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thermoelectric system integrated with parabolic trough collector
Energy Conversion and Management 159 (2018) 371–380
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Performance investigation of a hybrid photovoltaic/thermoelectric system integrated with parabolic trough collector
T
⁎
Shohreh Soltania, Alibakhsh Kasaeiana, , Tahmineh Sokhansefata, Mohammad Behshad Shafiib a b
Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran Faculty of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
A R T I C L E I N F O
A B S T R A C T
Keywords: Thermoelectric Photovoltaic Parabolic trough collector Efficiency
In this study, a non-dimensional model of a tri-generation unit consisting parabolic trough solar collector, integrated with solar cell and thermoelectric generator is presented. In order to obtain the effects of solar irradiance and ambient temperature on the performance of the system, a set of functions were coded in the MATLAB software. Eight nonlinear algebraic equations were derived and solved via the iterative Newton-Raphson technique. The thermal and electrical efficiencies, the electrical characteristics of the thermoelectric and photovoltaic modules, and the thermal and electrical power of the hybrid device were analyzed in this study. The results have reflected some improvements on the electrical efficiency by placing thermoelectric module and solar cell on the lateral area of the absorber tube. Furthermore, an electrical power of 22.714 W could be reached at the solar concentration of 998 W/m2. In order to validate the results of the mathematical model, two research works have been utilized. The evaluation of the obtained results shows a good agreement with the results in the literature.
1. Introduction Photovoltaic is recognized as the promising approach to exploit solar energy. However, the main part of solar energy is transformed into waste heat and the temperature increase of photovoltaic leads to diminish its electrical efficiency. An appropriate method to moderate the effects of this problem, is the integration of PV module with a converter of heat-to-electricity in the form of thermoelectric generator (TEG) [1]. To obtain this goal, it is necessary to heat one side, while keeping the other side cold. The temperature difference across the TEG provides energy for charging barriers (electron, hole) to depart from the hot side to the cold side of a thermoelectric element. Many research works have focused on the combination of thermoelectric modules with solar systems [2–4]. Miljkovic and Wang [5] numerically evaluated the performance of a hybrid solar thermoelectric system. They investigated the effects of three various types of thermoelectric materials on the efficiency of the system. They presented an energy-based model of the hybrid device to evaluate the overall performance. The effects of environmental parameters on the efficiency of a parabolic trough/TE unit were investigated by Li et al. [6]. They observed that rising the solar insolation, ambient temperature and wind velocity, increased the thermal losses of the system. Many researchers have investigated the effects of using
⁎
thermoelectric material on the efficiency of photovoltaic systems [7–10]. Su et al. [11] presented an electrical and thermal model for a dye-sensitized PV hybrid thermoelectric generator. They studied the temperature effects on the efficiency of the solar cell. The results indicated that the hybrid system could be used as a promising configuration to exploit solar energy. Lamba et al. [12] proposed a thermodynamic model for a concentrated photovoltaic cell and a thermoelectric module. The effects of some characteristics such as solar flux, PV current and TE current on the overall efficiency and total power were discussed. The results proved that the overall power of the hybrid system was reduced by 0.7% and 4.78% at the solar concentrations of 1 and 5, respectively. Hajji et al. [13] studied the efficiency of an indirect PV/TE coupling device. They placed a concentrator between the photovoltaic and thermoelectric modules. Their findings demonstrated that their design enhanced the overall efficiency of the hybrid PV/TE system. Studying the simultaneous use of thermoelectric cooler and solar cell has been received wide attention. Najafi et al. [14] investigated the application of thermoelectric cooler to control the solar cell temperature. They computed the required power to run the thermoelectric cooler, and applied genetic algorithm to optimize the thermoelectric current. It was found that using thermoelectric cooler dropped the temperature of solar cell. Kane et al. [15] utilized a thermoelectric tile
Corresponding author. E-mail address: [email protected] (A. Kasaeian).
https://doi.org/10.1016/j.enconman.2017.12.091 Received 19 September 2017; Received in revised form 26 December 2017; Accepted 27 December 2017 0196-8904/ © 2017 Elsevier Ltd. All rights reserved.
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Nomenclature
L D W α k R R0 Z T ΔTMax ṁ G t IMax VMax P Q e
amb air Sky Sol go gi co ci pi po M env Max in out The ele tot
length (m) diameter (m) width (m) seebeck coefficient (V/K) thermal conductivity (W/m·K) electrical resistance (Ω) load resistance (Ω) figure of merit for TEG temperature (°C) temperature gradient across TEG (°C) mass flow rate (kg/s) solar irradiance (W·m−2) time (hour) maximum current of TEG (A) maximum voltage of TEG (V) power (W) thermal energy (W) error
Greek Symbols
α λ β η τ θ ρ σ ε
Subscripts PV FF TEG H C f ref aper
ambient air sky solar outside area of glass envelope inside area of glass envelope outer surface of the PV inner surface of the PV inner surface of absorber tube outer surface of absorber tube mean envelope maximum input flow output flow thermal electrical total
photovoltaic fill factor thermoelectric generator hot side of the TEG cold side of the TEG fluid reference condition aperture area
to reduce the temperature of solar cell. They stated that the TE modules were able to operate at the optimal temperature of solar cell. The results showed that the electrical efficiency of the solar cell was increased in the range of 1–18% for the solar irradiation range of 800–1000 W·m−2
absorptance molecular mean free path angle of inclination efficiency (%) transmittance incidence angle reflectance Stephan Boltzmann constant (5.67 × 10−8 kg s−3 K−4) emissivity
and the temperature range of 25–45 °C. The integration of photovoltaic cell and solar collector is accounted as a novel design for improving the efficiency of hybrid systems. Some investigations have been conducted to improve the performance of Fig. 1a. Cross-sectional view of the evacuated tube.
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2.2. Description of the components
solar collectors with photovoltaic cells [16–18]. Garg et al. [19] evaluated a compound parabolic concentrator as the reflector of a photovoltaic/thermal collector. A numerical model of a two-stage parabolic trough PV/T system was introduced by Jiang et al. [20]. Various structural characteristics were considered to obtain the geometric concentration ratio and the size of solar image. They obtained that the heat load of the solar cell was decreased by 20.7%. Calise et al. [21] simulated a parabolic trough photovoltaic/thermal collector. In their model, solar cells were placed on the lateral areas of evacuated tubes. Their achievement showed that the performance was affected significantly by the temperature of working fluid. Tiwari et al. [22] evaluated the performance of a hybrid (PV/T-CPC) collector using MATLAB software. They developed an analytical model to compare the performance of inclined and horizontal PVT-CPC systems. Li et al. [23] investigated the efficiency of a hybrid PTC- PVT unit, using three different types of solar cells. Their achievements showed that the maximum electrical efficiency of the hybrid device was obtained by using GaAs solar cell. In this study, a numerical evaluation is carried out on the incorporation of PV-TEG with parabolic trough solar collector, under solar irradiance. The effects of solar irradiance and ambient temperature on the performance of the system are represented. Solar concentration is assumed to take place at the PV section of evacuated tubes. The small portion of thermal energy is transformed into electricity and the remaining part heats the hot side of thermoelectric generator. Meanwhile, the working fluid flows inside the absorber tube and creates temperature gradient for the TEG, which produces extra electricity. A 0-D mathematical model is introduced to investigate the system efficiency. Eight nonlinear algebraic equations are solved via the iterative Newton-Raphson technique. Although the modeling of hybrid solar thermoelectric collectors has been carried out in previous research works to determine the performance, this is the first time that the modeling of such system is performed with the help of experimental data for validation. Also, a novel mathematical method has been used based on the heat transfer and electrical equations.
