Photovoltaic and thermoelectric indirect coupling for maximum solar energy exploitation

Energy Conversion and Management 136 (2017) 184–191

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Photovoltaic and thermoelectric indirect coupling for maximum solar energy exploitation M. Hajji a,b, H. Labrim b,⇑, M. Benaissa a, A. Laazizi c, H. Ez-Zahraouy a, E. Ntsoenzok d, J. Meot e, A. Benyoussef a a

LMPHE, URAC-12, Faculty of Sciences, Mohammed V University in Rabat, 10000 Rabat, Morocco CNESTEN (National Centre for Energy, Sciences and Nuclear Techniques), Route de Kenitra – Maamora, Morocco c Department of Materials and Process, ENSAM, Moulay Ismail University, Meknes, Morocco d CEMHTI-CNRS, Site Cyclotron 3A, rue de la Férollerie, 45071 Orléans, France e SOLEMS S.A., 3 Rue Léon Blum, 91120 Palaiseau Paris, France b

a r t i c l e

i n f o

Article history: Received 30 September 2016 Received in revised form 28 December 2016 Accepted 29 December 2016

Keywords: Indirect coupling Photovoltaic Thermoelectric Hybrid system Heat transfer Efficiency

a b s t r a c t Advanced photovoltaic devices with a high performance/cost ratio is a major concern nowadays. In the present study, we investigate the energetic efficiency of a new concept based on an indirect (instead of direct) photovoltaic and thermoelectric coupling. Using state-of-the-art thermal transfer calculations, we have shown that such an indirect coupling is an interesting alternative to maximize solar energy exploitation. In our model, a concentrator is placed between photovoltaic and thermoelectric systems without any physical contact of the three components. Our major finding showed that the indirect coupling significantly improve the overall efficiency which is very promising for future photovoltaic developments. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction The design of advanced photovoltaic (PV) systems with high electricity generation efficiency and low total development cost is of importance for harvesting solar energy. In this context, enormous work has already helped increasing the charge mobility of photoelectric compounds [1–4] and improving the absorption of solar radiation [5]. As far as the performance/cost ratio is concerned, huge progress has been made to improve the efficiency [6–12] but the latter is still seriously suffering from phenomena such as reflection, transmission and thermalization. One way of overcoming such obstacles, a hybrid system that directly interconnects photovoltaic (PV) and thermoelectric (TE) systems was proposed in the literature [5,12]. Indeed, this PV-TE combination is an interesting alternative since the excess heat (or thermalization) in the PV system can though be transferred to the TE system where it is converted to an electric energy. The TE system has in addition another role that consists in reconverting the transmitted irradiation from the PV system to an additional electric energy. Currently, many efforts are devoted to develop this novel hybrid system [13–18]. Unfortunately, it was noticed that such a concept tends ⇑ Corresponding author. E-mail addresses: [email protected], [email protected] (H. Labrim). http://dx.doi.org/10.1016/j.enconman.2016.12.088 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.

to increase the temperature of the PV module (rather than reducing it) due to the low thermal conductivity of the used thermoelectric material [19–22]. Therefore a negative effect is obtained on the overall performance. These results motivated us to investigate the energetic efficiency of a new concept based on an indirect (instead of direct) PV-TE coupling using state-of-the-art thermal transfer calculations [12]. All along our investigation, comparison with direct coupling performances will be made. 2. Model and thermal transfer method 2.1. Presentation of general model In this part, we propose a new hybrid system that couples PV and TE systems to overcome the PV thermalization issue. We performed the coupling through two models; direct and indirect (see Fig. 1). Both models contain the same elements but differ in the coupling manner of the components. The elements are coupled as follows from top to bottom: a protective glass, photovoltaic system, a concentrator and a thermoelectric system. For the direct coupling (Fig. 1a), all components are physically connected, while in the indirect coupling (Fig. 1b), the concentrator is integrated without any direct physical contact with PV and TE systems. It is

