THERMAL SIMULATIONS OF A CPV POINT FOCUS MODULE USING COMSOL MULTIPHYSICS L.A. Oliverio*, G. Timò**, A. Minuto**, P. Groppelli** * Politecnico di Milano, e-mail: [email protected] ** RSE S.p.A. Via N. Bixio, 39 – Piacenza (Italy), e-mail: [email protected], [email protected], [email protected] Abstract – An investigation of the thermal performance of a Concentrating Photovoltaic (CPV) Point Focus module is presented. The modeling activity is based on Comsol Multiphysics software environment which uses the Finite Element Method (FEM). The goal of the simulation is to improve the module thermal management in order to reduce the solar cell’s temperature. The possibility to reduce the use of row material, in particular for the receiver, in order to reduce the module’s cost without affecting the cell’s temperature is also investigated. 2D and 3D models are realized and validated thanks to experimental indoor and outdoor measurements. The results of the FEM simulations show that an optimization of light spot area on the cell along with a better thermal contact downside the cell can lead to a significant reduction of cell’s operative temperature. A minimization of the quantity of copper and aluminum used for dissipating the heat can be obtained without increasing the cell working temperature. INTRODUCTION At high concentration levels, the use of high efficiency multi-junction solar cells could lead to the development of CPV systems with competitive costs, if compared to the current PV technologies. Advanced PV devices based on the III-V compounds, currently used in CPV modules, can reach conversion efficiency values grater than 40%; furthermore, efficiencies values around 50% are expected to be reached in a few years. However, the more the concentration ratio increases, the more is the heat flux to be dispersed from the device in order to keep junction temperature as lower as possible. In fact, it is well known that the temperature affects negatively the efficiency and the life time of cells. In this paper, the thermal analysis of a CPV Point Focus module is presented in order to understand the main obstacles to the heat exchange and to give technical advices and strategies to improve the heat dissipation. To perform an accurate analysis, a CPV module has been realized on purpose with thermocouples located in different places inside and outside the module itself and the developed Finite Element analysis has been validated throughout indoor and outdoor measurements. Once the CPV module thermal model has been validated, the simulating activity has been carried out in order to improve the module thermal management. CPV MODULE’S TYPE, GEOMETRY AND MATERIALS The CPV module utilized in the thermal analysis has been supplied by SolarTec Int. (Germany). It is made of sixteen series-connected receivers, each one containing nine parallel-connected Multijunction InGaP/InGaAs/Ge solar cells As shown in figure 1, the module’s base plate element consists of an aluminum substrate, a copper heat sink, a thin aluminum plate and polyamide tapes for electrical insulation between the conductive layers. The solar cells are electrically connected to Proceedings of the Solar Energy Tech 2010 ISBN 978-1-4467-3765-1 the copper heat sink through a conductive silver paste and to the thin aluminum upper plate through bond wires. Nitrogen is kept inside the enclosure, between the base plate and the lens to avoid moisture condensation. Heat transfer occurs by conduction from the cell through the base plate element and by convection and radiation inside the enclosure. The total heat produced is than dispersed from the external surfaces to the outside environment by convection and radiation. The total area of the cell is around 3 mm2 and its thickness is around 200 µm. Figure 1. Structure of the tested CPV module. The geometry used for the model is shown in figure 2, which is a cross section of the whole module, passing from the receiver to the cell. Figure 2. Entire geometry used for the model a) and detailed enlargement of the receiver b) and of the cell c). MODULE’S MODEL SETUP AND MESHING The simulations are performed using COMSOL Multiphysics software tool. A good FEM model has to be characterized by some features that often clash with each other: - easy parameters setting; - reasonable computing simulation time; - accuracy of the results. The trade-off among these features must be found, in order to perform an effective simulating activity: in the field of FEM simulation it's well-known that the “mesh“setup is strictly related to the global effectiveness of the model. As far as the 2D model is concerned, the fluid thermal interaction modeling requires a tight mesh in the gaseous domain constituting the inside part of the module; this kind of setup is necessary in order to obtain the convergence of the model; the 2D model’s mesh consists of 27000 elements. The physical properties of the materials, used to build up the module are taken from literature or 56 from available supplier’s datasheet and represent the input data of the model. In particular, the thermal conductivity is the most important parameter which defines the capability of the