The optical and geometrical properties of the parabolic trough collector are presented in Table 1. A set of crystalline silicon PV cells with the total area of (8 × 62.5) cm2 is used in this study. The characteristics of the PV cell, manufactured by the Aria Solar Co, are reported in Table 2. Also, a TEG, Model: TEC1-12706, produced by the Hebei I.T. (Shanghai) Co., is employed in the study. The specifications of the TEG are given in Table 3. 2.3. Governing equation 2.3.1. Thermal equation A non-dimensional model covers all the energy equations of the evacuated tube. The thermal resistances of the model are presented in Table 4. To investigate the effect of radiation between the outer surface of glass envelope and the sky, the heat transfer coefficient is determined by [4]: 2 2 hgo − sky . Rad = σεgo (Tgo + Tsky )(Tgo + Tsky )
(1)
where Tgo is the temperature of the outside area of glass envelope, εgo is the emissivity of glass cover, σ is the Stephan Boltzmann constant, and Tsky is the sky temperature which is calculated by the following equation [27]: 1.5 Tsky = 0.0552Tamb
(2)
Tamb is the ambient temperature, and hgo − air is the convection heat transfer coefficient between the outer surface of glass envelope and the ambient, which is calculated by Eq. (3) [27]: hgo − air =
kair Nugo Dgo
(3)
In the above equation, kair is the conduction heat transfer coefficient of the air, and Nugo is the Nusselt number for the external surface of glass envelope. The Nusselt number for the forced convection on an insulated cylinder is written as [26]:
2. Modeling of the hybrid system
1.5
m n ⎛ Prair ⎞ Nugo = CReDgo Prair ⎜ ⎟ ⎝ Prgo ⎠
2.1. Model description A cross-sectional view of the evacuated tube is indicated in Fig. 1a, while, Fig. 1b shows the thermal resistance model, gained from the energy balance of the evacuated tube. It is supposed that the temperature distribution, solar radiation and the properties of the PV and TEG sections are uniform along the axial and circumferential directions of the evacuated tube. Also, all the surfaces are gray surface in this investigation. As it can be seen, the evacuated tube consists of four main parts, namely glass envelope, photovoltaic tube, thermoelectric tube and absorber pipe. When solar radiation is received by the glass envelope, it is encapsulated in a vacuum space between the inner layer of glass cover and the outer layer of PV tube. After that, the photovoltaic cell absorbs the solar flux, and transforms it into electrical power. A TEG module is placed at the back side of the PV cell for using the waste heat. A single-phase working fluid flows inside the absorber tube to create temperature gradient across two ends of the TEG. Therefore, a temperature difference is provided within the TEG layer for producing electricity. According to Fig. 1b, R1 is the convection resistance between the working fluid and the absorber pipe, R2 is the radial conduction resistance through the absorber tube, and R3 and R4 are the radial thermal resistances through the TEG and PV tubes, respectively. Also, R5 and R6 are the radial convection and radiation resistances from the outer surface of the PV tube to the inner surface of glass envelope, and R7 is the radial conduction resistance through the glass envelope. Finally, R8 and R9 are the radial convection and radiation resistances between the outer surface of the glass envelope wall and the ambient or sky.
(4)
In Eq. (4), ReDgo is the Reynolds number of the wind which flows on the outer surface of the glass envelope, Prair is the Prandtl number at the ambient temperature, and Prgo is the Prandtl number at the temperature of the outer surface of the glass envelope. Also, n = 0.37 for Pr < 10, n = 0.36 for Pr > 10, and C and m are the experimental constants, which are represented in Table 5. In addition, hco − gi . Rad is the radiative heat transfer coefficient between the outer surface of the PV tube and the inner surface of the glass cover, which is calculated as bellow [4]:
hco − gi . Rad = σεgo (Tco2 + Tgi2 )(Tco + Tgi )
(5)
The free molecular convection happens between the inner surface of glass envelope and the outer surface of PV tube. The air pressure in the annular space is 0.013 Pa [34]. Also, hco − gi is the convective heat transfer coefficient between the inner surface of glass envelope and the
Fig. 1b. Thermal resistance model of the hybrid system.
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Table 1 Optical and geometrical properties of the evacuated tube and reflector of PTC [24]. Parameter
Symbol
Value
Parameter
Symbol
Value
Shadowing Tracking error Geometry effects Dirt mirror error Non computing error Dirt absorber error Absorbance of glass cover Angle of inclination Transmittance of glass cover Incident angle Emissivity of glass
esh etr ege edm enc eda α β Г θ ε
0.974 0.994 0.98 0.88–0.93 0.97 1 + edm/2 0.96 20 0.96 0 0.9
Glass cover outside diameter Glass cover inside diameter PV cell outside diameter PV cell inside diameter Absorber tube outside diameter Receiver tube inside diameter Aperture width Length of collector Reflectance of mirror Focal distance Conductivity of glass
0.085 0.08 0.03 0.029 0.027 0.025 1 1 0.67 0.21 1.04
Rim angle
φr
79.6°
Concentration ratio
Dgo (m) Dgi (m) Dco (m) Dci (m) Dpo (m) Dpi (m) W(m) L(m) ρcl f (m) kglass (W/m·K) C
Table 2 The PV cell characteristics [3,8,25].
8
Table 5 Experimental coefficients of Eq. (4) [34].
Parameter
Symbol
Value
ReDgo
C
m
Type of solar cell Number of solar cell Short circuit current Open circuit voltage Fill factor Area of one cell Active area of solar cells Efficiency (At the standard condition) Thermal coefficient Absorptivity Emissivity
C-Si n ISC (A) Voc (V) FF A (cm2) ACell (cm2) η (%) β αc εc
– 8 in series 8 4.44 0.73 62.5 500 15.75 0.0041 °C−1 0.85 0.9
1–40 40–1000 1000–200,000 200,000–1,000,000
0.75 0.51 0.26 0.076
0.4 0.5 0.6 0.7
outer surface of PV tube, which is calculated by Eq. (6) [29]:
hco − gi =
kstd Dco D
gi ⎞ 2ln ⎛ ⎝ Dco ⎠ ⎜
Symbol
Value
TE type Number of modules Maximum voltage Maximum current Maximum power Maximum temperature gradient Figure of merit Electrical resistance of a P-N couple Load resistance of a P-N couple Seebeck coefficient Thermal conductivity
– – VMax (V) IMax (A) QMax (W) ΔTMax (°C) Z(1/K) RTEG(Ω) R 0 (Ω) αTEG (V/K) kTEG (W/m·K)
TEC1-12706 20 in series 15.2 6 56.8 79 0.0021 0.0022 0.0022 3.9 × 10−4 3.2
λ=
b=
R1 =
R2 =
R3 =
R4 = R5 =
1 πLc hf Dpi ⎛ Dpo ⎞ Ln ⎜ D ⎟ ⎝ pi ⎠ 2πLc kpipe
R7 =
)
+1
(6)
2.331∗10−20 (Tco−Tgi + 273.15) Pair δ 2
(7)
(2−a)(9γ −5) 2a + (γ + 1)
(8)
2 QH . TEG = αTEG ITEG Tci−0.5RTEG ITEG + kTEG ΔTTEG
1 πLc hco − gi . Rad Dco ⎛ Dgo ⎞ Ln ⎜ D ⎟ ⎝ gi ⎠ 2πLc kglass
D Ln ⎛⎜ ci ⎞⎟ ⎝ Dpo ⎠ 2πLc kTEG
R8 =
1 πLc hgo − air Dgo
D Ln ⎛⎜ co ⎞⎟ ⎝ Dci ⎠ 2πLc kPv 1 πLc hco − gi . Conv Dco
R9 =
1 πLc hgo − sky . Rad Dco
(9)
where ITEG .αTEG and RTEG are the thermo electric current, the Seebeck coefficient, and the electrical resistance of the TEG, respectively. Also, Tci is the temperature of the inner surface of PV cell, and kTEG is the thermal conductivity of the thermoelectric material, which is calculated as bellow [14]:
Thermal Resistance Equation (R6–R9)
R6 =
Dco Dgi
Also, b is an interaction and accommodation coefficient, which is supposed to be 1.571[34]. To compute the conduction in the PV tube, it is necessary to know kPV . The values of this parameter are extracted from Table 6. The thermal energy, which is absorbed by the hot side of the thermoelectric generator, is calculated by [31]:
Table 4 Thermal resistances for the PV/TEG-PTC models [26]. Thermal Resistance Equation (R1–R5)
(
where kstd is the conductive heat transfer coefficient of gas in the annular space, λ is the free mean path, δ is the molecular diameter of air (3.55 × 10−8 cm), and Pa is the air pressure at this space [34].
Table 3 The characteristics of the thermoelectric module [3,8,40]. Parameter
+ bλ
⎟
Table 6 Conductivity of silicon [30].
–
374
Temperature (K)
kPv (W/m·K)
Temperature (K)
kPv (W/m·K)
200 300 400 500 600 700 800 900
266 156 105 80 64 52 43 36
1000 1100 1200 1300 1400 1500 1600 1681
31 28 26 25 24 23 22 22
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kTEG =
(Tamb−ΔTMax ) VMax IMax 2Tamb ΔTMax
where βref , ηcell . ref , and Tref represent the temperature coefficient of the solar cell, the PV cell's efficiency, and the temperature at the reference condition, which is commonly considered to be 25 °C. The electrical efficiency of the thermoelectric generator could be shown as followings [9]:
(10)
ΔTMax is the maximum temperature gradient across the TEG, and IMax is the current which can produce ΔTMax between two sides of the TEG. It should be noted that all the electrical and thermal properties of the TEG such as ΔTMax , IMax , VMax and IMax are reported in Table 3. Also, kpipe is the conductive heat transfer coefficient of the absorber tube, which is presented in Table 7. The Newton’s law should be used to compute the convection between the working fluid and the inner surface of the absorber tube. Here, hf is the convective heat transfer coefficient of the fluid, which flows through the absorber tube [26].
hf =
kf Dpi
NuDpi
ηmax . TEG =
TH and TC are the temperatures of the hot side and the cold side of the TEG, TM is the mean temperature of the TEG, and Z is the figure of merit for the TE material. ITEG is the thermoelectric current, which is given by [14]: ITEG =
(11)
Prf
f pi
Prpi
1 + 12.7
(Pr f2/3−1) 8
αTEG =
0.11
(12)
(13)
(16)
where Aaper is the aperture area of the reflector, G is the direct normal irradiance, and α is the absorptance of the reflector mirrors. The solar energy, which is absorbed by the glass envelope of the evacuated tube, is [35]:
Qenv . SolAbs = QSol ηenv α env
(17)
(18)
where αpv is the absorbance of the PV tube, and ηpv is the efficiency of the PV cell.
