Two-dimensional unsteady state performance analysis of a hybrid photovoltaic-thermoelectric generator

Accepted Manuscript Two-dimensional unsteady state performance analysis of a hybrid photovoltaicthermoelectric generator P. Motiei, M. Yaghoubi, E. GoshtashbiRad, A. Vadiee PII:

S0960-1481(17)31193-X

DOI:

10.1016/j.renene.2017.11.092

Reference:

RENE 9494

To appear in:

Renewable Energy

Received Date: 16 July 2017 Revised Date:

14 November 2017

Accepted Date: 30 November 2017

Please cite this article as: Motiei P, Yaghoubi M, GoshtashbiRad E, Vadiee A, Two-dimensional unsteady state performance analysis of a hybrid photovoltaic-thermoelectric generator, Renewable Energy (2018), doi: 10.1016/j.renene.2017.11.092. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Two-dimensional unsteady state performance analysis of a

2

hybrid photovoltaic-thermoelectric generator

3

P. Motiei, M. Yaghoubi∗, E. GoshtashbiRad, A. Vadiee

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Abstract

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This paper presents an unsteady, two-dimensional numerical model of a hybrid solar

6

power generation system (STEG) that integrates photovoltaic (PV) and thermoelectric

7

generator (TEG) technologies to harvest more solar energy under typical

8

environmental and operating conditions. The model takes into account solar

9

irradiation, wind speed and ambient temperature in addition to convective and

10

radiative heat losses from the front and rear surfaces of the system .The governing

11

equations are discretized using finite volume method and a fully implicit formulation

12

is adopted for the time dependent terms. Results of each part of the numerical

13

modeling were compared with the available experimental measurements and

14

satisfactory agreements were observed. In addition, the effects of wind speed and

15

ambient temperature, PN couples’ height and external load resistance variations on

16

the STEG performance are investigated. A monocrystalline photovoltaic cell (PV) is

17

used and a commercial TE module is selected. Meteorological information of the 6th

18

of July for the city of Shiraz, Iran with a latitude of 29.39° N are used which contain

19

ambient air temperature and average wind speed. Computation is made with the

20

developed code for a duration of 24 hours. Results show that adding TE module at the

21

back of PV can improve PV efficiency and PV electrical output power by 0.59% and

22

5.06%, respectively. Furthermore, it is found that as the wind speed increases, the PV

23

efficiency improves and the TEG efficiency decreases. Also, a rise in the ambient

24

temperature causes the PV efficiency to decrease but increases the TEG efficiency.

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Nomenclature ∗

Corresponding author. Tel.: +98 917 1184335; Fax: +98 713 6473538. E-mail address: [email protected] (M.Yaghoubi)

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Abbreviation PV

photovoltaic

TEG

thermoelectric generator

Symbols semiconductor cross section area (m2)

A

PV area (m2)

Ai

anisotropy index

CP

specific heat capacity (J/ kg K)

CF

clear sky factor

D

electric flux density vector (C/m2)

E

electric field (V/m)

F

radiation view factor

h

heat transfer coefficient (W/m2K)

IT

total solar radiation on tilted surface (W/m2)

I

total solar radiation on horizontal surface (W/m2) and electrical current (A)

Ib

diffuse components of solar radiation on horizontal surface (W/m2)

Id

beam components of solar radiation on horizontal surface (W/m2)

J

electrical current density vector (A/m2)

k

thermal conductivity (W/ m K)

H

semiconductor height (m)

N

numbers of p-n couples

n

numbers of PV layers

Pout

PV electrical output power (W)

PRL

TEG electrical output power (W)

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q

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An

heat flux vector (W/m2)

rate of heat generation per unit volume (W/m3)




heat generation rate (W/m3)

Qh

heat supplied to the hot side of TEG

RL

external load resistance (Ω)

Rin

internal resistance (Ω)

Rb

geometric factor

T

temperature (K)

t

time (s)

Vi

volume of each PV layer (m3)

V

electric scalar potential (V) and wind speed (m/s)

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Qi

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Voc

open circuit voltage (V)

VRL

output voltage (V)

Z

material thickness (m)

y

axis coordinate (m)

b

back

Ce

ceramic

CP

copper

C

cold

f

front

H

hot

in

internal

n

n-type semiconductor

p

p-type semiconductor

W

wind

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aluminum

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Subscript

angular position of the sun at solar noon

α

absorptance coefficient and Seebeck coefficient (V/K)

β

slope of PV



PV temperature coefficient

ε

emissivity coefficient and dielectric permittivity (F/m)

η

electrical efficiency (%)

ηref

reference efficiency (%)

λ

zenith angle

Thomson coefficient (V/K) material density (Kg/ m3)

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ρ

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θz

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δ

ρg

diffuse reflectance of ground

́

electrical resistivity (µΩm)

σ τ

Estefan-Boltzman constant and electrical conductivity (µ -1 Ω-1 m-1) transmissivity coefficient

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Keywords: Solar energy, PV module, TEG, STEG system, Hybrid solar power

29

generation, Waste heat recovery.

30

1. Introduction

32

The increased need for energy, environmental pollution and danger of global

33

warming are the main concerns that have led to the increased focus on renewable and

34

clean energies. Energy derived from fossil fuels is not sustainable due to their limited

35

resources. Climate change and energy security have forced governments to adopt

36

policies to extend the share of clean energies [1]. Among renewable energies, solar

37

energy has been given more consideration recently. One of the most prevailing

38

applications of solar energy is its direct conversion into electricity using a

39

photovoltaic (PV) cell. PVs are still not capable of meeting industrial requirements

40

due to their low efficiency. One of the main reasons for this issue is that PVs can

41

only utilize a fraction of the incident solar radiation due to their given bandgap [2].

42

The temperature of PV rises due to heat accumulation from solar radiation, which is

43

not actively converted into electricity. This temperature increment decreases PV

44

performance [3]. Therefore, any mechanism which reduces the cell temperature,

45

particularly at times of high irradiance, will increase PV efficiency and output. To

46

improve PV efficiency, its cooling with different schemes are investigated. Examples

47

of active cooling systems include air or water cooling. Water cooled systems may be

48

unsuitable due to the weight of water required to deliver appropriate cooling.

49

Moreover, in many places like remote areas or locations with great potential of solar

50

energy, such as deserts, water availability is limited and since they are activated, they

51

introduce a maintenance burden that could increase operating costs and system

52

downtime [4]. Active cooling systems not only need electric power to operate but

53

also they may waste more heat into the environment [5]. Hence alternative scheme of

54

passive cooling can be achieved by incorporating thermoelectric generator (TEG) to

55

harvest waste heat from PV [6]. TEG is a solid state heat engine which directly

56

converts thermal energy into electrical energy due to Seebeck effect [7]. Compared to

57

conventional mechanical providers of electricity, TE modules are clean, highly

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reliable, light weight, noiseless, portable and with the ability of working in a wide

59

range of operating temperatures. They have low maintenance cost, because they have

60

no moving parts or working fluids. They can be built in different dimensions, shapes

61

and be adapted easily with other systems of heat generation and waste heat recovery

62

systems [8];[9];[10]. To compensate the drop in PV efficiency, TE modules are

63

attached to the back of PV as a heat sink to remove waste heat from PV, improving

64

its efficiency. Through creating a temperature difference across TEG, direct

65

conversion of heat into electricity results in additional electricity generation [11];[12].

