A geometrical multi-scale numerical method for coupled hygro-thermo-mechanical problems in photovoltaic laminates

Abstract

A comprehensive computational framework based on the finite element method for the simulation of coupled hygro-thermo-mechanical problems in photovoltaic laminates is herein proposed. While the thermo-mechanical problem takes place in the three-dimensional space of the laminate, moisture diffusion occurs in a two-dimensional domain represented by the polymeric layers and by the vertical channel cracks in the solar cells. Therefore, a geometrical multi-scale solution strategy is pursued by solving the partial differential equations governing heat transfer and thermo-elasticity in the three-dimensional space, and the partial differential equation for moisture diffusion in the two dimensional domains. By exploiting a staggered scheme, the thermo-mechanical problem is solved first via a fully implicit solution scheme in space and time, with a specific treatment of the polymeric layers as zero-thickness interfaces whose constitutive response is governed by a novel thermo-visco-elastic cohesive zone model based on fractional calculus. Temperature and relative displacements along the domains where moisture diffusion takes place are then projected to the finite element model of diffusion, coupled with the thermo-mechanical problem by the temperature and crack opening dependent diffusion coefficient. The application of the proposed method to photovoltaic modules pinpoints two important physical aspects: (i) moisture diffusion in humidity freeze tests with a temperature dependent diffusivity is a much slower process than in the case of a constant diffusion coefficient; (ii) channel cracks through Silicon solar cells significantly enhance moisture diffusion and electric degradation, as confirmed by experimental tests.

Nondestructive monitoring of damage caused by accelerated ageing in photovoltaic modules

“…This can be primarily motivated by thermo-mechanical stresses which damage and break the gridline deposited onto solar cells, as observed in the thermal cycling tests for an amount of cycles above 200, plus the accelerated oxidation of the gridline induced by moisture whose diffusion within the encapsulant is accelerated by cracks. As shown in the numerical simulations in Lenarda and Paggi, 38 cracks connect the two layers of the encapsulating material above and below the solar cells and therefore enhance moisture diffusion.…”

Simulated hail impacts on flexible photovoltaic laminates: testing and modelling

“…In fact, a further propagation of cracks and an increase of their opening can lead to an expansion of the electrically inactive solar cell areas, with a consequent increase of power-loss [6]. In this regard, the crack pattern with partial electric insulation observed for the soft substrate (see Fig.…”

Effect of operating temperature on degradation of solder joints in crystalline silicon photovoltaic modules for improved reliability in hot climates

“…In ANSYS, all the respective material properties of component layers in the PV module are inputted as Engineering Data. Lenarda and Paggi, (2016), proposed a geometrical multi-scale numerical method for coupled hygro-thermo-mechanical problems in photovoltaic laminates. They presented advanced model schemes of imperfect sealing between PV component layer interfaces.…”

“…Kurnik et al (2011) in their outdoor testing of PV module temperature and performance under different mounting and operating conditions, reported that the temperature difference between ambient and module can be as high as 22 °C. The PV module has been described as a layered composite of different materials hence the different material combinations complicate stress distribution and concentration (Lenarda and Paggi, 2016;Ojo and Paggi, 2016a). Operations at high-temperatures increases the mismatch effect among crystalline silicon wafer, silver contacts, solder, copper ribbons and other component layers in the module occasioned by the differences in their coefficient of thermal expansion (CTE).…”