T solar collector under climatic conditions of semi-arid region

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Performance evaluation of a locally modified PV module to a PV/T solar collector under climatic conditions of semi-arid region Billel Boumaarafa,d ,∗, Houria Boumaarafb , Mohamed El-Amine Slimanic , Selma Tchoketch_Kebira , Mohamed Salah Ait-cheikha , Khaled Touafekd a

Laboratoire des Dispositifs de Communications et de Conversions Photovoltaïques, Département d’Electronique, Ecole Nationale Polytechnique d’Alger, Avenue Hacen Badi, 16200 El harrach Algiers, Algeria b Faculté d’Electronique et d’Informatique Université des Sciences et de la Technologie Houari Boumediene BP 32 El-Alia, 16111 Bab-Ezzouar Algiers, Algeria c Laboratoire de Mécanique des Fluides Théorique et Appliquée, Département Energétique et Mécanique des Fluides, Université des Sciences et de la Technologie Houari Boumediene, 16111 Algiers, Algeria d Unité de Recherche Appliquée en Energies Renouvelables, URAER, Centre de Développement des Energies Renouvelables, CDER, 47133 Ghardaïa, Algeria Received 10 February 2019; received in revised form 9 August 2019; accepted 13 September 2019 Available online xxxx

Abstract A hybrid photovoltaic/thermal (PV/T) collector is used to produce simultaneously electrical and heat energy from solar irradiation through electrical and thermal photo-conversion processes. In this paper, a mathematical model has been developed and detailed based on heat transfer balance equations, electrical and thermo-physical proprieties to draw the output behavior of both PV module and hybrid PV/T water-based system and estimate carefully their energy performance. The PV/T collector has been manufactured and built locally so as to be simple, flexible and efficient to meet the energy needs of an individual housing in a semi-arid region. A sample of meteorological conditions of semi-arid region (Ghardaia city, Algeria) is used to test and evaluate experimentally the performance of both PV module and the designed PV/T collector. Furthermore, the mathematical model has been converted into a numerical program under MATLAB environment. The simulation results have been compared and successfully validated through the experimental results under the same operating conditions. The obtained results show the evolution of thermal and electrical parameters (temperatures, Open-circuit voltage, Short circuit current) during the day test, and also the energy performances of the system (Thermal and electrical powers and efficiencies). The electrical, thermal, and overall efficiencies have reached 6.78%, 0 and 17.43% respectively for the PV module and 7%, 61% and 79.43% respectively for the PV/T collector. The results show that the presented collector can be effectively a simple and efficient energy solution for individual housing in semi-arid regions. c 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights ⃝ reserved. Keywords: PV/T collector; Photovoltaic module; Thermal performance; Numerical model; Semi-arid region; Experimentation

∗ Corresponding author at: Laboratoire des Dispositifs de Communications et de Conversions Photovolta¨ıques, D´epartement d’Electronique, Ecole Nationale Polytechnique d’Alger, Avenue Hacen Badi, 16200 El harrach Algiers, Algeria. E-mail address: [email protected] (B. Boumaaraf).

https://doi.org/10.1016/j.matcom.2019.09.013 c 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights 0378-4754/⃝ reserved.

Please cite this article as: B. Boumaaraf, H. Boumaaraf, M.E.-A. Slimani et al., Performance evaluation of a locally modified PV module to a PV/T solar collector under climatic conditions of semi-arid region, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.013.

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Nomenclature Acronyms Pac PV PV/T STC

Packing factor Photovoltaic Photovoltaic/Thermal Standard test conditions

Symbols A a cρ Eg G h I K m˙ N n Nu P Pac Q Qele Qth q R T r t V U

Surface area (m2 ) Modified diode ideality Specific heat (J/kg K) Semiconductor band gap energy, 1.12 (eV) Solar irradiance (W/m2 ) Heat transfer coefficient (W/m2 K) Current (A) Boltzmann’s constant, 1.3807.10−23 (J/K) Mass flow rate (kg/s) Number of cells in the PV module Ideality factor of the diode Nusselt number Electrical power (W) Packing factor Heat transfer energy (W) Electrical energy (W) Thermal energy (W) Electronic charge, 1,6.10−19 (C) Resistance () Temperature (◦ C) Radius (m) Time (s) Voltage (V) Overall heat loss coefficient

Greeksymbols η λ τ α ρ ε β δ µ σ

Efficiency Thermal conductivity (W/m K) Transmissivity Absorptivity Density (kg/m3 ) Emissivity Efficiency Temperature coefficient (1/K) Thickness (m) Temperature coefficient Stefan–Boltzmann constant, 5.670/108 (W/m2 K4 )

Please cite this article as: B. Boumaaraf, H. Boumaaraf, M.E.-A. Slimani et al., Performance evaluation of a locally modified PV module to a PV/T solar collector under climatic conditions of semi-arid region, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.013.

