with solar radiationand concentration ratio but the increment is less as compared tothat of PV and hot side of TEG module.

7. Conclusions

A theoretical model of an irreversible CPV–TEG hybrid systemincluding various conduction, convection and radiation heat lossesin PV module and Thomson effect in conjunction with Seebeck,Joule and Fourier heat conduction effects in TEG module has beendeveloped. The expressions for power output and efficiency ofhybrid PV–TEG system have been derived analytically and simu-lated in MATLAB environment. It has been observed that the hybridPV–TEG system generate more power than that of PV system alone.The overall efficiency and power output of hybrid system has beenimproved as compared to that of conventional PV system alone.The influence of Thomson effect is more dominant at higher con-centration ratio. Furthermore, the concentration ratio should beoptimized to get maximum power from hybrid system. Based onthe study, the following conclusions have been observed:

� At a given concentration ratio, the power output is maximum ata particular solar irradiance. In this study, the power outputs ofhybrid PV–TEG and PV system alone are maximum for solarirradiance of 600 W/m2 which are 110.5 W and 97.55 W respec-tively for C = 5 and n = 127. The efficiencies of hybrid PV–TEGand PV system alone at maximum power output are 0.058and 0.051 respectively for G = 600W/m2, C = 5 and n = 127.

� The Thomson effect reduces the power output of hybrid systemby 0.7% and 4.78% at C = 1 and 5 respectively for n = 127,G = 700 W/m2. The reduction in power output of TEG due toThomson effect is higher as compared to hybrid PV–TEG system.

� The efficiencies of hybrid PV–TEG and PV system alone decreaseslightly at lower concentration ratio values and the rate ofdecrement in efficiency is more at higher concentration ratiovalues. The efficiency of TE system increases with increase inconcentration ratio.

� The power output is maximum at an optimum value of concen-tration ratio. The maximum power outputs of hybrid PV–TEG,TE and PV system alone, corresponding to an optimum concen-tration ratio value of 3, are 111 W, 12.99 W and 97.97 W respec-tively for n = 127, and the efficiencies corresponding tomaximum power output of hybrid PV–TEG, TE and PV systemalone are 0.058, 0.043 and 0.052 respectively.

� The percentage increase in power output and efficiency ofhybrid PV–TEG system with respect to PV system alone are13.26% and 13.37% respectively at C = 3 and n = 127.

Thus, the results obtained in this study are helpful in optimiza-tion analysis for both design and performance of a practical irre-versible CPV–TEG hybrid system.

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