Penumbra shadow representation in photovoltaics : comparing dynamic and constant intensity

Abstract

This study is the first to directly compare natural dynamic penumbra shadows with experimentally replicated constant-intensity shadows on photovoltaic modules, providing new insights into the limitations of conventional shadow approximations found in the existing body of knowledge. Neutral density filters were deemed the most appropriate method for replicating a constant-intensity shadow, as they reduce visible light relatively uniformly across the primary silicon wavelength range. Preliminary experiments established the intensity values for each neutral density filter chosen to be able to match with the 29 dynamic penumbra shadows being replicated by both the size of shadow and the averaged intensity. The results revealed that while constant-intensity shadows and dynamic penumbra shadows produced similar overall power loss magnitudes, the constant-intensity shadows consistently led to higher losses, averaging 9.65% more, despite having the same average intensity and shadow size. Regression modelling showed similar curvature trends for both shading types (Adjusted R2 = 0.895 for constant-intensity shadows and Adjusted R2 = 0.743 for dynamic-intensity shadows), but statistical analyses, including the Mann–Whitney U-test (p = 0.00229), confirmed a significant difference between the power loss output for the two penumbra shadow conditions. Consequently, the null hypothesis was rejected, confirming that the simplified constant-intensity shadows represented in the literature cannot accurately replicate the behaviour of dynamic-intensity penumbra on photovoltaic modules.