A multi-physics and multi-scale numerical approach to microcracking and power-loss in photovoltaic modules

doi:10.1016/j.compstruct.2012.08.014

Composite Structures

Volume 95, January 2013, Pages 630-638

https://doi.org/10.1016/j.compstruct.2012.08.014 Get rights and content

Abstract

A multi-physics and multi-scale computational approach is proposed in the present work to study the evolution of microcracking in polycrystalline Silicon (Si) solar cells composing photovoltaic (PV) modules. Coupling between the elastic and the electric fields is provided according to an equivalent circuit model for the PV module where the electrically inactive area is determined from the analysis of the microcrack pattern. The structural scale of the PV laminate (the macro-model) is coupled to the scale of the polycrystals (the micro-model) using a multiscale nonlinear finite element approach where the macro-scale displacements of the Si cell borders are used as boundary conditions for the micro-model. Intergranular cracking in the Si cell is simulated using a nonlinear fracture mechanics cohesive zone model (CZM). A case-study shows the potentiality of the method, in particular as regards the analysis of the microcrack orientation and distribution, as well as of the effect of cracking on the electric characteristics of the PV module.

Introduction

Photovoltaics (PVs) based on Silicon (Si) semiconductors is one the most growing technology in the World for renewable, sustainable, non-polluting, widely available clean energy sources. Standard PV modules are laminates composed of a glass superstrate 4 mm thick, an encapsulating polymer layer (EVA) 0.5 mm thick, a layer of Si solar cells 0.166 mm thick, another layer of EVA with the same thickness as the previous one, and finally a thin multi-layered backsheet made of Tedlar/Aluminum/Tedlar 0.1 mm thick, see Fig. 1. For more details about the geometrical and mechanical properties of these constituent materials, the reader is referred to [1]. The majority of solar cells available on the market are made of either mono or polycrystalline Si and are separated by a thin amount of EVA in their plane. Two main semiconductors, called busbars, connect the cells together and are placed on the upper and the lower sides of the cells. The microstructure of a polycrystalline Si cell is shown in Fig. 2, where we note a significant elongation of the grains due to production issues.

So far, theoretical and applied research has focused on the increase of the solar energy conversion efficiency of the cells. Although efficiencies up to $40 %$ have been reached in the laboratory using single junction GaAs and multijunction concentrators, the technology based on mono and multicrystalline Si is still the most competitive on the market due to the low price of Si semiconductor and the widely established material processing developed in the field of electronics [2].

Another important issue is the problem of durability, which, however, has received much less attention by the scientific community so far. In the 1990s, warranties of PV producers allow one to replace PV modules in case of power losses larger than $10 %$ in the first 10 years, and then larger than $20 %$ in the next 15 years. The maximum life of PV modules is considered to be of 25 years. More recently, with more and more field data of installed modules available, a linear decreasing performance of the PV module is expected (see the comparison among various warranty specifics in Fig. 3).

The quality control of these composites is of primary concern from the industrial point of view. On the one hand, the aim is to develop new manufacturing processes able to reduce the number of cells or modules rejected by quality control [3]. On the other hand, even if all the damaged cells are theoretically discarded during manufacturing, it is impossible to avoid the occurrence of microcracking. Sources of damage in Si cells are transport, installation and use (in particular impacts, snow loads and environmental aging caused by temperature and relative humidity variations). The existing qualification standards IEC 61215 require passing of severe laboratory tests in a climate chamber. However, microcracking is not used as a quantitative indicator for the quality assessment of PV modules. Recently, Kajari-Schröder et al. [4] have analyzed microcracking resulting from snow tests and artificial aging in the laboratory using the electroluminescence technique, see Fig. 4. Microcracking can lead to large electrically disconnected cell areas, with up to $16 %$ of power-loss [5]. In addition to laboratory tests on single panels, field data published in [6] have shown that microcracked cells have a nonconstant current–voltage characteristics in time and an undesirable increase of the operating temperature.

The aim of the present work is to understand the phenomena leading to microcracking in Si cells and to quantify the connection between cracking and power-loss. In this study, an innovative multi-scale (multi-resolution) and multi-physics numerical method is proposed. Since Si cells operate in the presence of elastic, thermal and electric fields, a multi-field (multi-physics) perspective is considered to be essential to achieve a predictive stage of any computational model. The multi-resolution approach, on the other hand, is adopted to simplify the actual 3D problem in a simpler 2D one, where microcracking in Si cells is numerically simulated under plane stress conditions and nonlinear fracture mechanics formulations. To the knowledge of the present authors, the present model is the first proposed in the literature for the simulation of microcracking and the resulting prediction of power-loss of PV modules.

Section snippets

A multi-physics approach

The study of durability of PV modules requires the characterization of the effect of microcracking induced by mechanical loads and thermal excursions on the electric response of the solar panel. Mechanical loads are induced by vibrations and impacts during transportation, installation and use of the modules. Deformations are also induced by the night and day alternating temperature variation. Moreover, temperature affects the electric performance of the PV module, since the semiconductor

A multi-scale (multi-resolution) computational method

Photovoltaic modules are laminated composites where the thickness of the various layers are very different from each other, as outlined in the Introduction. Moreover, Si cells are separated by a thin interspace of EVA and are made of a polycrystalline material whose microstructure has to be considered to predict microcracking. These complexities suggest the use of 3D methods, which are however computationally expensive. In the present study, a simplified approach to reduce the computational

A numerical example

In this section, a numerical example showing the applicability of the proposed numerical method to a realistic case study is proposed. The aim is the determination of microcracking in Si cells, the quantification of the electrically inactive cell areas and finally the computation of the $I – V$ and $P – V$ characteristics of the PV module. The comparison between the characteristics of the intact and microcracked modules will provide a measure of power-loss due to cracking.

A square PV module composed of

Conclusion

In the present work, a multi-physics and multi-scale (multi-resolution) computational approach has been proposed for the study of the snow load-induced microcracking in polycrystalline Si solar cells and its effect on the electric response of PV modules. To the authors’ best knowledge, this is the first computational approach that attempts at studying the coupling between the elastic and the electric fields. Moreover, it is the first computational method that explicitly considers the

Acknowledgments

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007–2013)/ERC Grant Agreement No. 306622 (ERC Starting Grant “Multi-field and multi-scale Computational Approach to Design and Durability of PhotoVoltaic Modules” – CA2PVM). The support of the Italian Ministry of Education, University and Research to the Project FIRB 2010 Future in Research “Structural mechanics models for renewable energy

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A multi-physics and multi-scale numerical approach to microcracking and power-loss in photovoltaic modules

Abstract

Introduction

Section snippets

A multi-physics approach

A multi-scale (multi-resolution) computational method

A numerical example

Conclusion

Acknowledgments

Mater Sci Eng R

Solar Energy Mater Solar Cells

Solar Energy Mater Solar Cells

Solar Energy Mater Solar Cells

Comput Mater Sci

Thermomechanical deformations in photovoltaic laminates

J Strain Anal Eng Des