# Modeling and optimization of an air-cooled photovoltaic thermal (PV/T) system using genetic algorithms

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<ul><li><p>ISSN 0003701X, Applied Solar Energy, 2013, Vol. 49, No. 4, pp. 215224. Allerton Press, Inc., 2013.</p><p>215</p><p>1 INTRODUCTION</p><p>The Environmental problems have made seriousconcerns in the world. For solving the problems, therenewable energies have attracted much attention.Solar energy is one of the most important renewableenergy among all kinds of renewable energies. It can becategorized in three general groups: thermal systemsthat convert solar energy to the thermal energy, PVmodules which convert solar energy to electricity andsolar chimneys that convert solar energy to mechanical energy. The photovoltaic (PV) modules have beendeveloped to provide electricity in various types ofbuildings across the world and the recent developments on photovoltaic/thermal PV/T concept offeredan opportunity to increase the overall efficiency bymaking use of waste heat generated in the PV module.The main parts of the research and development workson the PV/T technology have been done in the last35 years.</p><p>PV/T systems have been the subject of intensivenumerical and experimental investigations duringthese years. The PV/T collector devices enable betterspace utilization, energy consumption, cost savingand simultaneous conversion of solar radiation intothe thermal and electrical energy. They can be used inhouses, offices, hospitals, schools and other places forheating the sanitary water and electrical energy generation.</p><p>1 The article is published in the original.</p><p>Kern and Russell [1] gave the concept of this system with results, by using water or air as the heatremoval fluid in 1978. The HottelWhiller analytical model for the analysis of PV/T systems was modified by Florschuetz [2]. Based on the extendedmodel, examples of both thermal and electrical performance of a combined collector as a function ofcollector design parameters were presented and discussed. Raghuraman [3] presented the numericalmethods predicting the performances of liquid andair PV/T flat plate collectors. A PV/T system consisting of a PV panel placed on a thermal collector,with a gap between them to achieve an effective PVcooling, was proposed by Takashima et al. [4], alsothe energy transfer analysis between the differentcomponents of a liquid type PV/T system for obtaining the electrical and thermal efficiencies were analyzed by Bergene and Lovvik [5]. Sopian et al. [6]presented a performance analysis of PV/T air heatersin 1996. Comparisons were made between the performances of the two types of combined photovoltaicthermal collectors (singlepass and doublepasswater), and the results showed that the doublepassphotovoltaic thermal collector had superior performance comparing to the singlepass PV/T collector.In the work of Sopian et al. [7], a doublepass photovoltaic thermal solar collector, suitable for solardrying applications, was developed and tested. Anew integrated design for water heating in a PV/Twas proposed by Huang et al. [8], where a commercial polycrystalline PV module was used. They intro</p><p>Modeling and Optimization of an AirCooled Photovoltaic Thermal (PV/T) System Using Genetic Algorithms1</p><p>A. B. Kasaeiana, M. M. Akhlaghia, S. Golzaria, and M. DehghanibaFaculty of New Science and Technologies, University of Tehran, Tehran, Iran</p><p>bResearch Institute of Petroleum Industry, Tehran, Iran</p><p>Received February 13, 2013</p><p>AbstractThe aim of this paper is to model and optimize an air PV/T system. There are some parametersthat affect on the efficiency of a PV/T solar system like thickness of the glass and Tedlar, temperature of theinlet flow, solar cell temperature and etc. All equations for PV cell and thermal collector have been derived.By genetic algorithms using, thermal efficiency and electrical efficiency of the system may be optimized. Allthe parameters that are used in genetic algorithms, are the parameters that could be changed, and the nonchangeable parameters, like solar radiation cannot be used in the algorithm. By compare to other methods,we found that the GaAs are very efficient technique to estimate the design parameters of PV/T solar systems.