Modeling the transmittance of anisotropic diffuse radiation towards estimating energy losses in solar panel coverings

The performance assessment of photovoltaic arrays involves estimating the energy that is lost due to different sources, such as optical losses in the protective coverings. These transparent coatings do not transmit all incoming solar radiation due to partial reflections and absorptions that intensify with the angle of solar incidence. In the case of beam radiation, which consists of parallel rays with a deterministic incidence, the transmittance can be assessed with well-known analytical models. Alternately, more complex diffuse radiation consists of scattered rays with stochastic and anisotropic distributions. Consequently, the transmittance of diffuse radiation is commonly ignored or oversimplified with limited models. This work presents a new set of general models for estimating the transmittance of anisotropic diffuse radiation. Transmittance was determined from surface integrals models solved over the geometrical regions corresponding to the diffuse radiation components, i.e., sky isotropic, circumsolar, horizon brightening, and albedo. This approach was validated against stochastic rays simulations, which converged with RMSE below 0.05% transmittance. The surface integrals were then solved for the relevant discretized input ranges, and regression models were fitted to capture the resulting behavior. With high flexibility, the inputs of these regression models allow for specifying the covering characteristics and the sun and panel angular positions. The proposed models allowed us to incorporate the estimation of transmittance losses to a broader energy harvesting analysis. In a case study, the effect on annual energy was calculated comparing four transmittance modeling approaches with three different covering specifications, three panel inclinations, three sky models, and in two locations. The range of variation due to the covering specifications can result in energy losses of 16.33% compared to using a covering with the highest transmittance. The findings and methods presented in this work have implications in areas ranging from the modeling of energy harvesting to the design and development of solar panels and protective transparent coatings.