Understanding Reverse I-V Characteristics of Solar Cells Using an Irradiance-dependent Bishop Model

Mismatch in photovoltaic (PV) modules—arising from shading, soiling, or latent defects—forces individual cells into reverse bias, where their characteristics govern module power loss, hotspot formation, and longterm reliability. Despite substantial changes in cell technology, most system models still adopt Bishop’s 1988 reversecharacteristic formulation, originally calibrated for Al-BSF cells. This work reassesses the adequacy of the Bishop model for modern architectures (PERC, TOPCon, HJT) and introduces an adapted formulation that captures the distinct irradiance dependencies observed in modern cells. The model’s avalanche and shunt terms are extended with physicsmotivated, irradiance-dependent multipliers and provide a stable parameter-extraction framework tailored to reversebias data. Model parameters are estimated via particle swarm optimization (PSO). Validation against measured I–V curves under controlled irradiance demonstrates materially improved fits in the reverse quadrant and more accurate prediction of module-level stress indicators, including hotspot onset and severity. The proposed approach supports more reliable system-level simulations under mismatch, enabling better thermal-risk assessment, bypass-diode coordination, and design margins for modern PV modules. Results indicate that updating reverse-bias models is critical to accurately forecasting field performance and mitigating reliability hazards in current and emerging PV technologies.