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Subscripts cond conv d ele f m r in I,sc Iso gc P Ph PV/T sc S Sc Sh th v,oc wi

Conduction Convection Diode Electrical Fluid Maximum Radiation Inlet, inside Short circuit current Insulation Glass cover Parallels Photo-generated Photovoltaic/Thermal Solar cells Series Short circuit, solar cells Shunt Thermal Open circuit voltage Wind

1. Introduction The sun is the natural source of light and heat, with the depletion of traditional sources, solar energy has become the energy that is used more and more to produce energy. Electricity and heat. Regarding the increasing of using the PV module to convert solar energy to electricity and thermal collectors to convert solar energy to heat, Great efforts are needed to hybrid both of them in the same system. The photo-thermal conversion could be happened by an upgrading system called photovoltaic thermal collector. During the last two decades, a number of PV/T collector designs and configurations have been examined by several research groups. Amori et al. [7] conducted a thermoelectric comparative theoretical and experimental study of various PV/Thermal collectors’ design where four collectors of different configurations have been constructed and tested under Iraq climate conditions. The studied configurations have been designed as follows: model I: PV module without cooling, model II: single duct double pass PV/T, model III: double duct single pass PV/T, and model IV: single duct single pass PV/T. The obtained results revealed that the highest efficiency is obtained with model III followed by model II than by model IV. They concluded that model III is the most suitable for rural areas in Iraq and is simple to construct. In a work dealing with a parametric optimization of an integrated PV solar house. Matrawy et al. [44] have concluded that there would be a significant enhancement in thermal efficiency at a high flow rate. Farshchimonfared et al. [28] claimed that PV/thermal collectors design requires an accurate determination of such key parameters as channel depth and air mass flow rate. In fact, in a work dealing with the optimization of channel depth, flow rate and air distribution duct diameter of PV/T collectors linked to residential buildings, they modeled collectors of various areas (Ac: 10, 15, 25 and 30 m2 ) and different length to width ratios (L/W: 0.5, 1, 1.5 and 2) for a constant temperature rise of 10 ◦ C. It was concluded that when maximizing the performance of the PV/T collector system for a fixed value of temperature rise (∆T: 10 ◦ C) and for different values of collector area and L/W ratios, the optimum channel depth is dependent on the collector L/W and area. Additionally, the air mass flow rate per unit area slightly decreases as a result of an increase in the collector L/W ratio and area. To improve the overall performance of an air-cooled PV/T collector, Tanui et al. [64] studied a modified system by the use of suspended thin flat metallic sheet (TMS) at the middle or fins at the back wall of the air duct as Please cite this article as: B. Boumaaraf, H. Boumaaraf, M.E.-A. Slimani et al., Performance evaluation of a locally modified PV module to a PV/T solar collector under climatic conditions of semi-arid region, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.013.