M. Hajji et al. / Energy Conversion and Management 136 (2017) 184–191

185

Nomenclature A C Eg e h1, h01 h3, h5 I k kTE ksub kg n Q PJ Ppv PTE req RT

area of the hybrid system (m2) concentrator coefficient bandgap of silicon material (eV) elementary charge 1.6
1019 (C) heat transfer coefficient for the bottom surface (W/m2 K) heat transfer coefficient for the top surface (W/m2 K) electrical current in thermoelectric module (A) Boltzmann constant (J K1) thermal conductivity of the thermoelectric module (W/m K) thermal conductivity of the substrate in solar cells (W/m K) thermal conductivity of the glass layer in solar cells (W/m K) number of p–n pairs in the thermoelectric module heat flow (W) energy of Joule heating (W) power output of photovoltaic solar cells (W) power output of thermoelectric module (W) equivalent resistance equal to the sum external and internal resistances of thermoelectric module circuit (O) room-temperature (°C)

S Seebeck coefficient of thermoelectric module (lV/K) Sc solar irradiance (W/m2) transmitted solar irradiation (W/m2) S0c T1, . . . , T5 nodal temperatures at node 1, . . . , 5 (K) Ta temperature of the ambient air (K) Th temperature of the hot side for thermoelectric module (K) Tc temperature of the cold side for thermoelectric module (K) Twater temperature of the cooling water (K) temperature of the surroundings (K) Tenv VTE voltage of the thermoelectric module circuit (V) DzTE half thickness of the thermoelectric module (m) Dzsub half thickness of the substrate (m) Dzg half thickness of the glass layer (m) Dzb half thickness of the concentrator layer (m) a, b constants related to bandgap e emissivity of the protective glass layer q reflectivity of the protective glass layer r Stefan–Boltzmann constant (5.67 ⁄ 108 W/(m2 K4)) gPV efficiency of the photovoltaic system gTE efficiency of the thermoelectric system ghyb efficiency of the hybrid system

Fig. 1. Sketch of PV-TE hybrid system model for (a) direct and (b) indirect coupling.

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worth noting that the proposed configurations are surrounded by an insulating system that traps all the accumulated solar energy inside the device. In order to study the performance of both hybrid systems, thermal transfer calculations are performed where the temperature distribution is considered homogeneous only if the thermal equilibrium is reached at each interface. Therefore, the temperature calculation will be carried out along z-axis so the conservation energy can then be written [23,24] as:

qC p

2

@T @ T ¼k @t @z2

! ð1Þ

where q, C p and k are mass density, specific heat and thermal conductivity respectively. In this study, the steady state is considered and the transferred heat flux propagates from the top to the bottom of the system. The limit conditions used in this work are illustrated in Table 1. Applying the first law of thermodynamics and after discretization, five algebraic equations can be extracted (Eqs. (2)–(6)).

Q 1 þ ½ASc  Q rad  qSc A  Q 2 ¼ 0;

ð2Þ

Q 2  Q 3  Ppv ¼ 0;

ð3Þ

1 Q 3  Q 4 ¼ 0; b

ð4Þ

Finally, Q 5 and Q 6 represent the flow of heat by conduction in the thermoelectric module and the convection of the cold side with ambient respectively, whose expressions are:

Q5 ¼

In the following, the development of Eqs. (2)–(6): For T1; which corresponds to the upper surface of the PV module.

Ah5 ðT a  T 1 Þ þ ½ASc  eArðT 41  T 4env Þ  qSc A 

ð5Þ

Q 5  Q 6 ¼ 0;

ð6Þ

where Q 1 ¼ Ah5 ðT a  T 1 Þ denotes the convection of the upper surA ðT 1  T 2 Þ and Q 3 ¼ KDsub ðT 2  T 3 Þ face with ambient. While Q 2 ¼ KgA Dzg z sub

correspond to heat transfer by conduction in glass and substrate respectively (see Fig. 1). The Q 4 term plays the role of conduction or convection according to the appropriate connection type. The Q 4 term can be written as:

Q4 ¼

KbA ðT 3  T 4 Þ; Dzb

KgA ðT 1  T 2 Þ ¼ 0; Dzg ð2aÞ

For T2: represents the temperature in the surface of the substrate.

