The impact of shading has been a prominent subject of discourse within the realm of photovoltaic (PV) energy harvesting and is recognized as a significant detriment to the system’s overall efficiency. Nevertheless, prevailing investigations, which predominantly focus on the hard shading originating from building structures and vegetation, singularly address the umbra shadow phenomenon while overlooking the complexity of shadow properties and their varying intensities. In this context, this present research aims to analyze the impact of shading caused by thin objects, wherein shadow formation deviates from a singular-intensity umbra to a blend of umbra and penumbra, exhibiting diverse intensities. In the initial experimental approach, outdoor trials produced statistically significant findings, identifying both the distance and thickness of shading objects as primary determinants influencing the impact of thin object shading on the power output of PV systems. Furthermore, the analysis of the results revealed that under the specified parameters and assumptions, when considering a thin object with a thickness-to-distance ratio of 2.3 mm/225 cm, the resulting power loss of 1.65% is statistically insignificant. Remarkably, laboratory investigations unveiled a notable correlation between penumbra and power loss, contrasting with outdoor experimentation results. The findings highlight the distinction between indoor and outdoor methodologies, stemming from discrepancies in shadow formation characteristics, thereby emphasizing the necessity of acknowledging and comprehending these variations.

This study aims to quantify the size and intensity of umbra and penumbra shadows on photovoltaic (PV) modules and assess the resulting potential power loss using image analysis techniques. An innovative algorithm, developed from open-source code, was employed to analyze shadow characteristics, alongside outdoor experiments to measure the raw power loss caused by thin objects shading the PV module. Spearman correlation analysis revealed a weak negative correlation between power loss and object distance, which strengthens with increased object thickness. For larger objects between the range of 10 and 16 mm, the raw power loss is predominantly influenced by umbra intensity, while smaller thin objects in the range between 2.8 and 8 mm are affected more by the intensity of the penumbra shadow. Moreover, beyond a distance of 225 cm, for object thicknesses up to 16mm, umbra shadows disappear, leaving only penumbra, which continues to cause power loss, though at a lower intensity. The study's key findings indicate that thicker objects generate stronger umbra shadows, correlating more significantly with power loss, while thinner objects create diffuse penumbra shadows with a reduced impact. Penumbra size and intensity play a critical role, as larger penumbras correspond to a slower reduction in power loss over distance. Shadow intensity, particularly for thicker objects, proves to be a more decisive factor in the raw power loss output than shadow size, as the increase in shadow size compensates for the loss in intensity. The image analysis techniques developed in this work provide an effective method for objectively quantifying the size and intensity of umbra and penumbra shadows, highlighting the importance of shadow dynamics.

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.