Thermal Stress and Strain of Solar Cells in Photovoltaic Modules

  • Ulrich EitnerEmail author
  • Sarah Kajari-Schröder
  • Marc Köntges
  • Holm Altenbach
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 15)


The long-term stability of photovoltaic (PV) modules is largely influenced by the module’s ability to withstand thermal cycling between −40°C and 85°C. Due to different coefficients of thermal expansion (CTE) of the different module materials the change in temperature creates stresses. We quantify these thermomechanical stresses by performing a Finite-Element-analysis of a 60 cell module during thermal cycling. We therefore start by the experimental characterization of each material layer. In particular, the polymeric encapsulant is characterized by three alternative models in order to stepwise consider the time- and temperature-dependence in the simulation. Experiments performed with laminated samples are used to validate the computational model. We find that taking into account the viscoelasticity of the encapsulation layers gives the best agreement with experiments. The Finite-Element-analysis of the complete module shows that the solar cells are under high compressive stress of up to 76 MPa as they are sandwiched between the stiff front glass and the strongly contracting plastic back sheet. The non-symmetrical structure of the 5.55 mm thick module with glass being the thickest component (4 mm) leads to bending during the thermal cycle.


Thermal Stress Solar cell Photovoltaic 


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The authors thank Prof. R.~Brendel for his guidance on the experimental parts and for his support of this work. Parts of this work were funded by the state of Lower-Saxony.


  1. 1.
    Iec 61215:2005, crystalline silicon terrestrial photovoltaic (pv) modules - design qualification and type approval. international electrochemical commission, 2005.Google Scholar
  2. 2.
    Althaus, J.: Quality assurance for pv modules: experience from type approval testing.. Photovoltaics International 3, 120–127 (2009)Google Scholar
  3. 3.
    Brueckner, R.: Materials Science and Technology: A Comprehensive Treatment, Vol. 9, Glasses and Amorphous Materials, chap. Mechanical properties of Glasses Wiley-VCH,   (1991)Google Scholar
  4. 4.
    Ehrenstein, G.: Polymer-Werkstoffe. Struktur - Eigenschaften - Anwendung Hanser Fachbuch,   (1999)Google Scholar
  5. 5.
    Eitner U., Altermatt P.P., Köntges M., Meyer R., Brendel, R.: A modeling approach to the optimization of interconnects for back contact cells by thermomechanical simulations of photovoltaic modules. In: Proceedings of the 23rd European Photovoltaic Solar Energy Conference, pp. 2815–2817. Valencia (2008)Google Scholar
  6. 6.
    Eitner U., Kajari-Schröder S., Köntges M., Brendel R (2010) Non-linear mechanical properties of ethylene-vinyl acetate (eva) and its relevance to thermomechanics of photovoltaic modules. In: Proceedings of the 25th European Photovoltaic Solar Energy Conference, pp. 4366–4368. ValenciaGoogle Scholar
  7. 7.
    Eitner U., Köntges M., Brendel, R.: Measuring thermomechanical displacements of solar cells in laminates using digital image correlation. In: Proceedings of the 34th IEEE PVSC, pp. 1280–1284. Philadelphia (2009)Google Scholar
  8. 8.
    Eitner, U., Köntges, M., Brendel, R.: Use of digital image correlation technique to determine thermomechanical deformations in photovoltaic laminates: Measurements and accuracy. Solar Energy Materials and Solar Cells 94(8), 1346–1351 (2010)CrossRefGoogle Scholar
  9. 9.
    Ferry, J.D: Properties of Polymers. Wiley,   (1980)Google Scholar
  10. 10.
    Greenwood, J.C.: Silicon in mechanical sensors. Journal of Physics E: Scientific Instruments 21(12), 1114–1128 (1988)CrossRefGoogle Scholar
  11. 11.
    Häberlin, H.: Photovoltaik: Strom aus Sonnenlicht für Verbundnetz und Inselanlagen. Electrosuisse,   (2010)Google Scholar
  12. 12.
    de Jong, P.: Achievements and challenges in crystalline silicon back-contact module technology. Photovoltaics International 7, 138–144 (2010)Google Scholar
  13. 13.
    Kempe, M.: Design criteria for photovoltaic back-sheet and front-sheet materials. Photovoltaics International 2, 100–104 (2008)Google Scholar
  14. 14.
    Kempe, M.: Evaluation of encapsulant materials for pv applications. Photovoltaics International 9, 170–176 (2010)Google Scholar
  15. 15.
    Lyon, K.G., Salinger, G.L., Swenson, C.A., White, G.K.: Linear thermal expansion measurements on silicon from 6 to 340 k. Journal of Applied Physics 48(3), 865–868 (1977)CrossRefGoogle Scholar
  16. 16.
    Meier R., Kraemer F., Schindler S., Bagdahn S.W.J. (2010) Thermal and mechanical induced loading on cell interconnectors in crystalline photovoltaic modules. In: Proceedings of the 25th European Photovoltaic Solar Energy Conference, pp. 3740–3744. ValenciaGoogle Scholar
  17. 17.
    Osterwald, C.R., McMahon, T.J.: History of accelerated and qualification testing of terrestrial photovoltaic modules: A literature review. Progress in Photovoltaics: Research and Applications 17, 11–33 (2009)CrossRefGoogle Scholar
  18. 18.
    Roberts, R.B.: Thermal expansion reference data: silicon 300-850 k. Journal of Physics D: Applied Physics 14(10), L163–L166 (1981)CrossRefGoogle Scholar
  19. 19.
    Tschoegl, N.W.: The Phenomenological Theory of Linear Viscoelastic Behavior: An Introduction. Springer,   (1989)Google Scholar
  20. 20.
    Williams, M.L., Landel, R.F., Ferry, J.D.: The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. Journal of the American Chemical Society 77, 3701–3707 (1955)CrossRefGoogle Scholar
  21. 21.
    Wohlgemuth J., Petersen R. (1993) Reliability of eva modules. In: Proceedings of the 23rd IEEE PVSC, pp. 1090–1094Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ulrich Eitner
    • 1
    Email author
  • Sarah Kajari-Schröder
    • 1
  • Marc Köntges
    • 1
  • Holm Altenbach
    • 2
  1. 1.Institute for Solar Energy Research Hamelin (ISFH)EmmerthalGermany
  2. 2.Martin-Luther-Universität Halle-WittenbergHalle (Saale)Germany

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