Improving Estimation of Parameters in Photovoltaic Models Using Two-Level Layered Physics-Informed Neural Networks

Accurate estimation of parameters in photovoltaic models is essential to improve system monitoring, control, and diagnostics. In this study, a novel two-level layered physics-informed neural network (PINN) architecture is proposed to estimate the parameters irradiance (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$G$</tex-math></inline-formula>) and temperature (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T$</tex-math></inline-formula>), and junction capacitance (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C_{j0}$</tex-math></inline-formula>) in a dynamic single-diode PV model. In case no noise affects the PV current and voltage waveforms, the proposed method achieves errors equal to <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.25% for <inline-formula><tex-math notation="LaTeX">$G$</tex-math></inline-formula></b>, <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1.5% for <inline-formula><tex-math notation="LaTeX">$T$</tex-math></inline-formula></b>, and <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2.1% for <inline-formula><tex-math notation="LaTeX">$C_{j0}$</tex-math></inline-formula></b>. Compared to traditional optimization methods, the two-level layered PINN shows a better performance, particularly in learning the nonlinear behavior of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C_{j0}$</tex-math></inline-formula>. Sensitivity analysis under additive Gaussian noise (0% –5% ) confirms the robustness of the approach, with a slight increase of the identification error. The results confirm the effectiveness of incorporating physical knowledge into neural networks for robust and reliable parameter estimation in dynamic photovoltaic systems.