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heat transfer improvers. They concluded that the suggested modifications yield higher thermal efficiency than the reference system with better electrical performance. In addition to that, they indicated that the fin type system gives a higher output than that containing TMS. Then, the choice of the modification depends on the application and on whether the system is used for air preheating or for PV module cooling. Mojumder et al. [45] performed an experimental comparative investigation to study the effect of TMS shape on the PV/T collector performance. The TMS shapes used in the different collectors were flat, saw tooth backward, saw tooth forward and trapezoidal. They observed that the efficiency of a flat sheet type collector was the lowest. Saw tooth forward and saw tooth backward sheets gave comparable collectors efficiencies but higher than in the case of trapezoidal one. Other configurations and designs can be found in the literature. In a study of the performance of a double pass PV/T collector with fins attached to the PV panel perpendicular to the air flow direction, Rosen et al. [49] reported that the addition of fins increases the heat transfer area and rate, reduces the cell temperature, and improves thermal and electrical efficiencies. Al-Ibrahim et al. [4] studied the performance of photovoltaic powered pumps in direct coupling with solar domestic hot water systems. An optimum configuration of the whole system has been presented and the proposed system was found to achieve outstanding performance if compared to conventional one. Zohri et al. [73] conducted a theoretical study of a PV/T system, based on steady state thermal analysis, to investigate the effect of attached fins to the back surface of the PV module on the hybrid collector thermal and electrical efficiencies and reported that thermal and electrical efficiencies of the finned collector are higher than that without fins. In a theoretical analysis of a PV/T collector, without and with fins attached to the back surface of the PV module, to develop a predictive model. Alfegi et al. [6] studied the effect of flow rate on the performance of a finned single pass and double duct PV/T collector. Obtained results under radiation conditions comprised between 400 and 700 W/m2 and inlet temperature between 30 ◦ C and 35 ◦ C have shown that when the collector is operated at high mass flow rates, electrical, thermal and overall efficiencies are increased. Zohri et al. [74] stated that fins increase the PV/T system efficiency by 7%. Al-Damook et al. [3] analyzed by Comsol a single pass PV/T collector with and without offset strip fins and results and concluded that the use of offset strip fins enhanced the thermal efficiency of the hybrid collector and maintained the electrical PV efficiency at an acceptable level. In 2003 Zondag et al. studied the yield of different combined PV-thermal collector designs [75]. Tiwari et al. have validated the theoretical and experimental results for PV module integrated with air duct for composite climate of India and concluded that an overall thermal efficiency of PV/T system has significantly increased (18%) due to the utilization of thermal energy from PV module [63]. An attempt, by Anand Joshi et al. [38], has been made in 2007 to study the energy efficiency of unglazed PV/T air heating module for the Srinagar cold and cloudy condition. Agrawal al. [1] presented a study about a life cycle cost assessment of a building integrated photovoltaic thermal (BIPVT) systems. The cost of power generation is found to be US $ 0.1009 per kWh which is much closer to that of the conventional grid power. Athienitis et al. designed a prototype photovoltaic/thermal system integrated with a transpired collector (Building-integrated photovoltaic/thermal (BIPV/T) system) which produces useful heat while simultaneously generating electricity from the same building envelope surface [12]. Agrawal et al. [2] presented an indoor experimental analysis of glazed hybrid photovoltaic thermal tiles air collector connected in series. In this paper, a design and experimental analysis of glaze photovoltaic thermal (PV/T) tile air collector has been discussed. Fabricated glazed PV/T tile consists of a single solar cell, duct, and fan for extraction of heat associated with the rear of the solar cell. In 2015 Ghadiri et al. realized an experimental prototype of a PV/T system using nanoferrofluids [31]. Another experimental study of the performance analysis of PV/T Combi with water and air heating system has been done in 2016 by Othman et al. [47]. In 2017 Fu Huide et al. presented a comparative study between a hybrid photovoltaic/thermal and a PV module with a thermal collector installed separately [35]. Shan et al. summarized the different applications and the performance evaluations of the photovoltaic thermal collectors with case studies [57]. In the same context many others review have been reported such as Kumar et al. [39], Sathe and Dhoble [55], and Joshi and Dhoble [37]. A study of glass cover technologies for photovoltaic thermal collector is made by Gorgolis [33]. In 2018 Hosseinzadeh presents and validate a 3D numerical model of nanofluid PV/T collector [34]. In 2019 Thinsurat et al. studied the performance of PV/T collector using a new correlations of PV module resistances [62]. In 2017 an attempt has been presented by Jakhar and Soni to investigate the performance of the PV/T system coupled with earth water heat exchanger [36]. Xiang et al. proposed a combination of Photovoltaic Thermal (PV/T) and soil heat storage technologies on the roadways [68]. Many factors influencing the energy efficiency of PV/T systems. Sun et al. [61] studied the tilt angle and connection mode of Please cite this article as: B. Boumaaraf, H. Boumaaraf, M.E.-A. Slimani et al., Performance evaluation of a locally modified PV module to a PV/T solar collector under climatic conditions of semi-arid region, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.013.

