23 rd EU PVSEC, 4AV.3.8
A MODELING APPROACH TO THE OPTIMIZATION OF INTERCONNECTS FOR BACK CONTACT CELLS
BY THERMOMECHANICAL SIMULATIONS OF PHOTOVOLTAIC MODULES
Ulrich Eitner 1 , Pietro P. Altermatt 2 , Marc Köntges 1 , Rüdiger Meyer 3 and Rolf Brendel 1,2
1 Institut für Solarenergieforschung Hameln (ISFH), Am Ohrberg 1, D-31860 Emmerthal, Germany
2 Institut für Festkörperphysik, Leibniz Universität Hannover, Appelstraße 2, D-30167 Hannover, Germany
3 Stiebel-Eltron GmbH & Co. KG, Dr.-Stiebel-Strasse, D-37603 Holzminden, Germany
Tel: +49 5151 999 415, Fax: +49 5151 999 400, Email: eitner@isfh.de
ABSTRACT: We present a thermomechanical model of a laminated string for the optimization of interconnects for modules with back contact silicon solar cells. First we calculate the thermal stresses in a laminate of 9 noninterconnected cells that result from the cooling process from lamination temperature of 150°C down to − 40°C. In a second step we add the interconnectors in a 2-dimensional geometry which is bidirectionally coupled to the original
3-dimensional geometry of the laminated cell string. Both simulations show the resulting stresses on the solar cells and all other module components. The first analysis shows the same stress distribution for every cell in the string. In the second simulation we find the cell stresses near the 3 soldered areas to depend significantly on the specific interconnector design. The model presented here consists of the equations from continuum mechanics and is solved by Finite Element Analysis. In this modeling approach we describe the mechanical material behavior by linear elasticity. The 2-dimensional plain-stress modeling of the interconnector allows fast and easy modifications of the interconnector’s design and helps to estimate the mechanical performance of the interconnector as a part of the 3dimensional string. In a last step the electrical performance of the interconnector is simulated.
Keywords: PV Module, mechanics, back-contact
1 ISSUES 2 MODELING
The aging of PV modules mainly results from mechanical loads, thermal loads and moisture. Thermal cycling tests are commonly used to investigate the influence of temperature variations on PV modules.
These aging tests provide the degree of degradation for the operating mode of the module depending on the
For reasons of computational complexity we focus on modeling a laminated string as depicted in figure 1 instead of a complete module. The geometry of the string requires a 3D model as it cannot be reduced to 2dimensional plane stress or plane strain. However, axial symmetries allow a further reduction of the model to number of thermal cycles, so that temperature induced mechanical failures cannot be locally identified. The use of materials with different coefficients of thermal expansion (CTE) leads to mechanical stresses. The quantification of these stresses is achieved by thermomechanical simulations. only 1/4 of the string. The interconnectors are simulated in a separate 2D-plain stress geometry. This way the details of the interconnectors can be accurately modeled and the large FEM-mesh of the 3D geometry remains unchanged. Another benefit of this submodeling technique is the easy modification of the interconnector design.
Rear-contact solar cells require a special design for their interconnection. Various techniques are currently investigated by module manufacturers and research institutes such as using adhesives and pre-structured lamination sheets as presented by de Jong et al. [1]. The interconnectors that we focus on join the rear sides of neighboring cells (as opposed to front-junction cells, where a front with a rear side is joined). Hence, such inplane interconnectors have no loop in the out-of-plane direction and are thus less flexible. This causes additional stresses on the soldering joints when the temperature changes. Making such interconnectors more elastic, e.g. by punching slits into them, usually results in an increased electrical resistance or makes them less suitable for handling by robots. For these reasons, finding an optimum design for the interconnector is not a straight forward task.
Here we present a computer model for the optimization. The Finite Element simulation considers the thermomechanical as well as the electrical performance of an interconnector design.
Figure 1: Schematic sketch of the laminated string used in our simulations. The interconnections between the solar cells are not shown.
We implement a bidirectional coupling mechanism between the solder areas on the cells in the 3D geometry and the solder areas of the 2D-interconnector. This coupling mechanism includes the imitation of elastic solder properties. The reason for this simplification is
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23 rd EU PVSEC, 4AV.3.8 first the different scales in dimension of the solder in comparison to the string and second the difficulty to access material parameters of complex material laws for the solder that would involve viscoplasticity. Residual stresses are not included and a stress free state is assumed at lamination temperature (as it is done in [2]) of 150°C, since the EVA is liquid at this temperature.
We use the generalized Hooke’s law for linear elasticity including thermal expansion or contraction respectively. The material parameters are either taken from literature, manufacturer’s data tables or are derived from stress-strain measurements. We measure the elasticity of silicon solar cells by four point bending experiments as suggested by Schoenfelder et al. [3] with the testing apparatus depicted in Figure 2. For the polymer sheets temperature dependent tensile tests of fully cured EVA strips were carried out at the Fraunhofer
Institute for Mechanics of Materials in Halle (IWMH).
As for this work we decided to use linear elastic material laws that are time-independent, the model can be solved by static Finite Element Computations using temperatures between − 40°C and 150°C as a parameter.
The electrical performance of the interconnector is simulated by applying the cell specific electrical current to the soldered areas. The voltage drop over the interconnector at constant current is then calculated as the difference of the voltage levels on two opposite solder areas and is interpreted as a measure of the interconnector’s electrical performance.