</p><p>DOI: 10.3103/S0003701X1304004X</p><p>SOLAR POWER PLANTS AND THEIR APPLICATION</p></li><li><p>216</p><p>APPLIED SOLAR ENERGY Vol. 49 No. 4 2013</p><p>KASAEIAN et al.</p><p>duced the concept of energysaving efficiency forthe evaluation of a PV/T system.</p><p>Raghuraman [9] presented the detailed numericalmodels for both liquid and air PV/T systems, then heand Cox [10] followed up the computer simulation onthe airtype PV/T system. Several experimental andtheoretical studies on PV/T air systems based on thedesign and operating parameters, such as channeldepth and mass flow rate, have been reported [1113].On the channel depth analysis for a singlepass PV/Tair system, Bhargava [14] suggested that the ductdepth should be at least 10 cm for achieving realisticresults.</p><p>The yield of nine different combined PV/T collector designs was considered by Zondag et al. [15]. He W.et al. presented the test results on aluminumalloy flatbox type hybrid solar collector functioned as a thermosyphon system [16]. They found that the daily thermal efficiency could reach around 40% when the initial water temperature in the system is the same as thedaily mean ambient temperature. An improved designof this hybrid PV/T collector and the sensitivity analysis of some key designelements were presented by Jiet al. [17]. An integrated combined system of a photovoltaic thermal solar water heater has been designedand tested in outdoor conditions for a variety of climate changes of New Delhi by Dubey and Tiwari [18].They also derived an analytical expression for thecharacteristic equation of this system for differentconditions as a function of design and climatic parameters and the obtained model showed good agreementwith the experimental results. An analytical expressionfor electrical efficiency of PV/T hybrid air collectorwas presented by Dubey et al. [19]. The optimizationof number of collectors for integrated PV/T hybridactive solar was considered by Gaur and Tiwari [20].As well the indoor test procedure for thermal and electrical testing of PV/T collectors connected in seriesproposed by Solanki et al. [21]. This test procedurecan be used by manufacturers for testing of differenttypes of PV modules in order to optimize their products. Also, Tiwari et al. [22] studied the energy payback time, the electricity production factor and the lifecycle conversion efficiency of hybrid photovoltaicmodules for the different climate changes in India.</p><p>The improvement of the system performance canbe achieved by an additional glazing using to increasethe thermal output, a booster diffuse reflector toincrease the electrical and thermal output, or both,giving the flexibility in the system design. The electrical and thermal efficiency and the annual energy output of watercooled PV/T solar systems under theweather conditions of Patras in Greece for horizontaland tilted building roof installation were determinedby Tripanagnostopoulos et al. [23]. They found thatPV/T systems were cost effective and of better envi</p><p>ronmental impact compared with the standard PVmodules. Experiments with dual type PV/T models ofalternative arrangement of the water and the air heatexchanging elements were performed by Tripanagnostopoulos [24].The modified dual PV/T collectorswere combined with booster diffuse reflectors, achieving a significant increase in the system thermal andelectrical energy output. Kostic et al. [25] presentedthe results of the influence of reflectance from flatplate solar radiation reflectors made of Al sheet andAl foil on energy efficiency of PV/T collector.Recently, Gaur and Tiwari [26] optimized a PV/Tsystem by changing the number of the collectors.Kostic et al. [27] optimized the system by orientation of the collector.