Learning a Generalized Model for Substation Level Voltage Estimation in Distribution Networks

Abstract--Accurate voltage estimation in distribution networks is critical for real-time monitoring and increasing the reliability of the grid. As DER penetration and distribution level voltage variability increase, robust distribution system state estimation (DSSE) has become more essential to maintain safe and efficient operations. This paper presents a hierarchical graph neural network for substation-level voltage estimation that exploits both electrical topology and physical features, while remaining robust to the low observability levels common to real-world distribution networks. Leveraging the public SMART -DS datasets, the model is trained and evaluated on thousands of buses across multiple substations and DER penetration scenarios. Comprehensive experiments demonstrate that the proposed method achieves up to 2 times lower RMSE than alternative data-driven models, and maintains high accuracy with as little as 1% measurement coverage. The results highlight the potential of GNNs to enable scalable, reproducible, and data-driven voltage monitoring for distribution systems. Distribution System State Estimation (DSSE) is the process of determining the state variables of a distribution network given a limited set of measurements [1], [2]. Historically, distribution networks were operated as a passive part of the grid, delivering electricity from transmission substations to customers in a unidirectional manner [3].