QC . TEG = Qpi − po . Cond
(24)
QH . TEG = QC . TEG + PTEG
(25)
QH . TEG = Qco − ci . Cond
(26)
Qcell . SolAbs = Qco − ci . Cond + Qco − gi . Conv + Qco −gi .Rad + PPV
(27)
Qgo − gi . Cond = Qco − gi . Conv + Qco − gi . Rad
(28)
Qgo . SolAbs = Qgo − air . Conv + Qgo − sky . Rad−Qgo − gi . Cond
(29)
QHeatLoss = Qgo − air . Conv + Qgo − sky . Rad
(30)
Table 7 Conductive heat transfer coefficient of the absorber tube [32].
2.3.3. Electrical equation The electrical efficiency of the photovoltaic cell may be expressed as bellow [36]:
ηcell = ηcell . ref [1−βref (T −Tref )]
(23)
where, Qf − pi . Conv is the convection between the working fluid and the inner surface of the absorber tube, Qpi − po . Cond and Qco − ci . Cond are the conduction through the absorber pipe and the PV tube, QC . TEG and QH . TEG are the thermal energy at the cold and hot junctions of the TEG, PTEG is the power of the thermoelectric generator, and Qco − gi . Conv and Qco − gi . Rad are the convection and radiation between the outer layer of the PV cell and the inner surface of the glass envelope. Also, Qgo − gi . Cond is the conduction between the inner and outer surfaces of the glass envelope, PPV is the PV cell power, Qgo − air . Conv is the convection between the outer surface of glass cover and the ambient, and Qgo − sky . Rad is the radiation between the outer surface of the glass envelope and the sky.
where α env is the absorbance of the reflector glass envelope, and ηenv is the optical efficiency of the glass envelope. The solar energy, which is absorbed by the PV tube, is:
Qcell . SolAbs = QSol ηpv αpv
Qf − pi . Conv = Qpi − po . Cond
(15)
The incoming solar energy on the reflector is given as followings:
QSol = Aaper G α
(22)
(14)
All parameters in Eq. (14) are taken from Table 1, and the incident angle modifier (K θ ) is given by [28,34]:
K θ = cosθ + 0.000884θ−0.00005369θ 2
VMax TH
2.3.4. Energy balance The numerical model utilizes an energy balance between the fluid flowing inside the absorber tube and the sky. Also, the energy equations are assigned by mentioning that the energy is kept at each surface of the evacuated tube. The energy balance equations can be written as followings [34]:
2.3.2. Solar flux absorption As the first step of the thermal computation, it is necessary to compute the optical efficiency of the glass envelope by the following equation [34]:
ηenv = esh etr edm ege eda eun ρcl K θ
(21)
where VMax is the DC voltage at the maximum temperature gradient of the TE material.
Prf is the Prandtl number of the working fluid, Prpi is the Prandtl number on the inner surface of the absorber tube, ReDpi is the Reynolds number on the inner surface of the absorber tube, and fpi is calculated by Eq. (13). This equation is valid for 0.5 ≤ Prf ≤ 2000 and 2300 ≤ ReDpi ≤ 5 × 106 [34]. The Reynolds number varies from 2730 to 5800 in this study. fpi = [1.821log(ReDpi )−1.64]−2
αTEG ΔT R 0 +RTEG
ΔT is the temperature difference between two sides of the TEG, and R 0 is the load resistance. The Seebeck coefficient can be calculated by the following equation [14].
f pi 8(ReDpi − 1000) Prf
(20)
C
where kf is the thermal resistance of the working fluid, and NuDpi is the Nusselt number for the forced convection in a cylindrical tube. If the Reynolds number is less than 2300, the flow is laminar and the Nusselt number becomes 4.36. If not, the Nusselt number would be calculated by Eq. (12) [33]:
NuDpi =
(TH −TC ) (1 + ZTM )0.5−1 T TH (1 + ZTM )0.5 + TH
(19) 375
Material
kpipe (W/m·K)
Stainless steel Copper
0.013 Tpi-po + 15.2 400
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2.4. Solution method
3.1. Thermal results
The modeling of the hybrid PV/TEG-PTC is carried out by implementing MATLAB codes. Eight nonlinear equations are solved via the iterative Newton-Raphson technique. The modeling procures are developed in the MATLAB (R2014b). The wind speed (UWind), the air pressure (Pair), the TEG and PV cell geometry, and the material properties are considered as the input parameters, to achieve the power of the PV cell (PPV) and the thermoelectric module (PTEG). The flowchart of the numerical modeling is indicated in Fig. 2.
3.1.1. Comparison between the ambient temperature and the photovoltaic temperature Fig. 4 shows the distribution of the solar cell and the ambient temperature versus time. It is assumed that water flows through the absorber tube with the flow rate of 0.03 kg·s−1 and the inlet temperature of 28 °C. The obtained results show that the maximum temperature of the PV cell is 96.2 °C at the ambient temperature of 36.2 °C. It should be noted that the ambient temperature has a positive impact on the efficiency of the solar cell. Also, it is clear that the reflected solar flux has a negative effect on the thermal efficiency of the hybrid system [38]. So, using glass envelope as the external cover of the evacuated tube, declines the rate of the dissipated heat. But, as the temperature of the solar cell increases, the electrical efficiency of the PV cell reduces, which is due to the higher thermal energy [15].
2.5. Validation In order to examine the accuracy of the numerical results, two available research works [3,6] were used.
3.1.2. Temperature of the hot side and cold side of the thermoelectric generator Fig. 5 indicates the variation of the temperatures through the TEG. It is seen from the figure that, the TEG’s hot side temperature is usually less than that of the PV cell’s temperature. The contact resistance
2.5.1. Solar PV/T, combined with thermoelectric module Mohsenzadeh et al. [3] introduced a new design of photovoltaic/ thermal system, integrated with thermoelectric module. They assumed that the evacuated tube consisted of a triangular channel, which was covered by photovoltaic cell and thermoelectric generator, and a glass envelope covered the solar cells. They examined the overall efficiency and total power of the hybrid system, experimentally.
2.5.2. Solar TEG, integrated with parabolic trough collectors Li et. al. [6] investigated the impacts of the environmental parameters on the efficiency of a hybrid solar thermoelectric collector. They supposed that the TEM array was located on the focal axis of the parabolic trough collector.
3. Results and discussions In the following, the modeling results are represented for the proposed tri-generation device. Fig. 3 shows the average solar radiation, which has been considered in this study. As it can be seen, the solar irradiance rises until noon and reduces in the afternoon. Also, the solar radiation reaches to a maximum value of about 998 W·m−2 at 1:30 p.m. The wind speed plays a significant role on the efficiency of solar systems. An increasing heat loss should be resulted by increasing the wind velocity [6]. In this study, the wind velocity and the air pressure are considered as 2.5 m/s and 101.3 kPa, respectively. As mentioned above, the geometrical and optical parameters of the evacuated tube and the reflector of the parabolic trough collector (PTC) are given in Table 1. Some important characteristics of the PTC, namely the focal distance (f), the aperture width (W), the rim angle (φr), and the incident angle (θ) are taken into account in the modeling process. In order to absorb the radiated solar flux, the appropriate diameters are calculated and considered in this study (Table 1). It is supposed that the sun tracking system radiates the solar flux on the evacuated tube continually, and the tracking error is considered to be small (0.994). The tracking error is an important factor to compute the optical efficiency of the glass envelope (Eq. (14)). The optical efficiency is low when the rim angle is small (at φr < 90). If the tracking error is too high, the reflected solar flux cannot be absorbed by the evacuated tube [37]. In this study, the evacuated tube is considered on the focal line, the rim angle is 79.6°, and the aperture width is 1 m. This section consists of two main parts; at the first part, the obtained thermal results are investigated and the results of photovoltaic temperature and the TEG temperature gradient are presented. Therefore, the thermal power and thermal efficiency of the hybrid PV/TEG-PTC system are explained. At the second part, the electrical results of the TEG and PV sections are represented. Finally, the total power and the overall efficiency of the proposed tri-generation unit are studied.
Fig. 2. Flowchart of numerical modeling.
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Fig. 6. Comparison of the thermal power with Mohsenzadeh et al. [3].
Fig. 3. The variation of solar irradiance.
It is worthy to notify that the TEG’s cold side temperature depends on the flow rate of the working fluid, which flows inside the absorber tube. In this study, the flow rate of the working fluid is considered as 0.03 kg·s−1. In order to demonstrate the conformity of the thermal results with the experimental data, the thermal power and thermal efficiency of the hybrid system were compared with the experimental works in the literature. 3.1.3. Thermal power of the hybrid unit According to Fig. 6, the thermal power of the hybrid unit initially increases and then, slightly decreases, which is due to the decrease on the solar irradiance. This issue clearly indicates the importance of solar radiation, especially at the mid time of the solving process. It is observed from the figure that the numerical and experimental results show a similar trend, and the deviation of the thermal power is less than 3%. As it was expected, considering the TEG and PV tubes decreases the portion of the absorbed heat by the working fluid.