</p><p>In all works there is not an optimization of thePV/T system that optimize simultaneously designparameters like Tedlar, glass and solar cell thickness,air flow rate, the length and width of the PV/T collector. However there were some works that just workedon optimizing the flow rate of the air or inlet air temperature or other parameters individually. Also thiswork is somehow because of using the genetic algorithms.</p><p>The aim of this paper is to design an optimal PV/Tsystem for using in different places. Since an optimaldesign is cost effective and reliable, the optimizationstudies about PV/T systems seem to be helpful.</p><p>SYSTEM DESCRIPTION</p><p>A schematic view of a photovoltaic thermal air collector is shown in Fig. 1. A parallel flat plate air duct isprovided below the glass base of the solar cell. Whensolar radiations fall on the solar cells of PV module,they get converted into electricity and heat, then theelectrical energy is stored in a battery. Due to the thermal energy of solar radiations, the PV modules getheated. Solar cells made up of electronic circuits losetheir efficiency when heated. In order to maintain agood electrical efficiency of the system, the heatremoval from the PV panel is essential. Therefore thethermal energy available on the back surface of the PVmodule is carried away by blowing air below thePV module by using DC fans. These DC fans consumea small amount of electricity from the battery itselfwhich is neglected in the present study. In the PVmodule with glasstoTedlar, solar radiation isabsorbed by solar cell and EVA and it is then conducted to the base of the Tedlar for thermal heating ofair flowing below the Tedlar as shown in Fig. 2. A partof solar energy is converted to electricity and the restto thermal energy as what available at the black surface. The air is considered as a working fluid in allanalyses.</p></li><li><p>APPLIED SOLAR ENERGY Vol. 49 No. 4 2013</p><p>MODELING AND OPTIMIZATION OF AN PHOTOVOLTAIC THERMAL SYSTEM 217</p><p>ELECTRICAL EQUATIONS</p><p>The thermal analysis of PV/T air collector and itselectrical analysis are dependent to each other. Thecalculation precision of the thermal parameters of aPV/T air collector will be improved if the electricalefficiency of PV module is calculated correctly.</p><p>The theoretical expression of the current flowing ina photovoltaic cell versus the applied voltage resultedfrom the Schottky diffusion model in a PN junction isgiven by [29]:</p><p>(1)</p><p>where the ideality factor of temperature</p><p> it changes with the cell temperature.</p><p>To solve the nonlinear Eq. (1), theoretically fiveindependent equations are required. These are considered as three cases including open circuit (OC), shortcircuit (SC) and maximum power (MP). In addition,the derivative at the peak of PV curve gets zero, so weobtain the fourth equation. Two resistance values Rshand Rs are usually measured from the SC point andOC point of the IV curve, so thereby another twoequations can be obtained. However, six equations areredundant for the fiveparameter IV characteristics.</p><p>Efficiency of the PV module will be calculate asbelow:</p><p>(2)</p><p>I IL Io( )V IRs+</p><p>a exp 1</p><p>V IRsh+</p><p>Rsh,=</p><p>aNsnIkTcell</p><p>q,=</p><p> VIS</p><p> .=</p><p>THERMAL EQUATIONS</p><p>The proof of governing equations on PV/T air collector thermal analysis is not included in this study inorder to have a brief note. More details of governingequations derivations are found in Ref. [30].</p><p>Air flow</p><p>Air inletDC fans</p><p>Solar radiation</p><p>PV modules </p><p>Digital temperature</p><p>indicators</p><p> Tedlar</p><p>Frame</p><p>Battery</p><p>Solar cells </p><p>Air outlet</p><p>Wooden support Air duct</p><p>1 & 2</p><p>with EVA</p><p>+</p><p>Fig. 1. Schematic diagram of hybrid PV/T air collector [30].</p><p> Glass</p><p>Solar cell </p><p>Tedlar</p><p> Air inlet Air outlet </p><p>and EVA</p><p>Insulation material</p><p>Tsky Tamb</p><p>Tg</p><p>Tcell</p><p>Tbs</p><p>Ti</p><p>Tamb</p><p>Fig. 2. Thermal resistance circuit diagram for a PV/T aircollector [28].