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PV/T collectors to evaluate their effect. Othman et al. calculated the performance of PV/T Combi with water and air heating system based on Hottel–Whillier–Bliss equation with experimental validation [47]. a Steady-state energy analysis was performed on a photovoltaic thermal (PV/T) by Fudholi et al. using V-groove [30]. Sakellariou and Axaopoulos present a dynamic model with experimental validation, this model utilizes the analytic solution to solve collector’s energy balance equation [51]. Ben youssef et al. designed a photovoltaic thermal collector with concentrator to evaluate its performances from energy and economic viewpoints [14]. Different working fluids has been used by Al-Shamani et al. [5] to evaluate thermal and electrical efficiency of PV/T collector. Shukla et al. present a review for various cooling techniques of photovoltaic module for enhancing electrical efficiency [58]. In 2016. Zahraee et al. present a summary of prior research concerning the use of optimization in artificially intelligent algorithms for designing, planning and controlling problems in the field of hybrid energy systems [71]. Elbreki et al. reviews the research studied the parameters affecting the PV/T collector performance [27]. Good presents a review of the published results about the life cycle assessments (LCA) of different PV/T concepts and installations [32]. Lamnatou et al. present a critical review about solar system modeling with emphasis on BIST configurations for Building-Integrated system [40]. Makki et al. collect various cooling methods for PV systems [43]. Amit Sahay et al. proposed a new developed Cooling System for central panel and compared it with various existing technologies [50]. Tyagia et al. give an overview on the research and the development in solar photovoltaic/thermal (PV/T) hybrid collector technology [66]. A review on the current state-of-the-art on the domestic technology available with energy saving system in the UK presented by Xie et al. [69]. This paper presents a thermal–electrical study with model validation of a hybrid photovoltaic thermal collector using a PV module locally fabricated. From the research papers mentioned above [1–7,12,14,27,28,30–40,43–45, 47,49–51,55,57,58,61–64,66,68,69,71,73–75], many results have been found depending of many factors especially climate conditions and exchanger geometry. In this work a PV/T collector with serpentine exchanger has been realized using a PV module locally fabricated and tested under Gharda¨ıa city climatic conditions (semi-arid region). The PV/T collector has been manufactured and built so as to be simple, flexible and efficient to meet the energy needs of an individual housing in a semi-arid region (far from cities). This context makes the study specific from construction and application point of view. A numerical simulation was developed, to evaluate the performance of the PV/T solar collector. The PV/T solar collector is represented by the model governing equations of the energy balance for each layer including PV module. According to this, the heat transfer within the PV/T collector is analyzed to determine the useful energy. Results, of the experimental PV/T system developed, are presented for validation and discussion. 2. Methodology and experimental setup 2.1. Setup description An experimental setup was built at the unit of applied research in renewable energies in Gharda¨ıa city. The pictures of the PV module used in this work and the PV/T collector realized are shown in Figs. 1 and 2 respectively. The collector has a 0.425 m2 surface. It consists of one multi-crystalline silicon PV module fabricated at the silicon technology development unit of Algiers city (UDTS) with 36 solar cells. The PV module is equipped with a thermal part. The heat exchanger consists of an absorber plate and a copper tube in serpentine geometry with black paint. 2.2. Experimental tests location The tests were performed in outdoor conditions with respect to time and location. The experimental tests have been registered on May 16th 2017 from 08:00 a.m to 08:00 p.m at the Unit of applied research in renewable energies in Gharda¨ıa city (Fig. 3). The site coordinates are: Latitude: 32.36◦ ; Altitude: 450 m and Longitude: 3.81◦ . Monthly climate datas of Gharda´’ia city are presented in Table 1. 2.3. Data gathering In the experiments, the global radiation measurements have been taken using a “Kipp and Zonen” type pyranometer with a sensibility of 0.00000457 V m2 /W. A K-type temperature thermocouples have been used to measure the ambient temperature, the PV solar cells glass-cover temperature and the PV/T insulation temperature. The collected Please cite this article as: B. Boumaaraf, H. Boumaaraf, M.E.-A. Slimani et al., Performance evaluation of a locally modified PV module to a PV/T solar collector under climatic conditions of semi-arid region, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.013.

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Fig. 1. A view of the PV module UDTS50.

Fig. 2. The PV/T collector serpentine prototype.

Fig. 3. Geographical location of experimental tests.

Please cite this article as: B. Boumaaraf, H. Boumaaraf, M.E.-A. Slimani et al., Performance evaluation of a locally modified PV module to a PV/T solar collector under climatic conditions of semi-arid region, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.013.

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B. Boumaaraf, H. Boumaaraf, M.E.-A. Slimani et al. / Mathematics and Computers in Simulation xxx (xxxx) xxx Table 1 Monthly climate datas of Ghardaïa city. Tempé. max mean Temp. mean mean Temp. mini mean Irradiation W/m2

Jan.

Feb.

Mar.

Apr.

May.

Jun.

Jul.

Aug.

Sep.

Oct.

Nov.

Dec.

14,9 10,1 5,2 3972

20,6 14,7 9,0 5181

24,4 18,3 12,2 6505

27,7 21,3 14,9 7728

34,9 28,5 22,2 8385

37,6 31,4 25,2 8557

40,5 33,9 27,4 8332

40,6 33,8 27,0 7735

34,5 28,2 21,9 6704

27,6 22,0 16,3 5457

22,3 16,4 10,3 4223

17,8 12,5 6,5 3628

Table 2 List of experimental testing and measure instruments. Device

Type/Model

Parameter

Experimental uncertainty & precision

Pyranometer Thermocouples Data acquisition

Kipp and Zonen K-type Agilent 34970 DATA

Irradiance Temperature Current/Voltage

1% with a Sensitivity of 4.57 µV/W/m2 0,5 ◦ C 0.004%

data of the K-types are then stored using a data acquisition card, Agilent 34 970 DATA Acquisition/Switch Unit. GPIB, RS232. Serial Number: MY44050878, while a second data acquisition, of same type, has been used to store the values of the I-V characteristics using a variable resistance. Experimental uncertainty & precision of the experimental testing and measure instruments are listed in Table 2. To find the experimental variation of the thermal power and thermal efficiency the following expressions are used: Q th = mcp ˙ f ∆T f Q th 6th = A gc G

(1) (2)

˙ is the mass flow rate, C p f is the specific heat (J/Kg K), ∆T f is the fluid temperature change, G is solar where m global irradiation and A gc is glass cover surface area. The expressions of electrical power and electrical efficiency used in the experimental setup are given by: P = IV 6ele =