Fig. 4. Distribution of the ambient temperature and solar cell temperature.
Fig. 5. Temperature variation within the thermoelectric generator.
3.1.4. Thermal efficiency of the hybrid unit The variations of thermal efficiency versus time and the flow rate of working fluid are illustrated in Figs. 7a and 7b. The maximum values for the thermal efficiency take place at the early and late hours. According to Fig. 7a, the thermal efficiency reaches to a maximum value of about 57%. The deviation of the thermal efficiency is about 2.5%, which shows a good agreement with the experimental results. As it is expected, higher thermal efficiencies are obtained by the higher flow rates. The flow rates of the working fluid are changed from 0.5 L·min−1 to 3 L·min−1 in Fig. 7b, while the mean temperature of the working fluid and the thermal capacity are fixed. The flow rate strongly influences on the performance of the hybrid PV/TEG-PTC unit. The value of the mass flow rate controls the temperature of the working fluid, which flows through the absorber tube. Since the temperature of the working fluid affects the electrical properties of the hybrid system,
between the back side of the solar cell and the hot junction of the thermoelectric generator, reduces the thermal energy at the hot surface of the TEG. The TEG’s cold side temperature, initially increases and then decreases by changing the intensity of solar radiation. Also, for the TEG section, the cold side temperature is less than the hot side temperature. There must be a temperature difference between two sides of the TEG to produce electricity. In this case, the charge barriers are excited by the heat flow through the TEG, and create the electromotive force [39]. This phenomenon causes transforming waste heat into electricity. It should be noted that the reduction in the working fluid temperature leads to a decrease in the cold side temperature of the thermoelectric generator [4]. The maximum temperature of the two sides of the TEG are 89.97 °C and 45 °C.
Fig. 7a. Comparison of the thermal efficiency with Mohsenzadeh et al. [3].
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3.2.4. The generated power by thermoelectric generator Fig. 11 shows the produced power of the thermoelectric generator. It is seen from the figure that the produced power of the thermoelectric directly depends on the temperature gradient across the module. Also, the higher temperature differences between two sides of the TEG leads to the higher power. At the beginning, the temperature difference is low because of the lower solar radiation; while, by increasing the solar flux during the solving process, the operating temperature of the solar cell rises. Consequently, by increasing the temperature difference through the thermoelectric generator, the higher power is obtained. The TEG current is almost constant in the afternoon; but, its voltage decreases and results in a drop in the generated power by the thermoelectric generator. 3.2.5. Electrical efficiency of the solar cell Fig. 12 shows the variation of the PV’s electrical efficiency versus time. According to Eq. (19), an increase in the solar cell temperature causes a reduction in the PV’s electrical efficiency. Finally, the efficiency of the solar cell is gradually improved due to the temperature decrease.
Fig. 7b. Comparison of the thermal efficiency versus flow rate between the numerical and experimental studies.
it is necessary to control it. 3.2. Electrical results
3.2.6. Electrical efficiency of the thermoelectric generator Fig. 13a and b show the efficiency of thermoelectric generator in the current study and those reported by Li et al. [6], respectively. The efficiency of the thermoelectric generator, depends on the temperature gradient between both sides of the device. It is observed from Fig. 13a that, at the beginning, the TEG’s efficiency is low, about 0.34%, due to lower solar flux and lower temperature gradient across the module; while, as the solar flux rises, the temperature gradient across the TEG increases, leading to the higher efficiencies. The maximum value of the TEG’s electrical efficiency is about 0.468%. Due to lack of data, the comparison of the TEG’s electrical efficiency with the reported results of Li et al. [6] has been done from 10 a.m. to 1:30 p.m. These two figures have the same trend, and show an acceptable conformity.
3.2.1. Current and voltage of the solar cell Fig. 8 shows the variation of the electrical current and electrical voltage of the solar cell. As it is anticipated, the solar irradiance strongly affects the solar cell current. When the sunlight is absorbed by the solar cell, electrons are excited from the valence band to the conduction band. So, if the incident photons are energetic enough to initiate the valance electron, they move toward the conduction band, and create the PV’s current [41]. As the solar flux is enhanced, the solar cell’s current is initially enhanced and then reduced, which is due to increasing of the number of the energetic photons until noon, and decreasing during the evening. The maximum value of solar cell current is about 6.6 A. According to Fig. 8, the variation of solar radiation has an inverse relation with the solar cell’s voltage. Also, an increase in the solar radiation as well as the solar cell’s temperature, causes a reduction in the solar cell’s voltage [42]. The minimum value of the solar cell’s voltage takes place at 1:30 p.m, which is about 3.15 V.
3.3. Error analysis For reporting the deviation of the numerical data with the results in the literature, the error percentage is calculated and reported, where the experimental results are considered as the base case. The root mean square error (RMSE) and the mean absolute error (MAE) methods are utilized to calculate the error percentage [43].
3.2.2. Current and voltage of the thermoelectric generator Fig. 9 outlines the variation of the current and voltage of the TEG versus time. The thermoelectric’s current is initially increased and then becomes fixed, by changing the intensity of solar radiation. It is clear that the thermoelectric’s current has a direct relation with the temperature gradient between two sides of the device, which is enhanced until noon and approximately fixed in the afternoon. As it can be seen, the TEG’s current varies from 1.64 A to 1.68 A. According to the figure, at the beginning of the iterations (10:00 a.m.), the value of the TEG’s voltage is low (about 1.28 V); but, as the solar flux increases during the day, the temperature difference through the TEG increases, which leads to a larger voltage. For the purpose of validating the electrical results of the current model, the power and efficiency of the solar cell and thermoelectric generator have been compared with the experimental results.
y
MAE =
3.2.3. The generated power by the solar cell Fig. 10 demonstrates the power produced by the solar cell. The solar cell’s power depends on its temperature, which in turn, depends on the solar radiation. As the solar flux rises, the solar cell’s temperature increases. It should be noted that the temperature rise of the solar cell has a negative effect on its produced power, despite the solar flux which has a positive influence. Thus, the generated power is obtained by considering these two phenomena. The maximum value of the PV’s power reaches to 20.4 W. The variation of the solar cell’s power, as a function of solar flux, is in a good agreement with the experimental results.
2
1⎛ e −m ∑ ⎜⎛ i i ⎞⎟ ⎞ y ⎜ i = 1 ⎝ mi ⎠ ⎟ ⎠ ⎝
RMSE =
1 y
∑
|ei−mi |
i=1
Fig. 8. Variation of the current and voltage of the solar cell.
378
(31)
y
(32)
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Fig. 9. Variation of the current and voltage of the thermoelectric generator.
Fig. 10. Comparison of the solar cell power with Mohsenzadeh et al. [3].
Fig. 13. Comparison of the thermoelectric efficiency of (a) present study with (b) the results of Li et al. [6].
Table 8 Error percentage for numerical and experimental results.
MAE (%) RMSE (%)
ηTEG (%)
ηCell (%)
PPV (W)
PTEG (W)
PThe (W)
ηThe (%)
1.85 3.29
2.73 3.27
1.36 1.61
2.71 3.11
2.02 2.87
1.84 2.37
Fig. 11. Comparison of the thermoelectric power with Mohsenzadeh et al. [3].
In the above equations, m is the value for the base case, y is the number of numerical data, and e is the deviation from the base value. In this study, y is 12, and the values of m and e are shown in Table 8. 4. Conclusion In this study, a tri-generation parabolic trough solar collector, integrated with a solar cell and thermoelectric generator was modeled. Also, the hybrid (PV/TEG-PTC) system was simulated by considering the influences of the solar radiation and ambient temperature. In order to improve the cooling efficiency of the TEG, it was supposed that the working fluid flew through the absorber tube. A non-dimensional numerical model was presented, considering steady state condition. Eight nonlinear equations were solved via the iterative Newton-Raphson technique. The modeling procures were developed in the MATLAB (R2014b) to evaluate the electrical and thermal characteristics of the PV and TEG sections. The key results are summarized as bellow:
Fig. 12. Comparison of the solar cell efficiency with Mohsenzadeh et al. [3].
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• Modeling of the hybrid system indicates that the electrical power of
• • • • •
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the device, as high as 22.714 W, could be achieved at the solar concentration of 998 W/m2. Also, the portion of the TEG‘s electrical power is about 2.3 W. It could be concluded that the TEG has low power values, which would be due to the low temperature differences of the TEG. The PV/TEG design mainly affects the energy conversion efficiency of solar energy. It can be concluded that the thermal power increases as the mass flow rate increases. The maximum amount of thermal power (240 W) is attained at 1:30 p.m, by increasing the solar irradiance. The maximum amount of thermal efficiency is about 57%. The electrical efficiency of thermoelectric generator has the highest error percentage (3.29%) among other cases in the validation.