66

A hybrid solar power generation system, briefly called STEG, is depicted in Fig. 1.

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Fig. 1. Schematic diagram of a STEG system

There are many models of hybridization that are developed to analyze heat transfer,

71

electrical output power and efficiency for both PV and TEs. The first group is a zero

72

dimensional model based on energy balance, without any need to solve differential

73

equations. These models are usually simpler in comparison to the other ones. The

74

second group consists of one, two or three dimensional models where energy

75

differential equation of the TEG includes Fourier’s heat, Joule heat and Thomson heat

76

as heat sources and Peltier heat as boundary fluxes. These modeling schemes need to

77

solve energy equation coupled with the TEG electric potential equation to obtain

78

temperature and potential distributions and system performance [13];[14]. Numerous

79

studies have been conducted on PV, TEG and also both direct and indirect

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combination of PV and TEG, with or without using solar concentrators or solar

81

tracking systems.

82

PVs may be used in different arrangement, such as PV-fixed, single-axis solar

83

tracker, dual/multi-axis solar tracker, and on parabolic solar concentrator (solar dish).

84

The electrical output power and efficiency of PV is maximum under maximum solar

85

radiation and solar tracking systems minimize the angle of incidence between the

86

incoming sunlight and a PV surface to deliver more electrical power by PV system.

87

Roth et al.[15], designed an electromechanical system to follow position of sun with a

88

pyrheliometer that operates automatically, guided by a closed loop servo system. A

89

four-quadrant photo detector senses the position of sun and two small DC motors

90

move the instrument platform keeping the sun’s image at the center of the four-

91

quadrant photo detectors. A computing program calculates the position of sun for

92

cloudy conditions and takes control of the movement, until the detector can sense the

93

sun again. The constructed system can be adapted to work with PVs, concentrators,

94

etc. Chin et al.[16] designed an active single axis solar tracker, enable to be mounted

95

onto the wall. Solar radiation is detected by two sensors located on the surface of the

96

PV. The tracker system operates at different modes to accommodate different weather

97

conditions. The PV rotates automatically based on the solar radiation during the day.

98

A computer model of the system is first modeled using MATLAB/Simulink.

99

Maneewan et al.[17], conducted a numerical study to investigate the amount of

100

reduction in the received thermal energy through a roof, using TE-RSC

101

(Thermoelectric roof solar collector) system, which is a direct combination of solar

102

collector and TEG, and used the electrical current generated by TEG to operate fans

103

in order to cool the TEGs. Lertsatitthanakornet al.[18], conducted a performance

104

analysis of a double passed thermoelectric generator solar air collector in order to

105

generate both thermal and electrical energies. In their work, TE modules were

106

embedded under an absorber plate and they used rectangular fins located in the lower

107

channel as heat sinks for TE cooling, and the flow of ambient air cooled both TEs and

108

the collector. Fan et al. [19], implemented a PV-TEG system for a hybrid electric

109

vehicle in which TEGs were used to remove heat from internal combustion engines

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and PVs for converting solar energy into electricity. Their study was mainly focused

111

on power controlling of PV-TEG. Jradi et al. [20], studied a photovoltaic-

112

thermoelectric cooling system for air dehumidification and fresh water production.

113

Fan et al.[21], designed a concentrating thermoelectric generator utilizing solar

114

thermal energy. The design consisted of a parabolic dish collector with an aperture

115

diameter of 1.8 m, used to concentrate sunlight onto a copper receiver plate with a

116

diameter of 260 mm. Four BiTe-based TEGs installed on the receiver plate were used

117

to convert the concentrated solar thermal energy directly into electric energy. A

118

microchannel heat sink was used to remove waste heat from the TEG cold side, and a

119

two-axis tracking system was used to track the sun continuously.

120

al.[22], performed modeling and optimization of a hybrid solar thermoelectric system

121

with thermosyphon. In their model, a parabolic through mirror concentrates sun light

122

onto a selective surface to produce electrical power using TEG. Meanwhile, a

123

thermosyphone was attached to the back of TEG to decrease temperature of the cold

124

side and carry the remaining thermal energy to the condenser and produce warm

125

water for various applications. EA Chávez Urbiola et al.[23], conducted an

126

experimental study of a solar-concentrating system based on thermoelectric

127

generators. The system included 6 serially connected TEGs, which were illuminated

128

by concentrated solar radiation on one side and cooled by water running on the other

129

side. A sun-tracking concentrator with a mosaic set of mirrors was used; which was

130

oriented towards the sun. A thermosiphon cooling system was designed to absorb the

131

heat passing through the TEGs and provide optimal working conditions. The system

132

generates 20 W of electrical energy and 200 W of thermal energy stored in water with

133

a temperature of around 50°C. Ju et al.[24], presented a numerical modeling and

134

optimization of a spectrum splitting for an indirect combination of PV-TEG. The

135

solar radiation is concentrated and split into two parts at cutoff wavelength. The wave

136

with shorter wavelength is converted to electricity by PV and the longer ones are used

137

in TEG. Results show that the maximum output power is produced when the cutoff

138

wavelength is between 850-950 nm and a higher concentration ratio delivers more

139

output power. Li et al.[25], proposed a power system that integrates indirect

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combination of PV-TEG to harvest solar energy from a wide spectral range, so that

141

by spectrum beam splitting technique, the short wavelength of sunlight is converted

142

directly into electricity in PV and the long wavelength is used to store thermal energy

143

in a separate unit as a heat source for TEG to generate electricity. Wu et al.[26],

144

established a theoretical model for assessing the performance of glazed/unglazed PV–

145

TEG system. Under the condition of enhanced transmissivity of glass cover, glazed

146

system may be competitive or even superior to the unglazed one. Bjork et al.[27],

147

examined the performance of a PV-TEG system for four different types of

148

commercial PVs and a commercial TEG (Bi2Te3). The considered PVs are c-Si, a-Si,

149

CIGS and CdTe cells. For c-Si, CIGS and CdTe PV cells, the combined system

150

produces a lower power and has a lower efficiency than the PV alone, whereas for an

151

a-Si cell, the total system performance may be slightly increased by the TEG. Zhang

152

et al.[28], carried out a thermal analysis of a highly concentrated PV-TE system using

153

the thermal resistance of the whole system. Firstly, the sensitivity analysis shows that

154

the thermal resistance between the TE module and the environment has a greater

155

effect on the output power than the thermal resistance between the PV and the TE.

