Hybrid Modeling for Photovoltaic Module Operating Temperature Estimation
Letícia de Oliveira Santos, Francisco Souza, Clodoaldo de Oliveira Carvalho Filho, Paulo César Marques de Carvalho, Tarek AlSkaif, Renata Imaculada Soares Pereira
Abstract
The performance and efficiency of photovoltaic (PV) modules are significantly impacted by their operating temperature. Therefore, accurately estimating the PV module temperature ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T_{m}$</tex-math></inline-formula> ) is a crucial factor in the assessment of PV systems. This article introduces a hybrid model for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T_{m}$</tex-math></inline-formula> estimation that combines both physical and data-driven modeling. The primary objective of our research is to enhance long-term <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T_{m}$</tex-math></inline-formula> estimation, a domain where steady-state physical models are conventionally applied. Model parameters are extracted for poly-Si modules using Bayesian optimization. The adaptivity of our approach is validated using data from three distinct PV plants, each featuring different installation types and operating under different climatic conditions. To evaluate the effectiveness of our model, we compare its results with two widely used models for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T_{m}$</tex-math></inline-formula> estimation: the Sandia and Faiman models. The comparative analysis further confirms that our model provides more accurate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T_{m}$</tex-math></inline-formula> estimations. Our model shows a mean absolute error (MAE) of 2.44 °C, surpassing the 3.82 °C and 4.14 °C MAE values obtained using Faiman and Sandia models, respectively. The results suggest a superior <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T_{m}$</tex-math></inline-formula> estimation even in scenarios of short-term irradiance variations. Model validation demonstrates its potential to improve the accuracy of PV conversion efficiency estimation by up to 1.05% compared with reference models.