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Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Performance investigation of a hybrid photovoltaic/thermoelectric system integrated with parabolic trough collector
T
⁎
Shohreh Soltania, Alibakhsh Kasaeiana, , Tahmineh Sokhansefata, Mohammad Behshad Shafiib a b
Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran Faculty of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
A R T I C L E I N F O
A B S T R A C T
Keywords: Thermoelectric Photovoltaic Parabolic trough collector Efficiency
In this study, a non-dimensional model of a tri-generation unit consisting parabolic trough solar collector, integrated with solar cell and thermoelectric generator is presented. In order to obtain the effects of solar irradiance and ambient temperature on the performance of the system, a set of functions were coded in the MATLAB software. Eight nonlinear algebraic equations were derived and solved via the iterative Newton-Raphson technique. The thermal and electrical efficiencies, the electrical characteristics of the thermoelectric and photovoltaic modules, and the thermal and electrical power of the hybrid device were analyzed in this study. The results have reflected some improvements on the electrical efficiency by placing thermoelectric module and solar cell on the lateral area of the absorber tube. Furthermore, an electrical power of 22.714 W could be reached at the solar concentration of 998 W/m2. In order to validate the results of the mathematical model, two research works have been utilized. The evaluation of the obtained results shows a good agreement with the results in the literature.
1. Introduction Photovoltaic is recognized as the promising approach to exploit solar energy. However, the main part of solar energy is transformed into waste heat and the temperature increase of photovoltaic leads to diminish its electrical efficiency. An appropriate method to moderate the effects of this problem, is the integration of PV module with a converter of heat-to-electricity in the form of thermoelectric generator (TEG) [1]. To obtain this goal, it is necessary to heat one side, while keeping the other side cold. The temperature difference across the TEG provides energy for charging barriers (electron, hole) to depart from the hot side to the cold side of a thermoelectric element. Many research works have focused on the combination of thermoelectric modules with solar systems [2–4]. Miljkovic and Wang [5] numerically evaluated the performance of a hybrid solar thermoelectric system. They investigated the effects of three various types of thermoelectric materials on the efficiency of the system. They presented an energy-based model of the hybrid device to evaluate the overall performance. The effects of environmental parameters on the efficiency of a parabolic trough/TE unit were investigated by Li et al. [6]. They observed that rising the solar insolation, ambient temperature and wind velocity, increased the thermal losses of the system. Many researchers have investigated the effects of using
⁎
thermoelectric material on the efficiency of photovoltaic systems [7–10]. Su et al. [11] presented an electrical and thermal model for a dye-sensitized PV hybrid thermoelectric generator. They studied the temperature effects on the efficiency of the solar cell. The results indicated that the hybrid system could be used as a promising configuration to exploit solar energy. Lamba et al. [12] proposed a thermodynamic model for a concentrated photovoltaic cell and a thermoelectric module. The effects of some characteristics such as solar flux, PV current and TE current on the overall efficiency and total power were discussed. The results proved that the overall power of the hybrid system was reduced by 0.7% and 4.78% at the solar concentrations of 1 and 5, respectively. Hajji et al. [13] studied the efficiency of an indirect PV/TE coupling device. They placed a concentrator between the photovoltaic and thermoelectric modules. Their findings demonstrated that their design enhanced the overall efficiency of the hybrid PV/TE system. Studying the simultaneous use of thermoelectric cooler and solar cell has been received wide attention. Najafi et al. [14] investigated the application of thermoelectric cooler to control the solar cell temperature. They computed the required power to run the thermoelectric cooler, and applied genetic algorithm to optimize the thermoelectric current. It was found that using thermoelectric cooler dropped the temperature of solar cell. Kane et al. [15] utilized a thermoelectric tile
Corresponding author. E-mail address: [email protected] (A. Kasaeian).
https://doi.org/10.1016/j.enconman.2017.12.091 Received 19 September 2017; Received in revised form 26 December 2017; Accepted 27 December 2017 0196-8904/ © 2017 Elsevier Ltd. All rights reserved.
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Nomenclature
L D W α k R R0 Z T ΔTMax ṁ G t IMax VMax P Q e
amb air Sky Sol go gi co ci pi po M env Max in out The ele tot
length (m) diameter (m) width (m) seebeck coefficient (V/K) thermal conductivity (W/m·K) electrical resistance (Ω) load resistance (Ω) figure of merit for TEG temperature (°C) temperature gradient across TEG (°C) mass flow rate (kg/s) solar irradiance (W·m−2) time (hour) maximum current of TEG (A) maximum voltage of TEG (V) power (W) thermal energy (W) error
Greek Symbols
α λ β η τ θ ρ σ ε
Subscripts PV FF TEG H C f ref aper
ambient air sky solar outside area of glass envelope inside area of glass envelope outer surface of the PV inner surface of the PV inner surface of absorber tube outer surface of absorber tube mean envelope maximum input flow output flow thermal electrical total
photovoltaic fill factor thermoelectric generator hot side of the TEG cold side of the TEG fluid reference condition aperture area
to reduce the temperature of solar cell. They stated that the TE modules were able to operate at the optimal temperature of solar cell. The results showed that the electrical efficiency of the solar cell was increased in the range of 1–18% for the solar irradiation range of 800–1000 W·m−2
absorptance molecular mean free path angle of inclination efficiency (%) transmittance incidence angle reflectance Stephan Boltzmann constant (5.67 × 10−8 kg s−3 K−4) emissivity
and the temperature range of 25–45 °C. The integration of photovoltaic cell and solar collector is accounted as a novel design for improving the efficiency of hybrid systems. Some investigations have been conducted to improve the performance of Fig. 1a. Cross-sectional view of the evacuated tube.
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2.2. Description of the components
solar collectors with photovoltaic cells [16–18]. Garg et al. [19] evaluated a compound parabolic concentrator as the reflector of a photovoltaic/thermal collector. A numerical model of a two-stage parabolic trough PV/T system was introduced by Jiang et al. [20]. Various structural characteristics were considered to obtain the geometric concentration ratio and the size of solar image. They obtained that the heat load of the solar cell was decreased by 20.7%. Calise et al. [21] simulated a parabolic trough photovoltaic/thermal collector. In their model, solar cells were placed on the lateral areas of evacuated tubes. Their achievement showed that the performance was affected significantly by the temperature of working fluid. Tiwari et al. [22] evaluated the performance of a hybrid (PV/T-CPC) collector using MATLAB software. They developed an analytical model to compare the performance of inclined and horizontal PVT-CPC systems. Li et al. [23] investigated the efficiency of a hybrid PTC- PVT unit, using three different types of solar cells. Their achievements showed that the maximum electrical efficiency of the hybrid device was obtained by using GaAs solar cell. In this study, a numerical evaluation is carried out on the incorporation of PV-TEG with parabolic trough solar collector, under solar irradiance. The effects of solar irradiance and ambient temperature on the performance of the system are represented. Solar concentration is assumed to take place at the PV section of evacuated tubes. The small portion of thermal energy is transformed into electricity and the remaining part heats the hot side of thermoelectric generator. Meanwhile, the working fluid flows inside the absorber tube and creates temperature gradient for the TEG, which produces extra electricity. A 0-D mathematical model is introduced to investigate the system efficiency. Eight nonlinear algebraic equations are solved via the iterative Newton-Raphson technique. Although the modeling of hybrid solar thermoelectric collectors has been carried out in previous research works to determine the performance, this is the first time that the modeling of such system is performed with the help of experimental data for validation. Also, a novel mathematical method has been used based on the heat transfer and electrical equations.