156

Secondly, decreasing the area of PV can improve the efficiency of the highly

157

concentrated PV-TE hybrid system. It should be pointed out that decreasing the area

158

of PV cells also increases the total thermal resistance, but the raise in the efficiency is

159

caused by the reduction of the heat transfer rate of the system. Luo et al.[29],

160

simulated an active building integrated photovoltaic thermoelectric (BIPVTE) wall

161

system that can use the electric power converted from solar energy by PV cells

162

directly and serves for the operation of thermoelectric radiant panel. This active

163

system is highly self-adaptive to ambient thermal environment and can reduce heat

164

gain to a considerable extent. Results showed that when indoor air temperature is

165

24°C, the thickness and thermal conductivity of insulation are 0.04 m and

166

0.05 W/m K, respectively and BIPVTE wall can reduce about 70% of daily heat gain

167

compared with a traditional wall in a typical day simulation. Li et al.[30], proposed a

168

one-dimensional model for analyzing the energy and exergy of a PV-TE hybrid

169

system using concentrated sunlight. The second law of thermodynamics is applied to

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the exergy analysis of the hybrid system. The exergy losses caused by the irreversible

171

process of solar radiation converted into electric power and thermal energy are

172

evaluated. The calculated results demonstrate that high concentration ratio and

173

suitable PV cell used in the PV-TE hybrid system can promote the system output

174

efficiency. Hajji et al.[31], investigated the energetic efficiency of a new concept

175

based on an indirect PV and TEG coupling. By using state-of-the-art thermal transfer

176

calculations, they showed that such an indirect coupling is an interesting alternative to

177

maximize solar energy exploitation. In the model a concentrator is placed between

178

PV and TEG systems without any physical contact of the three components. They

179

showed that the indirect coupling significantly improve the overall efficiency which

180

is very promising for future PV developments. Machrafi et al.[32], developed an

181

analytical mathematical model describing a cooled photovoltaic-thermoelectric

182

hybrid system using a nanocomposite as a thermoelectric material where the model

183

takes into account size-dependent non-local thermoelectric properties from an

184

extended thermodynamic point of view. The photovoltaic device powers also the

185

cooling system. The model determines first the optimum thickness of the photovoltaic

186

device, then analyse the influence of several size-related parameters on the

187

thermoelectric efficiency (also related to the figure of merit) and finally, coupled to a

188

cooling device, and the overall efficiency is determined. Liu et al.[33], investigated a

189

PV-TEG ventilator system, the outdoor fresh air is first heated up by PV airflow

190

channel, and then heated up further when it flows through the hot side heat sink of

191

thermoelectric ventilator into the indoor room. At the same time, the exhaust air

192

cooled down the heat sink on the other side of the TEM when it is pumped out of the

193

indoor environment. The electricity power of PV array is storage in battery, which

194

can used to power the thermoelectric ventilator through voltage controller. The results

195

show that the fresh air temperature supplied for indoor is increased as the solar

196

radiation intensity increased. Tan et al. [34], presented a comparative study of two

197

types of remote area power supply (RAPS) systems, which are the existing PV-based

198

configuration and the proposed TEG-based configuration. Both RAPS systems are

199

solar-based power generators and sized according to Melbourne weather conditions.

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The RAPS system designs for both PV and TE have no backup generator and the

201

batteries are the only device for electrical energy storage. Battery storage is used for

202

storing solar energy during the available days for meeting the energy demand.

203

Generally, both PV and TE cells are solar-based power generating cells but they have

204

different pre-conversion inputs. For electrical power generation, PV uses sunlight as

205

input energy while the TE uses concentrated solar heat. The results show that the total

206

setup cost for TE/Battery system is 66% higher than PV/Battery system under similar

207

design requirements. Despite having higher setup cost, the TE/Battery system has the

208

potential to harness both electrical and thermal energy for domestic purposes.

209

The above survey showed that an unsteady two-dimensional numerical modeling of a

210

hybrid system for duration of 24 hours by considering the effects of wind speed,

211

ambient temperature variations and also the effect of PN couples’ height and external

212

load resistance variations to find the optimum value for PN couples’ height and

213

external load resistance for the STEG system performance has not been reported yet,

214

while it would be interesting to be analyzed and employed in the corresponding

215

STEG industries.

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2. STEG modeling

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The purpose of present study is to model a STEG to determine the electrical output

219

power and efficiency of a PV alone, and also to calculate the electrical output power

220

and efficiency of PV and TEG as a hybrid system in order to assess the improvement

221

by adding TEG to PV. The modeling is conducted for a Klein day of July (6th) for

222

Shiraz, Iran. The PV cell’s temperature changes during the day because of changes in

223

the incident solar radiation and ambient temperature. Also, according to Seebeck,

224

Peltier and Thomson effects, output electrical power of TEG depends on temperature

225

distribution along the semiconductor legs, and any change in temperature distribution

226

leads to a change in open circuit voltage, generated electrical current and output

227

power of TEG. Therefore, an unsteady state model is used to determine temperature

228

distribution, output electrical power, efficiency and other outputs of the system by a

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computational code written in FORTRAN90. A STEG is composed of PV and TEG

230

device modules. The modeling is conducted in two parts: a single PV modeling,

231

followed by STEG modeling. Each part has its own governing and boundary

232

equations as described below.

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2.1. PV module

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The PV module’s layers in the present study is based on Boddaert and Caccaveli [35],

236

as shown in Fig. 2. Heat transfer and optical properties of PV layers are presented in

237

Tables 1 and 2.

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Fig. 2. Layer structure of a PV module

241 Table 1

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Thermal parameters of mono-crystalline PV [36]

C p (J/ kg Κ )

z(m)

3000

500

0.003

2330

677

960

2090

0.38×10−3

0.35

Material Glass cover PV cell

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k (W/ m Κ )

ρ (kg/ m 3 )

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−4

3×10

1.8 148

Aluminum

2700

900

0.0012

237

Tedlar

1200

1250

0.00017

0.2

244 245

Table 2

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Optical parameters of PV [36] 2

A

4 × 4 cm

α glass

0.05

α c ell

0.9

11

0.027

αtedlar

0.04

τ glass

0.95

τ c e ll

0.09

τ EV A

0.94

τ tedlar

0.92

σ

5.67 ×10−8 W/m2 K4

ε glass

0.95

ε Al

0.02

ε ce

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All layers are embedded in a metal framework. The effect of the frame is not included

249

because its side surface area is negligible compared to PV module’s area [37].

250

2.1.1. PV equations

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Heat transfer in a PV involves solid domains and Equation (1) applies for each layer. ∂T




 (1) ρ i c p ,i i = ∇ ⋅( ki ∇ Ti ) + Qi i = 1, 2, 3,...n ∂t

253 i = n −1

∏τ i =1

Vi

254

Qi = 256

(2)

For the PV cell layer, heat generation rate is:

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i

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Qi =

IT Aαi

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(I T A α i

i = n −1

∏τ i =1

i

(3)

) − Pout

Vi

257

where ρ , c p , k, T ( x , y ) , t, Q, n and i denote material density, specific heat capacity,

258

thermal conductivity, temperature field, time, the internal volumetric heat generation

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in each layer, number of layers and layer index. And also α , τ and V are:

260

absorptance , transmissivity and volume of PV layers, respectively.

