Computationally efficient gray-box modeling of photovoltaic parameters via higher-order degenerate Taylor polynomials and gradient boosting regression

Recent advances in photovoltaic I-V modeling still face trade-offs among accuracy, computational efficiency, parameter estimation, and applicability. This study introduces third- and fourth order Enhanced Degenerate Current Taylor Series Expansion (EDCTSE) formulations derived from the Single Diode Model and validated against literature data. EDCTSE was then used to generate a large synthetic dataset for a histogram gradient boosting regression model trained on RTC France Si, PVM 752 GaAs, PhotoWatt-PWP201, and STP6-120/36, and tested on STM6-40/36. The model learned the relationship between the degenerate variable λ and photovoltaic parameters and was integrated with EDCTSE to form a Hybrid Analytical-AI Model (HAAM). EDCTSE achieved RMSE values between 1.57 × 10−4 and 1.46 × 10−2 A, while HAAM reached an RMSE of 4.87 × 10−3 A, R2 of 0.99982, and MAPE of 0.279%. Results confirm EDCTSE as a highly accurate physics-based method and HAAM as an efficient gray-box solution for large-scale applications.