The optical and geometrical properties of the parabolic trough collector are presented in Table 1. A set of crystalline silicon PV cells with the total area of (8 × 62.5) cm2 is used in this study. The characteristics of the PV cell, manufactured by the Aria Solar Co, are reported in Table 2. Also, a TEG, Model: TEC1-12706, produced by the Hebei I.T. (Shanghai) Co., is employed in the study. The specifications of the TEG are given in Table 3. 2.3. Governing equation 2.3.1. Thermal equation A non-dimensional model covers all the energy equations of the evacuated tube. The thermal resistances of the model are presented in Table 4. To investigate the effect of radiation between the outer surface of glass envelope and the sky, the heat transfer coefficient is determined by [4]: 2 2 hgo − sky . Rad = σεgo (Tgo + Tsky )(Tgo + Tsky )
(1)
where Tgo is the temperature of the outside area of glass envelope, εgo is the emissivity of glass cover, σ is the Stephan Boltzmann constant, and Tsky is the sky temperature which is calculated by the following equation [27]: 1.5 Tsky = 0.0552Tamb
(2)
Tamb is the ambient temperature, and hgo − air is the convection heat transfer coefficient between the outer surface of glass envelope and the ambient, which is calculated by Eq. (3) [27]: hgo − air =
kair Nugo Dgo
(3)
In the above equation, kair is the conduction heat transfer coefficient of the air, and Nugo is the Nusselt number for the external surface of glass envelope. The Nusselt number for the forced convection on an insulated cylinder is written as [26]:
2. Modeling of the hybrid system
1.5
m n ⎛ Prair ⎞ Nugo = CReDgo Prair ⎜ ⎟ ⎝ Prgo ⎠
2.1. Model description A cross-sectional view of the evacuated tube is indicated in Fig. 1a, while, Fig. 1b shows the thermal resistance model, gained from the energy balance of the evacuated tube. It is supposed that the temperature distribution, solar radiation and the properties of the PV and TEG sections are uniform along the axial and circumferential directions of the evacuated tube. Also, all the surfaces are gray surface in this investigation. As it can be seen, the evacuated tube consists of four main parts, namely glass envelope, photovoltaic tube, thermoelectric tube and absorber pipe. When solar radiation is received by the glass envelope, it is encapsulated in a vacuum space between the inner layer of glass cover and the outer layer of PV tube. After that, the photovoltaic cell absorbs the solar flux, and transforms it into electrical power. A TEG module is placed at the back side of the PV cell for using the waste heat. A single-phase working fluid flows inside the absorber tube to create temperature gradient across two ends of the TEG. Therefore, a temperature difference is provided within the TEG layer for producing electricity. According to Fig. 1b, R1 is the convection resistance between the working fluid and the absorber pipe, R2 is the radial conduction resistance through the absorber tube, and R3 and R4 are the radial thermal resistances through the TEG and PV tubes, respectively. Also, R5 and R6 are the radial convection and radiation resistances from the outer surface of the PV tube to the inner surface of glass envelope, and R7 is the radial conduction resistance through the glass envelope. Finally, R8 and R9 are the radial convection and radiation resistances between the outer surface of the glass envelope wall and the ambient or sky.
(4)
In Eq. (4), ReDgo is the Reynolds number of the wind which flows on the outer surface of the glass envelope, Prair is the Prandtl number at the ambient temperature, and Prgo is the Prandtl number at the temperature of the outer surface of the glass envelope. Also, n = 0.37 for Pr < 10, n = 0.36 for Pr > 10, and C and m are the experimental constants, which are represented in Table 5. In addition, hco − gi . Rad is the radiative heat transfer coefficient between the outer surface of the PV tube and the inner surface of the glass cover, which is calculated as bellow [4]:
hco − gi . Rad = σεgo (Tco2 + Tgi2 )(Tco + Tgi )
(5)
The free molecular convection happens between the inner surface of glass envelope and the outer surface of PV tube. The air pressure in the annular space is 0.013 Pa [34]. Also, hco − gi is the convective heat transfer coefficient between the inner surface of glass envelope and the
Fig. 1b. Thermal resistance model of the hybrid system.
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Table 1 Optical and geometrical properties of the evacuated tube and reflector of PTC [24]. Parameter
Symbol
Value
Parameter
Symbol
Value
Shadowing Tracking error Geometry effects Dirt mirror error Non computing error Dirt absorber error Absorbance of glass cover Angle of inclination Transmittance of glass cover Incident angle Emissivity of glass
esh etr ege edm enc eda α β Г θ ε
0.974 0.994 0.98 0.88–0.93 0.97 1 + edm/2 0.96 20 0.96 0 0.9
Glass cover outside diameter Glass cover inside diameter PV cell outside diameter PV cell inside diameter Absorber tube outside diameter Receiver tube inside diameter Aperture width Length of collector Reflectance of mirror Focal distance Conductivity of glass
0.085 0.08 0.03 0.029 0.027 0.025 1 1 0.67 0.21 1.04
Rim angle
φr
79.6°
Concentration ratio
Dgo (m) Dgi (m) Dco (m) Dci (m) Dpo (m) Dpi (m) W(m) L(m) ρcl f (m) kglass (W/m·K) C
Table 2 The PV cell characteristics [3,8,25].
8
Table 5 Experimental coefficients of Eq. (4) [34].
Parameter
Symbol
Value
ReDgo
C
m
Type of solar cell Number of solar cell Short circuit current Open circuit voltage Fill factor Area of one cell Active area of solar cells Efficiency (At the standard condition) Thermal coefficient Absorptivity Emissivity
C-Si n ISC (A) Voc (V) FF A (cm2) ACell (cm2) η (%) β αc εc
– 8 in series 8 4.44 0.73 62.5 500 15.75 0.0041 °C−1 0.85 0.9
1–40 40–1000 1000–200,000 200,000–1,000,000
0.75 0.51 0.26 0.076
0.4 0.5 0.6 0.7
outer surface of PV tube, which is calculated by Eq. (6) [29]:
hco − gi =
kstd Dco D
gi ⎞ 2ln ⎛ ⎝ Dco ⎠ ⎜
Symbol
Value
TE type Number of modules Maximum voltage Maximum current Maximum power Maximum temperature gradient Figure of merit Electrical resistance of a P-N couple Load resistance of a P-N couple Seebeck coefficient Thermal conductivity
– – VMax (V) IMax (A) QMax (W) ΔTMax (°C) Z(1/K) RTEG(Ω) R 0 (Ω) αTEG (V/K) kTEG (W/m·K)
TEC1-12706 20 in series 15.2 6 56.8 79 0.0021 0.0022 0.0022 3.9 × 10−4 3.2
λ=
b=
R1 =
R2 =
R3 =
R4 = R5 =
1 πLc hf Dpi ⎛ Dpo ⎞ Ln ⎜ D ⎟ ⎝ pi ⎠ 2πLc kpipe
R7 =
)
+1
(6)
2.331∗10−20 (Tco−Tgi + 273.15) Pair δ 2
(7)
(2−a)(9γ −5) 2a + (γ + 1)
(8)
2 QH . TEG = αTEG ITEG Tci−0.5RTEG ITEG + kTEG ΔTTEG
1 πLc hco − gi . Rad Dco ⎛ Dgo ⎞ Ln ⎜ D ⎟ ⎝ gi ⎠ 2πLc kglass
D Ln ⎛⎜ ci ⎞⎟ ⎝ Dpo ⎠ 2πLc kTEG
R8 =
1 πLc hgo − air Dgo
D Ln ⎛⎜ co ⎞⎟ ⎝ Dci ⎠ 2πLc kPv 1 πLc hco − gi . Conv Dco
R9 =
1 πLc hgo − sky . Rad Dco
(9)
where ITEG .αTEG and RTEG are the thermo electric current, the Seebeck coefficient, and the electrical resistance of the TEG, respectively. Also, Tci is the temperature of the inner surface of PV cell, and kTEG is the thermal conductivity of the thermoelectric material, which is calculated as bellow [14]:
Thermal Resistance Equation (R6–R9)
R6 =
Dco Dgi
Also, b is an interaction and accommodation coefficient, which is supposed to be 1.571[34]. To compute the conduction in the PV tube, it is necessary to know kPV . The values of this parameter are extracted from Table 6. The thermal energy, which is absorbed by the hot side of the thermoelectric generator, is calculated by [31]:
Table 4 Thermal resistances for the PV/TEG-PTC models [26]. Thermal Resistance Equation (R1–R5)
(
where kstd is the conductive heat transfer coefficient of gas in the annular space, λ is the free mean path, δ is the molecular diameter of air (3.55 × 10−8 cm), and Pa is the air pressure at this space [34].
Table 3 The characteristics of the thermoelectric module [3,8,40]. Parameter
+ bλ
⎟
Table 6 Conductivity of silicon [30].
–
374
Temperature (K)
kPv (W/m·K)
Temperature (K)
kPv (W/m·K)
200 300 400 500 600 700 800 900
266 156 105 80 64 52 43 36
1000 1100 1200 1300 1400 1500 1600 1681
31 28 26 25 24 23 22 22
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kTEG =
(Tamb−ΔTMax ) VMax IMax 2Tamb ΔTMax
where βref , ηcell . ref , and Tref represent the temperature coefficient of the solar cell, the PV cell's efficiency, and the temperature at the reference condition, which is commonly considered to be 25 °C. The electrical efficiency of the thermoelectric generator could be shown as followings [9]:
(10)
ΔTMax is the maximum temperature gradient across the TEG, and IMax is the current which can produce ΔTMax between two sides of the TEG. It should be noted that all the electrical and thermal properties of the TEG such as ΔTMax , IMax , VMax and IMax are reported in Table 3. Also, kpipe is the conductive heat transfer coefficient of the absorber tube, which is presented in Table 7. The Newton’s law should be used to compute the convection between the working fluid and the inner surface of the absorber tube. Here, hf is the convective heat transfer coefficient of the fluid, which flows through the absorber tube [26].
hf =
kf Dpi
NuDpi
ηmax . TEG =
TH and TC are the temperatures of the hot side and the cold side of the TEG, TM is the mean temperature of the TEG, and Z is the figure of merit for the TE material. ITEG is the thermoelectric current, which is given by [14]: ITEG =
(11)
Prf
f pi
Prpi
1 + 12.7
(Pr f2/3−1) 8
αTEG =
0.11
(12)
(13)
(16)
where Aaper is the aperture area of the reflector, G is the direct normal irradiance, and α is the absorptance of the reflector mirrors. The solar energy, which is absorbed by the glass envelope of the evacuated tube, is [35]:
Qenv . SolAbs = QSol ηenv α env
(17)
(18)
where αpv is the absorbance of the PV tube, and ηpv is the efficiency of the PV cell.
