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

TL;DR

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 is presented.

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. Traditional DSSE techniques, however, struggle with sparse measurements and the scale of modern feeders, limiting their scalability to large networks. 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.

Figures (10)

• Figure 1: Data Generation and Algorithm Training Pipeline.
• Figure 2: Proposed GNN architecture for single-feeder training. Substation-level coupling is handled separately via the FiLM layer (not shown).
• Figure 3: Fine-tuning strategy for single-feeder voltage estimation. Early GNN layers are frozen, while the last layer and MLP head are updated to adapt the pretrained model to new substations or scenarios.
• Figure 4: Voltage estimation RMSE of the proposed model, DSS,RF and LR across twelve substations as a function of observability level (1--80%) (observability analysis case study).
• Figure 5: Voltage estimation RMSE of the proposed modeland benchmarks across twelve substations as a function of observability level (1--80%) with and without DER (DER case study).