material to conduce heat. For the gaseous subdomains it must be taken into account that the density is a function of temperature and it determines the fluid motion inside the enclosure. For the 2D model, the following thermal and fluid phenomena are considered: - heat conduction between layers; - convection and radiation outside of the module; - natural convection and radiation exchange inside the enclosure. For the heat conduction in solid domains the equation of pure conduction is used: Cp T ( k T ) Q t where ρ [kg/m3] is the fluid density, Cp [ J / kg K ] the specific heat, k [W / m K ] is the thermal conductivity, T [K] is the temperature and Q [J] is the produced heat. As far as the outside part of the module is concerned, the Neumann conditions for thermal exchange are imposed: 4 n k T h (Tinf T ) Tamb T 4 where the convection coefficient, h, is calculated using the dimensionless parameters for natural convection on a vertical plane, is the emissivity of the surface and is the Boltzmann constant. Tinf and Tamb are respectively the temperature of the cooling fluid (air) and the ambient surroundings temperature, that, in our case, have the same value. Inside the module, the fluid thermal interaction is modeled using the set of Navier-Stokes equations for weakly compressible fluids: t v 0 v p 2 v 1 v g v v 3 t T C p (k T ) Q C p (v T ) t where v is the velocity field, p is the pressure and g is the gravity field. The heat transfer phenomena and the fluid thermal interaction are solved simultaneously, so the simulation’s output are the profile of temperature in every point of the module and the velocity field of the fluid inside the enclosure. These kind of simulations also lead to understand what is the rate of error which is found when the fluid thermal interaction is neglected and it is a necessary step in order to build up an affordable 3D simplified model. Both transient and stationary simulations have been carried out. EXPERIMENTAL INDOOR VALIDATION OF THE 2D MODEL The available testing module has been made on-purpose, equipped with thermocouples able to measure the temperature in the following meaningful points: - underneath the cell; 57 - on the upper part of the cell; - on the lens; - on the module backside; - in the internal gas volume. During the indoor experimental tests, the module is kept in dark condition and heated by injecting a constant current; the environmental temperature is kept at a constant value. Thanks to joule effect, the cells heat up and after transient phenomena, a new stationary condition is reached. The transient lasts around 100 minutes and temperatures measured by thermocouples are imported into a database. Several experiments, with different values of the injecting current have been performed. With the hypothesis that all the electrical power injected in the cells is transformed in heat by Joule effect, the heat quantity, Q, is equal to: W Vm I where Vm is the mean value of the voltage produced at the terminals polarities of the module when the constant current, I, is injected. The module’s voltage decreases as the junction temperature rises up. Considering that the junctions have a very small thickness with respect to the total thickness of the substrate, the heat generated by the cells, due to joule effect is modeled as a boundary condition (on the cell’s surface); in this way a heat flux equal to the heat really produced, is injected on the upper face of the cell. A first validation of the FEM model, built up according to the above equations and assumptions, is possible by comparing a set of simulated results with the experimental ones. For example in figure 3 the result of an indoor simulation is shown. The most meaningful temperatures are compared with the measured ones (obtained by experimental tests). Figure 4 shows the good comparison of simulated upper cell’s temperature and back plate temperature with the experimental values, when a constant current of 750mA is injected. Several indoor measurements have been done in order to validate the model by using different values of the injected current. Figure 3. FEM Indoor simulation. 58 Figure 4. Comparison of simulated junction temperature (Tc) and back plate temperature (Tb) with the indoor experimental ones. OUTDOOR SIMULATIONS In outdoor conditions, the values of wind speed, environmental temperature, solar direct radiation and tilt angle are the input data that determine the operative junction temperature. It is possible to compare the back side module temperature that is measured outdoor, during different days of testing, with the one obtained by the FEM simulation, when the same environmental conditions are imposed. As an example, the figure 5 reports the trends of wind speed, environmental temperature and direct radiation during the day of July the 29th, 2009 from 9.50 am to 12.23 pm; the figure 5 shows also the fittings of the experimental data, whose values are used as input data to the FEM model. It's worthwhile to point out that a theoretical procedure has been developed for estimating the maximum and the minimum cell junction temperature [1] and considering current mismatch between receivers. In figure 6 the theoretical estimation of junction temperature developed in [1] and the experimental back temperature values are compared with the FEM simulated ones to allow a further validation of the FEM model. Figure 5. Measured values and fitted curves of wind speed, environmental temperature and DNI, as input data of simulations. 