QC . TEG = Qpi − po . Cond
(24)
QH . TEG = QC . TEG + PTEG
(25)
QH . TEG = Qco − ci . Cond
(26)
Qcell . SolAbs = Qco − ci . Cond + Qco − gi . Conv + Qco −gi .Rad + PPV
(27)
Qgo − gi . Cond = Qco − gi . Conv + Qco − gi . Rad
(28)
Qgo . SolAbs = Qgo − air . Conv + Qgo − sky . Rad−Qgo − gi . Cond
(29)
QHeatLoss = Qgo − air . Conv + Qgo − sky . Rad
(30)
Table 7 Conductive heat transfer coefficient of the absorber tube [32].
2.3.3. Electrical equation The electrical efficiency of the photovoltaic cell may be expressed as bellow [36]:
ηcell = ηcell . ref [1−βref (T −Tref )]
(23)
where, Qf − pi . Conv is the convection between the working fluid and the inner surface of the absorber tube, Qpi − po . Cond and Qco − ci . Cond are the conduction through the absorber pipe and the PV tube, QC . TEG and QH . TEG are the thermal energy at the cold and hot junctions of the TEG, PTEG is the power of the thermoelectric generator, and Qco − gi . Conv and Qco − gi . Rad are the convection and radiation between the outer layer of the PV cell and the inner surface of the glass envelope. Also, Qgo − gi . Cond is the conduction between the inner and outer surfaces of the glass envelope, PPV is the PV cell power, Qgo − air . Conv is the convection between the outer surface of glass cover and the ambient, and Qgo − sky . Rad is the radiation between the outer surface of the glass envelope and the sky.
where α env is the absorbance of the reflector glass envelope, and ηenv is the optical efficiency of the glass envelope. The solar energy, which is absorbed by the PV tube, is:
Qcell . SolAbs = QSol ηpv αpv
Qf − pi . Conv = Qpi − po . Cond
(15)
The incoming solar energy on the reflector is given as followings:
QSol = Aaper G α
(22)
(14)
All parameters in Eq. (14) are taken from Table 1, and the incident angle modifier (K θ ) is given by [28,34]:
K θ = cosθ + 0.000884θ−0.00005369θ 2
VMax TH
2.3.4. Energy balance The numerical model utilizes an energy balance between the fluid flowing inside the absorber tube and the sky. Also, the energy equations are assigned by mentioning that the energy is kept at each surface of the evacuated tube. The energy balance equations can be written as followings [34]:
2.3.2. Solar flux absorption As the first step of the thermal computation, it is necessary to compute the optical efficiency of the glass envelope by the following equation [34]:
ηenv = esh etr edm ege eda eun ρcl K θ
(21)
where VMax is the DC voltage at the maximum temperature gradient of the TE material.
Prf is the Prandtl number of the working fluid, Prpi is the Prandtl number on the inner surface of the absorber tube, ReDpi is the Reynolds number on the inner surface of the absorber tube, and fpi is calculated by Eq. (13). This equation is valid for 0.5 ≤ Prf ≤ 2000 and 2300 ≤ ReDpi ≤ 5 × 106 [34]. The Reynolds number varies from 2730 to 5800 in this study. fpi = [1.821log(ReDpi )−1.64]−2
αTEG ΔT R 0 +RTEG
ΔT is the temperature difference between two sides of the TEG, and R 0 is the load resistance. The Seebeck coefficient can be calculated by the following equation [14].
f pi 8(ReDpi − 1000) Prf
(20)
C
where kf is the thermal resistance of the working fluid, and NuDpi is the Nusselt number for the forced convection in a cylindrical tube. If the Reynolds number is less than 2300, the flow is laminar and the Nusselt number becomes 4.36. If not, the Nusselt number would be calculated by Eq. (12) [33]:
NuDpi =
(TH −TC ) (1 + ZTM )0.5−1 T TH (1 + ZTM )0.5 + TH
(19) 375
Material
kpipe (W/m·K)
Stainless steel Copper
0.013 Tpi-po + 15.2 400
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2.4. Solution method
3.1. Thermal results
The modeling of the hybrid PV/TEG-PTC is carried out by implementing MATLAB codes. Eight nonlinear equations are solved via the iterative Newton-Raphson technique. The modeling procures are developed in the MATLAB (R2014b). The wind speed (UWind), the air pressure (Pair), the TEG and PV cell geometry, and the material properties are considered as the input parameters, to achieve the power of the PV cell (PPV) and the thermoelectric module (PTEG). The flowchart of the numerical modeling is indicated in Fig. 2.
3.1.1. Comparison between the ambient temperature and the photovoltaic temperature Fig. 4 shows the distribution of the solar cell and the ambient temperature versus time. It is assumed that water flows through the absorber tube with the flow rate of 0.03 kg·s−1 and the inlet temperature of 28 °C. The obtained results show that the maximum temperature of the PV cell is 96.2 °C at the ambient temperature of 36.2 °C. It should be noted that the ambient temperature has a positive impact on the efficiency of the solar cell. Also, it is clear that the reflected solar flux has a negative effect on the thermal efficiency of the hybrid system [38]. So, using glass envelope as the external cover of the evacuated tube, declines the rate of the dissipated heat. But, as the temperature of the solar cell increases, the electrical efficiency of the PV cell reduces, which is due to the higher thermal energy [15].
2.5. Validation In order to examine the accuracy of the numerical results, two available research works [3,6] were used.
3.1.2. Temperature of the hot side and cold side of the thermoelectric generator Fig. 5 indicates the variation of the temperatures through the TEG. It is seen from the figure that, the TEG’s hot side temperature is usually less than that of the PV cell’s temperature. The contact resistance
2.5.1. Solar PV/T, combined with thermoelectric module Mohsenzadeh et al. [3] introduced a new design of photovoltaic/ thermal system, integrated with thermoelectric module. They assumed that the evacuated tube consisted of a triangular channel, which was covered by photovoltaic cell and thermoelectric generator, and a glass envelope covered the solar cells. They examined the overall efficiency and total power of the hybrid system, experimentally.
2.5.2. Solar TEG, integrated with parabolic trough collectors Li et. al. [6] investigated the impacts of the environmental parameters on the efficiency of a hybrid solar thermoelectric collector. They supposed that the TEM array was located on the focal axis of the parabolic trough collector.
3. Results and discussions In the following, the modeling results are represented for the proposed tri-generation device. Fig. 3 shows the average solar radiation, which has been considered in this study. As it can be seen, the solar irradiance rises until noon and reduces in the afternoon. Also, the solar radiation reaches to a maximum value of about 998 W·m−2 at 1:30 p.m. The wind speed plays a significant role on the efficiency of solar systems. An increasing heat loss should be resulted by increasing the wind velocity [6]. In this study, the wind velocity and the air pressure are considered as 2.5 m/s and 101.3 kPa, respectively. As mentioned above, the geometrical and optical parameters of the evacuated tube and the reflector of the parabolic trough collector (PTC) are given in Table 1. Some important characteristics of the PTC, namely the focal distance (f), the aperture width (W), the rim angle (φr), and the incident angle (θ) are taken into account in the modeling process. In order to absorb the radiated solar flux, the appropriate diameters are calculated and considered in this study (Table 1). It is supposed that the sun tracking system radiates the solar flux on the evacuated tube continually, and the tracking error is considered to be small (0.994). The tracking error is an important factor to compute the optical efficiency of the glass envelope (Eq. (14)). The optical efficiency is low when the rim angle is small (at φr < 90). If the tracking error is too high, the reflected solar flux cannot be absorbed by the evacuated tube [37]. In this study, the evacuated tube is considered on the focal line, the rim angle is 79.6°, and the aperture width is 1 m. This section consists of two main parts; at the first part, the obtained thermal results are investigated and the results of photovoltaic temperature and the TEG temperature gradient are presented. Therefore, the thermal power and thermal efficiency of the hybrid PV/TEG-PTC system are explained. At the second part, the electrical results of the TEG and PV sections are represented. Finally, the total power and the overall efficiency of the proposed tri-generation unit are studied.
Fig. 2. Flowchart of numerical modeling.
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Fig. 6. Comparison of the thermal power with Mohsenzadeh et al. [3].
Fig. 3. The variation of solar irradiance.
It is worthy to notify that the TEG’s cold side temperature depends on the flow rate of the working fluid, which flows inside the absorber tube. In this study, the flow rate of the working fluid is considered as 0.03 kg·s−1. In order to demonstrate the conformity of the thermal results with the experimental data, the thermal power and thermal efficiency of the hybrid system were compared with the experimental works in the literature. 3.1.3. Thermal power of the hybrid unit According to Fig. 6, the thermal power of the hybrid unit initially increases and then, slightly decreases, which is due to the decrease on the solar irradiance. This issue clearly indicates the importance of solar radiation, especially at the mid time of the solving process. It is observed from the figure that the numerical and experimental results show a similar trend, and the deviation of the thermal power is less than 3%. As it was expected, considering the TEG and PV tubes decreases the portion of the absorbed heat by the working fluid.
