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.
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.
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).
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
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
   (  k  T )  Q
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:
 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
 
  t
  C p 
   (k  T )  Q    C p  (v  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.
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;
- 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
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.
Figure 4. Comparison of simulated junction temperature (Tc)
and back plate temperature (Tb) with the indoor experimental
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
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
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.
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.
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.
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
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
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
, 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
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.
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.
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25rd European Photovoltaic Energy Conference - Valencia, Spain, September 2010.
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