IV Asc G

(3) (4)

where P is the electrical power; I, V are respectively the output current and output voltage of the PV solar cells and Asc is the PV solar cells surface area. Table 3 summarizes the design parameters of the collector. 3. Theoretical model 3.1. Electrical part The one-diode equivalent electrical circuit shown in Fig. 4 represents the mathematical model the most used in the literature. The output current depends on the current generator (I ph ), diode current (Id ) and parallel resistance current (I p ). The detailed current–voltage equation that is linked to the electrical circuit is given by [13,17,23,26,46,59]: { ( ) } ( )] V + I Rs NP G [ (V + I Rs ) I Ph,r e f + µ I,sc Tsc − Tsc,r e f − N P I0 ex p −1 − (5) I = Gr e f a RP In order to find the parameters I0 and n as a function of referential parameters, the following relationships are used [8,24,67,72]: [( )3 ( ( ))] Ns E g Tsc,r e f Tsc I0 = I0,r e f ex p 1− (6) Tsc,r e f nr e f Tsc Please cite this article as: B. Boumaaraf, H. Boumaaraf, M.E.-A. Slimani et al., Performance evaluation of a locally modified PV module to a PV/T solar collector under climatic conditions of semi-arid region, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.013.

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B. Boumaaraf, H. Boumaaraf, M.E.-A. Slimani et al. / Mathematics and Computers in Simulation xxx (xxxx) xxx Table 3 Thermo-physical parameter values of the PV module and the PV/T collector. Layers

Parameters

Values

PV glass-cover

Thickness, δg Heat conductivity, λg Heat capacity, C pg

0.003 m 0.95 W/m K 670 J/kg K

PV solar cells

Thickness, δ P V Packing factor, Pac

0.0002 m 0.88

Absorber

Thickness, δabs Heat conductivity, λabs Heat capacity, C pabs Density, ρabs Area, Aabs

0.003 m 390 W/K 903 J/kg K 2702 kg/m3 0.425 m2

Tube

Thickness, δtub Heat conductivity, λtub Heat capacity, C ptub Density, ρtub Outside diameter, Rout

0.0012 m 390 W/m K 903 J/kg K 2702 kg/m3 0.007 m

Insulation

Thickness, δiso Heat conductivity, λiso

0.05 m 0.45 W/m K

Fig. 4. Equivalent electrical circuit of a PV solar cell.

µV,ocTsc,r e f −Voc,r e f +Ns E g ) ( µ I,scT sc,r e f −3 I ph,r e f ( ) Tsc n = nr e f Tsc,r e f nr e f =

where N p /Ns is the number of cells in parallel/series in the branches, µ I,sc, is the temperature coefficient of short circuit current, Tsc is PV solar cells temperature, I0 is the diode reverse saturation current, Rs , R p are series and parallel resistances, n is the ideality factor of the diode, Eg is the gap energy = 1.12 eV, µv,oc is temperature coefficient of the open circuit voltage and Voc is the open circuit voltage. a is the modified diode ideality which is expressed by the equation as below: n s nkTsc a= q

(7)

(8) the the the

(9)

where k = 1.3807.10−23 J K−1 is Boltzmann’s constant and q = 1, 6.10−19 C is the electronic charge. The short circuit current (Isc ) and the open circuit voltage (Voc ) of a PV module (or PV/T system) can be found by the following equations [56]: ( ) [ ( )] G Isc (G, Tc ) = Isc,r e f + β I Tc − Tc,r e f (10) Gr e f ( ) ( ) G Vco (G, Tc ) = Vco,r e f + aln + βV Tc − Tc,r e f (11) Gr e f Please cite this article as: B. Boumaaraf, H. Boumaaraf, M.E.-A. Slimani et al., Performance evaluation of a locally modified PV module to a PV/T solar collector under climatic conditions of semi-arid region, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.013.

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Table 4 Electrical characteristics of the PV solar cells at STC (Tpv,ref = 25 ◦ C, and Gref = 1000 W/m2 ). Characteristics of PV panel (UDTS50)

Value

Power at MPP, Pmax Current at MPP, I mpp Short circuit current, I sc Voltage at MPP, V mpp Open circuit voltage, V oc Electrical efficiency, ηel

50 W 2.87 A 3.27 A 17.4 V 21.6 V 12%

Fig. 5. UDTS50 PV (I-V) and (P-V) characteristics at reference conditions.

