<p>With the increasing penetration of renewable energy, the stable operation of Static Var Generator (SVG) in weak grids heavily relies on the accurate estimation of grid impedance. Conventional impedance estimation methods frequently struggle to balance noise suppression with physical interpretability, often leading to severe noise amplification or poor transient robustness. To address these issues, this paper proposes a novel Adaptive Physics-Informed Neural Network (Adaptive-PINN) for fast and robust grid impedance estimation. By embedding Kirchhoff’s voltage laws into the loss function, the proposed method introduces a dynamic adaptive weighting mechanism for physical and smoothness constraints. The convergence and noise-suppression capabilities of this mechanism are rigorously justified through mathematical derivations, allowing the network to strike an optimal balance between data tracking and noise suppression. Simulation results demonstrate that the Adaptive-PINN offers a highly robust alternative to conventional baseline algorithms. Specifically, the proposed framework exhibits superior accuracy in the highly challenging grid resistance estimation, reducing the MAPE to 4.44%. Furthermore, regarding grid inductance estimation, the adaptive mechanism successfully prevents overfitting to the severe noise amplification inherent in discrete current differentiation, maintaining a structurally stable and comparable tracking trajectory. The proposed method exhibits excellent steady-state accuracy and transient tracking capability, providing a mathematically solid and validated parameter sensing solution for stable SVG operation in complex power grids.</p>