261

Total incident solar radiation on tilted surface of PV, IT is calculated from

262

anisotropic sky model represented by Hay and Davis [38]. Solar beam and diffuse

263

radiation are determined from modified Daneshyar model [39].

264

The electrical output power of PV is:

Pout = η PV I T A

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(4)

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where ηPV is PV electrical efficiency and A is PV module area.

267

Electrical efficiency of PV is a function of temperature and incident solar radiation

268

and can be calculated from the following experimental relation [40]:

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IT  ) 1000 

η PV = η ref 1 − β ′ (Tcell − 25 ) + γ log10 (

(5)

where Tcell is the average temperature of PV cells. Parameters β ′ and γ are basically

270

dependent on the material used in PV cell. β ′ is the temperature coefficient and

271

represents the amount of efficiency loss per each temperature degree rise in PV cells

272

and it is equal to 0.0045 (1/K), and γ = 0.1 is the adjustment factor in efficiency in

273

order to account for the performance decline for low light conditions, and

274

η ref = 15.6% is a reference efficiency at a cell temperature of 25ºC and intensity of

275

1000 (W/m2).

276

Also IT is calculated by [38]:

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I T = ( I b + I d Ai ) Rb + I d (1 − Ai )( 277

1 + cos β 1 − cos β ) + I ρg ( ) 2 2

I = Ib + Id

(6)

(7)

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I is the total solar radiation on horizontal surface. Beam I b and diffuse I d components

280

of solar radiation are calculated by modified Daneshyar model, suggested for various

281

cities of Iran using the following relations [41]:

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Ib' = (1.03964 − 0.005935×δ ) × ((1− CF) × 950× (1− exp(−0.075× (90 −θz ))

(8)

I d = (1.03964 − 0.005935 × δ ) × (1.432 + 2.107 × (90 − θz ) + 121.3×CF )

(9)

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I b = I b ' × cos θ z 285

(10)

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in the above relations, Rb is the geometric factor, Ai is an anisotropy index, β slope

287

of PV,

288

sun at solar noon), CF is clear sky factor( an index for indicating the degree of sky

289

clearness used as weighting factors to estimate the amount of solar radiation) that is

290

0.195 for July month in Shiraz [42], Iran and

TE D

ρg is diffuse reflectance of ground, δ is declination (angular position of the

is zenith angle.

EP

θz

291

2.2. TEG module

293

A conventional TE module includes a number of p-type and n-type semiconductor

294

couples. The PN couples are electrically series-connected by conducting copper

295

strips, to power the load but thermally in parallel-connected between the hot and cold

296

sources of heat. The semiconductor couples are sandwiched between two ceramic

297

layers which act as an electrical insulator [7], as shown in Fig. 3.

298

A commercial TE module HT6-12-40 is selected for modeling and its characteristics

299

parameters and electrical and thermal properties are respectively available in Tables 3

300

and 4.

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302 303

Fig. 3. Schematic of a TEG module

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Table 3

308

Electrical and thermal properties for TE module [7, 14]

C p (J/ kg Κ )

k (W / m K )

α (V/K)

Ceramic

3975

765

36

----

EP

ρ (kgm −3 )

ρ (µΩ m ) ---−6

11.196

P-type

7700

200

1.954

-163.546 ×10

N-type

7700

200

1.510

178.098 × 10 −6

10.896

Copper

8940

384.4

400

6.5 × 10 −6

1.7 × 10 −3

AC C

309

Material

310 311 312

15

ACCEPTED MANUSCRIPT

313 Table 4.

315

Characteristics of HT6-12-40 module [17]

HT6-12-40

Material of semiconductor

Bi2Te3

Leg length × width (mm)

1.35 × 1.35

Leg height (mm)

1.6

Ceramic insulator thickness (mm)

0.8

Conductor strip thickness (mm)

0.3

No. of p-n couples

RI PT

Parameter

SC

314

128

Maximum operating hot side temperature

160-170℃

M AN U

316 317

2.2.1 TEG equations

318

For thermoelectric analysis, energy equation and continuity equation of electric

319

charge are coupled by the following constitutive thermoelectric equations:

ρcp

i ∂T + ∇ .q = q ∂t

∂D )=0 ∂t

321 D = εE

322

323

(13)

(14)

AC C

E = −∇V

(12)

EP

∇ .( J +

TE D

320

(11)

324

where ρ , c p , T and t are material density, specific heat capacity, temperature field

325

and time, respectively. Additionally, q ,
 , J, D, E,

326

the rate of heat generation per unit volume, electrical current density vector, electric

327

flux density vector, electric field, dielectric permittivity and electric scalar potential,

328

respectively.

16

ε

and V denote heat flux vector,

ACCEPTED MANUSCRIPT

329

The heat flux at the interface between semiconductors and copper conducting strips is

330

calculated from the following relationship: q = − k ∇ T + α TJ

(15)

α and k are Seebeck coefficient and thermal conductivity, respectively. The first

332

term in the right hand side represents heat conduction due to Fourier effect and the

333

second term is associated with Seebeck effect and is known as Peltier heat:

RI PT

331

∇ .q = −∇ .( k ∇ T ) + J.∇ (α T ) + α T (∇ .J )

(16)

335

SC

334

The non-Ohmic current-voltage relation of the electric field is written as:

(17)

M AN U

∇ V = −α ∇ T − ρ J 336

the first term in the right side is the Seebeck electromotive force, increased due to the

338

temperature gradient, and the second term is the voltage drop due to current flowing

339

through TEG elements.

340

The heat generation term
 includes the electric power J.E spent on joule heating

341

and on work against the Seebeck field α ∇ T . So the heat generation term is written

342

as:

TE D

337

i

q = J.E = J.( −∇ V) = ρ ( J.J ) + α J.∇ T

(18)

The first term on the right hand side represents the joule heating and the second term

344

is associated with the work produced by electrical current against the Seebeck effect.

345

Substituting Equations (16) and (18) into Equation (11) and also Equations (13) and

346

(14) into Equation (12), leads to a system of coupled equations of thermoelectricity:

AC C

EP

343

(19)

2

J ∂T ρcp = ∇ .(k ∇ T ) + − τ J.∇ T ∂t σ

347

∇ (ε∇


 ∂V ) + ∇ .(σα ∇ T ) + ∇ .(σ∇ T ) = 0 ∂t

(20)

348

17

ACCEPTED MANUSCRIPT

1

(here ρ ′ is electrical resistivity), and

349

where ,electrical conductivity, is equal to

350

Thompson coefficient λ can be derived from Seebeck coefficient: dα dT

(21)

RI PT

λ =T

ρ′

Since charge carriers transfer due to the electric potential difference in thermoelectric

352

materials and as is clear from Equation (19), calculating the temperature field requires

353

calculation of the electrical current density vector J. Therefore, both Equations (19)

354

and (20) must be solved simultaneously and iteratively in order to determine the

355

temperature and electric potential field in thermoelectric materials. For STEG

356

modeling, solving Equations (1), (19) and (20) simultaneously and iteratively will

357

determine the temperature distribution and electric potential in TEG. All equations

358

for both PV and STEG modelings are discretized using finite volume method, and a

359

fully implicit formulation is adopted for time dependent terms. A line-by-line solver

360

based on the TDMA is used to iteratively solve the sets of linear equations.

