Improved modeling of real photovoltaic panel efficiency using a fractional-order error function family

Leonardo Martínez–Jiménez; Jorge Manuel Barrios–Sánchez; Roberto Baeza–Serrato; Leonardo Martínez–Jiménez; Jorge Manuel Barrios–Sánchez; Roberto Baeza–Serrato

doi:10.3934/energy.2025059

AIMS Energy

2025, Volume 13, Issue 6: 1583-1608. doi: 10.3934/energy.2025059

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Research article

Improved modeling of real photovoltaic panel efficiency using a fractional-order error function family

Leonardo Martínez–Jiménez ¹,
Jorge Manuel Barrios–Sánchez ^{1,2
,
,},
Roberto Baeza–Serrato ¹

1.
Department of Multidisciplinary Studies, DICIS, University of Guanajuato, Yuriria, Gto 38940, México
2.
Corporación Universitaria Rafael Núñez, Colombia

Received: 11 August 2025 Revised: 06 December 2025 Accepted: 11 December 2025 Published: 18 December 2025

In this study, we introduced a unified family of fractional-order derivatives of the error function, bridging classical error function ($ \alpha = 0 $) and Gaussian ($ \alpha = 1 $) through Maclaurin expansion and Lacroix's fractional calculus. The adaptive model was validated against cubic spline and Gaussian baselines using six days of real photovoltaic measurements from a tropical environment. Moving-window optimization achieved competitive accuracy (Root Mean Squared Error (RMSE): 0.0083–0.0104; Mean Absolute Error (MAE) 0.0068–0.0086) while preserving physical interpretability via the fractional order $ \alpha $. Comparative analysis demonstrated significant improvement over Gaussian fitting, with an average 14.17% reduction in RMSE across all test days. The fractional approach also delivered more consistent daily performance and better captured asymmetric transitions, despite spline's occasional marginal RMSE advantages. Graphical analysis revealed persistent diurnal $ \alpha $ patterns: from 0.50 at sunrise, peaking at 0.90–0.91 near noon, declining to 0.37 afternoon, with sunset rebound. Our results confirmed the model effectively captures photovoltaic memory effects while offering superior interpretability and dynamic adaptation versus traditional methods. The framework enables accurate energy forecasting and condition-based maintenance, with future work focusing on real-time $ \alpha $ tuning and machine learning integration.
- fractional calculus,
- error function,
- photovoltaic efficiency modeling,
- adaptive optimization,
- memory effects,
- solar energy,
- diurnal dynamics
Citation: Leonardo Martínez–Jiménez, Jorge Manuel Barrios–Sánchez, Roberto Baeza–Serrato. Improved modeling of real photovoltaic panel efficiency using a fractional-order error function family[J]. AIMS Energy, 2025, 13(6): 1583-1608. doi: 10.3934/energy.2025059

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Abstract

In this study, we introduced a unified family of fractional-order derivatives of the error function, bridging classical error function ($ \alpha = 0 $) and Gaussian ($ \alpha = 1 $) through Maclaurin expansion and Lacroix's fractional calculus. The adaptive model was validated against cubic spline and Gaussian baselines using six days of real photovoltaic measurements from a tropical environment. Moving-window optimization achieved competitive accuracy (Root Mean Squared Error (RMSE): 0.0083–0.0104; Mean Absolute Error (MAE) 0.0068–0.0086) while preserving physical interpretability via the fractional order $ \alpha $. Comparative analysis demonstrated significant improvement over Gaussian fitting, with an average 14.17% reduction in RMSE across all test days. The fractional approach also delivered more consistent daily performance and better captured asymmetric transitions, despite spline's occasional marginal RMSE advantages. Graphical analysis revealed persistent diurnal $ \alpha $ patterns: from 0.50 at sunrise, peaking at 0.90–0.91 near noon, declining to 0.37 afternoon, with sunset rebound. Our results confirmed the model effectively captures photovoltaic memory effects while offering superior interpretability and dynamic adaptation versus traditional methods. The framework enables accurate energy forecasting and condition-based maintenance, with future work focusing on real-time $ \alpha $ tuning and machine learning integration.

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