The term ref indicates that the parameter is calculated at the reference conditions, Table 4 represents the electrical characteristics of the PV solar cells of the UDTS50 PV module [16,19,20]. Fig. 5 shows the (I-V) and (P-V) characteristics curves of a UDTS50 PV module at reference conditions. 3.2. Thermal part It consists of a tube in a serpentine geometry, in which a coolant fluid circulates, mounted on the back of a copper absorber plate layer UDTS50 PV module. The last layer is a glass wool to minimize the heat loss. Fig. 6 shows a cross-sectional view of the studied serpentine PV/T collector. In order to simplify the mathematical model of the PV/T collector, the thermal energy balance has been made according to the following assumptions: • • • • •

A perfect contact is assumed between PV generator and thermal system. The materials thermo-physical properties are constant. The temperature is considered to be uniform in each layer of the PV/T collector The mass flow of the fluid is assumed constant throughout the day of tests. The temperatures of the fluid in the same direction are considered to be equal.

3.2.1. Governing equations The mathematical investigation of the governing equations given below was developed to predict the performance of the systems studied using the second law of thermodynamics. For the following equations, the nodal approach is used for modeling the thermal behavior of the hybrid collector. For the PV module In this context, a PV module can be treated as one component with two layers which are the PV glass-cover and PV solar cells Please cite this article as: B. Boumaaraf, H. Boumaaraf, M.E.-A. Slimani et al., Performance evaluation of a locally modified PV module to a PV/T solar collector under climatic conditions of semi-arid region, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.013.

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Fig. 6. Schematic view of a cross-sectional of the studied serpentine PV/T collector.

(a) PV glass cover The energy balance in each point of the glass cover takes into account the solar radiation energy absorbed by this layer, the losses, which are represented by the convection, the radiation energies, which are transferred from the glass cover to the environment, and the conduction energy, that is transferred from the glass cover to the solar cells. The thermal energy balance of this layer is described by Eq. (12): ( ) ( ) dTgc = Q gc − h r,gc→sky A g Tgc − Tsky − h conv,gc→amb A gc Tgc − Tamb ρgc A gc C pgc δgc dt ( ) − h cond,gc→ pv A gc Tgc − T pv (12) With [18]: Q gc= αgc A gc G

(13)

where C pgc is the glass cover specific heat, αgc the glass cover absorption coefficient and Q gc the solar radiation energy absorbed by the glass cover. The radiation heat transfer between the glass cover and the sky is given by [48,53]: )( ) ( 2 2 Tgc + Tsky (14) h r,gc→sky = εgc σ Tgc + Tsky where: Tsky is the sky temperature and it was estimated by Swinbank using the following expression [10,52]: 1.5 Tsky = 0.0552Tamb

(15)

Here Tamb is taking equal 25 ◦ C. In the another side the glass layer exchanges the heat with surrounding by convection heat transfer coefficients which is described by [11,29]: h conv,gc→amb = 2.8 + 3wi

(16)

The conduction heat transfer coefficient in the PV module between the glass cover and the solar cells is computed from [25,60]: ( ) egc esc + (17) h cond,gc→sc = 1/ λgc λsc where egc , λgc , esc , λsc are respectively the thickness, the conductivity of the PV glass cover, thickness and the conductivity of the PV solar cells. (b) PV solar cells The PV solar cells absorb the solar radiation transmitted from the glass cover, part of this energy is converted to electricity and the rest will be transformed into heat and transferred to the absorber plates by conduction. The thermal energy balance is then described by, Eq. (18): ( ) ( ) dT pv ρ pv A pv cp pv δ pv = Q sc + h cond,g→ pv A pv Tgc − T pv − h cond, pv→abs A pv T pv − Tabs − Q ele (18) dt With: Q sc= αsc τgc Asc G

(19)

Please cite this article as: B. Boumaaraf, H. Boumaaraf, M.E.-A. Slimani et al., Performance evaluation of a locally modified PV module to a PV/T solar collector under climatic conditions of semi-arid region, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.013.

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where αc is the PV solar cells absorption coefficient, Qsc is the solar radiation energy absorbed by PV solar cells and τgc is the glass cover transmittance. The conduction heat transfer coefficient between the PV solar cells and the absorber plate is computed from: ( ) e pv eabs h cond, pv→abs = 1/ + (20) λabs λ pv where eabs , λabs are respectively the thickness and the conductivity of the absorber plate. Using electrical data of Section 2, the PV solar cells energy output can be expressed as follows [15,22,54]: [ ] Q ele = Q sc ηr e f,sc 1 − β(T pv − 298) (21) For the Absorber plate The energy absorbed by the absorber plate can be calculated through the heat exchange between this layer and the PV module, the tube and insulation layers. The thermal energy balance is then described by, Eq. (22) as follows: ( ) dTabs = h cond, pv→abs Aabs T pv − Tabs − h cond,abs→tube Aabs,tube (Tabs − Ttube ) ρabs Aabs cpabs δabs dt − h cond,abs→iso Aabs,iso (Tabs − Tiso ) (22) With: The conduction heat transfer coefficients between the glass layer and surroundings are given, respectively, as: ) ( etub eabs h cond,abs→tub = 1/ + (23) λ λtub ) ( abs eiso eabs + (24) h cond, pv→iso = 1/ λabs λiso where etube , λtube , eiso , λiso are respectively the thickness, the conductivity of the tube, thickness and the conductivity of the Insulation. For the Tube The energy balance of the tube is considered as the energy transferred from the absorber plate, minus the energy transferred from the tube to the fluid and the insulation layers. The thermal energy balance is described by, Eq. (25) as follows: dTtube ρtube Atube cptube δtube = h cond,abs→tube Aabs,tube (Tabs − Ttube ) dt ( ) − h conv,tube→ f Atube, f Ttube − T f − h cond,tube→iso Atube,iso (Ttube − Tiso ) (25) With: The convection heat transfer coefficient into tube depends on the Nusslet number of the fluid Nu f , as illustrated by the following expression [9,21,42]: λf 1 Nu f 2 rin where λ f is the thermal conductivity and rin is the tube inner radius. The conduction heat transfer coefficient introduced in this layer is expressed by the following equation: ( ) etub eiso h cond, pv→iso = 1/ + λtub λiso h conv,tube→ f =