M AN U

SC

351

361

The following assumptions are considered for computational analysis:

TE D

362 363

•

The domain of study is two dimensional with transient heat conduction.

364

•

Due to low temperature variation, all thermal and electrical properties are assumed to be temperature independent and isotropic.

366

•

Since the rear side of the single PV module is not properly cooled compared to

EP

365

the front side, convective heat transfer coefficient at the rear side is assumed

368

to be half of that at the front.

AC C

367

369

•

No dust or any other agent is deposited on the PV surface.

370

•

Initial temperature of the system is taken to be equal to the ambient

371 372 373

temperature.

•

The study is focused on low-temperature systems, therefore, the Thomson effect is neglected.

374 375

3. Initial and boundary conditions

18

ACCEPTED MANUSCRIPT

376

Present modeling is made of two parts: PV modeling and STEG modeling.

377

3.1. PV initial and boundary conditions

378

Heat flow exchange between PV and ambient, as shown in Fig. 4, are given by:

380 381

M AN U

SC

RI PT

379

Fig. 4. Heat exchange elements between PV and ambient

qin = AIT 383 f

= hw ,f A (T glass −Tair )

qconv ,

b

= hw ,b A (TAl −Tair )

EP

qconv ,

4 qrad , f _ sky = σ Aε glass Ff _ sky (T glass −Tsky4 )

386

(22)

(23)

(24)

AC C

384

385

TE D

382

(25)

4 4 qrad , f _ ground = σ Aε glass Ff _ ground (T glass −T ground )

(26)

qrad , b _ sky = σ Aε Al Fb _ sky (T Al4 −Tsky4 )

(27)

387

388

19

ACCEPTED MANUSCRIPT

4 qrad , b _ ground = σ Aε Al Fb _ ground (T Al4 −T ground )

(28)

Equations (22-28) represent incident solar radiation from the sun, convective heat

390

loss due to heat transfer between front and back surface of PV and ambient, radiative

391

heat loss due to heat transfer between front surface of PV with ground and sky and

392

also between the back surface of PV with ground and sky. Where:

393

Ff

394

where ε glass , ε

395

Fb _ground , β denote emissivity of glass, emissivity of aluminum, Estefan-Boltzman

396

constant, temperature of rear surface of glass cover, ambient temperature, temperature

397

of rear surface of aluminum sheet, ground temperature, sky temperature, radiation

398

view factor of front surface to sky, radiation view factor of front surface to ground,

399

radiation view factor of back surface to sky, radiation view factor of front surface to

400

ground, tilt angle of PV with respect to the horizon (which is taken to be 29.39° ),

401

respectively. (For instance, the radiation view factor Ff _ sky is defined as the fraction

402

of the radiation leaving the front surface of PV that is intercepted by sky).

403

The average convection heat transfer coefficient for front and rear surfaces are:

1 + cos β , Ff 2 Al

_ground

=

1 − cos β 1 + cos(π − β ) 1 − cos(π − β ) , Fb _ sky = , Fb _ground = 2 2 2

, σ , Tglass , T a ir , T A l , Tground ,T

sk y

, Ff

_ sky

, Ff

_ground

, Fb _ sky ,

SC

=

TE D

M AN U

_ sky

RI PT

389

404

hw ,b = 0.5hw ,f

EP

hw ,f = 5.7 + 3.8 V, (W/m2K)

(29)

(30)

where V is wind speed (m/s) and additionally it is assumed thatTground =Tair . The sky

406

temperature is described by the below relationship [43]:

AC C

405

T sky = 0.0052T air1.5 (K) 407

(31)

408

Boundary conditions between consecutive PV layers, with assumption of perfect

409

contact, are:

20

ACCEPTED MANUSCRIPT

−K i

∂T i ∂y

= − K i +1 y =yi

∂ T i +1 ∂y

,

Ti

y =yi

y =yi

= T i +1

(32) y =yi

410

∂T = 0 ,where n is the ∂n

The side surfaces are assumed to be insulated, hence: − K

412

ʺ normal vector to the surface. Furthermore, a thermal contact resistance ( , ) of 0.01

413

m2.K/W is considered between Tedlar and aluminum back sheet [44].

414

The initial condition to solve energy equation for PV layers is assumed to be equal to

415

the ambient temperature at 12:00 A.M.

3.2. STEG initial and boundary conditions

418

3.2.1. Thermal initial and boundary conditions

419

A schematic of STEG modeling is depicted in Fig. 5.

EP

TE D

M AN U

417

SC

416

RI PT

411

420 421

AC C

422

Fig. 5. Heat exchange elements between STEG system and ambient

423

For a STEG model, the PV’s boundary conditions will remain unchanged but the

424

difference is for the lowest boundary, where Equations (27) and (28) will change to

425

conduction boundary condition by considering a thermal contact resistance of 8.5

426

× 10 − 3 m K/W, between aluminum back sheet and ceramic sublayer. The boundary

427

condition for the ceramic exposed to ambient is:

2

q rad ,b _ sky = σ Aεce Fb _ sky (Tce4 −T sky4 )

(33)

21

ACCEPTED MANUSCRIPT

428 4 qrad ,b _ ground = σ Aεce Fb _ ground (Tce4 −T ground )

(34)

430

Boundary condition between copper strip and ceramic sublayer:

−K ce

∂Tce ∂y

= −K cp

∂Tcp ∂y

y = y ce

,

Tce

y = y ce

y = y ce

=Tcp

(35)

y = y ce

431

− K cp

∂Tcp ∂y

+ αcpTJ y

= −K p

y = y cp

y = y cp

∂T p

433

where T

− K cp

cp

y = y

∂Tcp ∂y

= T

p

cp

+ αcpTJ y y = y cp

435

=Tn

y = y

y = y cp

cp

= −K n

y = y cp

∂T n ∂y

+ α nTJ y

y = y cp

(36)

y = y cp

(37)

y = y cp

TE D

434

∂y

+ α pTJ y

SC

Between copper strip and p-type and between copper strip and n-type semiconductor:

M AN U

432

RI PT

429

436

where T cp

437

The side surfaces are assumed to be thermally insulated as before. The initial

438

condition for solving energy equation for STEG system is also assumed to be equal to

439

the ambient temperature at 12:00 A.M.

