The stability of modern power grids is paramount, yet they are increasingly vulnerable to dynamic disturbances. While data-driven machine learning models are powerful, they often lack interpretability and require vast labeled fault data. This paper proposes a novel framework for real-time anomaly detection using Physics-Informed Neural Networks (PINNs). Our approach embeds the governing differential equation of power system dynamics—the swing equation—directly into the neural network’s loss function. We demonstrate that a standard PINN architecture fails to capture the system’s oscillatory nature and introduce a stabilized training methodology incorporating Fourier Feature Mapping and loss weight annealing to overcome this. By training the model on sparse data from only normal operating conditions, our framework accurately reconstructs the system’s state and uses the physics residual as a robust, interpretable anomaly signal. Experimental results on a simulated Single-Machine Infinite Bus system show that our method instantaneously detects fault conditions with high precision. A comparative analysis with an LSTM-based model highlights the PINN’s superior signal clarity and interpretability. This work presents a data-efficient and physically-grounded solution for next-generation smart grid monitoring, validated against a common data-driven approach.