KgA K sub A ðT 1  T 2 Þ  ðT 2  T 3 Þ  Ppv ¼ 0; Dz g Dzsub

ð3aÞ

For T 3 and T 4 we introduced a coupling coefficient (a and 1  a) that allows us to bind the two types of coupling (direct and indirect), respectively:

K sub A 1 KbA 0 ðT 2  T 3 Þ þ a ðT 3  T 4 Þ  ð1  aÞAh1 ðT 3  T a Þ ¼ 0; b Dz b Dzsub ð4aÞ

a 1 Q  Q 5  PTE ¼ 0; b 4

K TE A ðT 4  T 5 Þ and Q 6 ¼ Ah1 ðT 5  T a Þ: DzTE

1 KbA K TE A ðT 3  T 4 Þ  ðT 4  T 5 Þ þ ðAh3 ðT a  T h Þ b Dzb DzTE þ ½CASc  P pv Þð1  aÞ  P Te ðHÞ ¼ 0;

ð5aÞ

According to the a value, we were able to establish the governing equations for each type of coupling between PV and TE devices. If a ¼ 1: direct coupling is obtained and Eqs. (4a) and (5a) become:

K sub A 1 KbA ðT 2  T 3 Þ þ ðT 3  T 4 Þ ¼ 0 b Dz b Dzsub

ð4a Þ

1 KbA K TE A ðT 3  T 4 Þ  ðT 4  T 5 Þ  PTe ðHÞ ¼ 0 b Dz b DzTE

ð5a Þ

0

0

for the direct coupling

ð7Þ

if a ¼ 0: we got an indirect coupling, with Eqs. (4a) and (5a) becoming:

Q 4 ¼ Ah1 ðT 3  T a Þ;

for the indirect coupling

ð8Þ

Q 04 ¼ Ah3 ðT 4  T a Þ;

K sub A 0 ðT 2  T 3 Þ  Ah1 ðT 3  T a Þ ¼ 0; Dzsub

for the indirect coupling

ð9Þ

0

The first expression (Eq. (7)) corresponds to conduction inside the concentrator device for the direct coupling, while the rest presents the convection term in which we distinguish two surface expressions. In fact, the second (Eq. (8)) and the third Eq. (9) expressions assign their convection term of the lower surface of PV and of the top surface of TE respectively with ambient. This difference is shown below when integrating a binding coefficient (namely aÞ between the direct and indirect coupling in the development of the following Eqs. (2)–(6).

Table 1 The considered limit conditions for direct and indirect coupling between photovoltaic and thermoelectric devices. Limit conditions

Conduction heat equation Convection heat equation

Direct coupling

Indirect coupling

0 < z < Dzsub þ Dzg þ Dzb þ DzTE

0 < z < Dzsub þ Dzg 0 < z < DzTE z ¼ 0 or z ¼ Dzsub þ Dzg z ¼ 0 or z ¼ DzTE

z ¼ 0 or z ¼ Dzsub þ Dzg þ Dzb þ DzTE



00

ð4a Þ

K TE A ðT 4  T 5 Þ þ ðAh3 ðT a  T h Þ þ ½CASc  Ppv Þ  PTe ðHÞ ¼ 0; DzTE 00

ð5a Þ For T5: represents the cold side temperature of the TE

K TE A ðT 4  T 5 Þ  Ah1 ðT 5  T a Þ ¼ 0 DzTE

ð6aÞ

The above Eqs. (2a)–(6a) will be arranged in a general matrix that links both coupling types (see Table 2). 2.2. Simulation procedure and input parameters A computational study using the finite element method and the standard Matlab/Simulink software is carried out. In the case of the PV subsystem, we first determine the cell temperature (Tcell) by solving Eqs. (2a)–(4a) iteratively. Secondly, we calculate the PV output power which was initialized to zero since the system is considered to generate no energy at the beginning. In the case of the TE subsystem, Th (temperature of the hot side for thermoelectric module) and Tc (temperature of the cold side for thermoelectric