EP

y = y cp

AC C

440

y = y cp

441

3.2.2. Electrical boundary conditions

442

The “inlet” terminal is considered as the reference potential: Vout=0 V as shown in

443

Fig. 5 and constant current density condition is assumed at the “outlet” terminal,.

444 445

The generated current is calculated from the following relations:

446

22

ACCEPTED MANUSCRIPT

J=

(38)

Voc I = An An ( RL + Rin )

447 N

H ji

∑ ∑A

j =n, p i =1

∫ α ji

n ji An ji

(39)

dT dAn dy ji

RI PT

Voc = 448

Voc and PRL = VRL I . RL + Rin

also VRL =

450

where I is the load current, V oc is Seebeck voltage which is the open circuit voltage

451

produced when there is a temperature gradient across the junctions of the device at no

452

load condition. This open circuit voltage is the summation of Seebeck potentials with

453

reference to the hot side interface of TEG between copper strip and semiconductors.

454

VRL is the output voltage produced and depends on the external load resistance R L ,

455

and

456

represent total internal resistance of TEG, side area of copper strip, height of

457

semiconductors, and N is the number of p-n couples. By differentiating PRL with

458

respect to the load resistance, d PR L d R L = 0 , maximum output power will be find

459

when the external load resistance is equal to internal resistance [7].In addition, the

460

initial condition for solving electric potential equation for STEG system is V= 0V.

461

Electrical efficiency of a TEG can be obtained from the following relation:

M AN U

EP

TE D

PRL is electrical output power. In Equations (33-34) Rin, An, H respectively

PRL Qh

(40)

AC C

ηTEG = 462

SC

449

  dT  Qh = ∑ ∑ ∫ − k ji dAn ji + α jiTJ y  dy  j = n , p i =1  An  ji  N

463 464

where Q h is the heat supplied to the hot side of a TEG.

23

(41)

ACCEPTED MANUSCRIPT

465 466 467

4. Model validation

469

To validate the results of the presented modeling, computations are carried out

470

separately for both PV and TEG.

471

4.1. PV validation

472

The first comparison is made for PV modeling, using Usama et al.’s[45] experimental

473

measurement. The experimental data is for a site located in Tallahassee, Florida,

474

USA, at a latitude of 30° 28' N . The meteorological data for the PV site for one day

475

(15 May 2005) of the measurement is shown in Fig. 6.

476 477

Fig. 6. Irradiance, ambient temperature and wind speed data for Tallahassee, Florida on May 15,

478

2005[45]

AC C

479

EP

TE D

M AN U

SC

RI PT

468

480

The thermal properties used in this experimental study are presented in Table 5.

481

Table 5

482

Thermal parameters of multi-crystalline PV module[45] Material

ρ (kgm −3 )

C p (J/ kg Κ )

z(m)

k (W/ m Κ )

Glass cover

2450

500

0.003

2

PV cell

2330

677

2.5 × 10−4

130

EVA

950

2090

5 × 10 −4

0.311

24

ACCEPTED MANUSCRIPT

Aluminum

2702

903

1 × 10 − 5

237

polyester

1200

1250

0.0001

0.15

483

The initial condition for solving energy equation is taken to be equal to ambient

485

temperature at 12:00 A.M. The developed code is run for a duration of 24 hours based

486

on environmental data of Fig. 6. Fig. 7 illustrates variation of average temperature of

487

PV versus time, compared with experimental measurements, which shows an

488

acceptable agreement.

SC

RI PT

484

M AN U

489

Fig. 7. Comparison of computed PV temperature with experimental measurement

492

Maximum, average and minimum deviations from experimental measurements are

493

19.95%, 6.18% and 0.25% respectively.

TE D

490 491

EP

494

4.2. TEG validation

496

Due to lack of suitable experimental data for STEG, validation is made for TEG with

497

Massaguer et al.’s experimental measurements [7]. In their work, one TEG module is

498

placed on the top of a 23.6 W heater as a heat source. A water-cooled block cools the

499

top surface of the TEG by water of 16.45°C through a closed cooling loop, consisting

500

of a pump, a heat exchanger and liquid lines at ambient temperature of 16.17°C. TE

501

module consists of 98 thermocouples with cross sectional areas of 2.45 × 10-3 m2. The

502

schematic, geometry and material properties of TEG are explained in [7]. The

503

temperature difference between hot and cold junctions of TEG, ∆ and the load

AC C

495

25

ACCEPTED MANUSCRIPT

504

current are computed by the developed code and plotted versus time and load

505

resistance, respectively in Figs 8a and 8b.

506

measurements of [7] are made in Fig. 8.

507

Maximum, average and minimum deviations of ∆ from experimental measurements

508

are: 8.02%, 5.24% and 0.42%, respectively; and maximum, average and minimum

509

deviations of load current from experimental measurements are: 10.89%, 6.31% and

510

1.04%, respectively.

RI PT

Furthermore, comparisons with

M AN U

SC

511

512

(a)

513

(b)

Fig. 8. a) Comparison of computed and measured temperature difference between hot and cold

515

junctions of TEG versus time; b) Comparison of computed and measured load current versus load

516

resistance

TE D

514

517

Based on the comparisons presented in Figs. 7 and 8, the developed code is accurate

519

and can be used reliably for further computations of STEG system.

520

EP

518

5. Numerical scheme

522

The unsteady, two-dimensional numerical modeling is performed using the developed

523

code. The program contains the governing Equations (1), (19) and (20), which are

524

discretized using finite volume method, and a fully implicit formulation is adopted

525

for time dependent terms. A line-by-line solver based on the TDMA is used to

526

iteratively solve the sets of linear Equations. The system under consideration is the

527

same as Fig. 5 with properties and dimensions presented in Tables 1 to 4. Total

528

incident solar radiation on tilted surface is calculated by Equations (6-10).

AC C

521

26

ACCEPTED MANUSCRIPT

529

Meteorological information of the 6th of July are used which contain ambient air

530

temperature and averaged wind speed for the period 2012 to 2014. These are shown

531

in Fig. 9 for the city of Shiraz with a latitude of 29.39° N .

533 534

M AN U

SC

RI PT

532

Fig. 9. Average irradiance and ambient temperature data for July, 6th (2012-2014)

535

5.1. Grid independence study

537

The independency of the grid is investigated using four different meshes for each part

538

of modeling described in section 2. For PV modeling, the number of the grids in the

539

four tested meshes were: 14 × 5 , 26 × 5 , 32 ×10 and 32 × 20 . Maximum differences

540

were: 2.02%, 1.15%, and 0.53%, respectively. Hence, the third grid is chosen to save

541

the computational time without loss of accuracy.

542

For the second part (STEG modeling), the number of the grids in the four tested

543

meshes were: 25 ×136 , 43 × 136 , 53 × 136 and 65 × 136 . Maximum deviation

544

between them were 2.07%, 1.01%, 0.54%, respectively. Hence, the third grid is

545

selected to save computational time without loss of accuracy.

