Original Article

Modeling partial shading at the cell level on photovoltaic modules

¹ UCP, ENSTA, Institut Polytechnique de Paris, 828 Boulevard des Maréchaux, 91120 Palaiseau, France
² EPFL, PV-Lab, Maladière 71b, 2000 Neuchâtel, Switzerland
³ CSEM, Sustainable Energy Center, Jaquet-Droz 1, 2000 Neuchâtel, Switzerland

^* e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 1 October 2025
Accepted: 24 April 2026
Published online: 22 June 2026

Abstract

The growing integration of photovoltaic (PV) systems into complex environments—such as rooftops, façades, and vehicles—has introduced new shading patterns and the need for accurate performance modeling under these partial shading conditions. In particular, building-integrated photovoltaics (BIPV) are often subject to thin shadows from nearby building components, vegetation, or infrastructure. These shadings can impact only portions of individual cells, leading to inhomogeneous irradiances that are difficult to capture with conventional simulation tools. A few commercial tools consider the impact of near shading losses on photovoltaic arrays, a well-documented example being PVsyst. PVsyst incorporates a more sophisticated approach using four empirically derived I-V curve templates based on the number of shaded corners per sub-module, but the core logic remains: if at least one corner of a sub-module intersects a shadow, it is treated as electrically shaded. This assumption is valid for large open-rack systems with large shadows. The choice of points to check for shadow intersection could however be improved for thin shadows by considering partial shading at the cell level. This work presents a shadow modeling approach based on vertex projection, and the shadow positions were experimentally validated against photographs of shadows cast on an outdoor BIPV module in Neuchâtel, Switzerland. The near shading simulation is done at the cell level, and several strategies for selecting points to check for shadow intersection are compared to determine the shaded fraction and shading-adjusted plane-of-array irradiance of each cell. This irradiance is calculated by summing the diffuse plane-of-array irradiance and the direct plane-of-array irradiance adjusted for the shaded fraction. Compared with a conservative full-shading baseline, the cell-level model which captures partial cell shading may predict about 2% lower annual irradiance losses for a 25 cm shadow and even more for thinner shadows. At sufficient resolution, the model avoids missing thin shadows entirely—a key limitation of the submodule-level approach. The algorithm scales efficiently at low resolutions, simulating a full year of hourly cell irradiance data in about 17 s for a 40-cell module at 2 × 2 to 5 × 5 points per cell, and about 25 s for 1200 cells at 3 × 3 resolution.