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M. Hajji et al. / Energy Conversion and Management 136 (2017) 184–191 Table 2 General matrix coefficient for nonlinear equation linking the two types of direct and indirect coupling of PV-TE hybrid system. With A * X = B 2 h Dz 1  5K g g 6 Kg 6 6 Dzg 6 A¼6 0 6 6 6 0 4

1

0 K

 DKzsub  Dzgg sub K sub Dzsub

0

0

K sub Dzsub Þ  DKzsub sub 1 Kb b Dzb

h1 ð1  a

a

 a 1b Dzbb

0

0

0

0

a 1b DKzbb

K

0

h3 ð1  aÞ  DKzTeTe  a 1b Dzbb K

0 0 0 3 T1 6 T2 7 6 7 7 X¼6 6 T3 7 4 T4 5 T5 2 h Dzg 3 Dz  5K g T a þ ½Sc þ erðT 45  T 4env Þ þ qSc 
K gg 6 7 P pv 6 7 A 6 7 0 7 B¼6 T a h1 ð1  aÞ 6 7 6 7 PTE ðHÞ 0  ð1  aÞðh3 T a  CSc Þ 4 5 A DzTE h1  K TE T a

1

2

3

1

K TE DzTE  DzKTETeh1

7 7 7 7 7 7 7 7 5

Fig. 2. Mounting design of the photovoltaic module produced with Matlab/Simulink.

module) (corresponding to T4 and T5 respectively) were obtained from Eq. (6a), then we calculate the power PTE from Eqs. (7)–(9) and the performance gTE from Eq. (6). The parameters and assumptions used in the calculation for both subsystems are given as follows: – Thermal conductivities of the substrate (monocrystalline silicon), protection glass and thermoelectric compound (Bi2Te3) are 148 W/m K, 0.75 W/m K and 0.48 W/m K [12] respectively. A thickness of 0.1 mm as we reported in our previous study [25] for the two first layers (substrate and protective glass) and 3.9 mm for thermoelectric layer are considered. – The design of the PV module consists of a series of 36 solar cells (Fig. 2) to produce a maximum power, with a 1.1 eV bandgap energy and the cell characteristics are Voc = 22.3 V and Isc = 4.96 A [26]. – The cold side of the thermoelectric system is maintained constant at room temperature (300 K). – The heat transfer is considered along one dimension that is z-axis.

generation is ensured via the absorption process. These electrons are very often highly energetic provoking thermalization during energy excess release, a phenomenon that results in the heating of the cell. Therefore, it is important to estimate the temperature induced by such a heating as a function of solar flux. In fact, the maximum induced temperature (T2) can be found through the resolution of Eqs. (2a)–(4a), organized as a matrix in Table 3. Using the following limit conditions for the PV system:



0 < z < Dzsub þ Dzg ! conduction heat equation

z ¼ 0 or z ¼ Dzsub þ Dzg ! conv ection heat equation

Our calculations gives a value of about T2 = 53 °C for an irradiation flux around nominal functioning conditions (close to 1000 W/m2) of a PV system (see Fig. 3a). We recall that a was taken equal to 0 since the PV system is considered without any contact. As noticed, this temperature is very high with respect to the ideal functioning temperature that is 25 °C [12]. Such an increase in temperature is expected to have a negative impact on the produced open-circuit voltage [29] which results in a drop of the output power of the PV device as illustrated in Fig. 3b. In our case, this excess in tempera-

3. Results and discussion In order to show the efficiency of the proposed hybrid system, we need to identify the influencing parameters on the overall performance. For this reason, our strategy is to separately study photovoltaic and thermoelectric systems in the aim to fix the optimal functioning conditions in each system. 3.1. Thermalization and transmission problems of PV system In photovoltaic conversion (interaction of a photon with a semiconductor), there are three likely generated processes [8,27,28], which are reflection, transmission and absorption. The two first processes are considered as loss of energy, while electrons

