An ion-migration-considered fractional-order circuit model for perovskite solar cells

Perovskite solar cells (PSCs) are considered a next-generation photovoltaic technology, with a power conversion efficiency (PCE) upper limit of 33%, which is expected to overcome the efficiency bottleneck of silicon-based photovoltaics. However, ion migration induces pronounced hysteresis in PSCs, and these effects are sensitive to temperatures and bias voltages. This makes integer-order models inadequate for capturing PSCs' electrical behaviors. Here, we report a fractional-order circuit model for PSCs (PSC-FOCM) that addresses these effects and provides a more accurate representation of PSC behavior. Under standard test conditions, the error between simulated and measured PCEs decreases from 2.67% to 0.07%. Additionally, we develop a maximum power point tracking (MPPT) algorithm based on the PSC-FOCM, which improves MPPT efficiency by 2.23% and 0.80% for PSCs with hysteresis indices of 11.67% and 3.73%, respectively. The results confirm that the PSC-FOCM is particularly effective under strong hysteresis, highlighting its potential for practical designs and engineering applications.