The cooling of the string from lamination temperature of 150°C is assumed to be slow enough to be simulated by a parametric study of temperatures from
150°C to − 40°C so that the material laws and the equations of continuum mechanics solved here are all time-independent. Experimentally we observe temperature differences on different parts of the module to be sufficiently small (in comparison to the range from
150°C to − 40°C) to be neglected in our model. We therefore assume a homogeneous temperature distribution over the complete string. Our model cannot simulate aging itself but by applying failure criteria on the different parts in the module with the stresses we simulated, it is possible to detect the beginning of mechanical failures that will lead to complete breakdown in a temperature cycling test. These failure criteria must be valid for the solar cells in the condition directly before lamination. That is to assure that residual stresses in the cells are accounted for in the formulation of failure criteria.
4 RESULTS
Figure 3 shows typical mechanical stresses in noninterconnected cells at − 40°C. The simulation shows that the in-plane stresses dominate. Maximum compressive stress is observed in the center of a solar cell (point A).
Figure 2: Four-Line-Bending-Test for the determination of elastic constants of the silicon solar cells.
3 LIMITATIONS OF THE MODEL
Nonlinear material behavior such as viscoelastic and plastic deformation is not included in our model.
Especially the EVA polymer sheet is not modeled in its whole complexity in this first numerical approach.
Experimentally we find the mechanical behavior of the polymer to depend on time, temperature and curing conditions. However, in this computation of mechanics of solar modules we simplified the material laws for the polymer by fitting experimental stress strain curves with linear regression. We use the parameters of the regression as linear elastic constants. The tensile tests of fully cured EVA strips are run at low pulling speed of 5 mm/min in order to avoid large viscoelastic effects.
Figure 3: Simulated compressive stresses (coloured) and directions of principal stresses (arrows) in a noninterconnected solar cell at − 40°C (1/4 of the cell shown).
Figure 4: Simulated in-plane stress components of interconnected solar cells at − 40°C (1/2 of the cells shown).
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23 rd EU PVSEC, 4AV.3.8
Fig. 4 shows these in-plane stresses for all modelled solar cells in an interconnected string. The normal stresses (s stresses (s x
, s y
) are depicted as well as the in-plane shear xy
). As the stress distributions are almost identical for each interconnected cell we find the in-plane components of the cell stresses to be independent of the cell position within the string. The simulation yields maximum tensile and shear stresses close to the solder areas. The maximum compressive stress is in the center of the interconnected solar cells.
The exact interpretation of these stress values, i.e. the failure criteria for crack growth in solar cells or for delamination in a PV module are current research objectives.
The performance of five interconnector designs is shown in Fig. 5. The abscissa value gives the electrical power loss which is given by the voltage drop across the interconnector at a fix current flow. The ordinate value is a measure for the mechanical performance and is given as the maximum principle stress value on interconnected cells. Both values are normalized to the maximum number calculated for any of the investigated connectors.
The interconnector A shown in Fig. 5 exhibits a direct connection of the opposite solder areas which gives, of course, little electrical losses. However, the maximum principle stresses are large when compared to other connector shapes. A second interconnector B is mechanically optimized and thus shows low cell stresses but exhibits an enhanced electrical loss. The results for the three new designs (C, D, E, shapes are not shown) are also given in Fig. 5. According to the simulation these shapes have a compromising behaviour and are considered to be preferred over designs A and B.
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0.9
A
B
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0.7
C, D, E
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normalized electrical loss
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Figure 5: Simulated maximum mechanical stress in the cells vs. electrical loss over interconnector for different designs (normalized to worst examples)
5 CONCLUSIONS
A modeling approach that allows the optimization of interconnectors for back contact solar cells is presented.
The simulation for non-interconnected solar cells in a laminated string shows highest compressive stresses in the center of the cells, whereas for interconnected cells the areas of the solder joints is most stressed. Regarding mechanical stresses it seems to be of no importance on which position the solar cell is placed within the string.
As stated above, our model only includes linear elastic behaviour so far. Future work has to include more realistic material models. Experiments need to be carried out to evaluate the accuracy of the model and thus to assure realistic constraints for the optimization of the interconnector.
6 ACKNOWLEDGEMENTS
This work has been carried out in cooperation with
Stiebel-Eltron. Funding for this work was provided by
Stiebel-Eltron and the State of Lower Saxony.
5 REFERENCES
[1] P.C. de Jong, K.M. Broek, I.J. Bennett, M.J.H. Kloos,
Progress Made with Back-Contact Modules Using
Conductive Adhesive Interconnection Technology,
Proceedings of 22 nd European Photovoltaic Solar Energy
Conference, 3.-7. Sept. 2007, Milano, Italy, p.2679-2682.
[2] M. Meuwissen, M. van den Nieuwenhof, H.L.A.H.
Steijvers, T.L. Bots, K.M. Broek, M.J.H. Kloos,
Simulation Assisted Design of a PV Module
Incorporating Electrically Conductive Adhesive
Interconnections, Proceedings of 21 st European
Photovoltaic Solar Energy Conference, 4.-8. Sept. 2006,
Dresden, Germany, p.2485-2490.
[3] S. Schönfelder, A. Bohne, J. Bagdahn, Comparison of
Test Methods for Strength Characterisation of Thin Solar
Wafers, Proceedings of 22 nd European Photovoltaic Solar
Energy Conference, 3.-7. Sept. 2007, Milano, Italy, p.1636-1640.
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