Table 3 The matrix coefficients for the set of nonlinear equations governing the three temperatures T 1 ; T 2 ; T 3 and output power of photovoltaic system. With A * X = B 2 3 h Dz 1  5K g g 1 0 6 7 Kg K K sub 7 A¼6  DKzsub  Dzgg 4 5 Dzg Dzsub sub 0 K sub K sub 0 h  1 Dzsub Dzsub 2 3 T1 X ¼ 4 T2 5 T3 2 h Dzg 3 Dz  5K g T a þ ½Sc þ erðT 41  T 4env Þ þ qSc 
K gg 6 7 P p v B¼4 5 A 0

h1 Ta

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M. Hajji et al. / Energy Conversion and Management 136 (2017) 184–191 Table 4 The matrix coefficients for the set of nonlinear equations governing two temperatures T h ; T c and power output of thermoelectric module. With A * X = B: " # K Te h3  DKzTeTe DzTe A¼ 1 1  DzKTeTeh1   Th X¼ Tc " # PTE ðHÞ  h3 T a þ ½CSc þ erðT 4h  T 4env Þ þ qSc A B¼ DzTe h1  KTe T a

Fig. 3. The output power of a PV system as a function solar irradiation.

ture will be reduced by installing a cooling circulating water circuit so that the TE system is no more affected. However, the later must in principle only deal with the transmitted irradiation, which was not absorbed by the PV system. In the following section, a study on the optimum functioning conditions of this TE system is developed. 3.2. Optimization of the thermoelectric system Modeling parameters that affect the efficiency of the thermoelectric module is performed on the TE component shown in Fig. 1. The calculations are based on the following boundaries conditions and heat-transfer equations:



0 < z < DzTE ! conduction heat equation

z ¼ 0 or z ¼ DzTE ! conv ection heat equation

Q 04

þ ½CASc  Q rad  qSc A  Q 5  PTE ðHÞ ¼ 0;

Q 5  Q 6 ¼ 0;

ð6bÞ ð6cÞ

where Q5 corresponds to the losses by convection of the upper part of the thermoelectric module and C to the integrated concentrator coefficient. Since the system is assumed to be isolated, the radiation and reflection losses expressed respectively by Q rad ¼

½eAr  and ½qSc A are negligible. Eqs. (12) and (13) are developed below and organized as a matrix in Table 4: ðT 4h

T 4env Þ

Ah3 ðT a  T h Þ þ ½CASc  Ppv  

K TE A ðT h  T c Þ  PTe ðHÞ ¼ 0 DzTE

ð12aÞ

Fig. 4. Optical concentration effect on hot side temperature (a) and thermoelectric generator efficiency (b).

K TE A ðT h  T c Þ  Ah1 ðT c  T a Þ ¼ 0 DzTE

ð13aÞ

A thermoelectric system can directly convert thermal energy into electrical energy without a need for power generation devices. The maximum conversion efficiency of a thermoelectric system is limited by the Carnot efficiency equation [30]:

  pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ ZT 1 Tc pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T c g¼ 1 Th 1 þ ZT þ T

ð10Þ

h

where ZT stands for the thermoelectric figure of merit, which is a temperature dependent property describing the performance of thermoelectric systems [20]. However many efforts have been made to improve the ZT parameter for thermoelectric materials [21,22,31,32]:

ZT ¼ T S2

r k

;

ð11Þ

M. Hajji et al. / Energy Conversion and Management 136 (2017) 184–191

189

In our calculations, the considered thermoelectric material is bismuth telluride Bi2Te3 due to its relatively high thermoelectric efficiency under RT conditions [34,35], and its high factor of merit of about 0.9 at RT [32]. Our primary results without concentrator represented by the black line in the (Fig. 4a) were not very satisfactory in terms of efficiency that does not even exceed the 3%. These results are in a very good agreement with those found by other researchers [36]. However, the concentrator integration allows a significant increase in the temperature Th, as shown in Fig. 4a, which in turn greatly improve the efficiency of the TE system as a function of irradiation flux (Fig. 4b). In order to further enhance the temperature gradient between top and bottom plates of the TE system, the thickness of the later may be increased, as seen in Fig. 5, since an increase in the distance between the hot and cold plates should slow-down the heat flux transfer to the cold plate. Fig. 5. The thermoelectric module thickness effect on the temperature difference (DT).

