Multistage symbolic optimization for predictive thermal modeling of bifacial photovoltaic systems with solar tracking in tropical climates

Accurate prediction of module temperature in bifacial photovoltaic (PV) systems equipped with single-axis solar tracking is critical for optimizing energy yield and mitigating thermal stress, particularly in tropical climates. However, existing empirical and data-driven approaches often lack physical interpretability or fail to adequately represent the nonlinear thermal behavior of operating PV modules. This study presents a novel multistage symbolic optimization (MSO) framework for predictive thermal modeling that addresses these limitations. The proposed two-level hierarchical approach first derives a physically interpretable symbolic equation using genetic algorithms (GA), followed by a second corrective symbolic regression stage in which GA and Alpha Evolution (AE) are evaluated as competing optimizers. This work presents a novel application of the AE algorithm to symbolic regression in PV thermal modeling. The methodology is validated using one year of high-resolution (5-min) operational data from a utility-scale bifacial PV plant with solar tracking in Colombia. The MSO–AE model achieved an R² of 0.9439, an RMSE of 3.18 °C, and an MAE of 2.01 °C, outperforming the MSO–GA benchmark by 7.3% in MAE and 6.5% in RMSE, and surpassing recent single-stage symbolic regression models by 3.7–20%, while preserving closed-form, interpretable expressions suitable for real-time control applications. A field-derived heating coefficient of 0.034 °C/(W/m²) was identified. Observations show module temperatures exceeding 70 °C between 14:00 and 16:00, reducing electrical efficiency to 17.31%, corresponding to a 12.1% loss relative to standard test conditions. This thermal degradation resulted in average economic losses of USD 110.7 per hour during peak periods and an annual energy loss of 6738.6 MWh, equivalent to USD 336,929 at a benchmark electricity price of USD 50/MWh. These results define economic thresholds for thermal management investments in bifacial PV systems operating in tropical environments.