(26)

(27)

For the Fluid The fluid thermal balance is calculated assuming that the energy absorbed by the fluid is equal to the energy accumulated from the tube, by heat transfer convection, minus the thermal energy of the fluid. The thermal energy balance is described by, Eq. (28) as follows: ( ) dT f ρ f A f cp f = h conv,tube→ f Atube, f Ttube − T f − Q th (28) dt Please cite this article as: B. Boumaaraf, H. Boumaaraf, M.E.-A. Slimani et al., Performance evaluation of a locally modified PV module to a PV/T solar collector under climatic conditions of semi-arid region, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.013.

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Fig. 7. Meteorological data measured per hour during the test day.

With: The instantaneous thermal energy is obtained as [54,65]: ( ) ( ) Q th = τgc τsc αabs A gc G − U P V /T A gc (Ttube − Tamb )

(29)

where τgc is the glass cover transmittance, τsc is the PV solar cells transmittance αabs is the absorber plate absorption coefficient and U P V /T is the heat loss coefficient. For the Insulation The thermal energy balance of the last layer of the collector is the difference between the convection energy transferred to the environment and the total energy received from the absorber plate and the tube. The thermal energy balance is described by, Eq. (30) as follows: dTiso = h cond,abs→iso Aabs,iso (Tabs − Tiso ) + h cond,tube→iso Atube,iso (Ttube − Tiso ) dt − h conv,iso→amb Aiso (Tiso − Tamb )

ρiso Aiso cpiso δiso

(30)

3.3. Numerical simulation The Runge–Kutta method has been used to solve the system differential equations of the thermal energy balance under the MATLAB environment. The simulation allows us to evaluate the Thermal–electrical energies performance of the serpentine PV/T collector studied, using the experimental climatic conditions data of Gharda¨ıa city during the test day. 4. Results and validation 4.1. Experimental meteorological data In order to validate the PV/T system, the behavior under a meteorological data of the day of the experimental tests has been registered. It concerns the 16th day of May 2017 from 08:00 a.m to 08:00 p.m in Ghardaia city (south of Algeria). The variation of the overall radiation and temperature of this day is shown in Fig. 7. 4.2. Temperature distributions Fig. 8. describes the temperature computed during the day for the serpentine PV/T collector. The given Overall temperatures per day in this setup are respectively as follows: Please cite this article as: B. Boumaaraf, H. Boumaaraf, M.E.-A. Slimani et al., Performance evaluation of a locally modified PV module to a PV/T solar collector under climatic conditions of semi-arid region, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.013.

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Fig. 8. Temperature variations for the serpentine PV/T collector in each layer.

The temperatures of the PV module under study are: PV glass cover layer temperature (Tgc ) and PV solar cells layer temperature (Tsc ); the temperatures of the absorber plate layer (Tabs ); the temperatures of the tube layer (Ttube ); the temperatures of the fluid layer (T f ); the temperatures of the insulation layer (Tiso ). It is observed that the overall temperatures variation are dependent on solar irradiance conditions, the high value reached by the PV glass cover is 65 ◦ C between 12:00 and 14:00. The PV solar cells, the absorber plate, the tube and the fluid temperatures range between 67–68 ◦ C. They have almost the same value, which can be explained by their thermo-physical parameters values used in the numerical simulation. 4.3. Validation and discussion For the validation part, the experimental meteorological data shown in Fig. 7 are used. To compare the numerical simulation results and the experimental ones the mean absolute percent error (MAE) has been quantified [16,41,70]: ⏐ n ⏐ 100 ∑ ⏐⏐ X Sim,i − X E x p,i ⏐⏐ M AE (%) = ⏐ n 1 ⏐ X E x p,i