59 Figure 6. Results of simulation; the theoretical estimation of junction’s temperature and the back experimental temperature are compared with the simulated values of temperature. 2D THERMAL ANLYSIS Once the FEM model has been validated, it has been used to investigate the possibility to reduce the use of material for the receiver, without affecting junction’s temperature. In particular, the simulations show that the leading element of thermal dissipation is the back support while the dimensions of the plate of the receiver has little influence on cell’s temperature. Therefore, an optimization of the quantity of the dissipating materials can be evaluated to reduce the costs of the system. 2D simulations are made considering different rate of reduction of the receiver’s dimensions as shown in figure 7. The result is that no significant increase of the junction temperature is noticed, by changing the receiver dimension, as reported in figure 8; in fact, starting from a 90 mm receiver, no temperature increase of cell occurs reducing the dimension to a 20 mm receiver; while, in the smaller 9 mm receiver , an increase of less than 1 °C is predicted. Figure 7. 2D temperature simulations carried out considering different receiver’s dimensions. The first simulation represents the starting geometry ( 9i0 mm receiver). In the second and third simulations, smaller receivers are considered. 60 Figure 8. Results of the 2D temperature simulations made considering different receiver’s dimensions. The green line represents the starting geometry (90 mm receiver), while the yellow and the blue ones show the results obtained when the receiver’s base plate is reduced respectively at 20mm and at 9mm. The 2D model shows that the 90% of the heat flux generated by the junction goes to the receiver, passing through the conductive solder past. The conductive solder past is mostly responsible of the temperature drop between the junction and the back side of the module, as shown in figure 9. Figure 9. Temperature profile; the most part of temperature gap between the junction and the back side of the module is localized across the conductive solder paste. 3D THERMAL ANALYSIS A more detailed analysis can be performed with a 3D model. It is worth noting that the 2D model includes a complex modeling of fluid thermal interaction inside the module using the set of NavierStokes equations for weakly compressible fluids: this can be hardly considered in a 3D model for computation reasons. In three dimensions is necessary to introduce some simplification. In particular, it is possible to neglect the fluid-thermal interaction of the gas inside the enclosure and to simulate the convective heat transfer inside the module using a constant value of the convective coefficient. With 3D modeling has been possible to investigate the temperature cell distribution 61 when a non uniform distribution of the past is realized. In particular, it could happen that the past’s area is smaller than the total cell’s area, so that the cell is not effectively joined to the heating dissipative element. In this case there is an evident obstacle to heat dissipation and the junction temperature will be higher than expected. The positioning of the conductive solder past underneath the cell has been also analyzed by microscope observations. It has been checked that indeed the paste area is often smaller than the cell’s area. Therefore, different diameters of the past area have been considered in the 3D simulation, translating to different ratio of parte area to the cell’s area. It can ne showed that the temperature drop between the junction and the back side of the module is influenced by the thermal contact resistance, which is a function of the surface roughness and pressure of the contact. Contact spots are interspersed with gaps that are air filled. Heat transfer is therefore due to conduction across the actual contact area and to conduction and/or radiation across the gaps. The contact resistance may be seen as two parallel resistances, due to the contact spots and due to the gaps. The contact area is typically small, and especially for rough surfaces, the major contribution to the resistance is made by the gaps. When modeling the heat dissipation, it is taken into account that a portion of radiation hitting the designated cell area is converted into electricity, with an efficiency that is characteristic of the cell, while the remaining part of the radiation is converted in heat, or reflected. In our 3D simulation we consider a cell with a round active area (1.6 mm in diameter). The portion of radiation which goes on other areas of the cell, rather than the active one (for example on the metallization area), is not converted in electricity and it contributes to heat generation. An important factor that has a great impact on junction temperature is the