Genetic algorithm-supervised graph shadow estimation for low-observability distribution feeders: calibrated validation on a real feeder

Real distribution feeders often operate under partial observability, while physics-based state estimators can be too slow for frequent digital-twin updates. This paper proposes a Genetic Algorithm (GA)-supervised graph surrogate for shadow state estimation using feeder topology, sparse measurements, and physics-constrained GA pseudo-states. The model is trained with reliability-aware corrupted measurement views and deployed non-intrusively beside the operational GA estimator. Over an approximately eleven-day Terni feeder deployment, the mean estimation-call time decreased from 13.11 s to 0.655 s. At Fontana di Polo, the only hidden medium-voltage point with an independent active/reactive-power reference, the calibrated graph surrogate achieved weighted mean absolute percentage error (wMAPE) values of 12.64% and 12.80%, respectively, on the held-out test interval. Sensitivity tests showed progressive degradation as voltage-measurement availability decreased and negligible change under additive zero-mean noise within the trained corruption range. Controlled hidden-photovoltaic scenarios showed stable calibrated performance within the generated model-based operating groups. The results demonstrate short-term shadow-mode feasibility for the investigated Terni feeder; long-term robustness and cross-feeder transfer remain unverified.