Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for modeling and controlling complex energy systems by embedding physical laws into deep learning architectures. This review paper highlights the application of PINNs in grid-connected inverter systems (GCISs), categorizing them by key tasks: parameter estimation, state estimation, control strategies, fault diagnosis and detection, and system identification. Particular focus is given to the use of PINNs in enabling accurate parameter estimation for aging and degradation monitoring. Studies show that PINN-based approaches can outperform purely data-driven models and traditional methods in both computational efficiency and accuracy. However, challenges remain, mainly related to high training costs and limited uncertainty quantification. To address these, emerging strategies such as advanced PINN frameworks are explored. The paper also explores emerging solutions and outlines future research directions to support the integration of PINNs into practical inverter design and operation.

The growing deployment of renewable energy systems calls for accurate parameter estimation and compact modeling of grid-connected inverter systems (GCISs). This paper presents a framework for parameter estimation and physics-structured model compression using Physics-Structured-Informed Neural Networks (Ψ-NNs). A teacher physics-informed neural network (PINN) estimates LC-filter parameters by combining measurements with governing equations. A regularized student learns the teacher mapping through physics-informed distillation. Hierarchical clustering identifies shared weight magnitudes, enabling structured reconstruction and fine-tuning. The framework is evaluated on mathematical-model and MATLAB/Simulink datasets. The teacher achieves a mean relative parameter error below $5\%$ across all cases, outperforming the extended Kalman filter, remaining competitive with least squares on mathematical-model data, and outperforming both baselines on all MATLAB/Simulink records. The reconstructed networks retain only 23–78 trainable base coefficients (0.15–0.50% of the student’s 15,600 parameters): 23–55 (0.15–0.35%) on the mathematical-model records and 62–78 (0.40–0.50%) on the MATLAB/Simulink records. These ratios count tied magnitudes only; after cluster assignments and signs are stored, the packed footprint is about 19–22% of the student model. The representation is value-tying rather than sparsity, so dense inference is not automatically faster. Reconstruction reduces the student data residual by nearly two orders of magnitude on degraded mathematical-model data, while remaining comparable on MATLAB/Simulink data except under the strongest combined artifacts. These results demonstrate the framework’s potential to combine robust parameter estimation with compact representations of GCIS dynamics, revealing a compression–accuracy trade-off under severe measurement degradation.