EP

AC C

546

TE D

536

547

5.2. Time step independence study

548

The independency of the time step size was also conducted with ∆t =300, 600 and120

549

sec. Using the meshes selected in the previous section, maximum deviations for PV

27

ACCEPTED MANUSCRIPT

550

modeling were 2.9% and 0.87%, respectively and for STEG modeling, these values

551

were 2.6% and 0.75%, respectively. Therefore, ∆t =300 sec is selected.

552

RI PT

553 554 555

6. Results and discussion

557

The unsteady, two-dimensional modeling for the PV, TEG and STEG systems, has

558

made based on Tables 1-4.

SC

556

559

6.1. Effect of adding TE to PV module

561

The average temperature of PV cells for the single PV system, explained in section

562

2.1 with meteorological information (includes incident solar radiation on tilted

563

surface, ambient temperature and average wind speed) for the location of Shiraz, is

564

shown in Fig. 10.

567

AC C

565 566

EP

TE D

M AN U

560

Fig. 10. Variation of ambient temperature, solar incidence radiation and average temperature of PV

568

Addition of a TE module causes a decrease in PV temperature in comparison with

569

reference PV temperature, as shown in Fig. 11a. At the peak hour (about 12:30 P.M.),

570

when PV reaches to its maximum temperature of 79.6°C, temperature reduction is

571

about 8.4°C. Fig. 11b shows the photon-electric conversion efficiency of

572

monocrystalline PV cells and PV electrical output power during a day, with and

573

without TEG. According to Equation (5), PV efficiency decreases as PV cell

28

ACCEPTED MANUSCRIPT

temperature increases and leads to reduction of electrical output power of PV as

575

explained by [46]. A decrease of PV temperature by 8.48°C, leads to a 0.59%

576

improvement in PV cells’ efficiency and a 5.06% improvement in electrical output

577

power of PV module, as illustrated in Fig. 11b.

RI PT

574

579 580

(a) (b)

M AN U

SC

578

581

Fig. 11. a) Comparison of PV temperature with and without a TEG, variation of hot and cold

582

junctions temperature of semiconductors; b) Comparison of PV efficiency and electrical output power

583

with and without TEG

584

6.2. Electrical output and performance of TEG

586

In Fig. 11a, the temperatures of the hot and cold junctions of TE’s semiconductors are

587

illustrated versus time. For the same environmental condition and system component

588

specification, the maximum temperatures of hot and cold junctions of TE’s

589

semiconductors are 65.7°C and 63.2°C, respectively.

590

Fig. 12a shows the temperature difference between hot and cold junctions of the

591

semiconductors and TEG conversion efficiency during the day of operation. Fig.

592

12b shows corresponding electrical output power PRL and output voltage V RL of TEG.

593

TEG efficiency and electrical output power are functions of temperatures of hot and

594

cold junctions of semiconductors and the temperature difference between them, as

595

presented by Equations (39) and (40). Furthermore, by considering RL = Rin ,

596

Equations (39) and (40) show that the output power and efficiency continue to

597

increase as the temperature difference increases. The greater ∆, the larger the open

598

circuit voltage (Seebeck voltage), as shown in Fig 12.a, and a larger electrical current

AC C

EP

TE D

585

29

ACCEPTED MANUSCRIPT

can be produced which provides higher efficiency and more electrical output power,

600

Fig. 12c. Maximum power and conversion efficiency are 0.81 mW and 0.14%,

601

respectively at a temperature difference of 2.48°C. And maximum open circuit

602

voltage and electrical current are respectively 108.59 mV and 15.1 mA. The

603

temperature difference dropping below zero degree is due to the sky radiation

604

cooling, which makes the hot junctions cooler than the cold junctions.

RI PT

599

(a)

(b)

608 609

EP

TE D

606 607

M AN U

SC

605

(c)

Fig. 12. a) Variation of temperature difference between hot and cold junctions of semiconductors and

611

TEG efficiency during a day; b) Variation of TEG electrical output power; c) Variation of TEG

612

electrical current and Seebeck voltage.

613

AC C

610

614

In Fig. 13, comparison is made between TEG efficiency and Carnot cycle efficiency

615

, = ( −  )⁄ . As mentioned previously, TEG is a type of heat engine and

616

for an ideal and reversible case without any entropy production it could be considered

617

as a Carnot cycle, including two isothermal processes respectively at hot and cold

618

junctions and also two adiabatic processes from hot to cold and from cold to hot

30

ACCEPTED MANUSCRIPT

sides. However, the process that occurs in thermoelectric materials is not actually

620

ideal, and resources can be considered for entropy production and to justify the

621

irreversibility rise due to non-presence of two isothermal and adiabatic processes.

622

Non-adiabatic nature of this process is caused by the collision between particles and

623

also by the contact with crystalline network of substances. Since friction and collision

624

are factors of irreversibility, they cause the efficiency of TEG to be much lower than

625

that of Carnot ideal cycle. As shown in Fig. 13, the maximum Carnot efficiency is

626

3.77%. The negative efficiency is due to the reduction of temperature of hot side

627

which becomes less than the cold side during the night. Therefore, efficiency would

628

become positive, if the absolute values were considered.

629 630

TE D

M AN U

SC

RI PT

619

Fig. 13. Comparison of TEG and Carnot cycle efficiencies for STEG system

631

7. Sensitivity analysis

633

7.1. Effect of wind speed

634

Figs. 14a and b show the effect of wind speed on PV and TEG efficiency and also on

635

PV and TEG electrical output power in a STEG system. Computation is carried out

636

for PV and TEG performance and electrical output power when the wind speed

637

changes. Increasing wind speed, according to Equation (29), gives rise to the

638

convective heat transfer coefficient hw , hence, the temperatures of the STEG’s front

639

and rear surfaces reduce. However, since hw is greater for the front surface, the

640

temperature difference between hot and cold junctions of P/N legs decreases. With

641

the same amount of internal and external electrical resistance, smaller amount of

AC C

EP

632

31

ACCEPTED MANUSCRIPT

Seebeck voltage can be generated and smaller amount of electrical current and

643

electrical output power can be produced. In addition, by a decrease in PV

644

temperature, its conversion efficiency and electrical output power increase. From this

645

figure one can find that, as the wind speed increases from 1.4 m/s to 2.8 m/s and 5.6

646

m/s, the PV conversion efficiency at the peak hour increases by 0.28% and 0.56%,

647

respectively and TEG efficiency decreases by 0.01% and 0.02%, respectively.

648

Furthermore, PV electrical output power increases by 2.29% and 4.58% and TEG

649

electrical output power decreases by 12.3% and 27.5%, respectively.