</p></li><li><p>218</p><p>APPLIED SOLAR ENERGY Vol. 49 No. 4 2013</p><p>KASAEIAN et al.</p><p>The energy balance equation Writing for each component of a PV/T air collector gives the thermalparameters and thermal efficiency of a PV/T air collector as follows:</p><p>(3)</p><p>(4)</p><p>(5)</p><p>where Tcell, Tbs, Tamb, Tf, out, Tf; G, , Cp, L, W andth are solar cell temperature, back surface temperature, ambient temperature, outlet air temperature,average air temperature in flow duct, the rate of usefulthermal energy, solar radiation intensity, the mass flowrate of flowing air, the heat capacity of flowing air, thelength of air duct, the width of air duct and PV/T aircollector thermal efficiency, respectively.</p><p>In the above equations, the related heat transfercoefficients are defined as follows (more details of governing equations derivations are found in Ref. [28].):</p><p>(6)</p><p>(7)</p><p>(8)</p><p>(9)</p><p>(10)</p><p>Some assumption have been considered on heatloss coefficients in order to simplify the calculations ofPV/T air collector thermal parameters as follows:</p><p>(11)</p><p>(12)</p><p>(13)</p><p>Tcell( )effG UtTamb UTTbs+ +</p><p>Ut UT+,=</p><p>Tbshp1 ( )effG UtTTamb hfTf+ +</p><p>UtT hf+,=</p><p>Q u m Cp Tf out, Tf in,( )=</p><p>= m CpUL</p><p> hp1hp2 ( )effG UL Tf in, Tamb( )[ ]</p><p> 1WULL</p><p>m Cp exp ,</p><p>Q u, m</p><p>( )eff g cc T 1 c( ) cel+[ ],=</p><p>hp1UT</p><p>UT Ut+,=</p><p>hp2hf</p><p>UtT hf+,=</p><p>UtT1Ut 1</p><p>UT+</p><p>1 UtUTUt UT+,= =</p><p>Utf1hf 1</p><p>UtT+</p><p>1 hfUtThf UtT+ .= =</p><p>UTLsiKsi</p><p>LTKT+</p><p>1</p><p>,=</p><p>UtLgKg 1</p><p>hconv 1</p><p>hrad+ +</p><p>1</p><p>,=</p><p>hconv 2.8 3Vw,+=</p><p>where Vw is wind speed on the top surface of PV/T aircollector. The effective temperature of the sky (Tsky) iscalculated from the following empirical relation [14]:</p><p>(14)</p><p>In the estimation of the overall back loss coefficientfrom flowing air to the ambient (Ub), the convectiveheat transfer coefficient on the back surface of PV/Tair collector (hconv) has been calculated as below:</p><p>(15)</p><p>According to the aforementioned equation, Tcellmay be obtained and hrad can be calculated by following equation:</p><p>(16)</p><p>(17)</p><p>Having the electrical efficiency and thermal efficiency of the system now we can calculate the overallefficiency of the system as follow:</p><p>(18)</p><p>(19)</p><p>where Cf is the conversion factor of the thermal powerplant and it can be guessed as 0.4 for Iran.</p><p>RESULTS AND DISCUSSION</p><p>To treat with the overall efficiency curve numerically, we performed a fitting procedure based operation on the genetic algorithms (GAs); on the otherhand we used GAtool in MATLAB software to optimize the efficiency.</p><p>The procedure of the solving is defined as follow:</p><p>Choosing the parameters.Defining the target function.Defining some parameters like first population.Running the toolbox.Generally, ten parameters we chosen for GA: the</p><p>length of the air duct (L), the thickness of back insulation (Li), the Tedlar thickness (LT), the thickness ofsilicon solar cell (Lsi), the thickness of glass cover (Lg),the width of the PV/T air collector (W), inlet air temperature (Tf,in), the radiative heat transfer coefficient(hrad), the mass flow rate of flowing air ( ) and theelectrical efficiency.</p><p>Tsky Tamb 6.=</p><p>UbLiKi 1</p><p>hconv+</p><p>1</p><p>.=</p><p>hrad g Tsky Tcell+( ) Tsky2 Tcell</p><p>2+( ),=</p><p>UL Ub Utf.+=</p><p>thQ u</p><p>WLG,=</p><p>ov thelCf,+=</p><p>m</p></li><li><p>APPLIED SOLAR ENERGY Vol. 49 No. 4 2013</p><p>MODELING AND OPTIMIZATION OF AN PHOTOVOLTAIC THERMAL SYSTEM 219</p><p>Actually, solving the problem was finished after twosteps: optimizing the thermal system, step two: optimizing the electrical system by using the results of thestep one.</p><p>In step one, the electrical efficiency was consideredas a parameter and calculated the best overall effi...</p></li></ul>

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