3.3. PV-TE indirect coupling

where S, r, k represent, Seebeck coefficient, electrical and thermal conductivity respectively. According to Eq. (10) increasing the performance of TE must increase the temperature difference between the top (hot) and bottom (cold) plates. In our case, this will be achieved by integrating a series of transparent optical concentrators [33] which should heatup the top plate of the TE, increasing therefore its Th temperature, while the bottom plate must be kept at room-temperature (RT) Tc = 27 °C (using a ventilator, for example), as represented in Fig. 1b. In such a configuration, the TE system and the optical concentrator are isolated so that no energy exchange can occur with the outside.

From the above results, combination of both systems, namely; PV and TE, in an indirect way (see Fig. 6) is developed in the following. In principle, all temperatures (T1-T5) are strongly linked to the output powers PTE (of TE subsystem) and PPV (of PV subsystem). Such indirect-coupling approach (shown in Fig. 1b) poses a challenge in resolving the above non-linear equations, which are summarized in the matrix of Table 5 using similar boundary conditions. In such a configuration, the thermoelectric module receives concentrated light that only arises from transmitted (or not absorbed) irradiation from PV subsystem. This will lead to an increase of temperature at the TE top plate Th, which is a parameter directly related to the performance as it was shown in Fig. 4. The hybrid system performance is equal to the sum of PV and TE yields acting separately:

Fig. 6. Configuration of PV-TE hybrid system with an optical concentrator for indirect coupling.

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ghyb ¼ gPV þ gTE

ð14Þ

In our model, we opt for a substrate-silicon layer of 100 lm which basically increases the transmitted light and reduces the overall cost [25]. The simulation of the performance of our indirectcoupling model shows an important increase of the efficiency (Fig. 7). It should be recalled that this indirect coupling must integrate a circulating cooling-water system around the PV subsystem to reduce its temperature, and a ventilator beneath the TE subsystem. Indeed, an evaluation of the energy efficiency of PV-TE hybrid system with and without cooling-water is shown in Fig. 8. Table 5 The matrix coefficient for nonlinear equation governing all five temperatures and output power of PV-TE indirect coupling. 2 6 6 6 6 A¼6 6 6 4 2

1 

h5 Dzg Kg

1

Kg Dzg

 DKzsub  Dzgg sub

0

K sub Dzsub

K

0

0

0

K sub Dzsub 0 h1  DKzsub sub

0

0

0

0

0

0

0

h3  DKzTETE

0

0

0

1

3 T1 6 T2 7 6 7 7 X¼6 6 T3 7 4 T4 5 T5 3 2 h5 Dzg Dz  K g T a þ ½Sc þ erðT 45  T 4env Þ þ qSc 
K gg 7 6 P pv 7 6 A 7 6 0 7 6 B¼6 T a h1 7 7 6 PTE ðHÞ 0 5 4  h T  CS a 3 c A  DzKTETEh1 T a

K TE DzTE

1  DzKTETEh1

3 7 7 7 7 7 7 7 5

Fig. 8. assessing the energy efficiency of the hybrid system as a function of PV cooling.

4. Conclusions Using state-of-the-art thermal transfer calculations, we have proposed a new hybrid system that indirectly interconnects photovoltaic and thermoelectric systems as an alternative to maximize solar energy exploitation. Our indirect coupling was modeled in such a way that a concentrator is placed between photovoltaic and thermoelectric systems without any physical contact of the three components. Our major finding showed that the indirect coupling significantly improve the overall efficiency which is very promising for future photovoltaic developments. References

Fig. 7. Evaluation between the PV and PV-TE systems efficiency for indirect coupling (a) with and (b) without cooling.

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