diameter of the light spot, with respect to the cell’s active area. Indeed the rate of light that goes on the active area of the cell is the most important parameter in defining the optical efficiency (ratio of the light power incident on the cell with respect to light power incident on the lens) but it involves also the thermal phenomenon. As far as the heat generation is concerned, assuming a light spot with a Gaussian shape and considering a constant mean value, the more the variance of the focal spot increases, the more the light goes out from the active area. This portion of light is not converted into electricity and overheats the cell. Neglecting reflection phenomena it is possible to define two kinds of heat sources as follow: Heat generated in the boundary representing the cell’s active area: Qact [W m 2 ] Tlens DNI 1 cell G where Tlens is the transmittance of the lens that is assumed equal to 0.9; DNI is the direct radiation, cell is the PV efficiency of the cell and G is the Gaussian function which describes the light spot distribution produced by the Fresnel lens. In two dimensions, G is defined as: G x, y A e x x 0 2 y y 0 2 2 2 2 2 where A is the peak value of the function, and 2 its variance. Heat generated in the boundary representing the cell’s non-active area: Qdisp[W m 2 ] Tlens DNI G 62 Considering the same mean value of 705 suns, that is the concentration ratio of the tested module, different values of variance are considered, in order to figure out the impact of the spot distribution on the cell’s temperature. In particular, five different values of variance are considered, from to , which correspond to: - five different values of the concentration peak, from 2515 to 1125 suns; - five different values of the spot diameters, from 1.4mm to 2.8mm. The effect of the spot diameter and conductive paste positioning on the average temperature of the cell resulting from the 3D modeling is shown in figure 10. Figure 10. Overview of the effect of spot diameter and conductive paste positioning on the average temperature of the cell; an environmental temperature of 25 °C, wind speed of 1 m/s and a DNI of 750 W/m^2 are considered. In figure 11, the result of a 3 D temperature distribution simulation is reported as well. Figure 11. Detail of the image of the cell in the 3D model. In conclusion, the effect of the section of the bond wires on the heat dissipation has been analyzed. In this latter case, 3D FEM simulations shown that an over-sizing of bond wires does not lead to significant junction’s temperature reduction, also when the section is 10 times higher than the real section of . 63 CONCLUSIONS 2D FEM simulations of the whole geometry shows that the dimensions of the receiver’s plate has little role on thermal dissipation, while the main role of heat sink it is due to the back base plate. The 2D analysis leads to conclude that, from the strictly thermal point of view, a reduction of the row material used to build up the receiver can be obtained. 3D FEM simulations show that the dimensions of the light spot, produced by the Fresnel lens, with respect to the cell’s active area, along with the quality of the thermal contact underneath the cell, are the main factors determining the junction’s temperature. It is worthwhile to point out the validity of the FEM thermal analysis has been confirmed thanks to the availability of a properly designed prototype CPV module, equipped with several thermocouples which allowed the comparison of the output data of the modeling with experimental data coming from indoor and our door measurements. AKNOWLEDGMENT We are indebted to SolarTec Int. for the module preparation. The research has been partially supported by the Ministry of Economic Development with the Research Fund for the Italian Electrical System under the Contract Agreement established with the Ministry Decree of march 23, 2006 and by the European Commission under the Grant Agreement N.213514 (APOLLON Project) in the Seventh Framework Program. REFERENCES [1] G. Timò, A. Minuto, P. Groppelli, L. Oliverio, E. Malvisi, M. Sturm, “Modeling and New Identification Procedures to Evaluate Concentrating Photovoltaic Multi-junction (MJ) Module Equivalent Parameters and MJ-cells Junction Temperature in Operating Outdoor Conditions”, 25rd European Photovoltaic Energy Conference - Valencia, Spain, September 2010. [2] G. Timò, A. Minuto, P. Groppelli, E. Malvisi, G. Smekens, M. Sturm, “Thermal simulation and experimental identification of electro-thermal model parameters for a point-focus concentrating photovoltaic module”, 24th European Photovoltaic Solar Energy Conference and Exhibition, Germany, 2008. [3] E.S. Aronova, M.Z. Shvartz, A.A. Soluyanov, “The Effect of Temperature on the Efficiency of Concentrator PV Modules with MJ SC”, IEEE, 2008. [4] T. L. Chou, Z.H. Shih, H.F. Hong, C.N. Han, K.N. Chiang, “Investigation of Thermal Performance of High-Concentration Photovoltaic Solar Cell System”, 23th European Photovoltaic Solar Energy Conference, Spain, 2008. [5] Incropera, De Witt, Bergmann, Lavine, “Fundamentals of Heat and Mass Transfer”, 6th edition, ed. Wiley. 64

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