SC

RI PT

642

651 652

M AN U

650

(a)

(b)

Fig. 14. Effect of wind speed for a STEG system on, a) PV and TEG efficiency; b) PV and TEG

654

electrical output power

655

TE D

653

7.2. Effect of ambient temperature

657

Figs. 15a and b show the effect of ambient temperature on PV temperature, PV

658

efficiency, and TEG efficiency in a STEG system. Computations are conducted with

659

changing the ambient temperature by

660

wind speed (1.4 m/s), increasing the ambient temperature causes the PV temperature

661

to rise in a STEG system, and therefore, its conversion efficiency reduces due to the

662

decrease in convective and radiative heat transfer with ambient and sky and vice

663

versa. With an increase of 5°C in ambient temperature, there is an increase of 4.8°C

664

in PV temperature at the peak hour. As illustrated in Fig. 15b, this amount of increase

665

in ambient temperature, reduces the PV efficiency by 0.34%. Also, due to the smaller

666

hw on the rear surface, the rear surface temperature is less affected by the ambient

± 5 °C. As shown in Fig. 15a, with the same

AC C

EP

656

32

ACCEPTED MANUSCRIPT

temperature and the temperature difference between hot and junctions of P/N legs

668

decrease. This results in TEG efficiency reduction. For this amount of increase in

669

ambient temperature, the TEG efficiency increases 0.02% due to 0.05°C increase in

670

the temperature difference between hot and cold junctions of P/N legs.

RI PT

667

672 673

M AN U

SC

671

(a) (b)

674

Fig. 15. Effect of ambient temperature on a) PV and TEG efficiency for a STEG system;

675

b) PV temperature for a STEG system

676 677

7.3. Effect of height of PN couple

679

Fig. 16 shows the variation of TEG electrical output power PRL , with the height of

680

PN couples H in the PV-TEG system. There should be an optimal height at which

681

PRL maximizes. When all parameters are constant except H, a higher H because of

682

conduction heat transfer leads to larger temperature difference between hot and cold

683

junctions of P/N legs. However, there is a direct relation between H and internal

684

electrical resistance, Rin. Therefore, increasing the H may decrease the efficiency and

685

electrical output power of TEG. The ability of the thermoelectric materials to produce

686

electrical power effectively depends on the dimensionless figure of ZT merit defined

687

as:

688

ZT =

689

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α 2σ k

T , where T is the Kelvin temperature, α is Seebeck coefficient, σ is

electrical conductivity and k is thermal conductivity. According to the above relation,

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there are three ways to improve ZT. PRL at peak hour is demonstrated in Fig. 16 at

691

each height. By decreasing the value of k, the maximum output power moves toward

692

a smaller optimum H value, while by increasing α and σ , the maximum output

693

power moves toward a larger optimum H value. Although by increasing H, all

694

electrical output powers increase, the higher height results in a more required amount

695

of material (with the same cross sectional area), cost and occupied space. Hence,

696

choosing the optimum H is essential to design TEG modules and using a higher H is

697

not the best idea to reach better outputs.

700 701

Fig. 16. Effect of height of PN couple on TEG electrical output power for STEG system

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7.4. Effect of external load resistance connected to TEG

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The effect of the external load resistance RL on the PV-TEG system performance is

703

shown in Figs. 17 a, b and c. an increase in RL, according to Equation (38), causes a

704

decrease in electrical current, and any decrease in electrical current leads to an

705

increase in the temperature difference between hot and cold junctions due to smaller

706

values of the Peltier terms in Equations (36) and (37). (a decrease in electrical current

707

leads to reduction of absorbed and removed heat fluxes on the hot and cold sides of

708

TEG ). The same result is obtained in Ref [7]. As shown in Figs. 17 a and b, a higher

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∆T improves the TEG efficiency; however, as explained in Section (3.2.2), the

710

electrical output power and efficiency of TEG are the highest when RL = Rin , neraly

711

5 Ω . When RL is larger than Rin , TEG efficiency decreases because of the large

712

reduction in electrical current despite the larger ∆T . Because of the increase in ∆T ,

713

as RL increases, the hot side temperature of TEG increases and the temperature of PV

714

increases as a consequence and its efficiency decreases.

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718 719

Fig. 17.

720

junctions of semiconductors and electrical current; b) TEG efficiency; c) PV temperature and PV

721

temperature

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Effect of external load resistance on, a) temperature difference between hot and cold

723

8. Conclusion

724

An unsteady, two-dimensional model is developed in the present study to investigate

725

the thermal and electrical performances of PV and STEG systems by solving the

726

coupled energy and electric potential equations. All thermoelectric effects, including

727

Joule heating, Peltier effect, Fourier’s heat conduction, except Thomson effect, are

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considered in the simulations. All properties are assumed to be constant during

729

operation period. Temperature and electric potential distribution are determined for a

730

duration of 24 hours of a typical summer day (6th of July) in Shiraz, Iran. Results of

731

the numerical modelings are validated against experimental measurements and the

732

following conclusions are made. For the same environmental conditions:

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1- Directly adding a TE module to the back of PV leads to a decrease in PV

734

temperature by about 8.49°C, a 0.59% improvement in PV efficiency, and a

735

5.06% increase in its electrical output power at the peak hour.

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2- The maximum temperature difference at the peak hour is 2.48°C, where the

737

maximum amount of Seebeck voltage, electrical current, electrical output power

738

and TEG efficiency are 108.6 mW, 15.1 mA, 0.81 mW and 0.14%, respectively.

739

3- Factors of irreversibility, cause the efficiency of the TEG to be lower than

740

Carnot ideal cycle. At the peak hour, Carnot efficiency is about 26 times greater

741

than TEG efficiency.

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4- As the wind speed increases in a STEG system, PV efficiency increases as well

743

nearly by 0.28% for each doubling of the wind speed; and the TEG efficiency

744

decrease nearly by 0.01% for each doubling of the wind speed.

TE D

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5- A rise in the ambient temperature increases the PV temperature in a STEG

746

system, because of the decrease in convective and radiative heat transfer with

747

ambient and sky; therefore, its conversion efficiency reduces. There is a nearly

748

0.34% decrease in PV efficiency for a 5°C increase in ambient temperature and

749

there is also a 0.01% increase in TEG efficiency for a 5°C increase in ambient

750

temperature.

AC C

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745

751

6- By changing the height of PN couples, there is an optimum height at which the

752

electrical output power of TEG is maximum. This optimum height decreases

753 754

with the decrement of thermal conductivity and increases with increment of Seebeck coefficient and electrical conductivity.

755

7- The electrical output power and efficiency of TEG varies by the external load

756

resistance and there is a maximum value where external load resistance is equal

757

to internal load resistance. Also, the increment of external load resistance

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758

because of the decrease in electrical current causes an increase in the

759

temperature of PV and a decrease in its efficiency.

760

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An unsteady-two dimensional numerical model for a PV-TE system is developed Electric power and efficiency of hybrid PV-TE systems are presented during a Klein day The PV efficiency improved by adding TEG about 0.59%.

Comparison is made between TEG and Carnot cycle efficiency

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Effect of wind speed and ambient temperature variation on system performances are illustrated

Effect of height of PN couple on TEG electrical output power for STEG system

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Effect of external load resistance connected to TEG on TEG and PV efficiency