Fig. 4. Distribution of the ambient temperature and solar cell temperature.
Fig. 5. Temperature variation within the thermoelectric generator.
3.1.4. Thermal efficiency of the hybrid unit The variations of thermal efficiency versus time and the flow rate of working fluid are illustrated in Figs. 7a and 7b. The maximum values for the thermal efficiency take place at the early and late hours. According to Fig. 7a, the thermal efficiency reaches to a maximum value of about 57%. The deviation of the thermal efficiency is about 2.5%, which shows a good agreement with the experimental results. As it is expected, higher thermal efficiencies are obtained by the higher flow rates. The flow rates of the working fluid are changed from 0.5 L·min−1 to 3 L·min−1 in Fig. 7b, while the mean temperature of the working fluid and the thermal capacity are fixed. The flow rate strongly influences on the performance of the hybrid PV/TEG-PTC unit. The value of the mass flow rate controls the temperature of the working fluid, which flows through the absorber tube. Since the temperature of the working fluid affects the electrical properties of the hybrid system,
between the back side of the solar cell and the hot junction of the thermoelectric generator, reduces the thermal energy at the hot surface of the TEG. The TEG’s cold side temperature, initially increases and then decreases by changing the intensity of solar radiation. Also, for the TEG section, the cold side temperature is less than the hot side temperature. There must be a temperature difference between two sides of the TEG to produce electricity. In this case, the charge barriers are excited by the heat flow through the TEG, and create the electromotive force [39]. This phenomenon causes transforming waste heat into electricity. It should be noted that the reduction in the working fluid temperature leads to a decrease in the cold side temperature of the thermoelectric generator [4]. The maximum temperature of the two sides of the TEG are 89.97 °C and 45 °C.
Fig. 7a. Comparison of the thermal efficiency with Mohsenzadeh et al. [3].
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3.2.4. The generated power by thermoelectric generator Fig. 11 shows the produced power of the thermoelectric generator. It is seen from the figure that the produced power of the thermoelectric directly depends on the temperature gradient across the module. Also, the higher temperature differences between two sides of the TEG leads to the higher power. At the beginning, the temperature difference is low because of the lower solar radiation; while, by increasing the solar flux during the solving process, the operating temperature of the solar cell rises. Consequently, by increasing the temperature difference through the thermoelectric generator, the higher power is obtained. The TEG current is almost constant in the afternoon; but, its voltage decreases and results in a drop in the generated power by the thermoelectric generator. 3.2.5. Electrical efficiency of the solar cell Fig. 12 shows the variation of the PV’s electrical efficiency versus time. According to Eq. (19), an increase in the solar cell temperature causes a reduction in the PV’s electrical efficiency. Finally, the efficiency of the solar cell is gradually improved due to the temperature decrease.
Fig. 7b. Comparison of the thermal efficiency versus flow rate between the numerical and experimental studies.
it is necessary to control it. 3.2. Electrical results
3.2.6. Electrical efficiency of the thermoelectric generator Fig. 13a and b show the efficiency of thermoelectric generator in the current study and those reported by Li et al. [6], respectively. The efficiency of the thermoelectric generator, depends on the temperature gradient between both sides of the device. It is observed from Fig. 13a that, at the beginning, the TEG’s efficiency is low, about 0.34%, due to lower solar flux and lower temperature gradient across the module; while, as the solar flux rises, the temperature gradient across the TEG increases, leading to the higher efficiencies. The maximum value of the TEG’s electrical efficiency is about 0.468%. Due to lack of data, the comparison of the TEG’s electrical efficiency with the reported results of Li et al. [6] has been done from 10 a.m. to 1:30 p.m. These two figures have the same trend, and show an acceptable conformity.
3.2.1. Current and voltage of the solar cell Fig. 8 shows the variation of the electrical current and electrical voltage of the solar cell. As it is anticipated, the solar irradiance strongly affects the solar cell current. When the sunlight is absorbed by the solar cell, electrons are excited from the valence band to the conduction band. So, if the incident photons are energetic enough to initiate the valance electron, they move toward the conduction band, and create the PV’s current [41]. As the solar flux is enhanced, the solar cell’s current is initially enhanced and then reduced, which is due to increasing of the number of the energetic photons until noon, and decreasing during the evening. The maximum value of solar cell current is about 6.6 A. According to Fig. 8, the variation of solar radiation has an inverse relation with the solar cell’s voltage. Also, an increase in the solar radiation as well as the solar cell’s temperature, causes a reduction in the solar cell’s voltage [42]. The minimum value of the solar cell’s voltage takes place at 1:30 p.m, which is about 3.15 V.
3.3. Error analysis For reporting the deviation of the numerical data with the results in the literature, the error percentage is calculated and reported, where the experimental results are considered as the base case. The root mean square error (RMSE) and the mean absolute error (MAE) methods are utilized to calculate the error percentage [43].
3.2.2. Current and voltage of the thermoelectric generator Fig. 9 outlines the variation of the current and voltage of the TEG versus time. The thermoelectric’s current is initially increased and then becomes fixed, by changing the intensity of solar radiation. It is clear that the thermoelectric’s current has a direct relation with the temperature gradient between two sides of the device, which is enhanced until noon and approximately fixed in the afternoon. As it can be seen, the TEG’s current varies from 1.64 A to 1.68 A. According to the figure, at the beginning of the iterations (10:00 a.m.), the value of the TEG’s voltage is low (about 1.28 V); but, as the solar flux increases during the day, the temperature difference through the TEG increases, which leads to a larger voltage. For the purpose of validating the electrical results of the current model, the power and efficiency of the solar cell and thermoelectric generator have been compared with the experimental results.
y
MAE =
3.2.3. The generated power by the solar cell Fig. 10 demonstrates the power produced by the solar cell. The solar cell’s power depends on its temperature, which in turn, depends on the solar radiation. As the solar flux rises, the solar cell’s temperature increases. It should be noted that the temperature rise of the solar cell has a negative effect on its produced power, despite the solar flux which has a positive influence. Thus, the generated power is obtained by considering these two phenomena. The maximum value of the PV’s power reaches to 20.4 W. The variation of the solar cell’s power, as a function of solar flux, is in a good agreement with the experimental results.
2
1⎛ e −m ∑ ⎜⎛ i i ⎞⎟ ⎞ y ⎜ i = 1 ⎝ mi ⎠ ⎟ ⎠ ⎝
RMSE =
1 y
∑
|ei−mi |
i=1
Fig. 8. Variation of the current and voltage of the solar cell.
378
(31)
y
(32)
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Fig. 9. Variation of the current and voltage of the thermoelectric generator.
Fig. 10. Comparison of the solar cell power with Mohsenzadeh et al. [3].
Fig. 13. Comparison of the thermoelectric efficiency of (a) present study with (b) the results of Li et al. [6].
Table 8 Error percentage for numerical and experimental results.
MAE (%) RMSE (%)
ηTEG (%)
ηCell (%)
PPV (W)
PTEG (W)
PThe (W)
ηThe (%)
1.85 3.29
2.73 3.27
1.36 1.61
2.71 3.11
2.02 2.87
1.84 2.37
Fig. 11. Comparison of the thermoelectric power with Mohsenzadeh et al. [3].
In the above equations, m is the value for the base case, y is the number of numerical data, and e is the deviation from the base value. In this study, y is 12, and the values of m and e are shown in Table 8. 4. Conclusion In this study, a tri-generation parabolic trough solar collector, integrated with a solar cell and thermoelectric generator was modeled. Also, the hybrid (PV/TEG-PTC) system was simulated by considering the influences of the solar radiation and ambient temperature. In order to improve the cooling efficiency of the TEG, it was supposed that the working fluid flew through the absorber tube. A non-dimensional numerical model was presented, considering steady state condition. Eight nonlinear equations were solved via the iterative Newton-Raphson technique. The modeling procures were developed in the MATLAB (R2014b) to evaluate the electrical and thermal characteristics of the PV and TEG sections. The key results are summarized as bellow:
Fig. 12. Comparison of the solar cell efficiency with Mohsenzadeh et al. [3].
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• Modeling of the hybrid system indicates that the electrical power of
• • • • •
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the device, as high as 22.714 W, could be achieved at the solar concentration of 998 W/m2. Also, the portion of the TEG‘s electrical power is about 2.3 W. It could be concluded that the TEG has low power values, which would be due to the low temperature differences of the TEG. The PV/TEG design mainly affects the energy conversion efficiency of solar energy. It can be concluded that the thermal power increases as the mass flow rate increases. The maximum amount of thermal power (240 W) is attained at 1:30 p.m, by increasing the solar irradiance. The maximum amount of thermal efficiency is about 57%. The electrical efficiency of thermoelectric generator has the highest error percentage (3.29%) among other cases in the validation.
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