(31)

where X Sim,I X Exp,I and n are the simulation results, the experimental results and the data number respectively. Fig. 9 shows the simulated and experimental PV/T collector temperatures for the PV glass cover and the insulation. MAE value is almost 7% for the PV glass cover temperature and 9.55% for the insulation layer one. The results found in the study are very logical and almost accurate. Fig. 10a and b show the useful thermal power and thermal efficiency variations during the test day for the serpentine PV/T collector, respectively. Indeed, the results of experimental and theoretical are very close for the meteorological data variation of the 16th day of May in Ghardaia city. This closeness is due to the better design of the collector especially in the contact points between the layers. In addition, the higher solar energy values have an important factor on the thermal power, hence on the thermal efficiency. The thermal power efficiency takes the formal of the solar radiation; it reached its maximum value at 261 W. This is because the solar irradiation is maximal at this period of the day. However, the thermal efficiency of the system is about 61%. This showed that most of the solar irradiation is converted into heat and the thermal efficiency obtained from the experiment is significant. As depicted in Fig. 11a and b, it can be observed clearly that electrical power and efficiency vary during the day following the solar radiation. They reach their maximal values between 12:00 and 14:00 which is equal to 30.23 W and 7% respectively. Please cite this article as: B. Boumaaraf, H. Boumaaraf, M.E.-A. Slimani et al., Performance evaluation of a locally modified PV module to a PV/T solar collector under climatic conditions of semi-arid region, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.013.

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Fig. 9. Simulated and experimental variations of Back layer and PV glass cover layer temperature during the test day.

Fig. 10. Hourly variation of: (a) thermal power (b) thermal efficiency.

Please cite this article as: B. Boumaaraf, H. Boumaaraf, M.E.-A. Slimani et al., Performance evaluation of a locally modified PV module to a PV/T solar collector under climatic conditions of semi-arid region, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.013.

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Fig. 11. Hourly variation of: (a) electrical power (b) electrical efficiency.

4.4. Experimental comparison PV-PVT The performance of the studied PV/T collector is determined respectively by his thermal and electrical characteristics’, power and efficiencies. The experimental variations of Thermal–electrical results during the test day for PV/T are compared with ones of a PV module. The experimental chart of short-circuit current, open-circuit voltage, electrical power and electrical efficiency at the maximum power point (MPP) for the PV and the PV/T collector during the test day are shown in Fig. 12. From (I-V) and (P-V) characteristics curves of UDTS50 PV module it is clearly shown that when the voltage increases the current decreases. This is can be justified by the effect of solar radiation and the operating temperature of the PV cells. In the middle of the day, the solar radiation reaches important values which increases the current (effect of the solar radiation is dominant on the current), while at this time the temperature of the PV cells high which decreases the voltage relatively (effect of the temperature is dominant on the voltage). For the PV/T collector, the short-circuit current is improved by comparing with the PV module caused by the cooling of PV/T collector, while for both systems the open-circuit voltage almost has not changed. The electrical power for the PVT collector is higher than the PV system with a small difference (Fig. 12c) because the cooling system in the PV/T collector that decrease the PV cells temperature. According to the daily mean comparative histograms of electrical, thermal and overall thermal efficiencies for the PVT collector and the PV module respectively (Fig. 13). 7%, 61% and 79.43% are the electrical, thermal and overall thermal efficiencies of the PVT collector respectively and 6.78%, 0 and 17.43% are the electrical, thermal and overall thermal efficiencies of the PV module respectively. Please cite this article as: B. Boumaaraf, H. Boumaaraf, M.E.-A. Slimani et al., Performance evaluation of a locally modified PV module to a PV/T solar collector under climatic conditions of semi-arid region, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.013.

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Fig. 12. Experimental chart of: (a) short-circuit current and open-circuit voltage, (b) electrical power, and (c) electrical efficiency for the PV and the PV/T collector.

5. Conclusion The paper presents a theoretical and experimental study of a PV/T solar collector with a serpentine exchanger. A detailed numerical model based on the heat transfer equations of the collector is developed in MATLAB environment. The experimental tests were performed under outdoor condition and were used for verification and validation of the theoretical study. In addition to the electrical energy, the results show that the upgrading system by combining both types of heat and electrical offers a better thermal performance. The produced thermal and electrical energies reach Please cite this article as: B. Boumaaraf, H. Boumaaraf, M.E.-A. Slimani et al., Performance evaluation of a locally modified PV module to a PV/T solar collector under climatic conditions of semi-arid region, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.013.

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Fig. 13. Daily mean comparative histograms of electrical, thermal and overall thermal efficiencies for the PVT collector and classical PV generator respectively.

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Please cite this article as: B. Boumaaraf, H. Boumaaraf, M.E.-A. Slimani et al., Performance evaluation of a locally modified PV module to a PV/T solar collector under climatic conditions of semi-arid region, Mathematics and Computers in Simulation (2019), https://doi.org/10.1016/j.matcom.2019.09.013.