Partial Shading of Photovoltaic Modules with Thin Linear Objects: Modelling in MATLAB Environment and Measurement Experiments

This paper proposes a mathematical model for the shading profiles of a PV module with thin, long linear elements. The model includes the brightness distribution over the entire shading region (umbra, penumbra, and antumbra). A corresponding calculation code in the form of m-files has been prepared for the MATLAB environment. The input data for the calculations are the coordinates of the Sun’s position in the sky, the dimensions and spatial orientation of the shading element, and the spatial orientation of the shaded PV module. The correctness of the model was verified by a measurement experiment carried out under actual outdoor weather conditions. Statistical analysis of the comparison between the measurement data from the experiment and the model showed its high accuracy. As part of this research work, it was also checked how shading with thin linear elements affects the current–voltage characteristics of the module. It turned out that even a small linear shading could reduce the power output of the module by more than 6%, with the distribution of this shading across the individual cells of the module being extremely important.