This paper presents a real-time and interpretable framework for classifying power system stability in smart grids using current-only measurements. Traditional model-based approaches (e.g., voltage or power-flow driven) can be difficult to generalize and deploy under dynamic loads and renewable variability. We instead adopt a statistical labeling strategy based on the Sigma rule, categorizing each time point into Stable, Warning, or Critical via Z-score thresholds. The novelty lies in combining this parameter-light labeling with a single-step temporal feature (the previous label) and a lightweight XGBoost classifier, which together enable low-latency inference suitable for control-room and edge devices. We validate the approach on a city-scale case study (Laayoune, Morocco) using ampere-based data from five distribution zones sampled every 10 min between September 2022 and May 2024. With class balancing and calibrated decision thresholds, the framework delivers balanced multi-class performance and robust detection of the minority Critical state. Overall, the method bridges the gap between theoretical stability assessment and operational deployment by providing a simple, interpretable, and deployable pipeline for real-time situational awareness in distribution grids.